Properties

Label 150.2.l.a.47.2
Level $150$
Weight $2$
Character 150.47
Analytic conductor $1.198$
Analytic rank $0$
Dimension $80$
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] = [150,2,Mod(17,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.l (of order \(20\), degree \(8\), 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: \(1.19775603032\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 47.2
Character \(\chi\) \(=\) 150.47
Dual form 150.2.l.a.83.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.453990 - 0.891007i) q^{2} +(-1.06061 + 1.36935i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.483575 - 2.18315i) q^{5} +(1.70160 + 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-0.750223 - 2.90468i) q^{9} +O(q^{10})\) \(q+(-0.453990 - 0.891007i) q^{2} +(-1.06061 + 1.36935i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.483575 - 2.18315i) q^{5} +(1.70160 + 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-0.750223 - 2.90468i) q^{9} +(-2.16474 + 0.560262i) q^{10} +(3.57685 + 1.16219i) q^{11} +(-0.484416 - 1.66293i) q^{12} +(3.49677 + 1.78169i) q^{13} +(1.37043 - 4.21776i) q^{14} +(2.47661 + 2.97765i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.0644499 + 0.406920i) q^{17} +(-2.24749 + 1.98715i) q^{18} +(-2.93913 - 4.04536i) q^{19} +(1.48197 + 1.67445i) q^{20} +(-7.62006 + 0.968173i) q^{21} +(-0.588338 - 3.71462i) q^{22} +(-4.48117 + 2.28327i) q^{23} +(-1.26176 + 1.18657i) q^{24} +(-4.53231 - 2.11143i) q^{25} -3.92451i q^{26} +(4.77321 + 2.05341i) q^{27} +(-4.38021 + 0.693758i) q^{28} +(-1.49299 - 1.08472i) q^{29} +(1.52875 - 3.55850i) q^{30} +(2.69808 - 1.96027i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.38508 + 3.66532i) q^{33} +(0.391828 - 0.127313i) q^{34} +(8.36256 - 5.32968i) q^{35} +(2.79091 + 1.10038i) q^{36} +(-2.39714 + 4.70465i) q^{37} +(-2.27011 + 4.45534i) q^{38} +(-6.14845 + 2.89861i) q^{39} +(0.819141 - 2.08063i) q^{40} +(-3.24600 + 1.05469i) q^{41} +(4.32208 + 6.34998i) q^{42} +(3.71639 - 3.71639i) q^{43} +(-3.04265 + 2.21062i) q^{44} +(-6.70415 + 0.233223i) q^{45} +(4.06882 + 2.95617i) q^{46} +(-5.10512 + 0.808572i) q^{47} +(1.63007 + 0.585546i) q^{48} +12.6676i q^{49} +(0.176325 + 4.99689i) q^{50} +(-0.488859 - 0.519837i) q^{51} +(-3.49677 + 1.78169i) q^{52} +(-1.29952 - 8.20487i) q^{53} +(-0.337390 - 5.18519i) q^{54} +(4.26691 - 7.24681i) q^{55} +(2.60672 + 3.58784i) q^{56} +(8.65677 + 0.265855i) q^{57} +(-0.288689 + 1.82271i) q^{58} +(1.73564 + 5.34175i) q^{59} +(-3.86468 + 0.253402i) q^{60} +(4.43829 - 13.6596i) q^{61} +(-2.97152 - 1.51406i) q^{62} +(6.75613 - 11.4614i) q^{63} +(0.951057 + 0.309017i) q^{64} +(5.58065 - 6.77239i) q^{65} +(5.71060 + 3.13412i) q^{66} +(-6.11731 - 0.968887i) q^{67} +(-0.291323 - 0.291323i) q^{68} +(1.62617 - 8.55793i) q^{69} +(-8.54530 - 5.03147i) q^{70} +(0.992045 - 1.36543i) q^{71} +(-0.286595 - 2.98628i) q^{72} +(-1.62628 - 3.19175i) q^{73} +5.28015 q^{74} +(7.69829 - 3.96690i) q^{75} +5.00034 q^{76} +(7.57211 + 14.8611i) q^{77} +(5.37402 + 4.16237i) q^{78} +(-6.24842 + 8.60021i) q^{79} +(-2.22573 + 0.214725i) q^{80} +(-7.87433 + 4.35832i) q^{81} +(2.41339 + 2.41339i) q^{82} +(-7.00394 - 1.10932i) q^{83} +(3.69569 - 6.73384i) q^{84} +(0.857203 + 0.337480i) q^{85} +(-4.99854 - 1.62412i) q^{86} +(3.06883 - 0.893957i) q^{87} +(3.35101 + 1.70742i) q^{88} +(-0.324819 + 0.999689i) q^{89} +(3.25142 + 5.86756i) q^{90} +(5.37828 + 16.5526i) q^{91} +(0.786761 - 4.96742i) q^{92} +(-0.177314 + 5.77369i) q^{93} +(3.03812 + 4.18162i) q^{94} +(-10.2529 + 4.46033i) q^{95} +(-0.218312 - 1.71824i) q^{96} +(-1.20630 - 7.61627i) q^{97} +(11.2869 - 5.75096i) q^{98} +(0.692350 - 11.2615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{17}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.453990 0.891007i −0.321020 0.630037i
\(3\) −1.06061 + 1.36935i −0.612342 + 0.790593i
\(4\) −0.587785 + 0.809017i −0.293893 + 0.404508i
\(5\) 0.483575 2.18315i 0.216261 0.976336i
\(6\) 1.70160 + 0.323338i 0.694677 + 0.132002i
\(7\) 3.13589 + 3.13589i 1.18525 + 1.18525i 0.978364 + 0.206890i \(0.0663341\pi\)
0.206890 + 0.978364i \(0.433666\pi\)
\(8\) 0.987688 + 0.156434i 0.349201 + 0.0553079i
\(9\) −0.750223 2.90468i −0.250074 0.968227i
\(10\) −2.16474 + 0.560262i −0.684551 + 0.177171i
\(11\) 3.57685 + 1.16219i 1.07846 + 0.350413i 0.793778 0.608208i \(-0.208111\pi\)
0.284684 + 0.958622i \(0.408111\pi\)
\(12\) −0.484416 1.66293i −0.139839 0.480047i
\(13\) 3.49677 + 1.78169i 0.969828 + 0.494152i 0.865783 0.500420i \(-0.166821\pi\)
0.104046 + 0.994573i \(0.466821\pi\)
\(14\) 1.37043 4.21776i 0.366264 1.12724i
\(15\) 2.47661 + 2.97765i 0.639458 + 0.768826i
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) −0.0644499 + 0.406920i −0.0156314 + 0.0986927i −0.994271 0.106893i \(-0.965910\pi\)
0.978639 + 0.205585i \(0.0659098\pi\)
\(18\) −2.24749 + 1.98715i −0.529739 + 0.468376i
\(19\) −2.93913 4.04536i −0.674282 0.928070i 0.325565 0.945520i \(-0.394445\pi\)
−0.999848 + 0.0174495i \(0.994445\pi\)
\(20\) 1.48197 + 1.67445i 0.331378 + 0.374417i
\(21\) −7.62006 + 0.968173i −1.66283 + 0.211273i
\(22\) −0.588338 3.71462i −0.125434 0.791960i
\(23\) −4.48117 + 2.28327i −0.934389 + 0.476095i −0.853770 0.520650i \(-0.825690\pi\)
−0.0806186 + 0.996745i \(0.525690\pi\)
\(24\) −1.26176 + 1.18657i −0.257556 + 0.242208i
\(25\) −4.53231 2.11143i −0.906462 0.422287i
\(26\) 3.92451i 0.769660i
\(27\) 4.77321 + 2.05341i 0.918604 + 0.395179i
\(28\) −4.38021 + 0.693758i −0.827783 + 0.131108i
\(29\) −1.49299 1.08472i −0.277241 0.201427i 0.440472 0.897766i \(-0.354811\pi\)
−0.717713 + 0.696339i \(0.754811\pi\)
\(30\) 1.52875 3.55850i 0.279110 0.649690i
\(31\) 2.69808 1.96027i 0.484590 0.352075i −0.318510 0.947920i \(-0.603182\pi\)
0.803100 + 0.595844i \(0.203182\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −5.38508 + 3.66532i −0.937421 + 0.638051i
\(34\) 0.391828 0.127313i 0.0671980 0.0218340i
\(35\) 8.36256 5.32968i 1.41353 0.900881i
\(36\) 2.79091 + 1.10038i 0.465151 + 0.183397i
\(37\) −2.39714 + 4.70465i −0.394087 + 0.773440i −0.999752 0.0222802i \(-0.992907\pi\)
0.605664 + 0.795720i \(0.292907\pi\)
\(38\) −2.27011 + 4.45534i −0.368260 + 0.722751i
\(39\) −6.14845 + 2.89861i −0.984540 + 0.464149i
\(40\) 0.819141 2.08063i 0.129518 0.328976i
\(41\) −3.24600 + 1.05469i −0.506941 + 0.164715i −0.551310 0.834300i \(-0.685872\pi\)
0.0443698 + 0.999015i \(0.485872\pi\)
\(42\) 4.32208 + 6.34998i 0.666912 + 0.979824i
\(43\) 3.71639 3.71639i 0.566745 0.566745i −0.364470 0.931215i \(-0.618750\pi\)
0.931215 + 0.364470i \(0.118750\pi\)
\(44\) −3.04265 + 2.21062i −0.458697 + 0.333263i
\(45\) −6.70415 + 0.233223i −0.999395 + 0.0347668i
\(46\) 4.06882 + 2.95617i 0.599914 + 0.435863i
\(47\) −5.10512 + 0.808572i −0.744659 + 0.117942i −0.517223 0.855851i \(-0.673034\pi\)
−0.227436 + 0.973793i \(0.573034\pi\)
\(48\) 1.63007 + 0.585546i 0.235281 + 0.0845163i
\(49\) 12.6676i 1.80965i
\(50\) 0.176325 + 4.99689i 0.0249361 + 0.706667i
\(51\) −0.488859 0.519837i −0.0684540 0.0727917i
\(52\) −3.49677 + 1.78169i −0.484914 + 0.247076i
\(53\) −1.29952 8.20487i −0.178503 1.12703i −0.900412 0.435037i \(-0.856735\pi\)
0.721909 0.691988i \(-0.243265\pi\)
\(54\) −0.337390 5.18519i −0.0459130 0.705615i
\(55\) 4.26691 7.24681i 0.575350 0.977159i
\(56\) 2.60672 + 3.58784i 0.348337 + 0.479445i
\(57\) 8.65677 + 0.265855i 1.14662 + 0.0352134i
\(58\) −0.288689 + 1.82271i −0.0379068 + 0.239334i
\(59\) 1.73564 + 5.34175i 0.225961 + 0.695437i 0.998193 + 0.0600956i \(0.0191406\pi\)
−0.772231 + 0.635341i \(0.780859\pi\)
\(60\) −3.86468 + 0.253402i −0.498929 + 0.0327141i
\(61\) 4.43829 13.6596i 0.568264 1.74894i −0.0897825 0.995961i \(-0.528617\pi\)
0.658047 0.752977i \(-0.271383\pi\)
\(62\) −2.97152 1.51406i −0.377383 0.192286i
\(63\) 6.75613 11.4614i 0.851193 1.44400i
\(64\) 0.951057 + 0.309017i 0.118882 + 0.0386271i
\(65\) 5.58065 6.77239i 0.692195 0.840012i
\(66\) 5.71060 + 3.13412i 0.702926 + 0.385783i
\(67\) −6.11731 0.968887i −0.747349 0.118368i −0.228868 0.973458i \(-0.573502\pi\)
−0.518481 + 0.855089i \(0.673502\pi\)
\(68\) −0.291323 0.291323i −0.0353281 0.0353281i
\(69\) 1.62617 8.55793i 0.195768 1.03025i
\(70\) −8.54530 5.03147i −1.02136 0.601375i
\(71\) 0.992045 1.36543i 0.117734 0.162047i −0.746082 0.665854i \(-0.768068\pi\)
0.863817 + 0.503806i \(0.168068\pi\)
\(72\) −0.286595 2.98628i −0.0337755 0.351936i
\(73\) −1.62628 3.19175i −0.190342 0.373567i 0.776038 0.630686i \(-0.217227\pi\)
−0.966380 + 0.257120i \(0.917227\pi\)
\(74\) 5.28015 0.613805
\(75\) 7.69829 3.96690i 0.888922 0.458059i
\(76\) 5.00034 0.573579
\(77\) 7.57211 + 14.8611i 0.862922 + 1.69358i
\(78\) 5.37402 + 4.16237i 0.608488 + 0.471295i
\(79\) −6.24842 + 8.60021i −0.703002 + 0.967599i 0.296918 + 0.954903i \(0.404041\pi\)
−0.999919 + 0.0126959i \(0.995959\pi\)
\(80\) −2.22573 + 0.214725i −0.248845 + 0.0240069i
\(81\) −7.87433 + 4.35832i −0.874926 + 0.484258i
\(82\) 2.41339 + 2.41339i 0.266514 + 0.266514i
\(83\) −7.00394 1.10932i −0.768782 0.121763i −0.240290 0.970701i \(-0.577243\pi\)
−0.528493 + 0.848938i \(0.677243\pi\)
\(84\) 3.69569 6.73384i 0.403233 0.734722i
\(85\) 0.857203 + 0.337480i 0.0929767 + 0.0366049i
\(86\) −4.99854 1.62412i −0.539006 0.175134i
\(87\) 3.06883 0.893957i 0.329013 0.0958423i
\(88\) 3.35101 + 1.70742i 0.357219 + 0.182012i
\(89\) −0.324819 + 0.999689i −0.0344307 + 0.105967i −0.966795 0.255554i \(-0.917742\pi\)
0.932364 + 0.361521i \(0.117742\pi\)
\(90\) 3.25142 + 5.86756i 0.342730 + 0.618495i
\(91\) 5.37828 + 16.5526i 0.563797 + 1.73519i
\(92\) 0.786761 4.96742i 0.0820255 0.517889i
\(93\) −0.177314 + 5.77369i −0.0183866 + 0.598704i
\(94\) 3.03812 + 4.18162i 0.313358 + 0.431301i
\(95\) −10.2529 + 4.46033i −1.05193 + 0.457620i
\(96\) −0.218312 1.71824i −0.0222814 0.175367i
\(97\) −1.20630 7.61627i −0.122481 0.773315i −0.970099 0.242709i \(-0.921964\pi\)
0.847618 0.530607i \(-0.178036\pi\)
\(98\) 11.2869 5.75096i 1.14015 0.580935i
\(99\) 0.692350 11.2615i 0.0695838 1.13182i
\(100\) 4.37221 2.42565i 0.437221 0.242565i
\(101\) 11.0847i 1.10297i −0.834184 0.551487i \(-0.814061\pi\)
0.834184 0.551487i \(-0.185939\pi\)
\(102\) −0.241241 + 0.671578i −0.0238864 + 0.0664961i
\(103\) 2.42213 0.383628i 0.238660 0.0378000i −0.0359588 0.999353i \(-0.511448\pi\)
0.274618 + 0.961553i \(0.411448\pi\)
\(104\) 3.17500 + 2.30677i 0.311334 + 0.226197i
\(105\) −1.57120 + 17.1039i −0.153333 + 1.66917i
\(106\) −6.72062 + 4.88282i −0.652764 + 0.474261i
\(107\) 4.30681 4.30681i 0.416355 0.416355i −0.467590 0.883945i \(-0.654878\pi\)
0.883945 + 0.467590i \(0.154878\pi\)
\(108\) −4.46686 + 2.65464i −0.429824 + 0.255443i
\(109\) 4.46242 1.44993i 0.427422 0.138878i −0.0874029 0.996173i \(-0.527857\pi\)
0.514825 + 0.857295i \(0.327857\pi\)
\(110\) −8.39409 0.511864i −0.800345 0.0488043i
\(111\) −3.89988 8.27231i −0.370160 0.785173i
\(112\) 2.01336 3.95145i 0.190245 0.373377i
\(113\) −7.76223 + 15.2342i −0.730209 + 1.43312i 0.164459 + 0.986384i \(0.447412\pi\)
−0.894668 + 0.446732i \(0.852588\pi\)
\(114\) −3.69321 7.83393i −0.345901 0.733715i
\(115\) 2.81775 + 10.8872i 0.262756 + 1.01524i
\(116\) 1.75511 0.570270i 0.162958 0.0529483i
\(117\) 2.55189 11.4937i 0.235922 1.06259i
\(118\) 3.97157 3.97157i 0.365613 0.365613i
\(119\) −1.47816 + 1.07395i −0.135503 + 0.0984487i
\(120\) 1.98031 + 3.32842i 0.180777 + 0.303842i
\(121\) 2.54399 + 1.84832i 0.231272 + 0.168029i
\(122\) −14.1858 + 2.24681i −1.28432 + 0.203416i
\(123\) 1.99850 5.56352i 0.180199 0.501646i
\(124\) 3.33501i 0.299493i
\(125\) −6.80129 + 8.87369i −0.608326 + 0.793687i
\(126\) −13.2794 0.816407i −1.18302 0.0727313i
\(127\) −17.4755 + 8.90421i −1.55070 + 0.790121i −0.999034 0.0439442i \(-0.986008\pi\)
−0.551666 + 0.834065i \(0.686008\pi\)
\(128\) −0.156434 0.987688i −0.0138270 0.0873001i
\(129\) 1.14740 + 9.03067i 0.101023 + 0.795106i
\(130\) −8.56781 1.89779i −0.751447 0.166448i
\(131\) 12.0644 + 16.6052i 1.05407 + 1.45080i 0.885228 + 0.465158i \(0.154002\pi\)
0.168841 + 0.985643i \(0.445998\pi\)
\(132\) 0.199959 6.51104i 0.0174042 0.566713i
\(133\) 3.46903 21.9026i 0.300803 1.89919i
\(134\) 1.91392 + 5.89043i 0.165337 + 0.508856i
\(135\) 6.79111 9.42766i 0.584485 0.811404i
\(136\) −0.127313 + 0.391828i −0.0109170 + 0.0335990i
\(137\) −6.44062 3.28166i −0.550259 0.280371i 0.156675 0.987650i \(-0.449922\pi\)
−0.706935 + 0.707279i \(0.749922\pi\)
\(138\) −8.36344 + 2.43629i −0.711943 + 0.207391i
\(139\) 9.21867 + 2.99533i 0.781918 + 0.254060i 0.672659 0.739953i \(-0.265152\pi\)
0.109259 + 0.994013i \(0.465152\pi\)
\(140\) −0.603581 + 9.89816i −0.0510119 + 0.836547i
\(141\) 4.30732 7.84827i 0.362742 0.660943i
\(142\) −1.66699 0.264025i −0.139891 0.0221565i
\(143\) 10.4367 + 10.4367i 0.872765 + 0.872765i
\(144\) −2.53068 + 1.61110i −0.210890 + 0.134258i
\(145\) −3.09008 + 2.73488i −0.256617 + 0.227119i
\(146\) −2.10556 + 2.89805i −0.174257 + 0.239845i
\(147\) −17.3463 13.4353i −1.43070 1.10813i
\(148\) −2.39714 4.70465i −0.197044 0.386720i
\(149\) −4.14920 −0.339915 −0.169958 0.985451i \(-0.554363\pi\)
−0.169958 + 0.985451i \(0.554363\pi\)
\(150\) −7.02949 5.05829i −0.573955 0.413008i
\(151\) −9.50070 −0.773156 −0.386578 0.922257i \(-0.626343\pi\)
−0.386578 + 0.922257i \(0.626343\pi\)
\(152\) −2.27011 4.45534i −0.184130 0.361376i
\(153\) 1.23033 0.118075i 0.0994659 0.00954580i
\(154\) 9.80367 13.4936i 0.790002 1.08734i
\(155\) −2.97485 6.83827i −0.238946 0.549263i
\(156\) 1.26894 6.67796i 0.101597 0.534665i
\(157\) 2.98265 + 2.98265i 0.238041 + 0.238041i 0.816039 0.577997i \(-0.196166\pi\)
−0.577997 + 0.816039i \(0.696166\pi\)
\(158\) 10.4996 + 1.66297i 0.835300 + 0.132299i
\(159\) 12.6136 + 6.92265i 1.00032 + 0.549002i
\(160\) 1.20178 + 1.88566i 0.0950093 + 0.149075i
\(161\) −21.2125 6.89237i −1.67178 0.543195i
\(162\) 7.45816 + 5.03744i 0.585968 + 0.395779i
\(163\) −9.28593 4.73142i −0.727330 0.370593i 0.0507896 0.998709i \(-0.483826\pi\)
−0.778119 + 0.628116i \(0.783826\pi\)
\(164\) 1.05469 3.24600i 0.0823575 0.253470i
\(165\) 5.39788 + 13.5289i 0.420224 + 1.05322i
\(166\) 2.19132 + 6.74418i 0.170079 + 0.523450i
\(167\) 2.18995 13.8268i 0.169464 1.06995i −0.745527 0.666476i \(-0.767802\pi\)
0.914990 0.403476i \(-0.132198\pi\)
\(168\) −7.67770 0.235788i −0.592348 0.0181914i
\(169\) 1.41174 + 1.94309i 0.108595 + 0.149469i
\(170\) −0.0884649 0.916986i −0.00678495 0.0703296i
\(171\) −9.54548 + 11.5722i −0.729961 + 0.884945i
\(172\) 0.822184 + 5.19107i 0.0626910 + 0.395815i
\(173\) 6.24576 3.18237i 0.474856 0.241951i −0.200147 0.979766i \(-0.564142\pi\)
0.675003 + 0.737815i \(0.264142\pi\)
\(174\) −2.18974 2.32850i −0.166004 0.176523i
\(175\) −7.59160 20.8340i −0.573871 1.57491i
\(176\) 3.76092i 0.283490i
\(177\) −9.15555 3.28881i −0.688173 0.247202i
\(178\) 1.03819 0.164434i 0.0778159 0.0123248i
\(179\) −2.28996 1.66375i −0.171159 0.124355i 0.498908 0.866655i \(-0.333735\pi\)
−0.670067 + 0.742301i \(0.733735\pi\)
\(180\) 3.75192 5.56086i 0.279651 0.414482i
\(181\) −0.283169 + 0.205734i −0.0210478 + 0.0152921i −0.598259 0.801302i \(-0.704141\pi\)
0.577212 + 0.816595i \(0.304141\pi\)
\(182\) 12.3068 12.3068i 0.912243 0.912243i
\(183\) 13.9975 + 20.5651i 1.03473 + 1.52021i
\(184\) −4.78318 + 1.55415i −0.352621 + 0.114573i
\(185\) 9.11178 + 7.50837i 0.669911 + 0.552027i
\(186\) 5.22490 2.46321i 0.383108 0.180612i
\(187\) −0.703446 + 1.38059i −0.0514411 + 0.100959i
\(188\) 2.34657 4.60540i 0.171141 0.335883i
\(189\) 8.52898 + 21.4075i 0.620392 + 1.55717i
\(190\) 8.62892 + 7.11048i 0.626008 + 0.515849i
\(191\) 1.07980 0.350849i 0.0781318 0.0253866i −0.269690 0.962947i \(-0.586921\pi\)
0.347822 + 0.937561i \(0.386921\pi\)
\(192\) −1.43185 + 0.974581i −0.103335 + 0.0703343i
\(193\) 4.16176 4.16176i 0.299570 0.299570i −0.541275 0.840845i \(-0.682058\pi\)
0.840845 + 0.541275i \(0.182058\pi\)
\(194\) −6.23850 + 4.53254i −0.447898 + 0.325417i
\(195\) 3.35488 + 14.8247i 0.240248 + 1.06162i
\(196\) −10.2483 7.44581i −0.732020 0.531844i
\(197\) 18.9787 3.00593i 1.35218 0.214164i 0.562048 0.827105i \(-0.310014\pi\)
0.790129 + 0.612941i \(0.210014\pi\)
\(198\) −10.3484 + 4.49573i −0.735429 + 0.319498i
\(199\) 12.7124i 0.901157i −0.892737 0.450579i \(-0.851218\pi\)
0.892737 0.450579i \(-0.148782\pi\)
\(200\) −4.14621 2.79445i −0.293181 0.197597i
\(201\) 7.81481 7.34912i 0.551214 0.518367i
\(202\) −9.87658 + 5.03237i −0.694914 + 0.354076i
\(203\) −1.28028 8.08340i −0.0898583 0.567343i
\(204\) 0.707901 0.0899429i 0.0495630 0.00629726i
\(205\) 0.732866 + 7.59654i 0.0511856 + 0.530566i
\(206\) −1.44144 1.98397i −0.100430 0.138230i
\(207\) 9.99405 + 11.3034i 0.694634 + 0.785641i
\(208\) 0.613929 3.87619i 0.0425683 0.268766i
\(209\) −5.81135 17.8855i −0.401979 1.23716i
\(210\) 15.9530 6.36508i 1.10086 0.439232i
\(211\) −5.38805 + 16.5827i −0.370929 + 1.14160i 0.575255 + 0.817974i \(0.304903\pi\)
−0.946184 + 0.323628i \(0.895097\pi\)
\(212\) 7.40172 + 3.77136i 0.508352 + 0.259018i
\(213\) 0.817581 + 2.80664i 0.0560198 + 0.192308i
\(214\) −5.79265 1.88215i −0.395977 0.128661i
\(215\) −6.31630 9.91061i −0.430768 0.675898i
\(216\) 4.39322 + 2.77482i 0.298921 + 0.188803i
\(217\) 14.6081 + 2.31369i 0.991661 + 0.157064i
\(218\) −3.31779 3.31779i −0.224709 0.224709i
\(219\) 6.09547 + 1.15826i 0.411893 + 0.0782677i
\(220\) 3.35476 + 7.71157i 0.226178 + 0.519914i
\(221\) −0.950373 + 1.30808i −0.0639290 + 0.0879907i
\(222\) −5.60017 + 7.23036i −0.375859 + 0.485270i
\(223\) 10.2765 + 20.1688i 0.688167 + 1.35060i 0.925341 + 0.379136i \(0.123779\pi\)
−0.237174 + 0.971467i \(0.576221\pi\)
\(224\) −4.43481 −0.296313
\(225\) −2.73279 + 14.7490i −0.182186 + 0.983264i
\(226\) 17.0978 1.13733
\(227\) 8.76566 + 17.2036i 0.581797 + 1.14184i 0.974962 + 0.222373i \(0.0713804\pi\)
−0.393164 + 0.919468i \(0.628620\pi\)
\(228\) −5.30340 + 6.84721i −0.351226 + 0.453467i
\(229\) 9.58051 13.1864i 0.633098 0.871384i −0.365126 0.930958i \(-0.618974\pi\)
0.998224 + 0.0595738i \(0.0189742\pi\)
\(230\) 8.42135 7.45332i 0.555287 0.491458i
\(231\) −28.3810 5.39295i −1.86733 0.354830i
\(232\) −1.30492 1.30492i −0.0856721 0.0856721i
\(233\) −0.601093 0.0952038i −0.0393789 0.00623701i 0.136714 0.990611i \(-0.456346\pi\)
−0.176093 + 0.984374i \(0.556346\pi\)
\(234\) −11.3995 + 2.94426i −0.745205 + 0.192472i
\(235\) −0.703472 + 11.5363i −0.0458894 + 0.752543i
\(236\) −5.34175 1.73564i −0.347718 0.112981i
\(237\) −5.14955 17.6777i −0.334499 1.14829i
\(238\) 1.62797 + 0.829491i 0.105525 + 0.0537679i
\(239\) −2.47857 + 7.62825i −0.160325 + 0.493430i −0.998661 0.0517231i \(-0.983529\pi\)
0.838336 + 0.545154i \(0.183529\pi\)
\(240\) 2.06660 3.27554i 0.133398 0.211435i
\(241\) −2.23962 6.89284i −0.144267 0.444007i 0.852649 0.522484i \(-0.174994\pi\)
−0.996916 + 0.0784767i \(0.974994\pi\)
\(242\) 0.491916 3.10583i 0.0316215 0.199650i
\(243\) 2.38352 15.4052i 0.152903 0.988241i
\(244\) 8.44212 + 11.6196i 0.540452 + 0.743868i
\(245\) 27.6552 + 6.12572i 1.76683 + 0.391358i
\(246\) −5.86443 + 0.745110i −0.373903 + 0.0475065i
\(247\) −3.06986 19.3823i −0.195330 1.23327i
\(248\) 2.97152 1.51406i 0.188692 0.0961432i
\(249\) 8.94747 8.41428i 0.567023 0.533233i
\(250\) 10.9942 + 2.03143i 0.695337 + 0.128479i
\(251\) 14.5520i 0.918511i −0.888304 0.459256i \(-0.848116\pi\)
0.888304 0.459256i \(-0.151884\pi\)
\(252\) 5.30128 + 12.2026i 0.333949 + 0.768694i
\(253\) −18.6821 + 2.95895i −1.17453 + 0.186028i
\(254\) 15.8674 + 11.5284i 0.995611 + 0.723353i
\(255\) −1.37128 + 0.815874i −0.0858731 + 0.0510920i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 1.03830 1.03830i 0.0647675 0.0647675i −0.673981 0.738749i \(-0.735417\pi\)
0.738749 + 0.673981i \(0.235417\pi\)
\(258\) 7.52548 5.12218i 0.468516 0.318893i
\(259\) −22.2704 + 7.23610i −1.38382 + 0.449629i
\(260\) 2.19876 + 8.49555i 0.136361 + 0.526872i
\(261\) −2.03069 + 5.15043i −0.125696 + 0.318804i
\(262\) 9.31821 18.2880i 0.575681 1.12984i
\(263\) 10.1330 19.8871i 0.624825 1.22629i −0.334075 0.942546i \(-0.608424\pi\)
0.958901 0.283743i \(-0.0915761\pi\)
\(264\) −5.89216 + 2.77779i −0.362637 + 0.170961i
\(265\) −18.5409 1.13061i −1.13896 0.0694527i
\(266\) −21.0902 + 6.85264i −1.29313 + 0.420162i
\(267\) −1.02442 1.50507i −0.0626933 0.0921086i
\(268\) 4.37951 4.37951i 0.267521 0.267521i
\(269\) 20.2239 14.6936i 1.23308 0.895882i 0.235959 0.971763i \(-0.424177\pi\)
0.997117 + 0.0758813i \(0.0241770\pi\)
\(270\) −11.4832 1.77085i −0.698846 0.107771i
\(271\) −13.1402 9.54690i −0.798209 0.579933i 0.112179 0.993688i \(-0.464217\pi\)
−0.910388 + 0.413755i \(0.864217\pi\)
\(272\) 0.406920 0.0644499i 0.0246732 0.00390785i
\(273\) −28.3706 10.1911i −1.71706 0.616795i
\(274\) 7.22848i 0.436688i
\(275\) −13.7575 12.8197i −0.829609 0.773056i
\(276\) 5.96767 + 6.34583i 0.359212 + 0.381974i
\(277\) −6.13564 + 3.12626i −0.368655 + 0.187839i −0.628497 0.777812i \(-0.716330\pi\)
0.259842 + 0.965651i \(0.416330\pi\)
\(278\) −1.51633 9.57375i −0.0909436 0.574195i
\(279\) −7.71813 6.36643i −0.462072 0.381148i
\(280\) 9.09334 3.95588i 0.543431 0.236409i
\(281\) 14.3948 + 19.8128i 0.858723 + 1.18193i 0.981873 + 0.189542i \(0.0607004\pi\)
−0.123150 + 0.992388i \(0.539300\pi\)
\(282\) −8.94834 0.274810i −0.532866 0.0163647i
\(283\) −1.14551 + 7.23244i −0.0680933 + 0.429924i 0.929966 + 0.367646i \(0.119836\pi\)
−0.998059 + 0.0622774i \(0.980164\pi\)
\(284\) 0.521549 + 1.60516i 0.0309482 + 0.0952489i
\(285\) 4.76660 18.7705i 0.282349 1.11187i
\(286\) 4.56103 14.0374i 0.269699 0.830049i
\(287\) −13.4865 6.87171i −0.796083 0.405624i
\(288\) 2.58441 + 1.52343i 0.152288 + 0.0897690i
\(289\) 16.0065 + 5.20084i 0.941561 + 0.305932i
\(290\) 3.83966 + 1.51167i 0.225473 + 0.0887684i
\(291\) 11.7087 + 6.42603i 0.686378 + 0.376701i
\(292\) 3.53809 + 0.560378i 0.207051 + 0.0327936i
\(293\) 1.14628 + 1.14628i 0.0669662 + 0.0669662i 0.739797 0.672830i \(-0.234922\pi\)
−0.672830 + 0.739797i \(0.734922\pi\)
\(294\) −4.09590 + 21.5552i −0.238878 + 1.25712i
\(295\) 12.5012 1.20603i 0.727846 0.0702179i
\(296\) −3.10360 + 4.27173i −0.180393 + 0.248290i
\(297\) 14.6866 + 12.8921i 0.852203 + 0.748076i
\(298\) 1.88370 + 3.69696i 0.109120 + 0.214159i
\(299\) −19.7377 −1.14146
\(300\) −1.31565 + 8.55974i −0.0759590 + 0.494197i
\(301\) 23.3084 1.34347
\(302\) 4.31323 + 8.46519i 0.248198 + 0.487117i
\(303\) 15.1789 + 11.7566i 0.872003 + 0.675397i
\(304\) −2.93913 + 4.04536i −0.168571 + 0.232018i
\(305\) −27.6748 16.2949i −1.58466 0.933044i
\(306\) −0.663762 1.04262i −0.0379447 0.0596028i
\(307\) −8.29257 8.29257i −0.473282 0.473282i 0.429693 0.902975i \(-0.358622\pi\)
−0.902975 + 0.429693i \(0.858622\pi\)
\(308\) −16.4737 2.60917i −0.938673 0.148671i
\(309\) −2.04361 + 3.72362i −0.116257 + 0.211829i
\(310\) −4.74239 + 5.75512i −0.269349 + 0.326869i
\(311\) 31.4637 + 10.2232i 1.78414 + 0.579703i 0.999205 0.0398725i \(-0.0126952\pi\)
0.784937 + 0.619575i \(0.212695\pi\)
\(312\) −6.52620 + 1.90110i −0.369473 + 0.107628i
\(313\) 3.90255 + 1.98845i 0.220585 + 0.112394i 0.560791 0.827957i \(-0.310497\pi\)
−0.340206 + 0.940351i \(0.610497\pi\)
\(314\) 1.30346 4.01165i 0.0735587 0.226391i
\(315\) −21.7548 20.2921i −1.22574 1.14333i
\(316\) −3.28499 10.1102i −0.184795 0.568740i
\(317\) −4.38047 + 27.6572i −0.246032 + 1.55338i 0.487131 + 0.873329i \(0.338043\pi\)
−0.733163 + 0.680053i \(0.761957\pi\)
\(318\) 0.441669 14.3816i 0.0247676 0.806481i
\(319\) −4.07954 5.61501i −0.228411 0.314380i
\(320\) 1.13454 1.92687i 0.0634226 0.107715i
\(321\) 1.32968 + 10.4654i 0.0742157 + 0.584119i
\(322\) 3.48914 + 22.0296i 0.194442 + 1.22766i
\(323\) 1.83557 0.935268i 0.102134 0.0520397i
\(324\) 1.10246 8.93222i 0.0612479 0.496235i
\(325\) −12.0865 15.4584i −0.670439 0.857476i
\(326\) 10.4218i 0.577212i
\(327\) −2.74742 + 7.64841i −0.151933 + 0.422958i
\(328\) −3.37103 + 0.533919i −0.186134 + 0.0294807i
\(329\) −18.5447 13.4735i −1.02240 0.742818i
\(330\) 9.60375 10.9515i 0.528669 0.602862i
\(331\) 7.75360 5.63332i 0.426176 0.309635i −0.353942 0.935267i \(-0.615159\pi\)
0.780118 + 0.625632i \(0.215159\pi\)
\(332\) 5.01427 5.01427i 0.275194 0.275194i
\(333\) 15.4639 + 3.43338i 0.847416 + 0.188148i
\(334\) −13.3140 + 4.32598i −0.728510 + 0.236707i
\(335\) −5.07341 + 12.8865i −0.277190 + 0.704065i
\(336\) 3.27552 + 6.94793i 0.178694 + 0.379041i
\(337\) −7.11185 + 13.9578i −0.387407 + 0.760329i −0.999537 0.0304279i \(-0.990313\pi\)
0.612130 + 0.790757i \(0.290313\pi\)
\(338\) 1.09039 2.14002i 0.0593095 0.116401i
\(339\) −12.6283 26.7867i −0.685874 1.45485i
\(340\) −0.776879 + 0.495126i −0.0421322 + 0.0268520i
\(341\) 11.9289 3.87592i 0.645983 0.209893i
\(342\) 14.6444 + 3.25144i 0.791880 + 0.175818i
\(343\) −17.7729 + 17.7729i −0.959645 + 0.959645i
\(344\) 4.25201 3.08927i 0.229253 0.166562i
\(345\) −17.8969 7.68858i −0.963537 0.413939i
\(346\) −5.67103 4.12024i −0.304876 0.221506i
\(347\) −36.4678 + 5.77593i −1.95769 + 0.310068i −0.957963 + 0.286891i \(0.907378\pi\)
−0.999731 + 0.0231773i \(0.992622\pi\)
\(348\) −1.08059 + 3.00819i −0.0579255 + 0.161256i
\(349\) 15.0145i 0.803705i −0.915704 0.401853i \(-0.868366\pi\)
0.915704 0.401853i \(-0.131634\pi\)
\(350\) −15.1167 + 16.2226i −0.808024 + 0.867135i
\(351\) 13.0322 + 15.6847i 0.695610 + 0.837186i
\(352\) −3.35101 + 1.70742i −0.178609 + 0.0910060i
\(353\) 4.70953 + 29.7348i 0.250663 + 1.58263i 0.716392 + 0.697698i \(0.245792\pi\)
−0.465729 + 0.884927i \(0.654208\pi\)
\(354\) 1.22618 + 9.65074i 0.0651708 + 0.512931i
\(355\) −2.50122 2.82607i −0.132751 0.149992i
\(356\) −0.617842 0.850386i −0.0327456 0.0450704i
\(357\) 0.0971428 3.16316i 0.00514134 0.167412i
\(358\) −0.442795 + 2.79569i −0.0234024 + 0.147757i
\(359\) 1.07807 + 3.31797i 0.0568986 + 0.175116i 0.975467 0.220147i \(-0.0706536\pi\)
−0.918568 + 0.395263i \(0.870654\pi\)
\(360\) −6.65809 0.818408i −0.350912 0.0431339i
\(361\) −1.85517 + 5.70961i −0.0976403 + 0.300506i
\(362\) 0.311866 + 0.158904i 0.0163913 + 0.00835180i
\(363\) −5.22917 + 1.52327i −0.274460 + 0.0799508i
\(364\) −16.5526 5.37828i −0.867594 0.281898i
\(365\) −7.75452 + 2.00697i −0.405890 + 0.105049i
\(366\) 11.9689 21.8082i 0.625623 1.13993i
\(367\) 15.4679 + 2.44988i 0.807418 + 0.127882i 0.546479 0.837473i \(-0.315968\pi\)
0.260939 + 0.965355i \(0.415968\pi\)
\(368\) 3.55628 + 3.55628i 0.185384 + 0.185384i
\(369\) 5.49877 + 8.63735i 0.286254 + 0.449642i
\(370\) 2.55335 11.5274i 0.132742 0.599280i
\(371\) 21.6544 29.8047i 1.12424 1.54738i
\(372\) −4.56679 3.53714i −0.236777 0.183392i
\(373\) 2.89590 + 5.68352i 0.149944 + 0.294282i 0.953745 0.300616i \(-0.0971924\pi\)
−0.803801 + 0.594898i \(0.797192\pi\)
\(374\) 1.54947 0.0801213
\(375\) −4.93766 18.7248i −0.254980 0.966946i
\(376\) −5.16876 −0.266558
\(377\) −3.28799 6.45305i −0.169340 0.332349i
\(378\) 15.2021 17.3182i 0.781914 0.890751i
\(379\) −15.8374 + 21.7983i −0.813510 + 1.11970i 0.177262 + 0.984164i \(0.443276\pi\)
−0.990772 + 0.135537i \(0.956724\pi\)
\(380\) 2.41804 10.9165i 0.124043 0.560005i
\(381\) 6.34169 33.3739i 0.324895 1.70980i
\(382\) −0.802829 0.802829i −0.0410763 0.0410763i
\(383\) −29.5784 4.68475i −1.51138 0.239380i −0.654964 0.755660i \(-0.727316\pi\)
−0.856420 + 0.516280i \(0.827316\pi\)
\(384\) 1.51840 + 0.833337i 0.0774857 + 0.0425260i
\(385\) 36.1057 9.34462i 1.84012 0.476246i
\(386\) −5.59756 1.81876i −0.284908 0.0925723i
\(387\) −13.5831 8.00681i −0.690466 0.407009i
\(388\) 6.87074 + 3.50082i 0.348809 + 0.177727i
\(389\) 3.57268 10.9956i 0.181142 0.557497i −0.818719 0.574195i \(-0.805315\pi\)
0.999861 + 0.0166975i \(0.00531522\pi\)
\(390\) 11.6858 9.71949i 0.591735 0.492166i
\(391\) −0.640299 1.97064i −0.0323813 0.0996594i
\(392\) −1.98165 + 12.5116i −0.100088 + 0.631932i
\(393\) −35.5338 1.09127i −1.79244 0.0550472i
\(394\) −11.2945 15.5455i −0.569007 0.783170i
\(395\) 15.7540 + 17.8001i 0.792669 + 0.895620i
\(396\) 8.70380 + 7.17947i 0.437382 + 0.360782i
\(397\) −2.09608 13.2341i −0.105199 0.664203i −0.982781 0.184775i \(-0.940844\pi\)
0.877581 0.479427i \(-0.159156\pi\)
\(398\) −11.3268 + 5.77130i −0.567762 + 0.289289i
\(399\) 26.3130 + 27.9803i 1.31730 + 1.40077i
\(400\) −0.607532 + 4.96295i −0.0303766 + 0.248148i
\(401\) 22.2904i 1.11313i 0.830804 + 0.556565i \(0.187881\pi\)
−0.830804 + 0.556565i \(0.812119\pi\)
\(402\) −10.0960 3.62662i −0.503541 0.180879i
\(403\) 12.9272 2.04746i 0.643948 0.101991i
\(404\) 8.96775 + 6.51545i 0.446162 + 0.324156i
\(405\) 5.70705 + 19.2984i 0.283585 + 0.958947i
\(406\) −6.62112 + 4.81053i −0.328601 + 0.238742i
\(407\) −14.0419 + 14.0419i −0.696032 + 0.696032i
\(408\) −0.401520 0.589911i −0.0198782 0.0292050i
\(409\) 13.3939 4.35194i 0.662285 0.215190i 0.0414620 0.999140i \(-0.486798\pi\)
0.620823 + 0.783951i \(0.286798\pi\)
\(410\) 6.43586 4.10175i 0.317844 0.202571i
\(411\) 11.3247 5.33889i 0.558606 0.263348i
\(412\) −1.11333 + 2.18504i −0.0548499 + 0.107649i
\(413\) −11.3084 + 22.1939i −0.556448 + 1.09209i
\(414\) 5.53420 14.0364i 0.271991 0.689851i
\(415\) −5.80873 + 14.7542i −0.285139 + 0.724257i
\(416\) −3.73243 + 1.21274i −0.182998 + 0.0594595i
\(417\) −13.8790 + 9.44670i −0.679660 + 0.462607i
\(418\) −13.2978 + 13.2978i −0.650416 + 0.650416i
\(419\) −4.58918 + 3.33423i −0.224196 + 0.162888i −0.694213 0.719769i \(-0.744248\pi\)
0.470017 + 0.882657i \(0.344248\pi\)
\(420\) −12.9139 11.3246i −0.630132 0.552583i
\(421\) 5.16685 + 3.75393i 0.251817 + 0.182956i 0.706532 0.707682i \(-0.250259\pi\)
−0.454715 + 0.890637i \(0.650259\pi\)
\(422\) 17.2214 2.72761i 0.838327 0.132778i
\(423\) 6.17863 + 14.2221i 0.300415 + 0.691504i
\(424\) 8.30714i 0.403431i
\(425\) 1.15129 1.70821i 0.0558459 0.0828603i
\(426\) 2.12956 2.00266i 0.103178 0.0970292i
\(427\) 56.7531 28.9171i 2.74647 1.39940i
\(428\) 0.952804 + 6.01577i 0.0460555 + 0.290783i
\(429\) −25.3608 + 3.22224i −1.22443 + 0.155571i
\(430\) −5.96288 + 10.1272i −0.287555 + 0.488376i
\(431\) 11.7415 + 16.1608i 0.565568 + 0.778437i 0.992021 0.126072i \(-0.0402371\pi\)
−0.426453 + 0.904510i \(0.640237\pi\)
\(432\) 0.477906 5.17413i 0.0229932 0.248940i
\(433\) −3.62919 + 22.9138i −0.174408 + 1.10117i 0.732787 + 0.680458i \(0.238219\pi\)
−0.907195 + 0.420710i \(0.861781\pi\)
\(434\) −4.57041 14.0663i −0.219387 0.675203i
\(435\) −0.467637 7.13202i −0.0224215 0.341954i
\(436\) −1.44993 + 4.46242i −0.0694390 + 0.213711i
\(437\) 22.4074 + 11.4171i 1.07189 + 0.546156i
\(438\) −1.73527 5.95694i −0.0829144 0.284633i
\(439\) 10.7777 + 3.50189i 0.514393 + 0.167136i 0.554699 0.832051i \(-0.312833\pi\)
−0.0403065 + 0.999187i \(0.512833\pi\)
\(440\) 5.34803 6.49009i 0.254957 0.309403i
\(441\) 36.7952 9.50351i 1.75215 0.452548i
\(442\) 1.59696 + 0.252934i 0.0759598 + 0.0120309i
\(443\) −5.43418 5.43418i −0.258186 0.258186i 0.566130 0.824316i \(-0.308440\pi\)
−0.824316 + 0.566130i \(0.808440\pi\)
\(444\) 8.98473 + 1.70727i 0.426396 + 0.0810236i
\(445\) 2.02540 + 1.19255i 0.0960132 + 0.0565324i
\(446\) 13.3051 18.3129i 0.630015 0.867141i
\(447\) 4.40067 5.68169i 0.208144 0.268735i
\(448\) 2.01336 + 3.95145i 0.0951225 + 0.186688i
\(449\) 26.9459 1.27165 0.635827 0.771831i \(-0.280659\pi\)
0.635827 + 0.771831i \(0.280659\pi\)
\(450\) 14.3821 4.26095i 0.677978 0.200863i
\(451\) −12.8362 −0.604434
\(452\) −7.76223 15.2342i −0.365104 0.716558i
\(453\) 10.0765 13.0098i 0.473436 0.611252i
\(454\) 11.3490 15.6205i 0.532634 0.733108i
\(455\) 38.7378 3.73717i 1.81605 0.175201i
\(456\) 8.50860 + 1.61680i 0.398452 + 0.0757136i
\(457\) 24.1951 + 24.1951i 1.13180 + 1.13180i 0.989878 + 0.141919i \(0.0453271\pi\)
0.141919 + 0.989878i \(0.454673\pi\)
\(458\) −16.0987 2.54978i −0.752241 0.119143i
\(459\) −1.14321 + 1.80997i −0.0533603 + 0.0844823i
\(460\) −10.4642 4.11974i −0.487894 0.192084i
\(461\) −35.3066 11.4718i −1.64439 0.534295i −0.666877 0.745168i \(-0.732369\pi\)
−0.977513 + 0.210873i \(0.932369\pi\)
\(462\) 8.07957 + 27.7360i 0.375896 + 1.29040i
\(463\) 6.25735 + 3.18828i 0.290804 + 0.148172i 0.593307 0.804977i \(-0.297822\pi\)
−0.302503 + 0.953149i \(0.597822\pi\)
\(464\) −0.570270 + 1.75511i −0.0264741 + 0.0814790i
\(465\) 12.5191 + 3.17911i 0.580560 + 0.147428i
\(466\) 0.188063 + 0.578799i 0.00871187 + 0.0268124i
\(467\) 4.48899 28.3424i 0.207726 1.31153i −0.634718 0.772744i \(-0.718884\pi\)
0.842444 0.538785i \(-0.181116\pi\)
\(468\) 7.79860 + 8.82032i 0.360490 + 0.407719i
\(469\) −16.1449 22.2215i −0.745502 1.02609i
\(470\) 10.5983 4.61056i 0.488861 0.212669i
\(471\) −7.24770 + 0.920861i −0.333956 + 0.0424310i
\(472\) 0.878638 + 5.54750i 0.0404426 + 0.255344i
\(473\) 17.6121 8.97383i 0.809807 0.412617i
\(474\) −13.4131 + 12.6138i −0.616084 + 0.579371i
\(475\) 4.77953 + 24.5406i 0.219300 + 1.12600i
\(476\) 1.82711i 0.0837455i
\(477\) −22.8576 + 9.93018i −1.04658 + 0.454672i
\(478\) 7.92207 1.25473i 0.362347 0.0573901i
\(479\) −10.3928 7.55082i −0.474860 0.345006i 0.324473 0.945895i \(-0.394813\pi\)
−0.799332 + 0.600889i \(0.794813\pi\)
\(480\) −3.85674 0.354288i −0.176036 0.0161709i
\(481\) −16.7645 + 12.1801i −0.764394 + 0.555365i
\(482\) −5.12480 + 5.12480i −0.233428 + 0.233428i
\(483\) 31.9362 21.7372i 1.45315 0.989077i
\(484\) −2.99064 + 0.971718i −0.135938 + 0.0441690i
\(485\) −17.2108 1.04950i −0.781503 0.0476554i
\(486\) −14.8082 + 4.87006i −0.671713 + 0.220910i
\(487\) 9.39682 18.4423i 0.425810 0.835700i −0.574047 0.818822i \(-0.694627\pi\)
0.999858 0.0168777i \(-0.00537258\pi\)
\(488\) 6.52048 12.7972i 0.295168 0.579301i
\(489\) 16.3277 7.69748i 0.738363 0.348092i
\(490\) −7.09717 27.4220i −0.320617 1.23880i
\(491\) −26.5707 + 8.63333i −1.19912 + 0.389617i −0.839436 0.543459i \(-0.817114\pi\)
−0.359681 + 0.933075i \(0.617114\pi\)
\(492\) 3.32629 + 4.88697i 0.149961 + 0.220322i
\(493\) 0.537617 0.537617i 0.0242131 0.0242131i
\(494\) −15.8761 + 11.5346i −0.714298 + 0.518968i
\(495\) −24.2508 6.95729i −1.08999 0.312707i
\(496\) −2.69808 1.96027i −0.121148 0.0880188i
\(497\) 7.39279 1.17090i 0.331612 0.0525221i
\(498\) −11.5592 4.15225i −0.517982 0.186067i
\(499\) 0.405848i 0.0181683i −0.999959 0.00908413i \(-0.997108\pi\)
0.999959 0.00908413i \(-0.00289161\pi\)
\(500\) −3.18127 10.7182i −0.142271 0.479332i
\(501\) 16.6110 + 17.6636i 0.742126 + 0.789153i
\(502\) −12.9659 + 6.60645i −0.578696 + 0.294860i
\(503\) −0.948431 5.98816i −0.0422885 0.266999i 0.957480 0.288498i \(-0.0931560\pi\)
−0.999769 + 0.0214995i \(0.993156\pi\)
\(504\) 8.46590 10.2634i 0.377101 0.457167i
\(505\) −24.1997 5.36030i −1.07687 0.238530i
\(506\) 11.1179 + 15.3025i 0.494252 + 0.680280i
\(507\) −4.15807 0.127697i −0.184666 0.00567123i
\(508\) 3.06818 19.3717i 0.136129 0.859482i
\(509\) 1.17675 + 3.62167i 0.0521586 + 0.160528i 0.973743 0.227651i \(-0.0731044\pi\)
−0.921584 + 0.388178i \(0.873104\pi\)
\(510\) 1.34950 + 0.851423i 0.0597568 + 0.0377017i
\(511\) 4.90915 15.1088i 0.217168 0.668375i
\(512\) 0.891007 + 0.453990i 0.0393773 + 0.0200637i
\(513\) −5.72229 25.3446i −0.252645 1.11899i
\(514\) −1.39651 0.453755i −0.0615976 0.0200143i
\(515\) 0.333763 5.47339i 0.0147073 0.241187i
\(516\) −7.98039 4.37983i −0.351317 0.192811i
\(517\) −19.2000 3.04098i −0.844414 0.133742i
\(518\) 16.5580 + 16.5580i 0.727515 + 0.727515i
\(519\) −2.26652 + 11.9279i −0.0994894 + 0.523575i
\(520\) 6.57138 5.81601i 0.288174 0.255049i
\(521\) −1.70955 + 2.35299i −0.0748966 + 0.103086i −0.844822 0.535048i \(-0.820294\pi\)
0.769925 + 0.638134i \(0.220294\pi\)
\(522\) 5.51098 0.528892i 0.241209 0.0231490i
\(523\) 4.02250 + 7.89460i 0.175892 + 0.345207i 0.962074 0.272787i \(-0.0879455\pi\)
−0.786183 + 0.617994i \(0.787946\pi\)
\(524\) −20.5251 −0.896645
\(525\) 36.5807 + 11.7012i 1.59651 + 0.510682i
\(526\) −22.3198 −0.973188
\(527\) 0.623784 + 1.22424i 0.0271724 + 0.0533289i
\(528\) 5.15001 + 3.98886i 0.224125 + 0.173593i
\(529\) 1.34851 1.85606i 0.0586307 0.0806982i
\(530\) 7.41001 + 17.0333i 0.321870 + 0.739881i
\(531\) 14.2140 9.04899i 0.616833 0.392693i
\(532\) 15.6805 + 15.6805i 0.679837 + 0.679837i
\(533\) −13.2296 2.09537i −0.573040 0.0907606i
\(534\) −0.875950 + 1.59605i −0.0379060 + 0.0690678i
\(535\) −7.31976 11.4851i −0.316461 0.496544i
\(536\) −5.89043 1.91392i −0.254428 0.0826686i
\(537\) 4.70700 1.37116i 0.203122 0.0591699i
\(538\) −22.2735 11.3489i −0.960280 0.489287i
\(539\) −14.7221 + 45.3100i −0.634127 + 1.95164i
\(540\) 3.63543 + 11.0356i 0.156444 + 0.474895i
\(541\) −11.3923 35.0618i −0.489792 1.50742i −0.824919 0.565251i \(-0.808779\pi\)
0.335128 0.942173i \(-0.391221\pi\)
\(542\) −2.54083 + 16.0422i −0.109138 + 0.689071i
\(543\) 0.0186094 0.605959i 0.000798607 0.0260042i
\(544\) −0.242163 0.333309i −0.0103827 0.0142905i
\(545\) −1.00750 10.4433i −0.0431566 0.447342i
\(546\) 3.79961 + 29.9050i 0.162608 + 1.27982i
\(547\) 4.14971 + 26.2003i 0.177429 + 1.12024i 0.902221 + 0.431274i \(0.141936\pi\)
−0.724792 + 0.688968i \(0.758064\pi\)
\(548\) 6.44062 3.28166i 0.275130 0.140186i
\(549\) −43.0066 2.64402i −1.83548 0.112844i
\(550\) −5.17665 + 18.0781i −0.220733 + 0.770851i
\(551\) 9.22780i 0.393118i
\(552\) 2.94491 8.19818i 0.125344 0.348938i
\(553\) −46.5636 + 7.37495i −1.98009 + 0.313615i
\(554\) 5.57104 + 4.04760i 0.236691 + 0.171966i
\(555\) −19.9456 + 4.51375i −0.846643 + 0.191598i
\(556\) −7.84187 + 5.69745i −0.332569 + 0.241626i
\(557\) −20.9449 + 20.9449i −0.887465 + 0.887465i −0.994279 0.106814i \(-0.965935\pi\)
0.106814 + 0.994279i \(0.465935\pi\)
\(558\) −2.16857 + 9.76720i −0.0918029 + 0.413479i
\(559\) 19.6168 6.37389i 0.829703 0.269587i
\(560\) −7.65300 6.30630i −0.323398 0.266490i
\(561\) −1.14443 2.42753i −0.0483178 0.102490i
\(562\) 11.1182 21.8207i 0.468993 0.920450i
\(563\) −6.85128 + 13.4464i −0.288747 + 0.566698i −0.989126 0.147073i \(-0.953015\pi\)
0.700378 + 0.713772i \(0.253015\pi\)
\(564\) 3.81760 + 8.09779i 0.160750 + 0.340978i
\(565\) 29.5050 + 24.3130i 1.24129 + 1.02286i
\(566\) 6.96420 2.26281i 0.292727 0.0951128i
\(567\) −38.3602 11.0258i −1.61098 0.463041i
\(568\) 1.19343 1.19343i 0.0500753 0.0500753i
\(569\) 7.06373 5.13210i 0.296127 0.215149i −0.429794 0.902927i \(-0.641414\pi\)
0.725921 + 0.687778i \(0.241414\pi\)
\(570\) −18.8886 + 4.27455i −0.791157 + 0.179041i
\(571\) 19.6305 + 14.2624i 0.821513 + 0.596864i 0.917145 0.398553i \(-0.130487\pi\)
−0.0956328 + 0.995417i \(0.530487\pi\)
\(572\) −14.5781 + 2.30894i −0.609540 + 0.0965416i
\(573\) −0.664813 + 1.85074i −0.0277730 + 0.0773157i
\(574\) 15.1362i 0.631775i
\(575\) 25.1310 0.886795i 1.04804 0.0369819i
\(576\) 0.184091 2.99435i 0.00767044 0.124764i
\(577\) 32.6160 16.6187i 1.35782 0.691845i 0.384896 0.922960i \(-0.374237\pi\)
0.972927 + 0.231114i \(0.0742372\pi\)
\(578\) −2.63283 16.6231i −0.109511 0.691428i
\(579\) 1.28490 + 10.1129i 0.0533987 + 0.420277i
\(580\) −0.396260 4.10745i −0.0164538 0.170552i
\(581\) −18.4849 25.4423i −0.766882 1.05552i
\(582\) 0.409985 13.3499i 0.0169944 0.553372i
\(583\) 4.88741 30.8579i 0.202416 1.27800i
\(584\) −1.10696 3.40687i −0.0458062 0.140977i
\(585\) −23.8584 11.1292i −0.986422 0.460136i
\(586\) 0.500941 1.54174i 0.0206937 0.0636887i
\(587\) 10.1304 + 5.16169i 0.418126 + 0.213046i 0.650379 0.759609i \(-0.274610\pi\)
−0.232254 + 0.972655i \(0.574610\pi\)
\(588\) 21.0653 6.13637i 0.868719 0.253060i
\(589\) −15.8600 5.15324i −0.653501 0.212335i
\(590\) −6.75000 10.5911i −0.277893 0.436029i
\(591\) −16.0128 + 29.1766i −0.658678 + 1.20016i
\(592\) 5.21515 + 0.825998i 0.214341 + 0.0339483i
\(593\) 16.4362 + 16.4362i 0.674952 + 0.674952i 0.958854 0.283901i \(-0.0916288\pi\)
−0.283901 + 0.958854i \(0.591629\pi\)
\(594\) 4.81937 18.9388i 0.197741 0.777066i
\(595\) 1.62979 + 3.74639i 0.0668150 + 0.153587i
\(596\) 2.43884 3.35677i 0.0998986 0.137499i
\(597\) 17.4077 + 13.4829i 0.712449 + 0.551817i
\(598\) 8.96072 + 17.5864i 0.366431 + 0.719162i
\(599\) 16.9386 0.692094 0.346047 0.938217i \(-0.387524\pi\)
0.346047 + 0.938217i \(0.387524\pi\)
\(600\) 8.22407 2.71379i 0.335746 0.110790i
\(601\) −26.0220 −1.06146 −0.530730 0.847541i \(-0.678082\pi\)
−0.530730 + 0.847541i \(0.678082\pi\)
\(602\) −10.5818 20.7679i −0.431281 0.846437i
\(603\) 1.77504 + 18.4957i 0.0722854 + 0.753204i
\(604\) 5.58437 7.68623i 0.227225 0.312748i
\(605\) 5.26537 4.66012i 0.214068 0.189461i
\(606\) 3.58411 18.8618i 0.145595 0.766210i
\(607\) −29.4219 29.4219i −1.19420 1.19420i −0.975877 0.218322i \(-0.929942\pi\)
−0.218322 0.975877i \(-0.570058\pi\)
\(608\) 4.93878 + 0.782226i 0.200294 + 0.0317235i
\(609\) 12.4269 + 6.82016i 0.503562 + 0.276367i
\(610\) −1.95476 + 32.0562i −0.0791459 + 1.29792i
\(611\) −19.2921 6.26837i −0.780473 0.253591i
\(612\) −0.627642 + 1.06476i −0.0253709 + 0.0430402i
\(613\) 5.01575 + 2.55565i 0.202584 + 0.103222i 0.552339 0.833619i \(-0.313735\pi\)
−0.349755 + 0.936841i \(0.613735\pi\)
\(614\) −3.62398 + 11.1535i −0.146252 + 0.450118i
\(615\) −11.1796 7.05340i −0.450805 0.284421i
\(616\) 5.15409 + 15.8627i 0.207664 + 0.639125i
\(617\) 5.57460 35.1967i 0.224425 1.41696i −0.575960 0.817478i \(-0.695372\pi\)
0.800385 0.599486i \(-0.204628\pi\)
\(618\) 4.24555 + 0.130384i 0.170781 + 0.00524480i
\(619\) −20.2991 27.9393i −0.815889 1.12297i −0.990388 0.138317i \(-0.955831\pi\)
0.174499 0.984657i \(-0.444169\pi\)
\(620\) 7.28085 + 1.61273i 0.292406 + 0.0647687i
\(621\) −26.0780 + 1.69685i −1.04648 + 0.0680922i
\(622\) −5.17530 32.6756i −0.207511 1.31017i
\(623\) −4.15351 + 2.11632i −0.166407 + 0.0847885i
\(624\) 4.65672 + 4.95180i 0.186418 + 0.198231i
\(625\) 16.0837 + 19.1394i 0.643348 + 0.765574i
\(626\) 4.37993i 0.175057i
\(627\) 30.6550 + 11.0117i 1.22424 + 0.439766i
\(628\) −4.16617 + 0.659856i −0.166248 + 0.0263311i
\(629\) −1.75992 1.27866i −0.0701727 0.0509835i
\(630\) −8.20391 + 28.5961i −0.326851 + 1.13930i
\(631\) −6.95722 + 5.05472i −0.276963 + 0.201225i −0.717591 0.696464i \(-0.754755\pi\)
0.440629 + 0.897689i \(0.354755\pi\)
\(632\) −7.51686 + 7.51686i −0.299005 + 0.299005i
\(633\) −16.9929 24.9659i −0.675407 0.992305i
\(634\) 26.6314 8.65307i 1.05767 0.343657i
\(635\) 10.9885 + 42.4575i 0.436067 + 1.68488i
\(636\) −13.0146 + 6.13559i −0.516063 + 0.243292i
\(637\) −22.5697 + 44.2955i −0.894244 + 1.75505i
\(638\) −3.15094 + 6.18406i −0.124747 + 0.244829i
\(639\) −4.71040 1.85719i −0.186341 0.0734695i
\(640\) −2.23192 0.136101i −0.0882245 0.00537985i
\(641\) −12.9664 + 4.21305i −0.512144 + 0.166406i −0.553677 0.832732i \(-0.686776\pi\)
0.0415332 + 0.999137i \(0.486776\pi\)
\(642\) 8.72104 5.93593i 0.344192 0.234273i
\(643\) −11.4059 + 11.4059i −0.449806 + 0.449806i −0.895290 0.445484i \(-0.853032\pi\)
0.445484 + 0.895290i \(0.353032\pi\)
\(644\) 18.0445 13.1101i 0.711051 0.516609i
\(645\) 20.2702 + 1.86206i 0.798138 + 0.0733184i
\(646\) −1.66666 1.21090i −0.0655739 0.0476422i
\(647\) 30.9551 4.90280i 1.21697 0.192749i 0.485263 0.874368i \(-0.338724\pi\)
0.731707 + 0.681619i \(0.238724\pi\)
\(648\) −8.45917 + 3.07284i −0.332308 + 0.120713i
\(649\) 21.1238i 0.829181i
\(650\) −8.28635 + 17.7871i −0.325017 + 0.697668i
\(651\) −18.6617 + 17.5496i −0.731409 + 0.687823i
\(652\) 9.28593 4.73142i 0.363665 0.185297i
\(653\) −5.98789 37.8061i −0.234324 1.47947i −0.771626 0.636076i \(-0.780556\pi\)
0.537302 0.843390i \(-0.319444\pi\)
\(654\) 8.06209 1.02433i 0.315253 0.0400546i
\(655\) 42.0857 18.3085i 1.64442 0.715373i
\(656\) 2.00614 + 2.76122i 0.0783266 + 0.107807i
\(657\) −8.05095 + 7.11835i −0.314098 + 0.277713i
\(658\) −3.58587 + 22.6403i −0.139792 + 0.882610i
\(659\) 6.33270 + 19.4901i 0.246687 + 0.759225i 0.995354 + 0.0962789i \(0.0306941\pi\)
−0.748667 + 0.662946i \(0.769306\pi\)
\(660\) −14.1179 3.58511i −0.549539 0.139550i
\(661\) −13.4948 + 41.5327i −0.524887 + 1.61544i 0.239652 + 0.970859i \(0.422967\pi\)
−0.764539 + 0.644577i \(0.777033\pi\)
\(662\) −8.53939 4.35103i −0.331893 0.169108i
\(663\) −0.783237 2.68874i −0.0304184 0.104422i
\(664\) −6.74418 2.19132i −0.261725 0.0850395i
\(665\) −46.1391 18.1649i −1.78920 0.704406i
\(666\) −3.96130 15.3372i −0.153497 0.594303i
\(667\) 9.16704 + 1.45192i 0.354949 + 0.0562184i
\(668\) 9.89891 + 9.89891i 0.383000 + 0.383000i
\(669\) −38.5175 7.31907i −1.48917 0.282971i
\(670\) 13.7852 1.32991i 0.532570 0.0513789i
\(671\) 31.7502 43.7004i 1.22570 1.68703i
\(672\) 4.70360 6.07280i 0.181445 0.234263i
\(673\) −16.8283 33.0273i −0.648681 1.27311i −0.947792 0.318890i \(-0.896690\pi\)
0.299110 0.954219i \(-0.403310\pi\)
\(674\) 15.6652 0.603401
\(675\) −17.2980 19.3850i −0.665801 0.746129i
\(676\) −2.40180 −0.0923767
\(677\) −18.9516 37.1946i −0.728369 1.42951i −0.896182 0.443686i \(-0.853670\pi\)
0.167813 0.985819i \(-0.446330\pi\)
\(678\) −18.1340 + 23.4128i −0.696433 + 0.899163i
\(679\) 20.1010 27.6666i 0.771404 1.06175i
\(680\) 0.793856 + 0.467421i 0.0304430 + 0.0179248i
\(681\) −32.8546 6.24301i −1.25899 0.239233i
\(682\) −8.86905 8.86905i −0.339614 0.339614i
\(683\) 50.2616 + 7.96066i 1.92321 + 0.304606i 0.997318 0.0731865i \(-0.0233168\pi\)
0.925890 + 0.377793i \(0.123317\pi\)
\(684\) −3.75138 14.5244i −0.143437 0.555354i
\(685\) −10.2789 + 12.4739i −0.392736 + 0.476604i
\(686\) 23.9045 + 7.76703i 0.912677 + 0.296547i
\(687\) 7.89565 + 27.1047i 0.301238 + 1.03411i
\(688\) −4.68293 2.38607i −0.178535 0.0909681i
\(689\) 10.0744 31.0059i 0.383805 1.18123i
\(690\) 1.27444 + 19.4368i 0.0485172 + 0.739946i
\(691\) −9.91187 30.5056i −0.377065 1.16049i −0.942075 0.335403i \(-0.891128\pi\)
0.565010 0.825084i \(-0.308872\pi\)
\(692\) −1.09657 + 6.92347i −0.0416854 + 0.263191i
\(693\) 37.4860 33.1437i 1.42397 1.25902i
\(694\) 21.7024 + 29.8708i 0.823813 + 1.13388i
\(695\) 10.9972 18.6773i 0.417147 0.708471i
\(696\) 3.17089 0.402880i 0.120192 0.0152711i
\(697\) −0.219971 1.38884i −0.00833198 0.0526061i
\(698\) −13.3780 + 6.81642i −0.506364 + 0.258005i
\(699\) 0.767891 0.722131i 0.0290443 0.0273135i
\(700\) 21.3173 + 6.10421i 0.805719 + 0.230717i
\(701\) 32.1785i 1.21536i −0.794180 0.607682i \(-0.792100\pi\)
0.794180 0.607682i \(-0.207900\pi\)
\(702\) 8.05863 18.7325i 0.304153 0.707013i
\(703\) 26.0775 4.13027i 0.983533 0.155776i
\(704\) 3.04265 + 2.21062i 0.114674 + 0.0833157i
\(705\) −15.0511 13.1988i −0.566855 0.497094i
\(706\) 24.3558 17.6956i 0.916644 0.665981i
\(707\) 34.7605 34.7605i 1.30730 1.30730i
\(708\) 8.04220 5.47388i 0.302244 0.205721i
\(709\) −2.62130 + 0.851713i −0.0984451 + 0.0319867i −0.357825 0.933789i \(-0.616482\pi\)
0.259380 + 0.965775i \(0.416482\pi\)
\(710\) −1.38252 + 3.51162i −0.0518851 + 0.131789i
\(711\) 29.6686 + 11.6976i 1.11266 + 0.438693i
\(712\) −0.477205 + 0.936569i −0.0178840 + 0.0350994i
\(713\) −7.61474 + 14.9448i −0.285174 + 0.559686i
\(714\) −2.86250 + 1.34949i −0.107126 + 0.0505033i
\(715\) 27.8320 17.7381i 1.04086 0.663366i
\(716\) 2.69201 0.874686i 0.100605 0.0326886i
\(717\) −7.81693 11.4846i −0.291929 0.428900i
\(718\) 2.46690 2.46690i 0.0920639 0.0920639i
\(719\) −6.94235 + 5.04392i −0.258906 + 0.188106i −0.709665 0.704540i \(-0.751154\pi\)
0.450759 + 0.892646i \(0.351154\pi\)
\(720\) 2.29350 + 6.30395i 0.0854738 + 0.234935i
\(721\) 8.79854 + 6.39251i 0.327675 + 0.238070i
\(722\) 5.92953 0.939145i 0.220674 0.0349514i
\(723\) 11.8140 + 4.24378i 0.439369 + 0.157828i
\(724\) 0.350016i 0.0130082i
\(725\) 4.47637 + 8.06863i 0.166248 + 0.299661i
\(726\) 3.73123 + 3.96767i 0.138479 + 0.147254i
\(727\) −30.4942 + 15.5376i −1.13097 + 0.576257i −0.916325 0.400435i \(-0.868859\pi\)
−0.214644 + 0.976692i \(0.568859\pi\)
\(728\) 2.72266 + 17.1902i 0.100909 + 0.637111i
\(729\) 18.5670 + 19.6027i 0.687668 + 0.726026i
\(730\) 5.30870 + 5.99818i 0.196484 + 0.222003i
\(731\) 1.27276 + 1.75180i 0.0470746 + 0.0647926i
\(732\) −24.8650 0.763622i −0.919038 0.0282243i
\(733\) −6.22770 + 39.3201i −0.230025 + 1.45232i 0.554478 + 0.832198i \(0.312918\pi\)
−0.784504 + 0.620124i \(0.787082\pi\)
\(734\) −4.83943 14.8942i −0.178627 0.549756i
\(735\) −37.7196 + 31.3727i −1.39131 + 1.15720i
\(736\) 1.55415 4.78318i 0.0572867 0.176310i
\(737\) −20.7547 10.5750i −0.764509 0.389537i
\(738\) 5.19955 8.82071i 0.191398 0.324695i
\(739\) 19.6010 + 6.36874i 0.721033 + 0.234278i 0.646471 0.762939i \(-0.276244\pi\)
0.0745620 + 0.997216i \(0.476244\pi\)
\(740\) −11.4302 + 2.95827i −0.420181 + 0.108748i
\(741\) 29.7970 + 16.3533i 1.09462 + 0.600754i
\(742\) −36.3871 5.76314i −1.33581 0.211572i
\(743\) −25.7253 25.7253i −0.943771 0.943771i 0.0547306 0.998501i \(-0.482570\pi\)
−0.998501 + 0.0547306i \(0.982570\pi\)
\(744\) −1.07834 + 5.67487i −0.0395337 + 0.208051i
\(745\) −2.00645 + 9.05833i −0.0735105 + 0.331871i
\(746\) 3.74935 5.16053i 0.137273 0.188940i
\(747\) 2.03232 + 21.1764i 0.0743585 + 0.774806i
\(748\) −0.703446 1.38059i −0.0257205 0.0504794i
\(749\) 27.0114 0.986973
\(750\) −14.4423 + 12.9004i −0.527358 + 0.471055i
\(751\) −13.8571 −0.505654 −0.252827 0.967511i \(-0.581360\pi\)
−0.252827 + 0.967511i \(0.581360\pi\)
\(752\) 2.34657 + 4.60540i 0.0855705 + 0.167942i
\(753\) 19.9267 + 15.4339i 0.726169 + 0.562443i
\(754\) −4.25699 + 5.85925i −0.155031 + 0.213381i
\(755\) −4.59430 + 20.7415i −0.167204 + 0.754860i
\(756\) −22.3322 5.68292i −0.812216 0.206686i
\(757\) −28.7075 28.7075i −1.04339 1.04339i −0.999015 0.0443764i \(-0.985870\pi\)
−0.0443764 0.999015i \(-0.514130\pi\)
\(758\) 26.6124 + 4.21499i 0.966606 + 0.153095i
\(759\) 15.7625 28.7205i 0.572143 1.04249i
\(760\) −10.8245 + 2.80151i −0.392644 + 0.101621i
\(761\) 36.3818 + 11.8212i 1.31884 + 0.428517i 0.882096 0.471069i \(-0.156132\pi\)
0.436744 + 0.899586i \(0.356132\pi\)
\(762\) −32.6154 + 9.50095i −1.18153 + 0.344183i
\(763\) 18.5405 + 9.44684i 0.671210 + 0.341998i
\(764\) −0.350849 + 1.07980i −0.0126933 + 0.0390659i
\(765\) 0.337178 2.74309i 0.0121907 0.0991765i
\(766\) 9.25415 + 28.4814i 0.334366 + 1.02907i
\(767\) −3.44822 + 21.7712i −0.124508 + 0.786114i
\(768\) 0.0531674 1.73123i 0.00191851 0.0624705i
\(769\) 23.2438 + 31.9924i 0.838194 + 1.15368i 0.986342 + 0.164710i \(0.0526688\pi\)
−0.148148 + 0.988965i \(0.547331\pi\)
\(770\) −24.7178 27.9281i −0.890766 1.00646i
\(771\) 0.320565 + 2.52303i 0.0115449 + 0.0908646i
\(772\) 0.920714 + 5.81316i 0.0331372 + 0.209220i
\(773\) 32.0052 16.3075i 1.15115 0.586539i 0.229019 0.973422i \(-0.426448\pi\)
0.922129 + 0.386883i \(0.126448\pi\)
\(774\) −0.967539 + 15.7376i −0.0347775 + 0.565677i
\(775\) −16.3675 + 3.18774i −0.587939 + 0.114507i
\(776\) 7.71121i 0.276816i
\(777\) 13.7114 38.1706i 0.491895 1.36936i
\(778\) −11.4191 + 1.80860i −0.409394 + 0.0648416i
\(779\) 13.8070 + 10.0314i 0.494688 + 0.359412i
\(780\) −13.9654 5.99959i −0.500041 0.214820i
\(781\) 5.13529 3.73101i 0.183755 0.133506i
\(782\) −1.46516 + 1.46516i −0.0523940 + 0.0523940i
\(783\) −4.89897 8.24330i −0.175075 0.294592i
\(784\) 12.0476 3.91450i 0.430271 0.139803i
\(785\) 7.95390 5.06924i 0.283887 0.180929i
\(786\) 15.1597 + 32.1563i 0.540728 + 1.14698i
\(787\) −13.0206 + 25.5543i −0.464133 + 0.910913i 0.533735 + 0.845652i \(0.320788\pi\)
−0.997868 + 0.0652610i \(0.979212\pi\)
\(788\) −8.72355 + 17.1209i −0.310764 + 0.609908i
\(789\) 16.4852 + 34.9679i 0.586889 + 1.24489i
\(790\) 8.70783 22.1180i 0.309811 0.786922i
\(791\) −72.1143 + 23.4314i −2.56409 + 0.833123i
\(792\) 2.44551 11.0146i 0.0868976 0.391385i
\(793\) 39.8569 39.8569i 1.41536 1.41536i
\(794\) −10.8401 + 7.87580i −0.384701 + 0.279502i
\(795\) 21.2128 24.1898i 0.752341 0.857924i
\(796\) 10.2845 + 7.47216i 0.364526 + 0.264844i
\(797\) 9.56827 1.51547i 0.338926 0.0536805i 0.0153481 0.999882i \(-0.495114\pi\)
0.323578 + 0.946202i \(0.395114\pi\)
\(798\) 12.9848 36.1478i 0.459658 1.27962i
\(799\) 2.12949i 0.0753360i
\(800\) 4.69784 1.71182i 0.166094 0.0605219i
\(801\) 3.14746 + 0.193504i 0.111210 + 0.00683713i
\(802\) 19.8609 10.1196i 0.701313 0.357337i
\(803\) −2.10754 13.3065i −0.0743734 0.469575i
\(804\) 1.35213 + 10.6420i 0.0476859 + 0.375315i
\(805\) −25.3049 + 42.9772i −0.891881 + 1.51475i
\(806\) −7.69311 10.5887i −0.270978 0.372970i
\(807\) −1.32909 + 43.2777i −0.0467861 + 1.52345i
\(808\) 1.73404 10.9483i 0.0610032 0.385159i
\(809\) 17.2607 + 53.1231i 0.606855 + 1.86771i 0.483496 + 0.875346i \(0.339367\pi\)
0.123359 + 0.992362i \(0.460633\pi\)
\(810\) 14.6041 13.8463i 0.513135 0.486510i
\(811\) −6.13462 + 18.8804i −0.215416 + 0.662981i 0.783708 + 0.621129i \(0.213326\pi\)
−0.999124 + 0.0418519i \(0.986674\pi\)
\(812\) 7.29214 + 3.71553i 0.255904 + 0.130390i
\(813\) 27.0096 7.86795i 0.947268 0.275941i
\(814\) 18.8863 + 6.13654i 0.661965 + 0.215086i
\(815\) −14.8198 + 17.9846i −0.519116 + 0.629973i
\(816\) −0.343329 + 0.625571i −0.0120189 + 0.0218994i
\(817\) −25.9571 4.11120i −0.908125 0.143833i
\(818\) −9.95831 9.95831i −0.348184 0.348184i
\(819\) 44.0452 28.0404i 1.53906 0.979810i
\(820\) −6.57650 3.87224i −0.229661 0.135224i
\(821\) −22.0314 + 30.3236i −0.768899 + 1.05830i 0.227522 + 0.973773i \(0.426938\pi\)
−0.996421 + 0.0845263i \(0.973062\pi\)
\(822\) −9.89830 7.66658i −0.345243 0.267403i
\(823\) −17.9173 35.1647i −0.624559 1.22577i −0.959015 0.283355i \(-0.908553\pi\)
0.334456 0.942411i \(-0.391447\pi\)
\(824\) 2.45232 0.0854307
\(825\) 32.1459 5.24216i 1.11918 0.182508i
\(826\) 24.9088 0.866688
\(827\) −11.4419 22.4561i −0.397875 0.780874i 0.601969 0.798519i \(-0.294383\pi\)
−0.999844 + 0.0176456i \(0.994383\pi\)
\(828\) −15.0190 + 1.44138i −0.521946 + 0.0500915i
\(829\) −22.7111 + 31.2592i −0.788791 + 1.08568i 0.205467 + 0.978664i \(0.434129\pi\)
−0.994258 + 0.107013i \(0.965871\pi\)
\(830\) 15.7832 1.52266i 0.547844 0.0528525i
\(831\) 2.22656 11.7176i 0.0772386 0.406478i
\(832\) 2.77505 + 2.77505i 0.0962075 + 0.0962075i
\(833\) −5.15469 0.816423i −0.178600 0.0282874i
\(834\) 14.7180 + 8.07760i 0.509643 + 0.279705i
\(835\) −29.1271 11.4673i −1.00798 0.396842i
\(836\) 17.8855 + 5.81135i 0.618582 + 0.200990i
\(837\) 16.9038 3.81652i 0.584279 0.131918i
\(838\) 5.05427 + 2.57528i 0.174597 + 0.0889615i
\(839\) 1.11037 3.41736i 0.0383342 0.117980i −0.930058 0.367412i \(-0.880244\pi\)
0.968392 + 0.249432i \(0.0802438\pi\)
\(840\) −4.22750 + 16.6476i −0.145863 + 0.574396i
\(841\) −7.90910 24.3417i −0.272727 0.839369i
\(842\) 0.999080 6.30794i 0.0344306 0.217386i
\(843\) −42.3978 1.30207i −1.46026 0.0448455i
\(844\) −10.2487 14.1061i −0.352774 0.485552i
\(845\) 4.92475 2.14241i 0.169417 0.0737013i
\(846\) 9.86698 11.9619i 0.339234 0.411259i
\(847\) 2.18155 + 13.7738i 0.0749591 + 0.473273i
\(848\) −7.40172 + 3.77136i −0.254176 + 0.129509i
\(849\) −8.68879 9.23937i −0.298198 0.317095i
\(850\) −2.04470 0.250299i −0.0701326 0.00858518i
\(851\) 26.5557i 0.910317i
\(852\) −2.75118 0.988266i −0.0942540 0.0338574i
\(853\) 44.8288 7.10018i 1.53491 0.243106i 0.668983 0.743278i \(-0.266730\pi\)
0.865926 + 0.500172i \(0.166730\pi\)
\(854\) −51.5307 37.4393i −1.76334 1.28114i
\(855\) 20.6478 + 26.4352i 0.706141 + 0.904066i
\(856\) 4.92752 3.58005i 0.168419 0.122364i
\(857\) −5.49063 + 5.49063i −0.187556 + 0.187556i −0.794639 0.607082i \(-0.792340\pi\)
0.607082 + 0.794639i \(0.292340\pi\)
\(858\) 14.3846 + 21.1338i 0.491082 + 0.721496i
\(859\) 10.7387 3.48922i 0.366400 0.119051i −0.120030 0.992770i \(-0.538299\pi\)
0.486430 + 0.873720i \(0.338299\pi\)
\(860\) 11.7305 + 0.715314i 0.400006 + 0.0243920i
\(861\) 23.7136 11.1795i 0.808159 0.380996i
\(862\) 9.06883 17.7986i 0.308886 0.606222i
\(863\) −5.28199 + 10.3665i −0.179801 + 0.352880i −0.963263 0.268560i \(-0.913452\pi\)
0.783462 + 0.621440i \(0.213452\pi\)
\(864\) −4.82715 + 1.92319i −0.164223 + 0.0654282i
\(865\) −3.92731 15.1744i −0.133533 0.515944i
\(866\) 22.0640 7.16903i 0.749765 0.243613i
\(867\) −24.0984 + 16.4025i −0.818424 + 0.557056i
\(868\) −10.4582 + 10.4582i −0.354975 + 0.354975i
\(869\) −32.3447 + 23.4998i −1.09722 + 0.797177i
\(870\) −6.14237 + 3.65454i −0.208246 + 0.123900i
\(871\) −19.6646 14.2871i −0.666308 0.484101i
\(872\) 4.63430 0.734001i 0.156937 0.0248564i
\(873\) −21.2178 + 9.21782i −0.718115 + 0.311976i
\(874\) 25.1484i 0.850658i
\(875\) −49.1550 + 6.49880i −1.66174 + 0.219700i
\(876\) −4.51987 + 4.25053i −0.152712 + 0.143612i
\(877\) 22.0344 11.2271i 0.744049 0.379112i −0.0404992 0.999180i \(-0.512895\pi\)
0.784548 + 0.620068i \(0.212895\pi\)
\(878\) −1.77277 11.1928i −0.0598282 0.377740i
\(879\) −2.78540 + 0.353901i −0.0939492 + 0.0119368i
\(880\) −8.21067 1.81869i −0.276782 0.0613079i
\(881\) 7.08613 + 9.75322i 0.238738 + 0.328594i 0.911527 0.411240i \(-0.134904\pi\)
−0.672790 + 0.739834i \(0.734904\pi\)
\(882\) −25.1724 28.4703i −0.847598 0.958645i
\(883\) 1.11758 7.05614i 0.0376097 0.237458i −0.961721 0.274029i \(-0.911644\pi\)
0.999331 + 0.0365710i \(0.0116435\pi\)
\(884\) −0.499640 1.53774i −0.0168047 0.0517196i
\(885\) −11.6074 + 18.3976i −0.390177 + 0.618428i
\(886\) −2.37482 + 7.30895i −0.0797837 + 0.245549i
\(887\) 3.17069 + 1.61555i 0.106461 + 0.0542448i 0.506410 0.862293i \(-0.330972\pi\)
−0.399949 + 0.916537i \(0.630972\pi\)
\(888\) −2.55779 8.78054i −0.0858338 0.294655i
\(889\) −82.7238 26.8786i −2.77447 0.901479i
\(890\) 0.143060 2.34605i 0.00479539 0.0786399i
\(891\) −33.2305 + 6.43759i −1.11326 + 0.215667i
\(892\) −22.3573 3.54105i −0.748578 0.118563i
\(893\) 18.2756 + 18.2756i 0.611569 + 0.611569i
\(894\) −7.06028 1.34159i −0.236131 0.0448695i
\(895\) −4.73959 + 4.19478i −0.158427 + 0.140216i
\(896\) 2.60672 3.58784i 0.0870843 0.119861i
\(897\) 20.9339 27.0277i 0.698964 0.902430i
\(898\) −12.2332 24.0090i −0.408226 0.801189i
\(899\) −6.15455 −0.205266
\(900\) −10.3259 10.8801i −0.344195 0.362670i
\(901\) 3.42248 0.114019
\(902\) 5.82752 + 11.4372i 0.194035 + 0.380816i
\(903\) −24.7210 + 31.9173i −0.822665 + 1.06214i
\(904\) −10.0498 + 13.8324i −0.334252 + 0.460058i
\(905\) 0.312216 + 0.717688i 0.0103784 + 0.0238568i
\(906\) −16.1664 3.07193i −0.537093 0.102058i
\(907\) 1.89862 + 1.89862i 0.0630427 + 0.0630427i 0.737925 0.674883i \(-0.235806\pi\)
−0.674883 + 0.737925i \(0.735806\pi\)
\(908\) −19.0703 3.02044i −0.632871 0.100237i
\(909\) −32.1976 + 8.31603i −1.06793 + 0.275825i
\(910\) −20.9164 32.8190i −0.693372 1.08794i
\(911\) 2.38886 + 0.776187i 0.0791464 + 0.0257162i 0.348323 0.937375i \(-0.386751\pi\)
−0.269176 + 0.963091i \(0.586751\pi\)
\(912\) −2.42225 8.31523i −0.0802086 0.275345i
\(913\) −23.7628 12.1078i −0.786435 0.400708i
\(914\) 10.5736 32.5423i 0.349744 1.07640i
\(915\) 51.6655 20.6140i 1.70801 0.681477i
\(916\) 5.03677 + 15.5016i 0.166420 + 0.512187i
\(917\) −14.2395 + 89.9045i −0.470229 + 2.96891i
\(918\) 2.13170 + 0.196894i 0.0703567 + 0.00649846i
\(919\) −5.62589 7.74338i −0.185581 0.255430i 0.706082 0.708130i \(-0.250461\pi\)
−0.891663 + 0.452700i \(0.850461\pi\)
\(920\) 1.07992 + 11.1940i 0.0356040 + 0.369054i
\(921\) 20.1506 2.56024i 0.663983 0.0843629i
\(922\) 5.80740 + 36.6665i 0.191256 + 1.20755i
\(923\) 5.90173 3.00708i 0.194258 0.0989793i
\(924\) 21.0449 19.7908i 0.692328 0.651071i
\(925\) 20.7981 16.2615i 0.683839 0.534676i
\(926\) 7.02279i 0.230783i
\(927\) −2.93145 6.74771i −0.0962816 0.221624i
\(928\) 1.82271 0.288689i 0.0598335 0.00947670i
\(929\) 28.0139 + 20.3533i 0.919106 + 0.667770i 0.943301 0.331938i \(-0.107702\pi\)
−0.0241953 + 0.999707i \(0.507702\pi\)
\(930\) −2.85094 12.5979i −0.0934861 0.413101i
\(931\) 51.2449 37.2316i 1.67949 1.22022i
\(932\) 0.430335 0.430335i 0.0140961 0.0140961i
\(933\) −47.3697 + 32.2419i −1.55081 + 1.05555i
\(934\) −27.2912 + 8.86745i −0.892995 + 0.290152i
\(935\) 2.67387 + 2.20335i 0.0874449 + 0.0720572i
\(936\) 4.31847 10.9529i 0.141154 0.358008i
\(937\) 6.94494 13.6302i 0.226881 0.445280i −0.749302 0.662229i \(-0.769611\pi\)
0.976183 + 0.216949i \(0.0696106\pi\)
\(938\) −12.4699 + 24.4736i −0.407157 + 0.799090i
\(939\) −6.86194 + 3.23498i −0.223931 + 0.105570i
\(940\) −8.91955 7.34997i −0.290924 0.239730i
\(941\) −27.0255 + 8.78112i −0.881006 + 0.286256i −0.714375 0.699763i \(-0.753289\pi\)
−0.166631 + 0.986019i \(0.553289\pi\)
\(942\) 4.11088 + 6.03968i 0.133940 + 0.196783i
\(943\) 12.1378 12.1378i 0.395260 0.395260i
\(944\) 4.54397 3.30138i 0.147893 0.107451i
\(945\) 50.8602 8.26795i 1.65448 0.268956i
\(946\) −15.9915 11.6185i −0.519928 0.377750i
\(947\) 37.1437 5.88298i 1.20701 0.191171i 0.479669 0.877450i \(-0.340757\pi\)
0.727339 + 0.686279i \(0.240757\pi\)
\(948\) 17.3284 + 6.22461i 0.562800 + 0.202166i
\(949\) 14.0583i 0.456353i
\(950\) 19.6960 15.3998i 0.639022 0.499635i
\(951\) −33.2263 35.3318i −1.07744 1.14571i
\(952\) −1.62797 + 0.829491i −0.0527627 + 0.0268840i
\(953\) −4.16742 26.3120i −0.134996 0.852331i −0.958515 0.285042i \(-0.907992\pi\)
0.823519 0.567289i \(-0.192008\pi\)
\(954\) 19.2250 + 15.8580i 0.622432 + 0.513423i
\(955\) −0.243792 2.52704i −0.00788893 0.0817730i
\(956\) −4.71452 6.48898i −0.152478 0.209868i
\(957\) 12.0157 + 0.369010i 0.388412 + 0.0119284i
\(958\) −2.00959 + 12.6881i −0.0649269 + 0.409933i
\(959\) −9.90614 30.4880i −0.319886 0.984508i
\(960\) 1.43525 + 3.59723i 0.0463226 + 0.116100i
\(961\) −6.14254 + 18.9048i −0.198146 + 0.609832i
\(962\) 18.4635 + 9.40760i 0.595286 + 0.303313i
\(963\) −15.7410 9.27884i −0.507246 0.299006i
\(964\) 6.89284 + 2.23962i 0.222003 + 0.0721333i
\(965\) −7.07324 11.0983i −0.227696 0.357266i
\(966\) −33.8667 18.5869i −1.08964 0.598023i
\(967\) 41.4802 + 6.56982i 1.33391 + 0.211271i 0.782339 0.622853i \(-0.214027\pi\)
0.551576 + 0.834125i \(0.314027\pi\)
\(968\) 2.22353 + 2.22353i 0.0714670 + 0.0714670i
\(969\) −0.666109 + 3.50548i −0.0213985 + 0.112612i
\(970\) 6.87844 + 15.8114i 0.220853 + 0.507674i
\(971\) −8.52779 + 11.7375i −0.273670 + 0.376674i −0.923624 0.383299i \(-0.874788\pi\)
0.649955 + 0.759973i \(0.274788\pi\)
\(972\) 11.0620 + 10.9832i 0.354815 + 0.352287i
\(973\) 19.5157 + 38.3017i 0.625645 + 1.22790i
\(974\) −20.6983 −0.663215
\(975\) 33.9869 0.155361i 1.08845 0.00497554i
\(976\) −14.3626 −0.459736
\(977\) −0.545186 1.06999i −0.0174420 0.0342319i 0.882121 0.471023i \(-0.156115\pi\)
−0.899563 + 0.436791i \(0.856115\pi\)
\(978\) −14.2711 11.0535i −0.456340 0.353451i
\(979\) −2.32366 + 3.19824i −0.0742644 + 0.102216i
\(980\) −21.2112 + 18.7730i −0.677566 + 0.599680i
\(981\) −7.55939 11.8741i −0.241353 0.379112i
\(982\) 19.7552 + 19.7552i 0.630413 + 0.630413i
\(983\) −17.7113 2.80520i −0.564903 0.0894719i −0.132550 0.991176i \(-0.542317\pi\)
−0.432353 + 0.901704i \(0.642317\pi\)
\(984\) 2.84422 5.18239i 0.0906704 0.165209i
\(985\) 2.61521 42.8870i 0.0833276 1.36649i
\(986\) −0.723093 0.234947i −0.0230280 0.00748224i
\(987\) 38.1185 11.1040i 1.21333 0.353445i
\(988\) 17.4850 + 8.90907i 0.556273 + 0.283435i
\(989\) −8.16826 + 25.1393i −0.259736 + 0.799384i
\(990\) 4.81064 + 24.7662i 0.152892 + 0.787120i
\(991\) 14.9087 + 45.8841i 0.473589 + 1.45756i 0.847851 + 0.530234i \(0.177896\pi\)
−0.374262 + 0.927323i \(0.622104\pi\)
\(992\) −0.521711 + 3.29395i −0.0165643 + 0.104583i
\(993\) −0.509555 + 16.5921i −0.0161702 + 0.526535i
\(994\) −4.39954 6.05544i −0.139545 0.192067i
\(995\) −27.7531 6.14739i −0.879832 0.194885i
\(996\) 1.54810 + 12.1844i 0.0490535 + 0.386079i
\(997\) 3.38611 + 21.3791i 0.107239 + 0.677082i 0.981476 + 0.191583i \(0.0613621\pi\)
−0.874237 + 0.485499i \(0.838638\pi\)
\(998\) −0.361613 + 0.184251i −0.0114467 + 0.00583237i
\(999\) −21.1026 + 17.5340i −0.667657 + 0.554750i
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 150.2.l.a.47.2 80
3.2 odd 2 inner 150.2.l.a.47.6 yes 80
5.2 odd 4 750.2.l.a.743.9 80
5.3 odd 4 750.2.l.c.743.2 80
5.4 even 2 750.2.l.b.257.9 80
15.2 even 4 750.2.l.a.743.2 80
15.8 even 4 750.2.l.c.743.9 80
15.14 odd 2 750.2.l.b.257.5 80
25.6 even 5 750.2.l.c.107.9 80
25.8 odd 20 inner 150.2.l.a.83.6 yes 80
25.17 odd 20 750.2.l.b.143.5 80
25.19 even 10 750.2.l.a.107.2 80
75.8 even 20 inner 150.2.l.a.83.2 yes 80
75.17 even 20 750.2.l.b.143.9 80
75.44 odd 10 750.2.l.a.107.9 80
75.56 odd 10 750.2.l.c.107.2 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.l.a.47.2 80 1.1 even 1 trivial
150.2.l.a.47.6 yes 80 3.2 odd 2 inner
150.2.l.a.83.2 yes 80 75.8 even 20 inner
150.2.l.a.83.6 yes 80 25.8 odd 20 inner
750.2.l.a.107.2 80 25.19 even 10
750.2.l.a.107.9 80 75.44 odd 10
750.2.l.a.743.2 80 15.2 even 4
750.2.l.a.743.9 80 5.2 odd 4
750.2.l.b.143.5 80 25.17 odd 20
750.2.l.b.143.9 80 75.17 even 20
750.2.l.b.257.5 80 15.14 odd 2
750.2.l.b.257.9 80 5.4 even 2
750.2.l.c.107.2 80 75.56 odd 10
750.2.l.c.107.9 80 25.6 even 5
750.2.l.c.743.2 80 5.3 odd 4
750.2.l.c.743.9 80 15.8 even 4