Properties

Label 483.2.y.b.151.4
Level $483$
Weight $2$
Character 483.151
Analytic conductor $3.857$
Analytic rank $0$
Dimension $320$
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] = [483,2,Mod(4,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([0, 44, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.y (of order \(33\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(320\)
Relative dimension: \(16\) over \(\Q(\zeta_{33})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 151.4
Character \(\chi\) \(=\) 483.151
Dual form 483.2.y.b.16.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.620909 + 1.79400i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-1.26080 - 0.991503i) q^{4} +(-3.16803 + 0.302510i) q^{5} +(-0.270172 - 1.87909i) q^{6} +(1.40046 + 2.24471i) q^{7} +(-0.632491 + 0.406478i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\) \(q+(-0.620909 + 1.79400i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-1.26080 - 0.991503i) q^{4} +(-3.16803 + 0.302510i) q^{5} +(-0.270172 - 1.87909i) q^{6} +(1.40046 + 2.24471i) q^{7} +(-0.632491 + 0.406478i) q^{8} +(0.580057 - 0.814576i) q^{9} +(1.42436 - 5.87128i) q^{10} +(-0.842932 - 2.43549i) q^{11} +(1.57498 + 0.303552i) q^{12} +(-3.50062 + 1.02787i) q^{13} +(-4.89656 + 1.11867i) q^{14} +(2.67724 - 1.72056i) q^{15} +(-1.09280 - 4.50457i) q^{16} +(-1.43410 - 0.574128i) q^{17} +(1.10119 + 1.54640i) q^{18} +(2.71924 - 1.08862i) q^{19} +(4.29419 + 2.75971i) q^{20} +(-2.27336 - 1.35345i) q^{21} +4.89265 q^{22} +(2.95904 + 3.77413i) q^{23} +(0.375922 - 0.651116i) q^{24} +(5.03527 - 0.970470i) q^{25} +(0.329561 - 6.91833i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(0.459933 - 4.21868i) q^{28} +(-1.35096 - 9.39616i) q^{29} +(1.42436 + 5.87128i) q^{30} +(-0.0236884 - 0.497280i) q^{31} +(7.26285 + 0.693518i) q^{32} +(1.86523 + 1.77850i) q^{33} +(1.92043 - 2.21630i) q^{34} +(-5.11575 - 6.68765i) q^{35} +(-1.53899 + 0.451888i) q^{36} +(4.33020 - 6.08092i) q^{37} +(0.264582 + 5.55425i) q^{38} +(2.64048 - 2.51769i) q^{39} +(1.88079 - 1.47907i) q^{40} +(-3.04181 + 6.66063i) q^{41} +(3.83963 - 3.23805i) q^{42} +(2.95900 + 1.90163i) q^{43} +(-1.35203 + 3.90643i) q^{44} +(-1.59122 + 2.75608i) q^{45} +(-8.60808 + 2.96513i) q^{46} +(-4.58771 - 7.94615i) q^{47} +(3.03543 + 3.50307i) q^{48} +(-3.07742 + 6.28725i) q^{49} +(-1.38543 + 9.63585i) q^{50} +(1.53776 - 0.146838i) q^{51} +(5.43272 + 2.17493i) q^{52} +(-5.25639 + 5.01196i) q^{53} +(-1.68737 - 0.869902i) q^{54} +(3.40720 + 7.46072i) q^{55} +(-1.79820 - 0.850501i) q^{56} +(-1.91812 + 2.21363i) q^{57} +(17.6955 + 3.41053i) q^{58} +(-0.828341 + 3.41447i) q^{59} +(-5.08140 - 0.485215i) q^{60} +(-8.94618 - 4.61208i) q^{61} +(0.906828 + 0.266269i) q^{62} +(2.64083 + 0.161275i) q^{63} +(-1.90265 + 4.16622i) q^{64} +(10.7791 - 4.31532i) q^{65} +(-4.34877 + 2.24194i) q^{66} +(-4.79805 + 0.924749i) q^{67} +(1.23886 + 2.14578i) q^{68} +(-4.35951 - 1.99867i) q^{69} +(15.1741 - 5.02524i) q^{70} +(-0.887049 - 1.02371i) q^{71} +(-0.0357742 + 0.750992i) q^{72} +(-6.13279 - 4.82288i) q^{73} +(8.22050 + 11.5441i) q^{74} +(-4.03084 + 3.16988i) q^{75} +(-4.50779 - 1.32361i) q^{76} +(4.28647 - 5.30295i) q^{77} +(2.87724 + 6.30027i) q^{78} +(-5.24501 - 5.00111i) q^{79} +(4.82470 + 13.9400i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-10.0605 - 9.59264i) q^{82} +(-0.967975 - 2.11957i) q^{83} +(1.52431 + 3.96047i) q^{84} +(4.71696 + 1.38503i) q^{85} +(-5.24879 + 4.12770i) q^{86} +(5.50635 + 7.73259i) q^{87} +(1.52312 + 1.19779i) q^{88} +(0.309384 - 6.49478i) q^{89} +(-3.95639 - 4.56592i) q^{90} +(-7.20976 - 6.41837i) q^{91} +(0.0113038 - 7.69232i) q^{92} +(0.248922 + 0.431145i) q^{93} +(17.1039 - 3.29651i) q^{94} +(-8.28533 + 4.27138i) q^{95} +(-6.77326 + 2.71161i) q^{96} +(-6.82291 + 14.9401i) q^{97} +(-9.36853 - 9.42469i) q^{98} +(-2.47284 - 0.726092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 2 q^{11} + 18 q^{12} + 18 q^{14} - 18 q^{15} - 8 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 162 q^{20} - 4 q^{21} + 144 q^{22} - 26 q^{23} + 6 q^{24} - 8 q^{25} - 14 q^{26} - 32 q^{27} + 86 q^{28} - 74 q^{29} - 56 q^{31} - 28 q^{32} + 13 q^{33} + 40 q^{34} - 32 q^{35} - 14 q^{36} + 2 q^{37} - 39 q^{38} - 52 q^{40} + 60 q^{41} - 61 q^{42} + 16 q^{43} - 75 q^{44} - 2 q^{45} - 4 q^{46} - 40 q^{47} - 28 q^{48} - 100 q^{49} + 146 q^{50} - 18 q^{51} - 18 q^{52} + 34 q^{53} + 2 q^{54} + 36 q^{55} - 102 q^{56} + 28 q^{57} - 17 q^{58} - 102 q^{59} - 18 q^{60} - 18 q^{61} - 88 q^{62} + 2 q^{63} - 252 q^{64} - 78 q^{65} + 16 q^{66} + 12 q^{67} + 34 q^{68} + 8 q^{69} + 264 q^{70} + 160 q^{71} + 6 q^{72} - 8 q^{73} + 70 q^{74} + 14 q^{75} - 40 q^{76} - 90 q^{77} - 16 q^{78} + 26 q^{79} - 103 q^{80} + 16 q^{81} - 30 q^{82} - 80 q^{83} - 52 q^{84} - 128 q^{85} + 90 q^{86} + 4 q^{87} - 293 q^{88} - 36 q^{89} + 16 q^{91} - 174 q^{92} + 32 q^{93} + 57 q^{94} - 85 q^{95} - 50 q^{96} - 8 q^{97} - 193 q^{98} - 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.620909 + 1.79400i −0.439049 + 1.26855i 0.480991 + 0.876725i \(0.340277\pi\)
−0.920040 + 0.391824i \(0.871844\pi\)
\(3\) −0.888835 + 0.458227i −0.513169 + 0.264557i
\(4\) −1.26080 0.991503i −0.630399 0.495752i
\(5\) −3.16803 + 0.302510i −1.41679 + 0.135287i −0.775177 0.631744i \(-0.782339\pi\)
−0.641610 + 0.767031i \(0.721733\pi\)
\(6\) −0.270172 1.87909i −0.110297 0.767134i
\(7\) 1.40046 + 2.24471i 0.529325 + 0.848419i
\(8\) −0.632491 + 0.406478i −0.223619 + 0.143712i
\(9\) 0.580057 0.814576i 0.193352 0.271525i
\(10\) 1.42436 5.87128i 0.450421 1.85666i
\(11\) −0.842932 2.43549i −0.254154 0.734328i −0.997833 0.0657925i \(-0.979042\pi\)
0.743680 0.668536i \(-0.233079\pi\)
\(12\) 1.57498 + 0.303552i 0.454656 + 0.0876278i
\(13\) −3.50062 + 1.02787i −0.970897 + 0.285081i −0.728462 0.685086i \(-0.759764\pi\)
−0.242436 + 0.970168i \(0.577946\pi\)
\(14\) −4.89656 + 1.11867i −1.30866 + 0.298977i
\(15\) 2.67724 1.72056i 0.691261 0.444246i
\(16\) −1.09280 4.50457i −0.273199 1.12614i
\(17\) −1.43410 0.574128i −0.347821 0.139247i 0.191172 0.981556i \(-0.438771\pi\)
−0.538993 + 0.842310i \(0.681195\pi\)
\(18\) 1.10119 + 1.54640i 0.259552 + 0.364490i
\(19\) 2.71924 1.08862i 0.623837 0.249747i −0.0381382 0.999272i \(-0.512143\pi\)
0.661975 + 0.749526i \(0.269718\pi\)
\(20\) 4.29419 + 2.75971i 0.960210 + 0.617090i
\(21\) −2.27336 1.35345i −0.496089 0.295346i
\(22\) 4.89265 1.04312
\(23\) 2.95904 + 3.77413i 0.617003 + 0.786961i
\(24\) 0.375922 0.651116i 0.0767348 0.132908i
\(25\) 5.03527 0.970470i 1.00705 0.194094i
\(26\) 0.329561 6.91833i 0.0646321 1.35680i
\(27\) −0.142315 + 0.989821i −0.0273885 + 0.190491i
\(28\) 0.459933 4.21868i 0.0869192 0.797257i
\(29\) −1.35096 9.39616i −0.250868 1.74482i −0.593028 0.805182i \(-0.702068\pi\)
0.342161 0.939641i \(-0.388841\pi\)
\(30\) 1.42436 + 5.87128i 0.260051 + 1.07194i
\(31\) −0.0236884 0.497280i −0.00425456 0.0893141i 0.995741 0.0921914i \(-0.0293872\pi\)
−0.999996 + 0.00287728i \(0.999084\pi\)
\(32\) 7.26285 + 0.693518i 1.28390 + 0.122598i
\(33\) 1.86523 + 1.77850i 0.324696 + 0.309597i
\(34\) 1.92043 2.21630i 0.329352 0.380092i
\(35\) −5.11575 6.68765i −0.864720 1.13042i
\(36\) −1.53899 + 0.451888i −0.256498 + 0.0753147i
\(37\) 4.33020 6.08092i 0.711881 0.999697i −0.287243 0.957858i \(-0.592739\pi\)
0.999124 0.0418396i \(-0.0133218\pi\)
\(38\) 0.264582 + 5.55425i 0.0429208 + 0.901019i
\(39\) 2.64048 2.51769i 0.422815 0.403153i
\(40\) 1.88079 1.47907i 0.297379 0.233861i
\(41\) −3.04181 + 6.66063i −0.475050 + 1.04022i 0.508745 + 0.860917i \(0.330110\pi\)
−0.983795 + 0.179298i \(0.942618\pi\)
\(42\) 3.83963 3.23805i 0.592468 0.499641i
\(43\) 2.95900 + 1.90163i 0.451243 + 0.289996i 0.746455 0.665435i \(-0.231754\pi\)
−0.295213 + 0.955432i \(0.595390\pi\)
\(44\) −1.35203 + 3.90643i −0.203826 + 0.588917i
\(45\) −1.59122 + 2.75608i −0.237205 + 0.410852i
\(46\) −8.60808 + 2.96513i −1.26919 + 0.437184i
\(47\) −4.58771 7.94615i −0.669186 1.15906i −0.978132 0.207985i \(-0.933309\pi\)
0.308946 0.951080i \(-0.400024\pi\)
\(48\) 3.03543 + 3.50307i 0.438127 + 0.505625i
\(49\) −3.07742 + 6.28725i −0.439631 + 0.898179i
\(50\) −1.38543 + 9.63585i −0.195929 + 1.36272i
\(51\) 1.53776 0.146838i 0.215330 0.0205615i
\(52\) 5.43272 + 2.17493i 0.753383 + 0.301609i
\(53\) −5.25639 + 5.01196i −0.722021 + 0.688445i −0.959107 0.283043i \(-0.908656\pi\)
0.237086 + 0.971489i \(0.423808\pi\)
\(54\) −1.68737 0.869902i −0.229623 0.118379i
\(55\) 3.40720 + 7.46072i 0.459426 + 1.00600i
\(56\) −1.79820 0.850501i −0.240295 0.113653i
\(57\) −1.91812 + 2.21363i −0.254062 + 0.293203i
\(58\) 17.6955 + 3.41053i 2.32354 + 0.447825i
\(59\) −0.828341 + 3.41447i −0.107841 + 0.444526i −0.999974 0.00724715i \(-0.997693\pi\)
0.892133 + 0.451773i \(0.149208\pi\)
\(60\) −5.08140 0.485215i −0.656006 0.0626410i
\(61\) −8.94618 4.61208i −1.14544 0.590516i −0.222300 0.974978i \(-0.571357\pi\)
−0.923141 + 0.384462i \(0.874387\pi\)
\(62\) 0.906828 + 0.266269i 0.115167 + 0.0338162i
\(63\) 2.64083 + 0.161275i 0.332713 + 0.0203188i
\(64\) −1.90265 + 4.16622i −0.237831 + 0.520777i
\(65\) 10.7791 4.31532i 1.33699 0.535249i
\(66\) −4.34877 + 2.24194i −0.535296 + 0.275964i
\(67\) −4.79805 + 0.924749i −0.586176 + 0.112976i −0.473712 0.880680i \(-0.657086\pi\)
−0.112464 + 0.993656i \(0.535874\pi\)
\(68\) 1.23886 + 2.14578i 0.150234 + 0.260214i
\(69\) −4.35951 1.99867i −0.524823 0.240611i
\(70\) 15.1741 5.02524i 1.81365 0.600631i
\(71\) −0.887049 1.02371i −0.105273 0.121492i 0.700668 0.713488i \(-0.252886\pi\)
−0.805941 + 0.591996i \(0.798340\pi\)
\(72\) −0.0357742 + 0.750992i −0.00421603 + 0.0885053i
\(73\) −6.13279 4.82288i −0.717788 0.564475i 0.191072 0.981576i \(-0.438804\pi\)
−0.908860 + 0.417101i \(0.863046\pi\)
\(74\) 8.22050 + 11.5441i 0.955614 + 1.34197i
\(75\) −4.03084 + 3.16988i −0.465441 + 0.366027i
\(76\) −4.50779 1.32361i −0.517079 0.151828i
\(77\) 4.28647 5.30295i 0.488489 0.604327i
\(78\) 2.87724 + 6.30027i 0.325783 + 0.713365i
\(79\) −5.24501 5.00111i −0.590110 0.562668i 0.335072 0.942192i \(-0.391239\pi\)
−0.925182 + 0.379524i \(0.876088\pi\)
\(80\) 4.82470 + 13.9400i 0.539417 + 1.55854i
\(81\) −0.327068 0.945001i −0.0363409 0.105000i
\(82\) −10.0605 9.59264i −1.11099 1.05933i
\(83\) −0.967975 2.11957i −0.106249 0.232653i 0.849039 0.528331i \(-0.177182\pi\)
−0.955288 + 0.295678i \(0.904455\pi\)
\(84\) 1.52431 + 3.96047i 0.166316 + 0.432123i
\(85\) 4.71696 + 1.38503i 0.511627 + 0.150227i
\(86\) −5.24879 + 4.12770i −0.565992 + 0.445101i
\(87\) 5.50635 + 7.73259i 0.590343 + 0.829021i
\(88\) 1.52312 + 1.19779i 0.162365 + 0.127685i
\(89\) 0.309384 6.49478i 0.0327947 0.688445i −0.921284 0.388890i \(-0.872859\pi\)
0.954079 0.299555i \(-0.0968382\pi\)
\(90\) −3.95639 4.56592i −0.417041 0.481291i
\(91\) −7.20976 6.41837i −0.755788 0.672828i
\(92\) 0.0113038 7.69232i 0.00117850 0.801980i
\(93\) 0.248922 + 0.431145i 0.0258120 + 0.0447077i
\(94\) 17.1039 3.29651i 1.76414 0.340009i
\(95\) −8.28533 + 4.27138i −0.850057 + 0.438235i
\(96\) −6.77326 + 2.71161i −0.691293 + 0.276752i
\(97\) −6.82291 + 14.9401i −0.692762 + 1.51694i 0.155771 + 0.987793i \(0.450214\pi\)
−0.848532 + 0.529143i \(0.822513\pi\)
\(98\) −9.36853 9.42469i −0.946364 0.952038i
\(99\) −2.47284 0.726092i −0.248530 0.0729750i
\(100\) −7.31069 3.76892i −0.731069 0.376892i
\(101\) 1.92328 + 0.183651i 0.191374 + 0.0182740i 0.190303 0.981725i \(-0.439053\pi\)
0.00107111 + 0.999999i \(0.499659\pi\)
\(102\) −0.691382 + 2.84992i −0.0684571 + 0.282184i
\(103\) −8.04430 1.55041i −0.792628 0.152767i −0.223162 0.974781i \(-0.571638\pi\)
−0.569466 + 0.822015i \(0.692850\pi\)
\(104\) 1.79630 2.07305i 0.176142 0.203279i
\(105\) 7.61152 + 3.60005i 0.742809 + 0.351328i
\(106\) −5.72771 12.5419i −0.556324 1.21818i
\(107\) −12.1821 6.28028i −1.17768 0.607138i −0.245596 0.969372i \(-0.578984\pi\)
−0.932087 + 0.362234i \(0.882014\pi\)
\(108\) 1.16084 1.10686i 0.111702 0.106508i
\(109\) −13.4772 5.39546i −1.29088 0.516791i −0.378299 0.925683i \(-0.623491\pi\)
−0.912583 + 0.408892i \(0.865915\pi\)
\(110\) −15.5001 + 1.48008i −1.47788 + 0.141120i
\(111\) −1.06240 + 7.38915i −0.100839 + 0.701347i
\(112\) 8.58102 8.76149i 0.810830 0.827883i
\(113\) 6.10042 + 7.04026i 0.573879 + 0.662292i 0.966277 0.257504i \(-0.0829000\pi\)
−0.392398 + 0.919795i \(0.628355\pi\)
\(114\) −2.78027 4.81558i −0.260397 0.451020i
\(115\) −10.5161 11.0614i −0.980628 1.03148i
\(116\) −7.61303 + 13.1862i −0.706852 + 1.22430i
\(117\) −1.19328 + 3.44775i −0.110318 + 0.318744i
\(118\) −5.61123 3.60612i −0.516555 0.331970i
\(119\) −0.719656 4.02318i −0.0659708 0.368805i
\(120\) −0.993964 + 2.17648i −0.0907361 + 0.198684i
\(121\) 3.42550 2.69384i 0.311409 0.244895i
\(122\) 13.8288 13.1858i 1.25200 1.19378i
\(123\) −0.348411 7.31404i −0.0314151 0.659484i
\(124\) −0.463188 + 0.650457i −0.0415955 + 0.0584128i
\(125\) −0.390679 + 0.114714i −0.0349434 + 0.0102603i
\(126\) −1.92904 + 4.63751i −0.171853 + 0.413142i
\(127\) 0.00169518 0.00195634i 0.000150423 0.000173597i −0.755674 0.654948i \(-0.772691\pi\)
0.755825 + 0.654774i \(0.227236\pi\)
\(128\) 4.26773 + 4.06928i 0.377218 + 0.359677i
\(129\) −3.50144 0.334347i −0.308285 0.0294376i
\(130\) 1.04881 + 22.0172i 0.0919865 + 1.93103i
\(131\) 3.39385 + 13.9896i 0.296522 + 1.22228i 0.903857 + 0.427834i \(0.140723\pi\)
−0.607335 + 0.794446i \(0.707762\pi\)
\(132\) −0.588300 4.09171i −0.0512049 0.356138i
\(133\) 6.25183 + 4.57933i 0.542102 + 0.397078i
\(134\) 1.32016 9.18189i 0.114044 0.793195i
\(135\) 0.151427 3.17884i 0.0130327 0.273591i
\(136\) 1.14043 0.219799i 0.0977909 0.0188476i
\(137\) −10.1359 + 17.5559i −0.865971 + 1.49990i 0.000109725 1.00000i \(0.499965\pi\)
−0.866080 + 0.499905i \(0.833368\pi\)
\(138\) 6.29247 6.57996i 0.535651 0.560124i
\(139\) −14.8276 −1.25766 −0.628832 0.777541i \(-0.716467\pi\)
−0.628832 + 0.777541i \(0.716467\pi\)
\(140\) −0.180888 + 13.5041i −0.0152878 + 1.14130i
\(141\) 7.71886 + 4.96061i 0.650045 + 0.417759i
\(142\) 2.38731 0.955735i 0.200339 0.0802035i
\(143\) 5.45417 + 7.65930i 0.456100 + 0.640503i
\(144\) −4.30320 1.72274i −0.358600 0.143562i
\(145\) 7.12233 + 29.3587i 0.591478 + 2.43810i
\(146\) 12.4601 8.00764i 1.03121 0.662717i
\(147\) −0.145669 6.99848i −0.0120146 0.577225i
\(148\) −11.4888 + 3.37341i −0.944371 + 0.277292i
\(149\) 19.6202 + 3.78149i 1.60735 + 0.309792i 0.912411 0.409275i \(-0.134218\pi\)
0.694941 + 0.719067i \(0.255430\pi\)
\(150\) −3.18399 9.19953i −0.259971 0.751138i
\(151\) 3.16485 13.0457i 0.257552 1.06164i −0.685254 0.728304i \(-0.740309\pi\)
0.942806 0.333341i \(-0.108176\pi\)
\(152\) −1.27740 + 1.79385i −0.103611 + 0.145501i
\(153\) −1.29953 + 0.835159i −0.105061 + 0.0675186i
\(154\) 6.85197 + 10.9826i 0.552148 + 0.885001i
\(155\) 0.225478 + 1.56823i 0.0181108 + 0.125964i
\(156\) −5.82540 + 0.556259i −0.466406 + 0.0445363i
\(157\) −17.0632 13.4187i −1.36179 1.07093i −0.989765 0.142706i \(-0.954420\pi\)
−0.372030 0.928221i \(-0.621338\pi\)
\(158\) 12.2287 6.30431i 0.972859 0.501544i
\(159\) 2.37545 6.86342i 0.188386 0.544305i
\(160\) −23.2187 −1.83560
\(161\) −4.32779 + 11.9277i −0.341078 + 0.940035i
\(162\) 1.89841 0.149153
\(163\) −2.38537 + 6.89209i −0.186837 + 0.539830i −0.999052 0.0435280i \(-0.986140\pi\)
0.812215 + 0.583358i \(0.198261\pi\)
\(164\) 10.4391 5.38175i 0.815160 0.420244i
\(165\) −6.44714 5.07009i −0.501909 0.394706i
\(166\) 4.40353 0.420486i 0.341780 0.0326361i
\(167\) −2.11442 14.7061i −0.163619 1.13800i −0.891740 0.452547i \(-0.850515\pi\)
0.728121 0.685448i \(-0.240394\pi\)
\(168\) 1.98803 0.0680283i 0.153380 0.00524850i
\(169\) 0.261521 0.168069i 0.0201170 0.0129284i
\(170\) −5.41354 + 7.60225i −0.415200 + 0.583066i
\(171\) 0.690551 2.84649i 0.0528078 0.217677i
\(172\) −1.84523 5.33143i −0.140697 0.406518i
\(173\) −3.74263 0.721332i −0.284547 0.0548419i 0.0449808 0.998988i \(-0.485677\pi\)
−0.329528 + 0.944146i \(0.606889\pi\)
\(174\) −17.2912 + 5.07716i −1.31084 + 0.384898i
\(175\) 9.23013 + 9.94361i 0.697732 + 0.751666i
\(176\) −10.0497 + 6.45855i −0.757524 + 0.486831i
\(177\) −0.828341 3.41447i −0.0622619 0.256647i
\(178\) 11.4595 + 4.58770i 0.858928 + 0.343863i
\(179\) −12.4860 17.5341i −0.933246 1.31056i −0.950505 0.310709i \(-0.899433\pi\)
0.0172594 0.999851i \(-0.494506\pi\)
\(180\) 4.73887 1.89716i 0.353214 0.141406i
\(181\) 7.28731 + 4.68327i 0.541662 + 0.348105i 0.782688 0.622414i \(-0.213848\pi\)
−0.241027 + 0.970518i \(0.577484\pi\)
\(182\) 15.9912 8.94908i 1.18534 0.663350i
\(183\) 10.0651 0.744030
\(184\) −3.40567 1.18432i −0.251069 0.0873093i
\(185\) −11.8787 + 20.5745i −0.873338 + 1.51267i
\(186\) −0.928033 + 0.178864i −0.0680466 + 0.0131149i
\(187\) −0.189433 + 3.97670i −0.0138527 + 0.290805i
\(188\) −2.09445 + 14.5672i −0.152754 + 1.06242i
\(189\) −2.42117 + 1.06675i −0.176114 + 0.0775948i
\(190\) −2.51842 17.5160i −0.182706 1.27075i
\(191\) −1.08773 4.48369i −0.0787055 0.324428i 0.918825 0.394666i \(-0.129140\pi\)
−0.997530 + 0.0702372i \(0.977624\pi\)
\(192\) −0.217931 4.57493i −0.0157278 0.330167i
\(193\) 6.48118 + 0.618878i 0.466526 + 0.0445478i 0.325672 0.945483i \(-0.394409\pi\)
0.140853 + 0.990030i \(0.455015\pi\)
\(194\) −22.5661 21.5167i −1.62015 1.54481i
\(195\) −7.60349 + 8.77489i −0.544497 + 0.628383i
\(196\) 10.1138 4.87569i 0.722416 0.348264i
\(197\) 24.4429 7.17707i 1.74148 0.511345i 0.752399 0.658707i \(-0.228896\pi\)
0.989083 + 0.147362i \(0.0470782\pi\)
\(198\) 2.83802 3.98544i 0.201689 0.283233i
\(199\) 0.376062 + 7.89451i 0.0266583 + 0.559627i 0.972204 + 0.234137i \(0.0752263\pi\)
−0.945545 + 0.325490i \(0.894471\pi\)
\(200\) −2.79029 + 2.66054i −0.197304 + 0.188129i
\(201\) 3.84094 3.02055i 0.270919 0.213053i
\(202\) −1.52366 + 3.33634i −0.107204 + 0.234744i
\(203\) 19.1996 16.1915i 1.34755 1.13642i
\(204\) −2.08440 1.33956i −0.145937 0.0937881i
\(205\) 7.62163 22.0213i 0.532318 1.53803i
\(206\) 7.77622 13.4688i 0.541795 0.938416i
\(207\) 4.79073 0.221155i 0.332979 0.0153713i
\(208\) 8.45560 + 14.6455i 0.586291 + 1.01549i
\(209\) −4.94346 5.70506i −0.341946 0.394627i
\(210\) −11.1845 + 11.4198i −0.771807 + 0.788039i
\(211\) −2.66843 + 18.5593i −0.183702 + 1.27768i 0.664212 + 0.747544i \(0.268767\pi\)
−0.847914 + 0.530133i \(0.822142\pi\)
\(212\) 11.5966 1.10734i 0.796459 0.0760526i
\(213\) 1.25753 + 0.503439i 0.0861646 + 0.0344951i
\(214\) 18.8308 17.9551i 1.28724 1.22739i
\(215\) −9.94946 5.12930i −0.678548 0.349816i
\(216\) −0.312327 0.683901i −0.0212512 0.0465336i
\(217\) 1.08307 0.749595i 0.0735238 0.0508858i
\(218\) 18.0476 20.8280i 1.22234 1.41065i
\(219\) 7.66101 + 1.47654i 0.517683 + 0.0997752i
\(220\) 3.10154 12.7847i 0.209106 0.861945i
\(221\) 5.61038 + 0.535726i 0.377395 + 0.0360369i
\(222\) −12.5965 6.49394i −0.845420 0.435844i
\(223\) 9.04432 + 2.65565i 0.605652 + 0.177836i 0.570159 0.821534i \(-0.306882\pi\)
0.0354933 + 0.999370i \(0.488700\pi\)
\(224\) 8.61459 + 17.2742i 0.575587 + 1.15418i
\(225\) 2.13022 4.66454i 0.142015 0.310969i
\(226\) −16.4180 + 6.57278i −1.09211 + 0.437215i
\(227\) 0.460039 0.237167i 0.0305339 0.0157413i −0.442892 0.896575i \(-0.646047\pi\)
0.473426 + 0.880834i \(0.343017\pi\)
\(228\) 4.61319 0.889120i 0.305516 0.0588834i
\(229\) 11.4654 + 19.8587i 0.757655 + 1.31230i 0.944044 + 0.329821i \(0.106988\pi\)
−0.186389 + 0.982476i \(0.559678\pi\)
\(230\) 26.3737 11.9977i 1.73903 0.791102i
\(231\) −1.38002 + 6.67762i −0.0907984 + 0.439355i
\(232\) 4.67380 + 5.39385i 0.306850 + 0.354124i
\(233\) −0.197929 + 4.15503i −0.0129667 + 0.272205i 0.983068 + 0.183241i \(0.0586588\pi\)
−0.996035 + 0.0889645i \(0.971644\pi\)
\(234\) −5.44434 4.28148i −0.355908 0.279889i
\(235\) 16.9378 + 23.7858i 1.10490 + 1.55162i
\(236\) 4.42983 3.48365i 0.288357 0.226767i
\(237\) 6.95359 + 2.04176i 0.451684 + 0.132626i
\(238\) 7.66443 + 1.20697i 0.496811 + 0.0782362i
\(239\) 8.02607 + 17.5746i 0.519163 + 1.13681i 0.969755 + 0.244079i \(0.0784855\pi\)
−0.450592 + 0.892730i \(0.648787\pi\)
\(240\) −10.6761 10.1796i −0.689137 0.657091i
\(241\) 5.14856 + 14.8758i 0.331648 + 0.958234i 0.980363 + 0.197202i \(0.0631855\pi\)
−0.648715 + 0.761031i \(0.724693\pi\)
\(242\) 2.70583 + 7.81797i 0.173937 + 0.502558i
\(243\) 0.723734 + 0.690079i 0.0464276 + 0.0442686i
\(244\) 6.70644 + 14.6851i 0.429336 + 0.940115i
\(245\) 7.84739 20.8492i 0.501352 1.33200i
\(246\) 13.3377 + 3.91630i 0.850381 + 0.249694i
\(247\) −8.40007 + 6.60589i −0.534484 + 0.420322i
\(248\) 0.217116 + 0.304897i 0.0137869 + 0.0193610i
\(249\) 1.83161 + 1.44040i 0.116074 + 0.0912814i
\(250\) 0.0367798 0.772104i 0.00232616 0.0488321i
\(251\) −15.0134 17.3263i −0.947635 1.09363i −0.995499 0.0947747i \(-0.969787\pi\)
0.0478642 0.998854i \(-0.484759\pi\)
\(252\) −3.16965 2.82173i −0.199669 0.177752i
\(253\) 6.69759 10.3881i 0.421074 0.653092i
\(254\) 0.00245712 + 0.00425586i 0.000154174 + 0.000267037i
\(255\) −4.82726 + 0.930378i −0.302295 + 0.0582625i
\(256\) −18.0921 + 9.32712i −1.13076 + 0.582945i
\(257\) 25.4818 10.2014i 1.58951 0.636344i 0.602662 0.797997i \(-0.294107\pi\)
0.986848 + 0.161653i \(0.0516825\pi\)
\(258\) 2.77389 6.07398i 0.172695 0.378149i
\(259\) 19.7142 + 1.20394i 1.22498 + 0.0748093i
\(260\) −17.8690 5.24680i −1.10819 0.325393i
\(261\) −8.43752 4.34984i −0.522269 0.269249i
\(262\) −27.2047 2.59773i −1.68071 0.160488i
\(263\) −5.42934 + 22.3800i −0.334787 + 1.38001i 0.516937 + 0.856023i \(0.327072\pi\)
−0.851725 + 0.523989i \(0.824443\pi\)
\(264\) −1.90266 0.366709i −0.117101 0.0225694i
\(265\) 15.1362 17.4682i 0.929812 1.07306i
\(266\) −12.0971 + 8.37242i −0.741723 + 0.513346i
\(267\) 2.70109 + 5.91455i 0.165304 + 0.361965i
\(268\) 6.96627 + 3.59136i 0.425533 + 0.219377i
\(269\) 8.83399 8.42320i 0.538618 0.513571i −0.371214 0.928547i \(-0.621058\pi\)
0.909832 + 0.414976i \(0.136210\pi\)
\(270\) 5.60881 + 2.24543i 0.341341 + 0.136652i
\(271\) −5.64228 + 0.538772i −0.342744 + 0.0327281i −0.265009 0.964246i \(-0.585375\pi\)
−0.0777350 + 0.996974i \(0.524769\pi\)
\(272\) −1.01902 + 7.08742i −0.0617870 + 0.429738i
\(273\) 9.34936 + 2.40117i 0.565849 + 0.145325i
\(274\) −25.2018 29.0845i −1.52250 1.75706i
\(275\) −6.60797 11.4453i −0.398475 0.690179i
\(276\) 3.51478 + 6.84239i 0.211565 + 0.411863i
\(277\) 13.2937 23.0254i 0.798744 1.38347i −0.121691 0.992568i \(-0.538832\pi\)
0.920434 0.390897i \(-0.127835\pi\)
\(278\) 9.20662 26.6008i 0.552176 1.59541i
\(279\) −0.418813 0.269155i −0.0250737 0.0161139i
\(280\) 5.95405 + 2.15044i 0.355823 + 0.128513i
\(281\) −10.7964 + 23.6409i −0.644061 + 1.41030i 0.252597 + 0.967572i \(0.418715\pi\)
−0.896658 + 0.442725i \(0.854012\pi\)
\(282\) −13.6920 + 10.7675i −0.815349 + 0.641197i
\(283\) 2.07813 1.98150i 0.123532 0.117788i −0.625795 0.779987i \(-0.715225\pi\)
0.749327 + 0.662200i \(0.230377\pi\)
\(284\) 0.103379 + 2.17020i 0.00613444 + 0.128778i
\(285\) 5.40703 7.59311i 0.320285 0.449777i
\(286\) −17.1273 + 5.02904i −1.01276 + 0.297373i
\(287\) −19.2111 + 2.49999i −1.13399 + 0.147570i
\(288\) 4.77779 5.51386i 0.281534 0.324907i
\(289\) −10.5765 10.0846i −0.622144 0.593213i
\(290\) −57.0917 5.45160i −3.35254 0.320129i
\(291\) −0.781501 16.4057i −0.0458124 0.961721i
\(292\) 2.95031 + 12.1614i 0.172654 + 0.711689i
\(293\) 0.481436 + 3.34846i 0.0281258 + 0.195619i 0.999040 0.0438087i \(-0.0139492\pi\)
−0.970914 + 0.239428i \(0.923040\pi\)
\(294\) 12.6457 + 4.08409i 0.737513 + 0.238189i
\(295\) 1.59130 11.0677i 0.0926490 0.644388i
\(296\) −0.267059 + 5.60626i −0.0155225 + 0.325857i
\(297\) 2.53066 0.487746i 0.146844 0.0283019i
\(298\) −18.9664 + 32.8507i −1.09869 + 1.90299i
\(299\) −14.2378 10.1703i −0.823395 0.588162i
\(300\) 8.22502 0.474872
\(301\) −0.124644 + 9.30524i −0.00718438 + 0.536345i
\(302\) 21.4389 + 13.7779i 1.23367 + 0.792832i
\(303\) −1.79364 + 0.718064i −0.103042 + 0.0412517i
\(304\) −7.87535 11.0594i −0.451682 0.634299i
\(305\) 29.7370 + 11.9049i 1.70274 + 0.681672i
\(306\) −0.691382 2.84992i −0.0395237 0.162919i
\(307\) 7.49349 4.81577i 0.427676 0.274851i −0.309045 0.951047i \(-0.600009\pi\)
0.736721 + 0.676197i \(0.236373\pi\)
\(308\) −10.6623 + 2.43590i −0.607539 + 0.138798i
\(309\) 7.86050 2.30805i 0.447168 0.131300i
\(310\) −2.95341 0.569223i −0.167742 0.0323297i
\(311\) −5.32597 15.3884i −0.302008 0.872594i −0.989259 0.146174i \(-0.953304\pi\)
0.687251 0.726420i \(-0.258817\pi\)
\(312\) −0.646694 + 2.66571i −0.0366119 + 0.150916i
\(313\) −6.39686 + 8.98313i −0.361572 + 0.507757i −0.954788 0.297286i \(-0.903918\pi\)
0.593216 + 0.805043i \(0.297858\pi\)
\(314\) 34.6678 22.2797i 1.95642 1.25731i
\(315\) −8.41503 + 0.287954i −0.474133 + 0.0162243i
\(316\) 1.65429 + 11.5058i 0.0930610 + 0.647253i
\(317\) −12.8454 + 1.22659i −0.721472 + 0.0688922i −0.449331 0.893365i \(-0.648338\pi\)
−0.272141 + 0.962257i \(0.587732\pi\)
\(318\) 10.8380 + 8.52313i 0.607767 + 0.477953i
\(319\) −21.7455 + 11.2106i −1.21751 + 0.627672i
\(320\) 4.76733 13.7743i 0.266502 0.770006i
\(321\) 13.7056 0.764974
\(322\) −18.7111 15.1701i −1.04273 0.845395i
\(323\) −4.52468 −0.251760
\(324\) −0.524604 + 1.51574i −0.0291447 + 0.0842080i
\(325\) −16.6291 + 8.57288i −0.922414 + 0.475538i
\(326\) −10.8833 8.55872i −0.602770 0.474024i
\(327\) 14.4514 1.37994i 0.799162 0.0763107i
\(328\) −0.783479 5.44921i −0.0432604 0.300883i
\(329\) 11.4119 21.4263i 0.629156 1.18127i
\(330\) 13.0988 8.41810i 0.721066 0.463401i
\(331\) 2.25523 3.16703i 0.123959 0.174076i −0.747933 0.663774i \(-0.768954\pi\)
0.871892 + 0.489698i \(0.162893\pi\)
\(332\) −0.881138 + 3.63210i −0.0483587 + 0.199337i
\(333\) −2.44161 7.05456i −0.133799 0.386588i
\(334\) 27.6957 + 5.33790i 1.51544 + 0.292077i
\(335\) 14.9206 4.38110i 0.815202 0.239365i
\(336\) −3.61237 + 11.7196i −0.197071 + 0.639355i
\(337\) −2.65967 + 1.70927i −0.144882 + 0.0931097i −0.611073 0.791574i \(-0.709262\pi\)
0.466192 + 0.884684i \(0.345626\pi\)
\(338\) 0.139135 + 0.573523i 0.00756796 + 0.0311956i
\(339\) −8.64830 3.46226i −0.469711 0.188044i
\(340\) −4.57388 6.42312i −0.248054 0.348343i
\(341\) −1.19115 + 0.476866i −0.0645046 + 0.0258237i
\(342\) 4.67783 + 3.00626i 0.252948 + 0.162560i
\(343\) −18.4228 + 1.89716i −0.994740 + 0.102437i
\(344\) −2.64451 −0.142582
\(345\) 14.4157 + 5.01305i 0.776114 + 0.269894i
\(346\) 3.61790 6.26639i 0.194500 0.336883i
\(347\) −14.6930 + 2.83185i −0.788762 + 0.152021i −0.567697 0.823238i \(-0.692165\pi\)
−0.221065 + 0.975259i \(0.570953\pi\)
\(348\) 0.724485 15.2088i 0.0388365 0.815278i
\(349\) −1.80168 + 12.5310i −0.0964418 + 0.670767i 0.883049 + 0.469280i \(0.155487\pi\)
−0.979491 + 0.201487i \(0.935423\pi\)
\(350\) −23.5699 + 10.3848i −1.25986 + 0.555089i
\(351\) −0.519222 3.61127i −0.0277140 0.192755i
\(352\) −4.43303 18.2732i −0.236281 0.973964i
\(353\) −0.804454 16.8876i −0.0428168 0.898835i −0.913462 0.406924i \(-0.866601\pi\)
0.870645 0.491911i \(-0.163702\pi\)
\(354\) 6.63988 + 0.634031i 0.352905 + 0.0336984i
\(355\) 3.11988 + 2.97480i 0.165586 + 0.157886i
\(356\) −6.82966 + 7.88185i −0.361971 + 0.417737i
\(357\) 2.48319 + 3.24618i 0.131424 + 0.171806i
\(358\) 39.2088 11.5127i 2.07225 0.608468i
\(359\) −6.33141 + 8.89122i −0.334159 + 0.469261i −0.947132 0.320843i \(-0.896034\pi\)
0.612973 + 0.790104i \(0.289973\pi\)
\(360\) −0.113849 2.38999i −0.00600038 0.125964i
\(361\) −7.54176 + 7.19106i −0.396935 + 0.378477i
\(362\) −12.9265 + 10.1655i −0.679404 + 0.534289i
\(363\) −1.81031 + 3.96403i −0.0950168 + 0.208058i
\(364\) 2.72623 + 15.2408i 0.142893 + 0.798833i
\(365\) 20.8878 + 13.4238i 1.09332 + 0.702634i
\(366\) −6.24949 + 18.0567i −0.326666 + 0.943839i
\(367\) 10.8960 18.8725i 0.568769 0.985137i −0.427919 0.903817i \(-0.640753\pi\)
0.996688 0.0813198i \(-0.0259135\pi\)
\(368\) 13.7672 17.4536i 0.717665 0.909831i
\(369\) 3.66117 + 6.34132i 0.190593 + 0.330116i
\(370\) −29.5350 34.0852i −1.53545 1.77201i
\(371\) −18.6117 4.78000i −0.966274 0.248165i
\(372\) 0.113642 0.790395i 0.00589204 0.0409800i
\(373\) −18.4623 + 1.76294i −0.955943 + 0.0912815i −0.561354 0.827576i \(-0.689719\pi\)
−0.394589 + 0.918858i \(0.629113\pi\)
\(374\) −7.01657 2.80901i −0.362818 0.145250i
\(375\) 0.294684 0.280981i 0.0152174 0.0145098i
\(376\) 6.13162 + 3.16107i 0.316214 + 0.163020i
\(377\) 14.3873 + 31.5038i 0.740983 + 1.62253i
\(378\) −0.410428 5.00592i −0.0211101 0.257477i
\(379\) −11.7913 + 13.6079i −0.605678 + 0.698989i −0.972922 0.231135i \(-0.925756\pi\)
0.367244 + 0.930125i \(0.380301\pi\)
\(380\) 14.6812 + 2.82957i 0.753131 + 0.145154i
\(381\) −0.000610288 0.00251564i −3.12660e−5 0.000128880i
\(382\) 8.71912 + 0.832575i 0.446109 + 0.0425982i
\(383\) −31.7085 16.3469i −1.62023 0.835287i −0.998650 0.0519368i \(-0.983461\pi\)
−0.621581 0.783350i \(-0.713509\pi\)
\(384\) −5.65796 1.66133i −0.288732 0.0847793i
\(385\) −11.9755 + 18.0966i −0.610327 + 0.922289i
\(386\) −5.13449 + 11.2430i −0.261339 + 0.572252i
\(387\) 3.26541 1.30727i 0.165990 0.0664524i
\(388\) 23.4155 12.0715i 1.18874 0.612838i
\(389\) −12.2013 + 2.35161i −0.618632 + 0.119232i −0.488932 0.872322i \(-0.662613\pi\)
−0.129700 + 0.991553i \(0.541401\pi\)
\(390\) −11.0211 19.0891i −0.558074 0.966612i
\(391\) −2.07674 7.11136i −0.105025 0.359637i
\(392\) −0.609187 5.22753i −0.0307686 0.264030i
\(393\) −9.42699 10.8793i −0.475529 0.548790i
\(394\) −2.30114 + 48.3068i −0.115930 + 2.43366i
\(395\) 18.1292 + 14.2570i 0.912181 + 0.717347i
\(396\) 2.39783 + 3.36729i 0.120496 + 0.169212i
\(397\) 15.9820 12.5684i 0.802113 0.630789i −0.130589 0.991437i \(-0.541687\pi\)
0.932702 + 0.360648i \(0.117444\pi\)
\(398\) −14.3962 4.22712i −0.721619 0.211886i
\(399\) −7.65521 1.20552i −0.383240 0.0603514i
\(400\) −9.87408 21.6212i −0.493704 1.08106i
\(401\) 1.44809 + 1.38075i 0.0723143 + 0.0689515i 0.725374 0.688355i \(-0.241667\pi\)
−0.653060 + 0.757306i \(0.726515\pi\)
\(402\) 3.03398 + 8.76612i 0.151321 + 0.437214i
\(403\) 0.594066 + 1.71644i 0.0295925 + 0.0855020i
\(404\) −2.24278 2.13849i −0.111583 0.106394i
\(405\) 1.32203 + 2.89485i 0.0656924 + 0.143846i
\(406\) 17.1263 + 44.4976i 0.849962 + 2.20838i
\(407\) −18.4601 5.42038i −0.915033 0.268678i
\(408\) −0.912935 + 0.717940i −0.0451970 + 0.0355433i
\(409\) 13.7131 + 19.2574i 0.678072 + 0.952218i 0.999985 + 0.00544927i \(0.00173457\pi\)
−0.321914 + 0.946769i \(0.604326\pi\)
\(410\) 34.7738 + 27.3464i 1.71735 + 1.35054i
\(411\) 0.964573 20.2489i 0.0475789 0.998804i
\(412\) 8.60500 + 9.93070i 0.423938 + 0.489251i
\(413\) −8.82454 + 2.92245i −0.434227 + 0.143804i
\(414\) −2.57786 + 8.73188i −0.126695 + 0.429149i
\(415\) 3.70777 + 6.42204i 0.182007 + 0.315246i
\(416\) −26.1373 + 5.03755i −1.28149 + 0.246986i
\(417\) 13.1793 6.79442i 0.645395 0.332724i
\(418\) 13.3043 5.32624i 0.650735 0.260515i
\(419\) 1.17223 2.56684i 0.0572674 0.125398i −0.878835 0.477126i \(-0.841679\pi\)
0.936102 + 0.351728i \(0.114406\pi\)
\(420\) −6.02714 12.0858i −0.294094 0.589726i
\(421\) −31.4616 9.23795i −1.53334 0.450230i −0.597272 0.802039i \(-0.703749\pi\)
−0.936072 + 0.351809i \(0.885567\pi\)
\(422\) −31.6386 16.3108i −1.54014 0.793999i
\(423\) −9.13387 0.872179i −0.444104 0.0424068i
\(424\) 1.28737 5.30663i 0.0625204 0.257713i
\(425\) −7.77827 1.49914i −0.377302 0.0727189i
\(426\) −1.68398 + 1.94342i −0.0815892 + 0.0941590i
\(427\) −2.17602 26.5406i −0.105305 1.28439i
\(428\) 9.13219 + 19.9967i 0.441421 + 0.966578i
\(429\) −8.35755 4.30862i −0.403506 0.208022i
\(430\) 15.3797 14.6645i 0.741674 0.707185i
\(431\) 8.34214 + 3.33969i 0.401827 + 0.160867i 0.563768 0.825933i \(-0.309351\pi\)
−0.161941 + 0.986800i \(0.551775\pi\)
\(432\) 4.61424 0.440607i 0.222003 0.0211987i
\(433\) 0.356831 2.48182i 0.0171482 0.119268i −0.979449 0.201691i \(-0.935356\pi\)
0.996598 + 0.0824221i \(0.0262656\pi\)
\(434\) 0.672283 + 2.40846i 0.0322706 + 0.115610i
\(435\) −19.7835 22.8314i −0.948546 1.09468i
\(436\) 11.6424 + 20.1653i 0.557571 + 0.965741i
\(437\) 12.1549 + 7.04150i 0.581450 + 0.336841i
\(438\) −7.40570 + 12.8270i −0.353858 + 0.612900i
\(439\) 10.3592 29.9310i 0.494419 1.42853i −0.371542 0.928416i \(-0.621171\pi\)
0.865961 0.500112i \(-0.166708\pi\)
\(440\) −5.18764 3.33389i −0.247311 0.158937i
\(441\) 3.33637 + 6.15375i 0.158875 + 0.293036i
\(442\) −4.44463 + 9.73238i −0.211409 + 0.462922i
\(443\) −12.9916 + 10.2167i −0.617252 + 0.485412i −0.877145 0.480225i \(-0.840555\pi\)
0.259894 + 0.965637i \(0.416313\pi\)
\(444\) 8.66584 8.26286i 0.411263 0.392138i
\(445\) 0.984598 + 20.6693i 0.0466744 + 0.979817i
\(446\) −10.3799 + 14.5766i −0.491504 + 0.690221i
\(447\) −19.1719 + 5.62939i −0.906802 + 0.266261i
\(448\) −12.0165 + 1.56374i −0.567727 + 0.0738798i
\(449\) 19.2339 22.1971i 0.907703 1.04755i −0.0909602 0.995855i \(-0.528994\pi\)
0.998663 0.0516905i \(-0.0164609\pi\)
\(450\) 7.04551 + 6.71788i 0.332128 + 0.316684i
\(451\) 18.7859 + 1.79384i 0.884595 + 0.0844686i
\(452\) −0.710962 14.9249i −0.0334408 0.702010i
\(453\) 3.16485 + 13.0457i 0.148698 + 0.612941i
\(454\) 0.139834 + 0.972568i 0.00656274 + 0.0456449i
\(455\) 24.7824 + 18.1526i 1.16182 + 0.851005i
\(456\) 0.313405 2.17978i 0.0146765 0.102077i
\(457\) 0.455352 9.55902i 0.0213005 0.447152i −0.962874 0.269951i \(-0.912993\pi\)
0.984175 0.177201i \(-0.0567044\pi\)
\(458\) −42.7454 + 8.23850i −1.99736 + 0.384960i
\(459\) 0.772378 1.33780i 0.0360515 0.0624431i
\(460\) 2.29120 + 24.3729i 0.106828 + 1.13639i
\(461\) 8.09333 0.376944 0.188472 0.982079i \(-0.439647\pi\)
0.188472 + 0.982079i \(0.439647\pi\)
\(462\) −11.1228 6.62195i −0.517479 0.308081i
\(463\) 20.3159 + 13.0563i 0.944162 + 0.606776i 0.919572 0.392922i \(-0.128536\pi\)
0.0245900 + 0.999698i \(0.492172\pi\)
\(464\) −40.8493 + 16.3536i −1.89638 + 0.759197i
\(465\) −0.919019 1.29058i −0.0426185 0.0598493i
\(466\) −7.33123 2.93498i −0.339613 0.135960i
\(467\) 5.40507 + 22.2800i 0.250117 + 1.03100i 0.948879 + 0.315641i \(0.102220\pi\)
−0.698762 + 0.715354i \(0.746265\pi\)
\(468\) 4.92293 3.16378i 0.227563 0.146246i
\(469\) −8.79528 9.47515i −0.406128 0.437522i
\(470\) −53.1886 + 15.6176i −2.45341 + 0.720385i
\(471\) 21.3152 + 4.10817i 0.982153 + 0.189294i
\(472\) −0.863986 2.49632i −0.0397682 0.114903i
\(473\) 2.13718 8.80956i 0.0982674 0.405064i
\(474\) −7.98046 + 11.2070i −0.366555 + 0.514754i
\(475\) 12.6357 8.12044i 0.579764 0.372591i
\(476\) −3.08166 + 5.78597i −0.141248 + 0.265199i
\(477\) 1.03362 + 7.18895i 0.0473260 + 0.329159i
\(478\) −36.5123 + 3.48650i −1.67004 + 0.159469i
\(479\) 10.2078 + 8.02750i 0.466406 + 0.366786i 0.823531 0.567271i \(-0.192001\pi\)
−0.357125 + 0.934057i \(0.616243\pi\)
\(480\) 20.6376 10.6394i 0.941974 0.485622i
\(481\) −8.90798 + 25.7379i −0.406169 + 1.17355i
\(482\) −29.8839 −1.36118
\(483\) −1.61890 12.5849i −0.0736625 0.572632i
\(484\) −6.98981 −0.317719
\(485\) 17.0957 49.3947i 0.776275 2.24290i
\(486\) −1.68737 + 0.869902i −0.0765409 + 0.0394596i
\(487\) −5.23754 4.11884i −0.237335 0.186643i 0.492406 0.870365i \(-0.336117\pi\)
−0.729742 + 0.683723i \(0.760360\pi\)
\(488\) 7.53309 0.719323i 0.341007 0.0325622i
\(489\) −1.03793 7.21897i −0.0469369 0.326453i
\(490\) 32.5309 + 27.0237i 1.46959 + 1.22080i
\(491\) −22.3232 + 14.3463i −1.00743 + 0.647437i −0.936727 0.350060i \(-0.886161\pi\)
−0.0707050 + 0.997497i \(0.522525\pi\)
\(492\) −6.81261 + 9.56698i −0.307136 + 0.431313i
\(493\) −3.45718 + 14.2507i −0.155703 + 0.641818i
\(494\) −6.63528 19.1714i −0.298535 0.862561i
\(495\) 8.05369 + 1.55222i 0.361987 + 0.0697672i
\(496\) −2.21415 + 0.650132i −0.0994181 + 0.0291918i
\(497\) 1.05565 3.42483i 0.0473523 0.153625i
\(498\) −3.72134 + 2.39156i −0.166757 + 0.107168i
\(499\) −7.78675 32.0974i −0.348583 1.43688i −0.828710 0.559679i \(-0.810924\pi\)
0.480127 0.877199i \(-0.340591\pi\)
\(500\) 0.606306 + 0.242728i 0.0271148 + 0.0108551i
\(501\) 8.61812 + 12.1025i 0.385029 + 0.540698i
\(502\) 40.4054 16.1759i 1.80338 0.721964i
\(503\) −29.6030 19.0247i −1.31993 0.848268i −0.324700 0.945817i \(-0.605263\pi\)
−0.995231 + 0.0975494i \(0.968900\pi\)
\(504\) −1.73586 + 0.971433i −0.0773213 + 0.0432711i
\(505\) −6.14859 −0.273608
\(506\) 14.4776 + 18.4655i 0.643607 + 0.820892i
\(507\) −0.155435 + 0.269221i −0.00690311 + 0.0119565i
\(508\) −0.00407700 0.000785777i −0.000180888 3.48632e-5i
\(509\) −0.855622 + 17.9617i −0.0379248 + 0.796140i 0.897158 + 0.441710i \(0.145628\pi\)
−0.935083 + 0.354430i \(0.884675\pi\)
\(510\) 1.32819 9.23778i 0.0588133 0.409056i
\(511\) 2.23721 20.5206i 0.0989684 0.907776i
\(512\) −3.82089 26.5749i −0.168861 1.17445i
\(513\) 0.690551 + 2.84649i 0.0304886 + 0.125676i
\(514\) 2.47937 + 52.0484i 0.109360 + 2.29576i
\(515\) 25.9536 + 2.47827i 1.14365 + 0.109206i
\(516\) 4.08310 + 3.89323i 0.179749 + 0.171390i
\(517\) −15.4857 + 17.8714i −0.681058 + 0.785983i
\(518\) −14.4006 + 34.6197i −0.632725 + 1.52110i
\(519\) 3.65711 1.07383i 0.160529 0.0471357i
\(520\) −5.06363 + 7.11088i −0.222055 + 0.311833i
\(521\) −0.0627227 1.31671i −0.00274793 0.0576862i 0.997077 0.0764052i \(-0.0243442\pi\)
−0.999825 + 0.0187190i \(0.994041\pi\)
\(522\) 13.0426 12.4360i 0.570857 0.544311i
\(523\) −14.2330 + 11.1930i −0.622367 + 0.489435i −0.878840 0.477116i \(-0.841682\pi\)
0.256473 + 0.966551i \(0.417440\pi\)
\(524\) 9.59180 21.0031i 0.419020 0.917526i
\(525\) −12.7605 4.60874i −0.556913 0.201142i
\(526\) −36.7787 23.6362i −1.60363 1.03059i
\(527\) −0.251531 + 0.726751i −0.0109569 + 0.0316578i
\(528\) 5.97305 10.3456i 0.259943 0.450235i
\(529\) −5.48812 + 22.3356i −0.238614 + 0.971114i
\(530\) 21.9396 + 38.0006i 0.952997 + 1.65064i
\(531\) 2.30086 + 2.65533i 0.0998487 + 0.115232i
\(532\) −3.34188 11.9723i −0.144889 0.519066i
\(533\) 3.80192 26.4429i 0.164679 1.14537i
\(534\) −12.2878 + 1.17335i −0.531747 + 0.0507756i
\(535\) 40.4930 + 16.2109i 1.75066 + 0.700860i
\(536\) 2.65884 2.53520i 0.114844 0.109504i
\(537\) 19.1326 + 9.86352i 0.825631 + 0.425642i
\(538\) 9.62610 + 21.0782i 0.415011 + 0.908746i
\(539\) 17.9066 + 2.19530i 0.771292 + 0.0945581i
\(540\) −3.34275 + 3.85774i −0.143849 + 0.166010i
\(541\) 11.0662 + 2.13284i 0.475775 + 0.0916981i 0.421501 0.906828i \(-0.361503\pi\)
0.0542740 + 0.998526i \(0.482716\pi\)
\(542\) 2.53678 10.4568i 0.108964 0.449157i
\(543\) −8.62322 0.823418i −0.370058 0.0353362i
\(544\) −10.0175 5.16438i −0.429497 0.221421i
\(545\) 44.3284 + 13.0160i 1.89882 + 0.557544i
\(546\) −10.1128 + 15.2818i −0.432788 + 0.654002i
\(547\) −6.93692 + 15.1897i −0.296601 + 0.649466i −0.997994 0.0633089i \(-0.979835\pi\)
0.701393 + 0.712775i \(0.252562\pi\)
\(548\) 30.1861 12.0847i 1.28949 0.516233i
\(549\) −8.94618 + 4.61208i −0.381814 + 0.196839i
\(550\) 24.6359 4.74817i 1.05048 0.202463i
\(551\) −13.9024 24.0797i −0.592264 1.02583i
\(552\) 3.56977 0.507902i 0.151939 0.0216177i
\(553\) 3.88058 18.7774i 0.165019 0.798495i
\(554\) 33.0534 + 38.1457i 1.40431 + 1.62065i
\(555\) 1.13042 23.7305i 0.0479837 1.00730i
\(556\) 18.6947 + 14.7017i 0.792831 + 0.623489i
\(557\) −4.40651 6.18807i −0.186710 0.262197i 0.710602 0.703594i \(-0.248423\pi\)
−0.897312 + 0.441397i \(0.854483\pi\)
\(558\) 0.742908 0.584229i 0.0314498 0.0247324i
\(559\) −12.3130 3.61541i −0.520783 0.152916i
\(560\) −24.5345 + 30.3525i −1.03677 + 1.28263i
\(561\) −1.65385 3.62143i −0.0698257 0.152897i
\(562\) −35.7081 34.0476i −1.50626 1.43621i
\(563\) 1.70657 + 4.93082i 0.0719235 + 0.207809i 0.975233 0.221180i \(-0.0709909\pi\)
−0.903309 + 0.428990i \(0.858870\pi\)
\(564\) −4.81347 13.9076i −0.202683 0.585615i
\(565\) −21.4561 20.4583i −0.902664 0.860688i
\(566\) 2.26447 + 4.95850i 0.0951828 + 0.208421i
\(567\) 1.66320 2.05761i 0.0698480 0.0864114i
\(568\) 0.977165 + 0.286922i 0.0410009 + 0.0120390i
\(569\) 21.1772 16.6539i 0.887792 0.698168i −0.0662616 0.997802i \(-0.521107\pi\)
0.954054 + 0.299635i \(0.0968648\pi\)
\(570\) 10.2648 + 14.4148i 0.429944 + 0.603771i
\(571\) −14.7755 11.6196i −0.618336 0.486265i 0.259169 0.965832i \(-0.416551\pi\)
−0.877505 + 0.479567i \(0.840794\pi\)
\(572\) 0.717618 15.0647i 0.0300051 0.629885i
\(573\) 3.02136 + 3.48683i 0.126219 + 0.145665i
\(574\) 7.44336 36.0169i 0.310680 1.50332i
\(575\) 18.5623 + 16.1321i 0.774100 + 0.672756i
\(576\) 2.29006 + 3.96650i 0.0954190 + 0.165271i
\(577\) 20.4040 3.93255i 0.849429 0.163714i 0.254082 0.967183i \(-0.418227\pi\)
0.595347 + 0.803469i \(0.297015\pi\)
\(578\) 24.6588 12.7125i 1.02567 0.528771i
\(579\) −6.04429 + 2.41977i −0.251192 + 0.100562i
\(580\) 20.1294 44.0772i 0.835827 1.83021i
\(581\) 3.40220 5.14120i 0.141147 0.213293i
\(582\) 29.9171 + 8.78445i 1.24010 + 0.364127i
\(583\) 16.6374 + 8.57716i 0.689049 + 0.355230i
\(584\) 5.83932 + 0.557588i 0.241633 + 0.0230732i
\(585\) 2.73736 11.2836i 0.113176 0.466518i
\(586\) −6.30607 1.21539i −0.260501 0.0502075i
\(587\) 20.1542 23.2592i 0.831852 0.960008i −0.167815 0.985818i \(-0.553671\pi\)
0.999667 + 0.0258104i \(0.00821663\pi\)
\(588\) −6.75536 + 8.96811i −0.278586 + 0.369839i
\(589\) −0.605763 1.32644i −0.0249600 0.0546549i
\(590\) 18.8674 + 9.72684i 0.776760 + 0.400448i
\(591\) −18.4370 + 17.5796i −0.758395 + 0.723128i
\(592\) −32.1240 12.8605i −1.32029 0.528563i
\(593\) 35.6212 3.40141i 1.46279 0.139679i 0.666909 0.745139i \(-0.267617\pi\)
0.795876 + 0.605460i \(0.207011\pi\)
\(594\) −0.696297 + 4.84285i −0.0285694 + 0.198705i
\(595\) 3.49695 + 12.5279i 0.143361 + 0.513593i
\(596\) −20.9878 24.2212i −0.859694 0.992140i
\(597\) −3.95173 6.84460i −0.161734 0.280131i
\(598\) 27.0859 19.2278i 1.10762 0.786284i
\(599\) 8.95674 15.5135i 0.365962 0.633865i −0.622968 0.782248i \(-0.714073\pi\)
0.988930 + 0.148382i \(0.0474066\pi\)
\(600\) 1.26098 3.64337i 0.0514794 0.148740i
\(601\) −29.7973 19.1495i −1.21546 0.781126i −0.233893 0.972262i \(-0.575146\pi\)
−0.981564 + 0.191136i \(0.938783\pi\)
\(602\) −16.6162 6.00132i −0.677226 0.244596i
\(603\) −2.02987 + 4.44479i −0.0826625 + 0.181006i
\(604\) −16.9251 + 13.3100i −0.688673 + 0.541578i
\(605\) −10.0372 + 9.57042i −0.408069 + 0.389093i
\(606\) −0.174521 3.66364i −0.00708941 0.148825i
\(607\) −26.3572 + 37.0136i −1.06981 + 1.50233i −0.219813 + 0.975542i \(0.570545\pi\)
−0.849994 + 0.526792i \(0.823395\pi\)
\(608\) 20.5044 6.02064i 0.831564 0.244169i
\(609\) −9.64596 + 23.1893i −0.390874 + 0.939680i
\(610\) −39.8213 + 45.9563i −1.61232 + 1.86072i
\(611\) 24.2275 + 23.1009i 0.980139 + 0.934561i
\(612\) 2.46651 + 0.235523i 0.0997028 + 0.00952046i
\(613\) 1.76535 + 37.0592i 0.0713017 + 1.49681i 0.697186 + 0.716890i \(0.254435\pi\)
−0.625884 + 0.779916i \(0.715262\pi\)
\(614\) 3.98672 + 16.4335i 0.160891 + 0.663201i
\(615\) 3.31635 + 23.0657i 0.133728 + 0.930099i
\(616\) −0.555627 + 5.09642i −0.0223869 + 0.205341i
\(617\) −5.34837 + 37.1987i −0.215317 + 1.49756i 0.539699 + 0.841858i \(0.318538\pi\)
−0.755017 + 0.655706i \(0.772371\pi\)
\(618\) −0.740014 + 15.5348i −0.0297677 + 0.624902i
\(619\) 21.2060 4.08712i 0.852342 0.164275i 0.255673 0.966763i \(-0.417703\pi\)
0.596668 + 0.802488i \(0.296491\pi\)
\(620\) 1.27063 2.20079i 0.0510296 0.0883858i
\(621\) −4.15683 + 2.39181i −0.166808 + 0.0959800i
\(622\) 30.9137 1.23953
\(623\) 15.0121 8.40121i 0.601449 0.336587i
\(624\) −14.2266 9.14289i −0.569520 0.366008i
\(625\) −22.6001 + 9.04772i −0.904004 + 0.361909i
\(626\) −12.1439 17.0537i −0.485366 0.681602i
\(627\) 7.00813 + 2.80563i 0.279878 + 0.112046i
\(628\) 8.20865 + 33.8365i 0.327561 + 1.35022i
\(629\) −9.70118 + 6.23457i −0.386812 + 0.248589i
\(630\) 4.70838 15.2753i 0.187586 0.608584i
\(631\) 11.1742 3.28104i 0.444838 0.130616i −0.0516398 0.998666i \(-0.516445\pi\)
0.496477 + 0.868050i \(0.334627\pi\)
\(632\) 5.35026 + 1.03118i 0.212822 + 0.0410181i
\(633\) −6.13259 17.7189i −0.243748 0.704265i
\(634\) 5.77535 23.8063i 0.229369 0.945470i
\(635\) −0.00477857 + 0.00671056i −0.000189632 + 0.000266301i
\(636\) −9.80008 + 6.29813i −0.388598 + 0.249737i
\(637\) 4.31036 25.1725i 0.170783 0.997370i
\(638\) −6.60980 45.9722i −0.261684 1.82006i
\(639\) −1.34843 + 0.128759i −0.0533430 + 0.00509364i
\(640\) −14.7513 11.6006i −0.583097 0.458553i
\(641\) −39.2181 + 20.2183i −1.54902 + 0.798575i −0.999323 0.0367890i \(-0.988287\pi\)
−0.549697 + 0.835364i \(0.685257\pi\)
\(642\) −8.50995 + 24.5879i −0.335861 + 0.970407i
\(643\) 14.0642 0.554639 0.277320 0.960778i \(-0.410554\pi\)
0.277320 + 0.960778i \(0.410554\pi\)
\(644\) 17.2828 10.7474i 0.681039 0.423508i
\(645\) 11.1938 0.440756
\(646\) 2.80941 8.11727i 0.110535 0.319370i
\(647\) 8.75746 4.51479i 0.344291 0.177495i −0.277405 0.960753i \(-0.589474\pi\)
0.621696 + 0.783259i \(0.286444\pi\)
\(648\) 0.590989 + 0.464759i 0.0232163 + 0.0182575i
\(649\) 9.01414 0.860746i 0.353836 0.0337873i
\(650\) −5.05460 35.1555i −0.198258 1.37891i
\(651\) −0.619189 + 1.16256i −0.0242679 + 0.0455643i
\(652\) 9.84100 6.32443i 0.385403 0.247684i
\(653\) −6.46279 + 9.07571i −0.252908 + 0.355160i −0.921438 0.388525i \(-0.872985\pi\)
0.668530 + 0.743686i \(0.266924\pi\)
\(654\) −6.49737 + 26.7825i −0.254067 + 1.04728i
\(655\) −14.9838 43.2929i −0.585467 1.69159i
\(656\) 33.3273 + 6.42332i 1.30121 + 0.250788i
\(657\) −7.48596 + 2.19808i −0.292055 + 0.0857552i
\(658\) 31.3531 + 33.7767i 1.22227 + 1.31675i
\(659\) 25.5981 16.4509i 0.997162 0.640837i 0.0631221 0.998006i \(-0.479894\pi\)
0.934040 + 0.357169i \(0.116258\pi\)
\(660\) 3.10154 + 12.7847i 0.120727 + 0.497644i
\(661\) −44.0084 17.6183i −1.71173 0.685273i −0.711874 0.702308i \(-0.752153\pi\)
−0.999855 + 0.0170348i \(0.994577\pi\)
\(662\) 4.28136 + 6.01232i 0.166400 + 0.233676i
\(663\) −5.23219 + 2.09465i −0.203201 + 0.0813496i
\(664\) 1.47379 + 0.947149i 0.0571943 + 0.0367565i
\(665\) −21.1913 12.6162i −0.821763 0.489236i
\(666\) 14.1719 0.549150
\(667\) 31.4648 32.9024i 1.21832 1.27398i
\(668\) −11.9153 + 20.6379i −0.461018 + 0.798506i
\(669\) −9.25580 + 1.78391i −0.357850 + 0.0689699i
\(670\) −1.40468 + 29.4879i −0.0542676 + 1.13922i
\(671\) −3.69165 + 25.6760i −0.142515 + 0.991212i
\(672\) −15.5725 11.4065i −0.600720 0.440015i
\(673\) 2.69375 + 18.7355i 0.103837 + 0.722199i 0.973522 + 0.228593i \(0.0734124\pi\)
−0.869686 + 0.493606i \(0.835678\pi\)
\(674\) −1.41501 5.83275i −0.0545041 0.224669i
\(675\) 0.243997 + 5.12213i 0.00939146 + 0.197151i
\(676\) −0.496366 0.0473972i −0.0190910 0.00182297i
\(677\) −0.910290 0.867960i −0.0349853 0.0333584i 0.672385 0.740202i \(-0.265270\pi\)
−0.707370 + 0.706843i \(0.750119\pi\)
\(678\) 11.5811 13.3653i 0.444769 0.513291i
\(679\) −43.0914 + 5.60759i −1.65369 + 0.215200i
\(680\) −3.54642 + 1.04132i −0.135999 + 0.0399329i
\(681\) −0.300223 + 0.421604i −0.0115046 + 0.0161559i
\(682\) −0.115899 2.43302i −0.00443800 0.0931651i
\(683\) −19.2285 + 18.3344i −0.735760 + 0.701545i −0.962159 0.272489i \(-0.912153\pi\)
0.226399 + 0.974035i \(0.427305\pi\)
\(684\) −3.69295 + 2.90417i −0.141203 + 0.111044i
\(685\) 26.8001 58.6840i 1.02398 2.24220i
\(686\) 8.03541 34.2285i 0.306793 1.30685i
\(687\) −19.2906 12.3973i −0.735983 0.472987i
\(688\) 5.33245 15.4071i 0.203298 0.587390i
\(689\) 13.2490 22.9479i 0.504745 0.874244i
\(690\) −17.9442 + 22.7491i −0.683126 + 0.866043i
\(691\) −14.2987 24.7660i −0.543947 0.942145i −0.998672 0.0515127i \(-0.983596\pi\)
0.454725 0.890632i \(-0.349738\pi\)
\(692\) 4.00350 + 4.62028i 0.152190 + 0.175637i
\(693\) −1.83326 6.56767i −0.0696397 0.249485i
\(694\) 4.04270 28.1176i 0.153459 1.06733i
\(695\) 46.9745 4.48552i 1.78184 0.170145i
\(696\) −6.62585 2.65259i −0.251152 0.100546i
\(697\) 8.18631 7.80564i 0.310079 0.295660i
\(698\) −21.3619 11.0128i −0.808558 0.416841i
\(699\) −1.72802 3.78384i −0.0653597 0.143118i
\(700\) −1.77821 21.6886i −0.0672102 0.819752i
\(701\) 4.55214 5.25345i 0.171932 0.198420i −0.663243 0.748404i \(-0.730821\pi\)
0.835175 + 0.549984i \(0.185366\pi\)
\(702\) 6.80101 + 1.31079i 0.256687 + 0.0494725i
\(703\) 5.15506 21.2494i 0.194427 0.801438i
\(704\) 11.7506 + 1.12205i 0.442867 + 0.0422887i
\(705\) −25.9542 13.3803i −0.977493 0.503932i
\(706\) 30.7958 + 9.04246i 1.15901 + 0.340317i
\(707\) 2.28124 + 4.57441i 0.0857950 + 0.172038i
\(708\) −2.34108 + 5.12626i −0.0879833 + 0.192657i
\(709\) 35.1679 14.0791i 1.32076 0.528752i 0.399155 0.916883i \(-0.369303\pi\)
0.921604 + 0.388131i \(0.126879\pi\)
\(710\) −7.27395 + 3.74998i −0.272987 + 0.140734i
\(711\) −7.11618 + 1.37153i −0.266878 + 0.0514365i
\(712\) 2.44430 + 4.23365i 0.0916039 + 0.158663i
\(713\) 1.80670 1.56088i 0.0676616 0.0584553i
\(714\) −7.36548 + 2.43925i −0.275646 + 0.0912866i
\(715\) −19.5960 22.6150i −0.732849 0.845752i
\(716\) −1.64281 + 34.4869i −0.0613947 + 1.28883i
\(717\) −15.1870 11.9432i −0.567169 0.446027i
\(718\) −12.0196 16.8792i −0.448568 0.629926i
\(719\) −1.91361 + 1.50488i −0.0713655 + 0.0561225i −0.653205 0.757182i \(-0.726576\pi\)
0.581839 + 0.813304i \(0.302333\pi\)
\(720\) 14.1538 + 4.15594i 0.527482 + 0.154883i
\(721\) −7.78551 20.2284i −0.289948 0.753344i
\(722\) −8.21800 17.9949i −0.305842 0.669701i
\(723\) −11.3927 10.8629i −0.423699 0.403996i
\(724\) −4.54436 13.1301i −0.168890 0.487975i
\(725\) −15.9212 46.0012i −0.591297 1.70844i
\(726\) −5.98743 5.70901i −0.222215 0.211881i
\(727\) 3.63519 + 7.95996i 0.134822 + 0.295219i 0.964986 0.262300i \(-0.0844809\pi\)
−0.830165 + 0.557518i \(0.811754\pi\)
\(728\) 7.16903 + 1.12896i 0.265702 + 0.0418419i
\(729\) −0.959493 0.281733i −0.0355368 0.0104345i
\(730\) −37.0517 + 29.1378i −1.37135 + 1.07844i
\(731\) −3.15172 4.42598i −0.116571 0.163701i
\(732\) −12.6900 9.97954i −0.469036 0.368854i
\(733\) −0.976038 + 20.4896i −0.0360508 + 0.756800i 0.906393 + 0.422435i \(0.138825\pi\)
−0.942444 + 0.334364i \(0.891478\pi\)
\(734\) 27.0918 + 31.2656i 0.999977 + 1.15403i
\(735\) 2.57860 + 22.1274i 0.0951130 + 0.816180i
\(736\) 18.8736 + 29.4631i 0.695692 + 1.08602i
\(737\) 6.29665 + 10.9061i 0.231940 + 0.401732i
\(738\) −13.6496 + 2.63074i −0.502448 + 0.0968389i
\(739\) 12.2949 6.33849i 0.452277 0.233165i −0.217009 0.976170i \(-0.569630\pi\)
0.669286 + 0.743005i \(0.266600\pi\)
\(740\) 35.3763 14.1625i 1.30046 0.520625i
\(741\) 4.43929 9.72068i 0.163081 0.357098i
\(742\) 20.1315 30.4215i 0.739051 1.11681i
\(743\) −43.5011 12.7731i −1.59590 0.468598i −0.641498 0.767124i \(-0.721687\pi\)
−0.954402 + 0.298526i \(0.903505\pi\)
\(744\) −0.332692 0.171515i −0.0121971 0.00628803i
\(745\) −63.3015 6.04456i −2.31919 0.221456i
\(746\) 8.30072 34.2160i 0.303911 1.25274i
\(747\) −2.28803 0.440982i −0.0837147 0.0161347i
\(748\) 4.18174 4.82599i 0.152900 0.176456i
\(749\) −2.96310 36.1404i −0.108269 1.32054i
\(750\) 0.321107 + 0.703127i 0.0117252 + 0.0256746i
\(751\) 20.5302 + 10.5840i 0.749157 + 0.386217i 0.790127 0.612943i \(-0.210015\pi\)
−0.0409701 + 0.999160i \(0.513045\pi\)
\(752\) −30.7806 + 29.3492i −1.12245 + 1.07026i
\(753\) 21.2838 + 8.52074i 0.775624 + 0.310513i
\(754\) −65.4509 + 6.24981i −2.38358 + 0.227605i
\(755\) −6.07990 + 42.2866i −0.221270 + 1.53897i
\(756\) 4.11029 + 1.05563i 0.149490 + 0.0383930i
\(757\) −10.6921 12.3394i −0.388611 0.448481i 0.527410 0.849611i \(-0.323163\pi\)
−0.916021 + 0.401130i \(0.868618\pi\)
\(758\) −17.0912 29.6028i −0.620780 1.07522i
\(759\) −1.19297 + 12.3023i −0.0433021 + 0.446545i
\(760\) 3.50418 6.06941i 0.127110 0.220161i
\(761\) −12.6569 + 36.5698i −0.458813 + 1.32565i 0.444156 + 0.895949i \(0.353504\pi\)
−0.902970 + 0.429705i \(0.858618\pi\)
\(762\) −0.00413413 0.00265684i −0.000149764 9.62472e-5i
\(763\) −6.76308 37.8085i −0.244840 1.36876i
\(764\) −3.07418 + 6.73152i −0.111220 + 0.243538i
\(765\) 3.86432 3.03893i 0.139715 0.109873i
\(766\) 49.0144 46.7352i 1.77096 1.68861i
\(767\) −0.609939 12.8042i −0.0220236 0.462332i
\(768\) 11.8070 16.5806i 0.426047 0.598299i
\(769\) −18.4555 + 5.41903i −0.665524 + 0.195415i −0.597009 0.802235i \(-0.703644\pi\)
−0.0685149 + 0.997650i \(0.521826\pi\)
\(770\) −25.0296 32.7204i −0.902005 1.17916i
\(771\) −17.9746 + 20.7438i −0.647338 + 0.747068i
\(772\) −7.55785 7.20639i −0.272013 0.259364i
\(773\) −26.5797 2.53806i −0.956006 0.0912875i −0.394623 0.918843i \(-0.629125\pi\)
−0.561384 + 0.827556i \(0.689731\pi\)
\(774\) 0.317724 + 6.66984i 0.0114203 + 0.239742i
\(775\) −0.601873 2.48095i −0.0216199 0.0891184i
\(776\) −1.75738 12.2228i −0.0630862 0.438774i
\(777\) −18.0743 + 7.96345i −0.648413 + 0.285687i
\(778\) 3.35713 23.3493i 0.120359 0.837114i
\(779\) −1.02051 + 21.4232i −0.0365637 + 0.767567i
\(780\) 18.2868 3.52449i 0.654772 0.126197i
\(781\) −1.74551 + 3.02332i −0.0624594 + 0.108183i
\(782\) 14.0472 + 0.689843i 0.502328 + 0.0246687i
\(783\) 9.49278 0.339244
\(784\) 31.6844 + 6.99175i 1.13158 + 0.249705i
\(785\) 58.1162 + 37.3490i 2.07426 + 1.33304i
\(786\) 25.3708 10.1569i 0.904947 0.362286i
\(787\) 16.1366 + 22.6606i 0.575206 + 0.807764i 0.995002 0.0998545i \(-0.0318377\pi\)
−0.419796 + 0.907619i \(0.637898\pi\)
\(788\) −37.9336 15.1863i −1.35133 0.540991i
\(789\) −5.42934 22.3800i −0.193290 0.796751i
\(790\) −36.8336 + 23.6715i −1.31048 + 0.842196i
\(791\) −7.25991 + 23.5533i −0.258133 + 0.837457i
\(792\) 1.85919 0.545908i 0.0660635 0.0193980i
\(793\) 36.0578 + 6.94957i 1.28045 + 0.246787i
\(794\) 12.6243 + 36.4755i 0.448019 + 1.29447i
\(795\) −5.44926 + 22.4622i −0.193265 + 0.796650i
\(796\) 7.35329 10.3263i 0.260631 0.366004i
\(797\) −40.9442 + 26.3132i −1.45032 + 0.932062i −0.451102 + 0.892473i \(0.648969\pi\)
−0.999216 + 0.0395899i \(0.987395\pi\)
\(798\) 6.91589 12.9849i 0.244820 0.459662i
\(799\) 2.01714 + 14.0295i 0.0713613 + 0.496329i
\(800\) 37.2435 3.55632i 1.31676 0.125735i
\(801\) −5.11103 4.01936i −0.180589 0.142017i
\(802\) −3.37621 + 1.74055i −0.119218 + 0.0614611i
\(803\) −6.57655 + 19.0017i −0.232082 + 0.670556i
\(804\) −7.83753 −0.276408
\(805\) 10.1023 39.0966i 0.356060 1.37797i
\(806\) −3.44815 −0.121456
\(807\) −3.99224 + 11.5348i −0.140533 + 0.406044i
\(808\) −1.29111 + 0.665614i −0.0454211 + 0.0234162i
\(809\) −20.5891 16.1914i −0.723874 0.569261i 0.186794 0.982399i \(-0.440190\pi\)
−0.910668 + 0.413138i \(0.864433\pi\)
\(810\) −6.01423 + 0.574289i −0.211318 + 0.0201785i
\(811\) 0.742277 + 5.16265i 0.0260649 + 0.181285i 0.998695 0.0510742i \(-0.0162645\pi\)
−0.972630 + 0.232359i \(0.925355\pi\)
\(812\) −40.2608 + 1.37768i −1.41288 + 0.0483472i
\(813\) 4.76818 3.06432i 0.167227 0.107470i
\(814\) 21.1862 29.7518i 0.742576 1.04280i
\(815\) 5.47201 22.5560i 0.191676 0.790101i
\(816\) −2.34191 6.76649i −0.0819831 0.236875i
\(817\) 10.1164 + 1.94977i 0.353927 + 0.0682139i
\(818\) −43.0624 + 12.6443i −1.50564 + 0.442096i
\(819\) −9.41032 + 2.14988i −0.328823 + 0.0751229i
\(820\) −31.4435 + 20.2075i −1.09805 + 0.705677i
\(821\) 6.89679 + 28.4289i 0.240699 + 0.992177i 0.956002 + 0.293361i \(0.0947739\pi\)
−0.715302 + 0.698815i \(0.753711\pi\)
\(822\) 35.7276 + 14.3032i 1.24614 + 0.498880i
\(823\) −17.7230 24.8885i −0.617785 0.867558i 0.380578 0.924749i \(-0.375725\pi\)
−0.998363 + 0.0571907i \(0.981786\pi\)
\(824\) 5.71816 2.28920i 0.199201 0.0797482i
\(825\) 11.1179 + 7.14507i 0.387077 + 0.248759i
\(826\) 0.236366 17.6458i 0.00822424 0.613975i
\(827\) 32.3895 1.12629 0.563146 0.826357i \(-0.309591\pi\)
0.563146 + 0.826357i \(0.309591\pi\)
\(828\) −6.25942 4.47119i −0.217530 0.155385i
\(829\) −24.1423 + 41.8157i −0.838498 + 1.45232i 0.0526531 + 0.998613i \(0.483232\pi\)
−0.891151 + 0.453707i \(0.850101\pi\)
\(830\) −13.8233 + 2.66423i −0.479815 + 0.0924767i
\(831\) −1.26508 + 26.5574i −0.0438853 + 0.921265i
\(832\) 2.37810 16.5400i 0.0824457 0.573422i
\(833\) 8.02302 7.24973i 0.277981 0.251188i
\(834\) 4.00601 + 27.8624i 0.138717 + 0.964797i
\(835\) 11.1473 + 45.9499i 0.385769 + 1.59016i
\(836\) 0.576127 + 12.0944i 0.0199258 + 0.418293i
\(837\) 0.495590 + 0.0473231i 0.0171301 + 0.00163572i
\(838\) 3.87705 + 3.69676i 0.133930 + 0.127702i
\(839\) 9.74730 11.2490i 0.336514 0.388358i −0.562121 0.827055i \(-0.690014\pi\)
0.898635 + 0.438697i \(0.144560\pi\)
\(840\) −6.27756 + 0.816915i −0.216596 + 0.0281863i
\(841\) −58.6374 + 17.2175i −2.02198 + 0.593707i
\(842\) 36.1077 50.7061i 1.24435 1.74745i
\(843\) −1.23663 25.9601i −0.0425918 0.894112i
\(844\) 21.7660 20.7538i 0.749216 0.714376i
\(845\) −0.777663 + 0.611561i −0.0267524 + 0.0210383i
\(846\) 7.23600 15.8446i 0.248779 0.544749i
\(847\) 10.8442 + 3.91662i 0.372610 + 0.134576i
\(848\) 28.3209 + 18.2007i 0.972543 + 0.625016i
\(849\) −0.939144 + 2.71348i −0.0322313 + 0.0931264i
\(850\) 7.51906 13.0234i 0.257902 0.446699i
\(851\) 35.7635 1.65095i 1.22596 0.0565940i
\(852\) −1.08633 1.88158i −0.0372171 0.0644619i
\(853\) 13.4320 + 15.5014i 0.459904 + 0.530757i 0.937576 0.347781i \(-0.113065\pi\)
−0.477672 + 0.878538i \(0.658519\pi\)
\(854\) 48.9649 + 12.5755i 1.67554 + 0.430325i
\(855\) −1.32660 + 9.22667i −0.0453686 + 0.315546i
\(856\) 10.2578 0.979505i 0.350606 0.0334788i
\(857\) 43.4468 + 17.3935i 1.48412 + 0.594150i 0.965395 0.260793i \(-0.0839841\pi\)
0.518721 + 0.854944i \(0.326408\pi\)
\(858\) 12.9189 12.3182i 0.441045 0.420536i
\(859\) 36.0261 + 18.5727i 1.22919 + 0.633694i 0.945625 0.325258i \(-0.105451\pi\)
0.283569 + 0.958952i \(0.408482\pi\)
\(860\) 7.45855 + 16.3319i 0.254334 + 0.556915i
\(861\) 15.9299 11.0251i 0.542891 0.375735i
\(862\) −11.1711 + 12.8921i −0.380490 + 0.439108i
\(863\) −18.5943 3.58376i −0.632958 0.121993i −0.137327 0.990526i \(-0.543851\pi\)
−0.495631 + 0.868533i \(0.665063\pi\)
\(864\) −1.72007 + 7.09022i −0.0585179 + 0.241214i
\(865\) 12.0750 + 1.15302i 0.410562 + 0.0392039i
\(866\) 4.23082 + 2.18114i 0.143769 + 0.0741181i
\(867\) 14.0218 + 4.11716i 0.476204 + 0.139826i
\(868\) −2.10876 0.128782i −0.0715761 0.00437114i
\(869\) −7.75897 + 16.9898i −0.263205 + 0.576338i
\(870\) 53.2432 21.3154i 1.80511 0.722659i
\(871\) 15.8456 8.16900i 0.536909 0.276796i
\(872\) 10.7173 2.06560i 0.362935 0.0699500i
\(873\) 8.21216 + 14.2239i 0.277940 + 0.481406i
\(874\) −20.1796 + 17.4338i −0.682584 + 0.589708i
\(875\) −0.804629 0.716307i −0.0272014 0.0242156i
\(876\) −8.19499 9.45753i −0.276883 0.319540i
\(877\) 1.83434 38.5075i 0.0619412 1.30031i −0.727342 0.686276i \(-0.759244\pi\)
0.789283 0.614030i \(-0.210453\pi\)
\(878\) 47.2640 + 37.1689i 1.59508 + 1.25439i
\(879\) −1.96227 2.75562i −0.0661858 0.0929449i
\(880\) 29.8840 23.5010i 1.00739 0.792219i
\(881\) −12.2670 3.60193i −0.413287 0.121352i 0.0684777 0.997653i \(-0.478186\pi\)
−0.481765 + 0.876301i \(0.660004\pi\)
\(882\) −13.1114 + 2.16452i −0.441484 + 0.0728831i
\(883\) −4.27175 9.35384i −0.143756 0.314782i 0.824034 0.566540i \(-0.191718\pi\)
−0.967790 + 0.251759i \(0.918991\pi\)
\(884\) −6.54239 6.23815i −0.220044 0.209812i
\(885\) 3.65712 + 10.5666i 0.122933 + 0.355191i
\(886\) −10.2622 29.6507i −0.344765 0.996134i
\(887\) 15.8186 + 15.0830i 0.531137 + 0.506438i 0.907510 0.420030i \(-0.137980\pi\)
−0.376373 + 0.926468i \(0.622829\pi\)
\(888\) −2.33157 5.10542i −0.0782422 0.171327i
\(889\) 0.00676545 + 0.00106540i 0.000226906 + 3.57324e-5i
\(890\) −37.6920 11.0674i −1.26344 0.370979i
\(891\) −2.02585 + 1.59314i −0.0678684 + 0.0533723i
\(892\) −8.76998 12.3157i −0.293641 0.412361i
\(893\) −21.1254 16.6132i −0.706936 0.555940i
\(894\) 1.80491 37.8898i 0.0603653 1.26722i
\(895\) 44.8602 + 51.7715i 1.49951 + 1.73053i
\(896\) −3.15753 + 15.2787i −0.105486 + 0.510425i
\(897\) 17.3154 + 2.51555i 0.578143 + 0.0839918i
\(898\) 27.8791 + 48.2879i 0.930336 + 1.61139i
\(899\) −4.64052 + 0.894387i −0.154770 + 0.0298295i
\(900\) −7.31069 + 3.76892i −0.243690 + 0.125631i
\(901\) 10.4157 4.16982i 0.346998 0.138917i
\(902\) −14.8825 + 32.5881i −0.495533 + 1.08507i
\(903\) −4.15312 8.32794i −0.138207 0.277137i
\(904\) −6.72017 1.97322i −0.223509 0.0656283i
\(905\) −24.5032 12.6323i −0.814513 0.419911i
\(906\) −25.3691 2.42245i −0.842831 0.0804806i
\(907\) 2.85905 11.7851i 0.0949331 0.391319i −0.904445 0.426591i \(-0.859714\pi\)
0.999378 + 0.0352715i \(0.0112296\pi\)
\(908\) −0.815168 0.157111i −0.0270523 0.00521390i
\(909\) 1.26521 1.46013i 0.0419645 0.0484296i
\(910\) −47.9533 + 33.1885i −1.58964 + 1.10019i
\(911\) 3.41973 + 7.48816i 0.113301 + 0.248094i 0.957784 0.287487i \(-0.0928199\pi\)
−0.844484 + 0.535581i \(0.820093\pi\)
\(912\) 12.0676 + 6.22127i 0.399598 + 0.206007i
\(913\) −4.34626 + 4.14415i −0.143840 + 0.137151i
\(914\) 16.8662 + 6.75219i 0.557883 + 0.223343i
\(915\) −31.8864 + 3.04479i −1.05413 + 0.100657i
\(916\) 5.23435 36.4057i 0.172948 1.20288i
\(917\) −26.6497 + 27.2101i −0.880049 + 0.898558i
\(918\) 1.92043 + 2.21630i 0.0633837 + 0.0731487i
\(919\) 1.95358 + 3.38369i 0.0644425 + 0.111618i 0.896447 0.443152i \(-0.146140\pi\)
−0.832004 + 0.554770i \(0.812806\pi\)
\(920\) 11.1475 + 2.72172i 0.367524 + 0.0897323i
\(921\) −4.45376 + 7.71414i −0.146756 + 0.254190i
\(922\) −5.02522 + 14.5194i −0.165497 + 0.478172i
\(923\) 4.15747 + 2.67184i 0.136845 + 0.0879447i
\(924\) 8.36081 7.05085i 0.275050 0.231956i
\(925\) 15.9024 34.8214i 0.522868 1.14492i
\(926\) −36.0373 + 28.3400i −1.18426 + 0.931311i
\(927\) −5.92908 + 5.65336i −0.194736 + 0.185681i
\(928\) −3.29544 69.1798i −0.108178 2.27094i
\(929\) 0.963092 1.35247i 0.0315980 0.0443732i −0.798475 0.602028i \(-0.794359\pi\)
0.830073 + 0.557655i \(0.188299\pi\)
\(930\) 2.88593 0.847385i 0.0946333 0.0277869i
\(931\) −1.52381 + 20.4467i −0.0499408 + 0.670113i
\(932\) 4.36928 5.04241i 0.143120 0.165170i
\(933\) 11.7853 + 11.2372i 0.385832 + 0.367890i
\(934\) −43.3264 4.13717i −1.41768 0.135372i
\(935\) −0.602861 12.6556i −0.0197157 0.413883i
\(936\) −0.646694 2.66571i −0.0211379 0.0871315i
\(937\) 2.41378 + 16.7882i 0.0788547 + 0.548446i 0.990505 + 0.137479i \(0.0438999\pi\)
−0.911650 + 0.410967i \(0.865191\pi\)
\(938\) 22.4595 9.89552i 0.733328 0.323100i
\(939\) 1.56945 10.9157i 0.0512169 0.356222i
\(940\) 2.22855 46.7830i 0.0726873 1.52589i
\(941\) 17.1991 3.31485i 0.560674 0.108061i 0.0989627 0.995091i \(-0.468448\pi\)
0.461712 + 0.887030i \(0.347235\pi\)
\(942\) −20.6049 + 35.6887i −0.671343 + 1.16280i
\(943\) −34.1389 + 8.22891i −1.11172 + 0.267970i
\(944\) 16.2859 0.530062
\(945\) 7.34763 4.11193i 0.239018 0.133761i
\(946\) 14.4773 + 9.30403i 0.470699 + 0.302500i
\(947\) −55.5276 + 22.2299i −1.80440 + 0.722374i −0.814585 + 0.580044i \(0.803035\pi\)
−0.989819 + 0.142330i \(0.954540\pi\)
\(948\) −6.74267 9.46875i −0.218992 0.307531i
\(949\) 26.4259 + 10.5793i 0.857820 + 0.343419i
\(950\) 6.72247 + 27.7104i 0.218106 + 0.899045i
\(951\) 10.8554 6.97636i 0.352012 0.226224i
\(952\) 2.09051 + 2.25211i 0.0677538 + 0.0729911i
\(953\) −12.9182 + 3.79313i −0.418462 + 0.122872i −0.484184 0.874966i \(-0.660883\pi\)
0.0657214 + 0.997838i \(0.479065\pi\)
\(954\) −13.5388 2.60938i −0.438333 0.0844818i
\(955\) 4.80233 + 13.8754i 0.155400 + 0.448998i
\(956\) 7.30605 30.1159i 0.236294 0.974019i
\(957\) 14.1912 19.9287i 0.458736 0.644204i
\(958\) −20.7394 + 13.3284i −0.670061 + 0.430622i
\(959\) −53.6029 + 1.83424i −1.73093 + 0.0592306i
\(960\) 2.07437 + 14.4276i 0.0669501 + 0.465648i
\(961\) 30.6129 2.92318i 0.987513 0.0942961i
\(962\) −40.6427 31.9618i −1.31037 1.03049i
\(963\) −12.1821 + 6.28028i −0.392561 + 0.202379i
\(964\) 8.25809 23.8602i 0.265975 0.768485i
\(965\) −20.7198 −0.666994
\(966\) 23.5825 + 4.90976i 0.758753 + 0.157969i
\(967\) 11.7557 0.378039 0.189019 0.981973i \(-0.439469\pi\)
0.189019 + 0.981973i \(0.439469\pi\)
\(968\) −1.07161 + 3.09622i −0.0344429 + 0.0995162i
\(969\) 4.02170 2.07333i 0.129195 0.0666049i
\(970\) 77.9992 + 61.3392i 2.50440 + 1.96948i
\(971\) 57.9290 5.53155i 1.85903 0.177516i 0.895490 0.445083i \(-0.146826\pi\)
0.963539 + 0.267567i \(0.0862196\pi\)
\(972\) −0.228267 1.58764i −0.00732168 0.0509234i
\(973\) −20.7655 33.2837i −0.665713 1.06703i
\(974\) 10.6412 6.83871i 0.340967 0.219126i
\(975\) 10.8522 15.2398i 0.347548 0.488063i
\(976\) −10.9991 + 45.3388i −0.352072 + 1.45126i
\(977\) −7.37880 21.3197i −0.236069 0.682076i −0.999351 0.0360113i \(-0.988535\pi\)
0.763283 0.646065i \(-0.223586\pi\)
\(978\) 13.5953 + 2.62028i 0.434729 + 0.0837872i
\(979\) −16.0788 + 4.72115i −0.513880 + 0.150889i
\(980\) −30.5660 + 18.5059i −0.976395 + 0.591149i
\(981\) −12.2126 + 7.84853i −0.389917 + 0.250584i
\(982\) −11.8765 48.9555i −0.378994 1.56223i
\(983\) 13.7180 + 5.49185i 0.437536 + 0.175163i 0.579964 0.814642i \(-0.303067\pi\)
−0.142428 + 0.989805i \(0.545491\pi\)
\(984\) 3.19336 + 4.48444i 0.101801 + 0.142959i
\(985\) −75.2647 + 30.1314i −2.39813 + 0.960067i
\(986\) −23.4191 15.0506i −0.745817 0.479307i
\(987\) −0.325148 + 24.2737i −0.0103496 + 0.772641i
\(988\) 17.1406 0.545314
\(989\) 1.57879 + 16.7946i 0.0502027 + 0.534039i
\(990\) −7.78530 + 13.4845i −0.247433 + 0.428567i
\(991\) 6.70350 1.29199i 0.212944 0.0410415i −0.0816635 0.996660i \(-0.526023\pi\)
0.294607 + 0.955618i \(0.404811\pi\)
\(992\) 0.172828 3.62810i 0.00548728 0.115192i
\(993\) −0.553313 + 3.84838i −0.0175589 + 0.122125i
\(994\) 5.48868 + 4.02034i 0.174090 + 0.127517i
\(995\) −3.57955 24.8963i −0.113479 0.789266i
\(996\) −0.881138 3.63210i −0.0279199 0.115088i
\(997\) 2.19472 + 46.0728i 0.0695075 + 1.45914i 0.717002 + 0.697071i \(0.245514\pi\)
−0.647494 + 0.762070i \(0.724183\pi\)
\(998\) 62.4176 + 5.96016i 1.97580 + 0.188666i
\(999\) 5.40277 + 5.15153i 0.170936 + 0.162987i
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 483.2.y.b.151.4 yes 320
7.2 even 3 inner 483.2.y.b.289.13 yes 320
23.16 even 11 inner 483.2.y.b.361.13 yes 320
161.16 even 33 inner 483.2.y.b.16.4 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.y.b.16.4 320 161.16 even 33 inner
483.2.y.b.151.4 yes 320 1.1 even 1 trivial
483.2.y.b.289.13 yes 320 7.2 even 3 inner
483.2.y.b.361.13 yes 320 23.16 even 11 inner