Properties

Label 429.2.bg.b.334.6
Level $429$
Weight $2$
Character 429.334
Analytic conductor $3.426$
Analytic rank $0$
Dimension $112$
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] = [429,2,Mod(16,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 12, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bg (of order \(15\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 334.6
Character \(\chi\) \(=\) 429.334
Dual form 429.2.bg.b.289.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.769531 + 0.342617i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.863470 + 0.958981i) q^{4} +(-0.666110 + 0.483957i) q^{5} +(-0.769531 - 0.342617i) q^{6} +(3.51709 - 3.90612i) q^{7} +(0.856508 - 2.63606i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\) \(q+(-0.769531 + 0.342617i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.863470 + 0.958981i) q^{4} +(-0.666110 + 0.483957i) q^{5} +(-0.769531 - 0.342617i) q^{6} +(3.51709 - 3.90612i) q^{7} +(0.856508 - 2.63606i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.346780 - 0.600641i) q^{10} +(3.11370 + 1.14232i) q^{11} -1.29044 q^{12} +(-0.177160 - 3.60120i) q^{13} +(-1.36820 + 4.21089i) q^{14} +(-0.805365 - 0.171186i) q^{15} +(-0.0257243 - 0.244750i) q^{16} +(5.47333 + 2.43688i) q^{17} +(-0.260302 - 0.801128i) q^{18} +(-0.00808041 + 0.00171754i) q^{19} +(0.111060 - 1.05667i) q^{20} +5.25620 q^{21} +(-2.78746 + 0.187756i) q^{22} +(-2.79306 + 4.83773i) q^{23} +(2.53209 - 1.12736i) q^{24} +(-1.33560 + 4.11054i) q^{25} +(1.37016 + 2.71053i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.708995 + 6.74564i) q^{28} +(-0.127017 - 0.0269983i) q^{29} +(0.678404 - 0.144199i) q^{30} +(-3.58192 - 2.60242i) q^{31} +(2.87537 + 4.98029i) q^{32} +(1.23456 + 3.07829i) q^{33} -5.04681 q^{34} +(-0.452371 + 4.30403i) q^{35} +(-0.863470 - 0.958981i) q^{36} +(11.0759 + 2.35425i) q^{37} +(0.00562966 - 0.00409019i) q^{38} +(2.55767 - 2.54133i) q^{39} +(0.705212 + 2.17042i) q^{40} +(-5.18688 - 5.76061i) q^{41} +(-4.04481 + 1.80087i) q^{42} +(-1.44781 - 2.50767i) q^{43} +(-3.78405 + 1.99962i) q^{44} +(-0.411679 - 0.713048i) q^{45} +(0.491859 - 4.67973i) q^{46} +(-0.510447 + 1.57099i) q^{47} +(0.164672 - 0.182887i) q^{48} +(-2.15618 - 20.5147i) q^{49} +(-0.380560 - 3.62079i) q^{50} +(1.85142 + 5.69807i) q^{51} +(3.60645 + 2.93963i) q^{52} +(4.40780 + 3.20246i) q^{53} +(0.421178 - 0.729502i) q^{54} +(-2.62690 + 0.745986i) q^{55} +(-7.28436 - 12.6169i) q^{56} +(-0.00668323 - 0.00485565i) q^{57} +(0.106994 - 0.0227422i) q^{58} +(2.18957 - 2.43176i) q^{59} +(0.859573 - 0.624516i) q^{60} +(4.46497 + 1.98793i) q^{61} +(3.64803 + 0.775412i) q^{62} +(3.51709 + 3.90612i) q^{63} +(-3.52082 - 2.55803i) q^{64} +(1.86083 + 2.31306i) q^{65} +(-2.00471 - 1.94586i) q^{66} +(0.836562 - 1.44897i) q^{67} +(-7.06298 + 3.14464i) q^{68} +(-5.46405 + 1.16142i) q^{69} +(-1.12652 - 3.46707i) q^{70} +(9.63838 + 4.29128i) q^{71} +(2.53209 + 1.12736i) q^{72} +(-2.34562 - 7.21907i) q^{73} +(-9.32982 + 1.98312i) q^{74} +(-3.94842 + 1.75795i) q^{75} +(0.00533010 - 0.00923201i) q^{76} +(15.4132 - 8.14484i) q^{77} +(-1.09750 + 2.83193i) q^{78} +(1.46533 + 1.06463i) q^{79} +(0.135584 + 0.150581i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(5.96514 + 2.65585i) q^{82} +(-8.36299 + 6.07606i) q^{83} +(-4.53858 + 5.04060i) q^{84} +(-4.82519 + 1.02563i) q^{85} +(1.97330 + 1.43369i) q^{86} +(-0.0649274 - 0.112458i) q^{87} +(5.67813 - 7.22949i) q^{88} +(-3.03103 + 5.24989i) q^{89} +(0.561102 + 0.407664i) q^{90} +(-14.6898 - 11.9737i) q^{91} +(-2.22756 - 6.85573i) q^{92} +(-0.462799 - 4.40324i) q^{93} +(-0.145445 - 1.38382i) q^{94} +(0.00455122 - 0.00505465i) q^{95} +(-1.77708 + 5.46928i) q^{96} +(-1.25388 + 11.9298i) q^{97} +(8.68793 + 15.0479i) q^{98} +(-1.46153 + 2.97723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q + 14 q^{3} + 8 q^{4} - 6 q^{5} - 24 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q + 14 q^{3} + 8 q^{4} - 6 q^{5} - 24 q^{8} + 14 q^{9} - 24 q^{10} + q^{11} + 104 q^{12} - 15 q^{13} - 30 q^{14} - 2 q^{15} + 24 q^{16} + 4 q^{17} - 28 q^{20} + 7 q^{22} + 8 q^{23} - 18 q^{24} - 42 q^{25} + 7 q^{26} - 28 q^{27} - 6 q^{28} - 2 q^{29} + 6 q^{30} + 12 q^{31} - 6 q^{32} + 6 q^{33} + 64 q^{34} - 8 q^{35} + 8 q^{36} + 4 q^{37} - 6 q^{38} + 12 q^{39} - 36 q^{40} - 26 q^{41} - 20 q^{42} - 76 q^{43} + 12 q^{44} - 2 q^{45} + 18 q^{46} + 50 q^{47} - 6 q^{48} + 32 q^{49} + 17 q^{50} - 18 q^{51} - 39 q^{52} - 54 q^{53} - 36 q^{55} + 12 q^{56} + 48 q^{58} + 20 q^{59} + 56 q^{60} + 34 q^{61} + 33 q^{62} - 68 q^{64} - 44 q^{65} - 4 q^{66} - 36 q^{67} + 4 q^{68} + 3 q^{69} - 92 q^{70} + 22 q^{71} - 18 q^{72} - 34 q^{73} - 4 q^{74} - 4 q^{75} + 4 q^{76} + 32 q^{77} - 18 q^{78} - 20 q^{79} + 30 q^{80} + 14 q^{81} - 41 q^{82} + 56 q^{83} + 9 q^{84} + 6 q^{85} - 86 q^{86} - 52 q^{87} - 70 q^{88} - 96 q^{89} - 12 q^{90} - 7 q^{91} - 126 q^{92} - 6 q^{93} - 10 q^{94} + 52 q^{95} - 88 q^{96} - 5 q^{97} + 104 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.769531 + 0.342617i −0.544140 + 0.242267i −0.660350 0.750958i \(-0.729592\pi\)
0.116210 + 0.993225i \(0.462925\pi\)
\(3\) 0.669131 + 0.743145i 0.386323 + 0.429055i
\(4\) −0.863470 + 0.958981i −0.431735 + 0.479491i
\(5\) −0.666110 + 0.483957i −0.297894 + 0.216432i −0.726684 0.686971i \(-0.758940\pi\)
0.428791 + 0.903404i \(0.358940\pi\)
\(6\) −0.769531 0.342617i −0.314160 0.139873i
\(7\) 3.51709 3.90612i 1.32933 1.47637i 0.578973 0.815347i \(-0.303454\pi\)
0.750361 0.661028i \(-0.229880\pi\)
\(8\) 0.856508 2.63606i 0.302821 0.931988i
\(9\) −0.104528 + 0.994522i −0.0348428 + 0.331507i
\(10\) 0.346780 0.600641i 0.109661 0.189939i
\(11\) 3.11370 + 1.14232i 0.938815 + 0.344422i
\(12\) −1.29044 −0.372517
\(13\) −0.177160 3.60120i −0.0491353 0.998792i
\(14\) −1.36820 + 4.21089i −0.365667 + 1.12541i
\(15\) −0.805365 0.171186i −0.207944 0.0441999i
\(16\) −0.0257243 0.244750i −0.00643106 0.0611875i
\(17\) 5.47333 + 2.43688i 1.32748 + 0.591031i 0.943212 0.332191i \(-0.107788\pi\)
0.384266 + 0.923223i \(0.374455\pi\)
\(18\) −0.260302 0.801128i −0.0613539 0.188828i
\(19\) −0.00808041 + 0.00171754i −0.00185377 + 0.000394032i −0.208838 0.977950i \(-0.566968\pi\)
0.206985 + 0.978344i \(0.433635\pi\)
\(20\) 0.111060 1.05667i 0.0248339 0.236279i
\(21\) 5.25620 1.14700
\(22\) −2.78746 + 0.187756i −0.594289 + 0.0400296i
\(23\) −2.79306 + 4.83773i −0.582394 + 1.00874i 0.412801 + 0.910821i \(0.364550\pi\)
−0.995195 + 0.0979144i \(0.968783\pi\)
\(24\) 2.53209 1.12736i 0.516861 0.230121i
\(25\) −1.33560 + 4.11054i −0.267119 + 0.822109i
\(26\) 1.37016 + 2.71053i 0.268711 + 0.531579i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 0.708995 + 6.74564i 0.133988 + 1.27481i
\(29\) −0.127017 0.0269983i −0.0235865 0.00501347i 0.196103 0.980583i \(-0.437171\pi\)
−0.219690 + 0.975570i \(0.570505\pi\)
\(30\) 0.678404 0.144199i 0.123859 0.0263271i
\(31\) −3.58192 2.60242i −0.643331 0.467408i 0.217662 0.976024i \(-0.430157\pi\)
−0.860993 + 0.508617i \(0.830157\pi\)
\(32\) 2.87537 + 4.98029i 0.508298 + 0.880399i
\(33\) 1.23456 + 3.07829i 0.214909 + 0.535861i
\(34\) −5.04681 −0.865521
\(35\) −0.452371 + 4.30403i −0.0764647 + 0.727513i
\(36\) −0.863470 0.958981i −0.143912 0.159830i
\(37\) 11.0759 + 2.35425i 1.82086 + 0.387036i 0.986444 0.164097i \(-0.0524711\pi\)
0.834417 + 0.551133i \(0.185804\pi\)
\(38\) 0.00562966 0.00409019i 0.000913252 0.000663516i
\(39\) 2.55767 2.54133i 0.409555 0.406938i
\(40\) 0.705212 + 2.17042i 0.111504 + 0.343174i
\(41\) −5.18688 5.76061i −0.810054 0.899656i 0.186512 0.982453i \(-0.440282\pi\)
−0.996566 + 0.0827964i \(0.973615\pi\)
\(42\) −4.04481 + 1.80087i −0.624128 + 0.277880i
\(43\) −1.44781 2.50767i −0.220788 0.382416i 0.734259 0.678869i \(-0.237530\pi\)
−0.955048 + 0.296453i \(0.904196\pi\)
\(44\) −3.78405 + 1.99962i −0.570467 + 0.301454i
\(45\) −0.411679 0.713048i −0.0613694 0.106295i
\(46\) 0.491859 4.67973i 0.0725207 0.689988i
\(47\) −0.510447 + 1.57099i −0.0744564 + 0.229153i −0.981358 0.192190i \(-0.938441\pi\)
0.906901 + 0.421343i \(0.138441\pi\)
\(48\) 0.164672 0.182887i 0.0237683 0.0263974i
\(49\) −2.15618 20.5147i −0.308026 2.93067i
\(50\) −0.380560 3.62079i −0.0538193 0.512057i
\(51\) 1.85142 + 5.69807i 0.259250 + 0.797890i
\(52\) 3.60645 + 2.93963i 0.500125 + 0.407654i
\(53\) 4.40780 + 3.20246i 0.605458 + 0.439891i 0.847812 0.530297i \(-0.177919\pi\)
−0.242354 + 0.970188i \(0.577919\pi\)
\(54\) 0.421178 0.729502i 0.0573151 0.0992726i
\(55\) −2.62690 + 0.745986i −0.354211 + 0.100589i
\(56\) −7.28436 12.6169i −0.973414 1.68600i
\(57\) −0.00668323 0.00485565i −0.000885216 0.000643147i
\(58\) 0.106994 0.0227422i 0.0140490 0.00298620i
\(59\) 2.18957 2.43176i 0.285058 0.316589i −0.583561 0.812069i \(-0.698341\pi\)
0.868619 + 0.495480i \(0.165008\pi\)
\(60\) 0.859573 0.624516i 0.110970 0.0806247i
\(61\) 4.46497 + 1.98793i 0.571681 + 0.254529i 0.672155 0.740411i \(-0.265369\pi\)
−0.100473 + 0.994940i \(0.532036\pi\)
\(62\) 3.64803 + 0.775412i 0.463300 + 0.0984774i
\(63\) 3.51709 + 3.90612i 0.443111 + 0.492125i
\(64\) −3.52082 2.55803i −0.440103 0.319753i
\(65\) 1.86083 + 2.31306i 0.230808 + 0.286899i
\(66\) −2.00471 1.94586i −0.246762 0.239518i
\(67\) 0.836562 1.44897i 0.102202 0.177020i −0.810389 0.585892i \(-0.800744\pi\)
0.912592 + 0.408872i \(0.134078\pi\)
\(68\) −7.06298 + 3.14464i −0.856513 + 0.381344i
\(69\) −5.46405 + 1.16142i −0.657795 + 0.139819i
\(70\) −1.12652 3.46707i −0.134645 0.414394i
\(71\) 9.63838 + 4.29128i 1.14387 + 0.509282i 0.889096 0.457720i \(-0.151334\pi\)
0.254769 + 0.967002i \(0.418000\pi\)
\(72\) 2.53209 + 1.12736i 0.298410 + 0.132861i
\(73\) −2.34562 7.21907i −0.274534 0.844928i −0.989342 0.145608i \(-0.953486\pi\)
0.714808 0.699320i \(-0.246514\pi\)
\(74\) −9.32982 + 1.98312i −1.08457 + 0.230532i
\(75\) −3.94842 + 1.75795i −0.455924 + 0.202991i
\(76\) 0.00533010 0.00923201i 0.000611405 0.00105898i
\(77\) 15.4132 8.14484i 1.75650 0.928190i
\(78\) −1.09750 + 2.83193i −0.124268 + 0.320653i
\(79\) 1.46533 + 1.06463i 0.164863 + 0.119780i 0.667158 0.744917i \(-0.267511\pi\)
−0.502295 + 0.864696i \(0.667511\pi\)
\(80\) 0.135584 + 0.150581i 0.0151587 + 0.0168355i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) 5.96514 + 2.65585i 0.658740 + 0.293290i
\(83\) −8.36299 + 6.07606i −0.917957 + 0.666935i −0.943015 0.332751i \(-0.892023\pi\)
0.0250577 + 0.999686i \(0.492023\pi\)
\(84\) −4.53858 + 5.04060i −0.495199 + 0.549975i
\(85\) −4.82519 + 1.02563i −0.523365 + 0.111245i
\(86\) 1.97330 + 1.43369i 0.212787 + 0.154599i
\(87\) −0.0649274 0.112458i −0.00696095 0.0120567i
\(88\) 5.67813 7.22949i 0.605291 0.770666i
\(89\) −3.03103 + 5.24989i −0.321288 + 0.556488i −0.980754 0.195247i \(-0.937449\pi\)
0.659466 + 0.751735i \(0.270783\pi\)
\(90\) 0.561102 + 0.407664i 0.0591453 + 0.0429716i
\(91\) −14.6898 11.9737i −1.53991 1.25519i
\(92\) −2.22756 6.85573i −0.232239 0.714759i
\(93\) −0.462799 4.40324i −0.0479900 0.456595i
\(94\) −0.145445 1.38382i −0.0150015 0.142730i
\(95\) 0.00455122 0.00505465i 0.000466946 0.000518596i
\(96\) −1.77708 + 5.46928i −0.181372 + 0.558206i
\(97\) −1.25388 + 11.9298i −0.127312 + 1.21129i 0.725184 + 0.688556i \(0.241755\pi\)
−0.852495 + 0.522735i \(0.824912\pi\)
\(98\) 8.68793 + 15.0479i 0.877613 + 1.52007i
\(99\) −1.46153 + 2.97723i −0.146889 + 0.299223i
\(100\) −2.78869 4.83015i −0.278869 0.483015i
\(101\) −4.22315 + 1.88027i −0.420219 + 0.187094i −0.605943 0.795508i \(-0.707204\pi\)
0.185723 + 0.982602i \(0.440537\pi\)
\(102\) −3.37698 3.75051i −0.334371 0.371356i
\(103\) −2.66360 8.19772i −0.262452 0.807745i −0.992269 0.124103i \(-0.960395\pi\)
0.729817 0.683643i \(-0.239605\pi\)
\(104\) −9.64471 2.61745i −0.945742 0.256662i
\(105\) −3.50121 + 2.54378i −0.341683 + 0.248247i
\(106\) −4.48915 0.954199i −0.436025 0.0926800i
\(107\) −9.36663 10.4027i −0.905506 1.00567i −0.999949 0.0101364i \(-0.996773\pi\)
0.0944422 0.995530i \(-0.469893\pi\)
\(108\) 0.134887 1.28337i 0.0129795 0.123492i
\(109\) −1.98684 −0.190305 −0.0951526 0.995463i \(-0.530334\pi\)
−0.0951526 + 0.995463i \(0.530334\pi\)
\(110\) 1.76589 1.47408i 0.168371 0.140548i
\(111\) 5.66165 + 9.80627i 0.537380 + 0.930770i
\(112\) −1.04650 0.760325i −0.0988847 0.0718440i
\(113\) −5.26846 + 1.11985i −0.495615 + 0.105346i −0.448937 0.893564i \(-0.648197\pi\)
−0.0466788 + 0.998910i \(0.514864\pi\)
\(114\) 0.00680658 + 0.00144678i 0.000637495 + 0.000135504i
\(115\) −0.480766 4.57418i −0.0448317 0.426545i
\(116\) 0.135566 0.0984948i 0.0125870 0.00914502i
\(117\) 3.59999 + 0.200238i 0.332819 + 0.0185120i
\(118\) −0.851777 + 2.62150i −0.0784124 + 0.241329i
\(119\) 28.7689 12.8088i 2.63725 1.17418i
\(120\) −1.14106 + 1.97637i −0.104164 + 0.180417i
\(121\) 8.39021 + 7.11367i 0.762746 + 0.646698i
\(122\) −4.11703 −0.372739
\(123\) 0.810270 7.70920i 0.0730596 0.695115i
\(124\) 5.58855 1.18788i 0.501866 0.106675i
\(125\) −2.37183 7.29975i −0.212143 0.652909i
\(126\) −4.04481 1.80087i −0.360340 0.160434i
\(127\) −0.377689 3.59348i −0.0335145 0.318869i −0.998416 0.0562582i \(-0.982083\pi\)
0.964902 0.262611i \(-0.0845837\pi\)
\(128\) −7.66434 1.62911i −0.677439 0.143994i
\(129\) 0.894793 2.75389i 0.0787821 0.242466i
\(130\) −2.22446 1.14241i −0.195098 0.100196i
\(131\) −19.3330 −1.68913 −0.844565 0.535453i \(-0.820141\pi\)
−0.844565 + 0.535453i \(0.820141\pi\)
\(132\) −4.01803 1.47409i −0.349724 0.128303i
\(133\) −0.0217106 + 0.0376038i −0.00188255 + 0.00326066i
\(134\) −0.147319 + 1.40164i −0.0127264 + 0.121084i
\(135\) 0.254431 0.783059i 0.0218980 0.0673950i
\(136\) 11.1117 12.3408i 0.952823 1.05822i
\(137\) −16.7123 7.44079i −1.42783 0.635709i −0.460136 0.887849i \(-0.652199\pi\)
−0.967691 + 0.252139i \(0.918866\pi\)
\(138\) 3.80683 2.76583i 0.324059 0.235443i
\(139\) 6.98449 7.75706i 0.592416 0.657945i −0.370156 0.928970i \(-0.620696\pi\)
0.962572 + 0.271025i \(0.0873625\pi\)
\(140\) −3.73687 4.15022i −0.315823 0.350757i
\(141\) −1.50903 + 0.671865i −0.127083 + 0.0565812i
\(142\) −8.88730 −0.745805
\(143\) 3.56210 11.4154i 0.297877 0.954604i
\(144\) 0.246098 0.0205082
\(145\) 0.0976735 0.0434870i 0.00811134 0.00361140i
\(146\) 4.27840 + 4.75165i 0.354083 + 0.393249i
\(147\) 13.8026 15.3294i 1.13842 1.26434i
\(148\) −11.8214 + 8.58872i −0.971710 + 0.705989i
\(149\) 1.24736 + 0.555362i 0.102188 + 0.0454970i 0.457194 0.889367i \(-0.348855\pi\)
−0.355006 + 0.934864i \(0.615521\pi\)
\(150\) 2.43613 2.70559i 0.198909 0.220911i
\(151\) −5.03245 + 15.4883i −0.409535 + 1.26042i 0.507514 + 0.861643i \(0.330565\pi\)
−0.917049 + 0.398775i \(0.869435\pi\)
\(152\) −0.00239339 + 0.0227715i −0.000194129 + 0.00184702i
\(153\) −2.99565 + 5.18862i −0.242184 + 0.419475i
\(154\) −9.07035 + 11.5485i −0.730910 + 0.930606i
\(155\) 3.64541 0.292806
\(156\) 0.228614 + 4.64711i 0.0183037 + 0.372067i
\(157\) −1.55754 + 4.79360i −0.124305 + 0.382571i −0.993774 0.111416i \(-0.964461\pi\)
0.869469 + 0.493988i \(0.164461\pi\)
\(158\) −1.49238 0.317214i −0.118727 0.0252362i
\(159\) 0.569507 + 5.41850i 0.0451648 + 0.429715i
\(160\) −4.32556 1.92586i −0.341966 0.152253i
\(161\) 9.07330 + 27.9247i 0.715076 + 2.20078i
\(162\) 0.823949 0.175136i 0.0647355 0.0137600i
\(163\) −0.620864 + 5.90713i −0.0486298 + 0.462682i 0.942926 + 0.333002i \(0.108062\pi\)
−0.991556 + 0.129680i \(0.958605\pi\)
\(164\) 10.0030 0.781105
\(165\) −2.31211 1.45300i −0.179998 0.113116i
\(166\) 4.35381 7.54102i 0.337921 0.585297i
\(167\) 1.46275 0.651256i 0.113191 0.0503957i −0.349360 0.936989i \(-0.613601\pi\)
0.462551 + 0.886593i \(0.346934\pi\)
\(168\) 4.50198 13.8557i 0.347335 1.06899i
\(169\) −12.9372 + 1.27598i −0.995171 + 0.0981519i
\(170\) 3.36173 2.44244i 0.257833 0.187327i
\(171\) −0.000863502 0.00821568i −6.60337e−5 0.000628268i
\(172\) 3.65495 + 0.776883i 0.278687 + 0.0592368i
\(173\) 1.56886 0.333471i 0.119278 0.0253533i −0.147886 0.989004i \(-0.547247\pi\)
0.267164 + 0.963651i \(0.413914\pi\)
\(174\) 0.0884935 + 0.0642943i 0.00670868 + 0.00487414i
\(175\) 11.3589 + 19.6741i 0.858650 + 1.48723i
\(176\) 0.199485 0.791462i 0.0150368 0.0596587i
\(177\) 3.27226 0.245958
\(178\) 0.533765 5.07844i 0.0400074 0.380645i
\(179\) −4.21697 4.68342i −0.315191 0.350055i 0.564644 0.825335i \(-0.309014\pi\)
−0.879835 + 0.475279i \(0.842347\pi\)
\(180\) 1.03927 + 0.220904i 0.0774628 + 0.0164652i
\(181\) −14.7211 + 10.6955i −1.09421 + 0.794991i −0.980105 0.198478i \(-0.936400\pi\)
−0.114105 + 0.993469i \(0.536400\pi\)
\(182\) 15.4066 + 4.18116i 1.14202 + 0.309928i
\(183\) 1.51033 + 4.64831i 0.111647 + 0.343613i
\(184\) 10.3603 + 11.5062i 0.763769 + 0.848251i
\(185\) −8.51710 + 3.79206i −0.626190 + 0.278798i
\(186\) 1.86476 + 3.22986i 0.136731 + 0.236825i
\(187\) 14.2586 + 13.8400i 1.04269 + 1.01208i
\(188\) −1.06580 1.84602i −0.0777313 0.134635i
\(189\) −0.549423 + 5.22741i −0.0399646 + 0.380238i
\(190\) −0.00177050 + 0.00544903i −0.000128445 + 0.000395314i
\(191\) 13.5289 15.0253i 0.978915 1.08719i −0.0172634 0.999851i \(-0.505495\pi\)
0.996178 0.0873440i \(-0.0278379\pi\)
\(192\) −0.454905 4.32813i −0.0328300 0.312356i
\(193\) 2.61706 + 24.8996i 0.188380 + 1.79231i 0.525439 + 0.850831i \(0.323901\pi\)
−0.337059 + 0.941484i \(0.609432\pi\)
\(194\) −3.12247 9.60997i −0.224180 0.689955i
\(195\) −0.473795 + 2.93061i −0.0339291 + 0.209865i
\(196\) 21.5350 + 15.6461i 1.53821 + 1.11758i
\(197\) 1.41595 2.45249i 0.100882 0.174733i −0.811166 0.584816i \(-0.801167\pi\)
0.912048 + 0.410083i \(0.134500\pi\)
\(198\) 0.104642 2.79182i 0.00743659 0.198406i
\(199\) 1.15386 + 1.99855i 0.0817953 + 0.141674i 0.904021 0.427488i \(-0.140601\pi\)
−0.822226 + 0.569161i \(0.807268\pi\)
\(200\) 9.69170 + 7.04143i 0.685307 + 0.497904i
\(201\) 1.63656 0.347862i 0.115434 0.0245363i
\(202\) 2.60563 2.89385i 0.183332 0.203610i
\(203\) −0.552189 + 0.401189i −0.0387561 + 0.0281580i
\(204\) −7.06298 3.14464i −0.494508 0.220169i
\(205\) 6.24292 + 1.32697i 0.436025 + 0.0926799i
\(206\) 4.85840 + 5.39580i 0.338501 + 0.375943i
\(207\) −4.51927 3.28344i −0.314111 0.228215i
\(208\) −0.876835 + 0.135998i −0.0607976 + 0.00942976i
\(209\) −0.0271219 0.00388250i −0.00187606 0.000268558i
\(210\) 1.82275 3.15709i 0.125781 0.217860i
\(211\) 9.89679 4.40634i 0.681323 0.303345i −0.0367376 0.999325i \(-0.511697\pi\)
0.718061 + 0.695980i \(0.245030\pi\)
\(212\) −6.87710 + 1.46177i −0.472321 + 0.100395i
\(213\) 3.26029 + 10.0341i 0.223391 + 0.687528i
\(214\) 10.7721 + 4.79603i 0.736362 + 0.327850i
\(215\) 2.17800 + 0.969710i 0.148539 + 0.0661337i
\(216\) 0.856508 + 2.63606i 0.0582780 + 0.179361i
\(217\) −22.7633 + 4.83848i −1.54527 + 0.328458i
\(218\) 1.52894 0.680727i 0.103553 0.0461046i
\(219\) 3.79529 6.57364i 0.256462 0.444205i
\(220\) 1.55286 3.16328i 0.104694 0.213268i
\(221\) 7.80604 20.1423i 0.525091 1.35491i
\(222\) −7.71661 5.60645i −0.517905 0.376280i
\(223\) −5.61135 6.23204i −0.375764 0.417328i 0.525367 0.850876i \(-0.323928\pi\)
−0.901131 + 0.433548i \(0.857261\pi\)
\(224\) 29.5665 + 6.28456i 1.97550 + 0.419905i
\(225\) −3.94842 1.75795i −0.263228 0.117197i
\(226\) 3.67057 2.66682i 0.244162 0.177394i
\(227\) 18.8133 20.8942i 1.24868 1.38680i 0.357018 0.934097i \(-0.383793\pi\)
0.891662 0.452702i \(-0.149540\pi\)
\(228\) 0.0104273 0.00221638i 0.000690562 0.000146783i
\(229\) −18.6913 13.5800i −1.23515 0.897392i −0.237888 0.971293i \(-0.576455\pi\)
−0.997266 + 0.0739009i \(0.976455\pi\)
\(230\) 1.93716 + 3.35525i 0.127732 + 0.221239i
\(231\) 16.3662 + 6.00427i 1.07682 + 0.395052i
\(232\) −0.179961 + 0.311701i −0.0118150 + 0.0204642i
\(233\) −9.15620 6.65237i −0.599842 0.435811i 0.245981 0.969275i \(-0.420890\pi\)
−0.845823 + 0.533464i \(0.820890\pi\)
\(234\) −2.83890 + 1.07933i −0.185585 + 0.0705579i
\(235\) −0.420281 1.29349i −0.0274161 0.0843780i
\(236\) 0.441386 + 4.19951i 0.0287318 + 0.273365i
\(237\) 0.189327 + 1.80133i 0.0122981 + 0.117009i
\(238\) −17.7501 + 19.7135i −1.15057 + 1.27783i
\(239\) −0.122277 + 0.376329i −0.00790943 + 0.0243427i −0.954933 0.296820i \(-0.904074\pi\)
0.947024 + 0.321163i \(0.104074\pi\)
\(240\) −0.0211803 + 0.201517i −0.00136718 + 0.0130078i
\(241\) −1.70364 2.95079i −0.109741 0.190077i 0.805924 0.592019i \(-0.201669\pi\)
−0.915665 + 0.401942i \(0.868335\pi\)
\(242\) −8.89379 2.59956i −0.571714 0.167106i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −5.76176 + 2.56530i −0.368859 + 0.164227i
\(245\) 11.3645 + 12.6215i 0.726050 + 0.806361i
\(246\) 2.01778 + 6.21008i 0.128649 + 0.395940i
\(247\) 0.00761674 + 0.0287949i 0.000484641 + 0.00183217i
\(248\) −9.92807 + 7.21317i −0.630433 + 0.458036i
\(249\) −10.1113 2.14923i −0.640779 0.136202i
\(250\) 4.32621 + 4.80475i 0.273614 + 0.303879i
\(251\) −0.137873 + 1.31177i −0.00870246 + 0.0827984i −0.998011 0.0630387i \(-0.979921\pi\)
0.989309 + 0.145837i \(0.0465875\pi\)
\(252\) −6.78280 −0.427276
\(253\) −14.2230 + 11.8726i −0.894191 + 0.746427i
\(254\) 1.52183 + 2.63589i 0.0954881 + 0.165390i
\(255\) −3.99087 2.89954i −0.249918 0.181576i
\(256\) 14.9699 3.18194i 0.935616 0.198871i
\(257\) −6.93739 1.47459i −0.432743 0.0919823i −0.0136102 0.999907i \(-0.504332\pi\)
−0.419133 + 0.907925i \(0.637666\pi\)
\(258\) 0.254959 + 2.42577i 0.0158731 + 0.151022i
\(259\) 48.1508 34.9836i 2.99194 2.17377i
\(260\) −3.82495 0.212751i −0.237213 0.0131943i
\(261\) 0.0401274 0.123499i 0.00248382 0.00764442i
\(262\) 14.8773 6.62381i 0.919124 0.409220i
\(263\) −11.4151 + 19.7715i −0.703883 + 1.21916i 0.263211 + 0.964738i \(0.415219\pi\)
−0.967093 + 0.254422i \(0.918115\pi\)
\(264\) 9.17197 0.617798i 0.564496 0.0380228i
\(265\) −4.48593 −0.275569
\(266\) 0.00382324 0.0363757i 0.000234418 0.00223034i
\(267\) −5.92958 + 1.26037i −0.362885 + 0.0771335i
\(268\) 0.667186 + 2.05339i 0.0407549 + 0.125431i
\(269\) 10.7287 + 4.77671i 0.654139 + 0.291241i 0.706845 0.707369i \(-0.250118\pi\)
−0.0527059 + 0.998610i \(0.516785\pi\)
\(270\) 0.0724968 + 0.689761i 0.00441201 + 0.0419775i
\(271\) 0.309791 + 0.0658480i 0.0188184 + 0.00399998i 0.217311 0.976102i \(-0.430271\pi\)
−0.198493 + 0.980102i \(0.563605\pi\)
\(272\) 0.455630 1.40228i 0.0276266 0.0850260i
\(273\) −0.931189 18.9286i −0.0563581 1.14561i
\(274\) 15.4100 0.930949
\(275\) −8.85420 + 11.2733i −0.533928 + 0.679806i
\(276\) 3.60427 6.24278i 0.216952 0.375771i
\(277\) −0.340889 + 3.24334i −0.0204820 + 0.194874i −0.999978 0.00658881i \(-0.997903\pi\)
0.979496 + 0.201462i \(0.0645694\pi\)
\(278\) −2.71708 + 8.36230i −0.162959 + 0.501537i
\(279\) 2.96257 3.29027i 0.177365 0.196983i
\(280\) 10.9582 + 4.87891i 0.654879 + 0.291571i
\(281\) −12.1535 + 8.83007i −0.725020 + 0.526758i −0.887984 0.459874i \(-0.847894\pi\)
0.162964 + 0.986632i \(0.447894\pi\)
\(282\) 0.931054 1.03404i 0.0554435 0.0615762i
\(283\) −10.3905 11.5398i −0.617649 0.685969i 0.350437 0.936586i \(-0.386033\pi\)
−0.968086 + 0.250617i \(0.919366\pi\)
\(284\) −12.4377 + 5.53763i −0.738043 + 0.328598i
\(285\) 0.00680170 0.000402898
\(286\) 1.16997 + 10.0049i 0.0691819 + 0.591604i
\(287\) −40.7443 −2.40506
\(288\) −5.25356 + 2.33904i −0.309569 + 0.137829i
\(289\) 12.6437 + 14.0423i 0.743749 + 0.826017i
\(290\) −0.0602633 + 0.0669292i −0.00353879 + 0.00393022i
\(291\) −9.70460 + 7.05080i −0.568894 + 0.413325i
\(292\) 8.94833 + 3.98405i 0.523661 + 0.233149i
\(293\) 6.91426 7.67906i 0.403935 0.448615i −0.506517 0.862230i \(-0.669067\pi\)
0.910452 + 0.413615i \(0.135734\pi\)
\(294\) −5.36943 + 16.5254i −0.313152 + 0.963782i
\(295\) −0.281625 + 2.67948i −0.0163968 + 0.156005i
\(296\) 15.6925 27.1802i 0.912109 1.57982i
\(297\) −3.19047 + 0.906029i −0.185130 + 0.0525731i
\(298\) −1.15016 −0.0666270
\(299\) 17.9164 + 9.20132i 1.03613 + 0.532126i
\(300\) 1.72350 5.30440i 0.0995065 0.306249i
\(301\) −14.8873 3.16440i −0.858091 0.182393i
\(302\) −1.43393 13.6429i −0.0825133 0.785061i
\(303\) −4.22315 1.88027i −0.242614 0.108019i
\(304\) 0.000628231 0.00193350i 3.60315e−5 0.000110894i
\(305\) −3.93624 + 0.836674i −0.225388 + 0.0479078i
\(306\) 0.527536 5.01917i 0.0301572 0.286927i
\(307\) 32.6731 1.86475 0.932375 0.361492i \(-0.117732\pi\)
0.932375 + 0.361492i \(0.117732\pi\)
\(308\) −5.49808 + 21.8138i −0.313282 + 1.24296i
\(309\) 4.30980 7.46479i 0.245176 0.424657i
\(310\) −2.80525 + 1.24898i −0.159328 + 0.0709373i
\(311\) −5.29910 + 16.3089i −0.300484 + 0.924795i 0.680840 + 0.732433i \(0.261615\pi\)
−0.981324 + 0.192363i \(0.938385\pi\)
\(312\) −4.50843 8.91883i −0.255240 0.504930i
\(313\) −1.59734 + 1.16054i −0.0902872 + 0.0655975i −0.632013 0.774958i \(-0.717771\pi\)
0.541726 + 0.840555i \(0.317771\pi\)
\(314\) −0.443799 4.22246i −0.0250450 0.238287i
\(315\) −4.23316 0.899787i −0.238512 0.0506972i
\(316\) −2.28623 + 0.485952i −0.128610 + 0.0273370i
\(317\) −8.59423 6.24408i −0.482700 0.350702i 0.319670 0.947529i \(-0.396428\pi\)
−0.802370 + 0.596827i \(0.796428\pi\)
\(318\) −2.29472 3.97458i −0.128682 0.222883i
\(319\) −0.364652 0.229159i −0.0204166 0.0128304i
\(320\) 3.58323 0.200309
\(321\) 1.46321 13.9215i 0.0816685 0.777024i
\(322\) −16.5497 18.3803i −0.922277 1.02429i
\(323\) −0.0484122 0.0102903i −0.00269373 0.000572569i
\(324\) 1.04398 0.758499i 0.0579992 0.0421389i
\(325\) 15.0395 + 4.08152i 0.834241 + 0.226402i
\(326\) −1.54611 4.75843i −0.0856310 0.263545i
\(327\) −1.32946 1.47651i −0.0735192 0.0816513i
\(328\) −19.6279 + 8.73892i −1.08377 + 0.482526i
\(329\) 4.34121 + 7.51919i 0.239339 + 0.414547i
\(330\) 2.27707 + 0.325962i 0.125348 + 0.0179436i
\(331\) −11.3991 19.7439i −0.626553 1.08522i −0.988238 0.152921i \(-0.951132\pi\)
0.361685 0.932300i \(-0.382201\pi\)
\(332\) 1.39436 13.2664i 0.0765254 0.728091i
\(333\) −3.49909 + 10.7691i −0.191749 + 0.590143i
\(334\) −0.902496 + 1.00232i −0.0493824 + 0.0548447i
\(335\) 0.143996 + 1.37003i 0.00786735 + 0.0748528i
\(336\) −0.135212 1.28646i −0.00737642 0.0701819i
\(337\) 6.06377 + 18.6624i 0.330315 + 1.01660i 0.968984 + 0.247123i \(0.0794851\pi\)
−0.638670 + 0.769481i \(0.720515\pi\)
\(338\) 9.51842 5.41442i 0.517734 0.294505i
\(339\) −4.35750 3.16591i −0.236667 0.171949i
\(340\) 3.18285 5.51286i 0.172614 0.298977i
\(341\) −8.18021 12.1948i −0.442983 0.660387i
\(342\) 0.00347932 + 0.00602636i 0.000188140 + 0.000325868i
\(343\) −57.9498 42.1030i −3.12900 2.27335i
\(344\) −7.85044 + 1.66866i −0.423267 + 0.0899682i
\(345\) 3.07758 3.41800i 0.165692 0.184019i
\(346\) −1.09303 + 0.794133i −0.0587617 + 0.0426928i
\(347\) −15.6313 6.95950i −0.839132 0.373606i −0.0582636 0.998301i \(-0.518556\pi\)
−0.780868 + 0.624696i \(0.785223\pi\)
\(348\) 0.163908 + 0.0348396i 0.00878637 + 0.00186760i
\(349\) −9.43436 10.4779i −0.505010 0.560870i 0.435696 0.900094i \(-0.356502\pi\)
−0.940706 + 0.339224i \(0.889836\pi\)
\(350\) −15.4817 11.2481i −0.827532 0.601237i
\(351\) 2.26006 + 2.80930i 0.120633 + 0.149949i
\(352\) 3.26395 + 18.7917i 0.173969 + 1.00160i
\(353\) −3.47566 + 6.02003i −0.184991 + 0.320414i −0.943573 0.331163i \(-0.892559\pi\)
0.758583 + 0.651577i \(0.225892\pi\)
\(354\) −2.51810 + 1.12113i −0.133836 + 0.0595875i
\(355\) −8.49702 + 1.80610i −0.450975 + 0.0958577i
\(356\) −2.41735 7.43982i −0.128119 0.394310i
\(357\) 28.7689 + 12.8088i 1.52261 + 0.677912i
\(358\) 4.84971 + 2.15923i 0.256315 + 0.114119i
\(359\) −4.95742 15.2574i −0.261643 0.805253i −0.992448 0.122667i \(-0.960855\pi\)
0.730805 0.682586i \(-0.239145\pi\)
\(360\) −2.23225 + 0.474478i −0.117650 + 0.0250072i
\(361\) −17.3573 + 7.72797i −0.913542 + 0.406735i
\(362\) 7.66387 13.2742i 0.402804 0.697677i
\(363\) 0.327657 + 10.9951i 0.0171976 + 0.577094i
\(364\) 24.1668 3.74829i 1.26668 0.196464i
\(365\) 5.05616 + 3.67352i 0.264652 + 0.192281i
\(366\) −2.75483 3.05955i −0.143997 0.159925i
\(367\) 28.0352 + 5.95906i 1.46342 + 0.311060i 0.869689 0.493600i \(-0.164319\pi\)
0.593735 + 0.804661i \(0.297653\pi\)
\(368\) 1.25588 + 0.559155i 0.0654674 + 0.0291480i
\(369\) 6.27123 4.55631i 0.326467 0.237192i
\(370\) 5.25495 5.83621i 0.273192 0.303410i
\(371\) 28.0118 5.95409i 1.45430 0.309121i
\(372\) 4.62224 + 3.35825i 0.239652 + 0.174117i
\(373\) −8.21984 14.2372i −0.425607 0.737173i 0.570870 0.821041i \(-0.306606\pi\)
−0.996477 + 0.0838675i \(0.973273\pi\)
\(374\) −15.7142 5.76507i −0.812564 0.298105i
\(375\) 3.83770 6.64710i 0.198178 0.343255i
\(376\) 3.70404 + 2.69114i 0.191021 + 0.138785i
\(377\) −0.0747240 + 0.462197i −0.00384848 + 0.0238044i
\(378\) −1.36820 4.21089i −0.0703727 0.216585i
\(379\) 0.116309 + 1.10660i 0.00597437 + 0.0568424i 0.997103 0.0760646i \(-0.0242355\pi\)
−0.991129 + 0.132907i \(0.957569\pi\)
\(380\) 0.000917463 0.00872908i 4.70649e−5 0.000447792i
\(381\) 2.41775 2.68518i 0.123865 0.137566i
\(382\) −5.26294 + 16.1977i −0.269276 + 0.828745i
\(383\) −1.39309 + 13.2544i −0.0711835 + 0.677266i 0.899503 + 0.436915i \(0.143929\pi\)
−0.970686 + 0.240351i \(0.922738\pi\)
\(384\) −3.91778 6.78580i −0.199929 0.346286i
\(385\) −6.32512 + 12.8847i −0.322358 + 0.656664i
\(386\) −10.5449 18.2644i −0.536724 0.929633i
\(387\) 2.64527 1.17775i 0.134467 0.0598685i
\(388\) −10.3578 11.5035i −0.525837 0.584002i
\(389\) 7.90238 + 24.3210i 0.400667 + 1.23312i 0.924460 + 0.381279i \(0.124516\pi\)
−0.523793 + 0.851845i \(0.675484\pi\)
\(390\) −0.639476 2.41752i −0.0323811 0.122416i
\(391\) −27.0763 + 19.6721i −1.36931 + 0.994861i
\(392\) −55.9248 11.8872i −2.82463 0.600393i
\(393\) −12.9363 14.3672i −0.652550 0.724730i
\(394\) −0.249349 + 2.37240i −0.0125620 + 0.119520i
\(395\) −1.49131 −0.0750357
\(396\) −1.59312 3.97234i −0.0800574 0.199617i
\(397\) −3.79840 6.57902i −0.190636 0.330191i 0.754825 0.655926i \(-0.227722\pi\)
−0.945461 + 0.325735i \(0.894388\pi\)
\(398\) −1.57267 1.14261i −0.0788309 0.0572740i
\(399\) −0.0424723 + 0.00902776i −0.00212627 + 0.000451953i
\(400\) 1.04041 + 0.221147i 0.0520206 + 0.0110573i
\(401\) −1.95791 18.6282i −0.0977732 0.930250i −0.927939 0.372733i \(-0.878421\pi\)
0.830165 0.557517i \(-0.188246\pi\)
\(402\) −1.14020 + 0.828404i −0.0568680 + 0.0413170i
\(403\) −8.73724 + 13.3602i −0.435233 + 0.665521i
\(404\) 1.84343 5.67348i 0.0917138 0.282266i
\(405\) 0.752174 0.334890i 0.0373758 0.0166408i
\(406\) 0.287472 0.497917i 0.0142670 0.0247112i
\(407\) 31.7976 + 19.9826i 1.57615 + 0.990500i
\(408\) 16.6062 0.822130
\(409\) −1.40976 + 13.4129i −0.0697079 + 0.663227i 0.902753 + 0.430160i \(0.141543\pi\)
−0.972461 + 0.233067i \(0.925124\pi\)
\(410\) −5.25876 + 1.11778i −0.259712 + 0.0552034i
\(411\) −5.65312 17.3985i −0.278848 0.858205i
\(412\) 10.1614 + 4.52415i 0.500616 + 0.222889i
\(413\) −1.79786 17.1054i −0.0884667 0.841704i
\(414\) 4.60268 + 0.978330i 0.226209 + 0.0480823i
\(415\) 2.63011 8.09466i 0.129107 0.397351i
\(416\) 17.4256 11.2371i 0.854360 0.550943i
\(417\) 10.4382 0.511158
\(418\) 0.0222014 0.00630473i 0.00108590 0.000308375i
\(419\) −14.3151 + 24.7944i −0.699337 + 1.21129i 0.269359 + 0.963040i \(0.413188\pi\)
−0.968697 + 0.248248i \(0.920145\pi\)
\(420\) 0.583757 5.55407i 0.0284844 0.271011i
\(421\) 5.58981 17.2037i 0.272431 0.838456i −0.717457 0.696603i \(-0.754694\pi\)
0.989888 0.141853i \(-0.0453061\pi\)
\(422\) −6.10620 + 6.78162i −0.297245 + 0.330124i
\(423\) −1.50903 0.671865i −0.0733717 0.0326672i
\(424\) 12.2172 8.87631i 0.593319 0.431072i
\(425\) −17.3271 + 19.2437i −0.840487 + 0.933455i
\(426\) −5.94676 6.60455i −0.288122 0.319991i
\(427\) 23.4688 10.4490i 1.13574 0.505662i
\(428\) 18.0638 0.873147
\(429\) 10.8668 4.99124i 0.524654 0.240980i
\(430\) −2.00828 −0.0968479
\(431\) 18.8532 8.39398i 0.908126 0.404324i 0.101125 0.994874i \(-0.467756\pi\)
0.807001 + 0.590550i \(0.201089\pi\)
\(432\) 0.164672 + 0.182887i 0.00792278 + 0.00879913i
\(433\) −17.8730 + 19.8499i −0.858920 + 0.953927i −0.999346 0.0361639i \(-0.988486\pi\)
0.140426 + 0.990091i \(0.455153\pi\)
\(434\) 15.8593 11.5224i 0.761270 0.553095i
\(435\) 0.0976735 + 0.0434870i 0.00468309 + 0.00208504i
\(436\) 1.71558 1.90535i 0.0821614 0.0912495i
\(437\) 0.0142601 0.0438880i 0.000682152 0.00209945i
\(438\) −0.668352 + 6.35895i −0.0319351 + 0.303842i
\(439\) −14.3255 + 24.8125i −0.683719 + 1.18424i 0.290119 + 0.956991i \(0.406305\pi\)
−0.973838 + 0.227245i \(0.927028\pi\)
\(440\) −0.283497 + 7.56361i −0.0135152 + 0.360581i
\(441\) 20.6277 0.982271
\(442\) 0.894093 + 18.1746i 0.0425277 + 0.864476i
\(443\) −0.398085 + 1.22518i −0.0189136 + 0.0582100i −0.960068 0.279767i \(-0.909743\pi\)
0.941154 + 0.337977i \(0.109743\pi\)
\(444\) −14.2927 3.03801i −0.678302 0.144177i
\(445\) −0.521726 4.96390i −0.0247322 0.235311i
\(446\) 6.45331 + 2.87320i 0.305573 + 0.136050i
\(447\) 0.421935 + 1.29858i 0.0199568 + 0.0614208i
\(448\) −22.3750 + 4.75595i −1.05712 + 0.224698i
\(449\) −2.50127 + 23.7980i −0.118042 + 1.12310i 0.761793 + 0.647820i \(0.224319\pi\)
−0.879836 + 0.475278i \(0.842348\pi\)
\(450\) 3.64073 0.171626
\(451\) −9.56990 23.8619i −0.450629 1.12361i
\(452\) 3.47525 6.01931i 0.163462 0.283125i
\(453\) −14.8774 + 6.62385i −0.699001 + 0.311215i
\(454\) −7.31866 + 22.5245i −0.343482 + 1.05713i
\(455\) 15.5798 + 0.866577i 0.730392 + 0.0406258i
\(456\) −0.0185240 + 0.0134585i −0.000867468 + 0.000630252i
\(457\) 1.51322 + 14.3973i 0.0707853 + 0.673477i 0.971171 + 0.238384i \(0.0766177\pi\)
−0.900386 + 0.435093i \(0.856716\pi\)
\(458\) 19.0362 + 4.04628i 0.889505 + 0.189070i
\(459\) −5.86038 + 1.24566i −0.273539 + 0.0581426i
\(460\) 4.80168 + 3.48863i 0.223880 + 0.162658i
\(461\) 17.8294 + 30.8814i 0.830397 + 1.43829i 0.897724 + 0.440558i \(0.145219\pi\)
−0.0673274 + 0.997731i \(0.521447\pi\)
\(462\) −14.6515 + 0.986882i −0.681648 + 0.0459139i
\(463\) 21.2668 0.988352 0.494176 0.869362i \(-0.335470\pi\)
0.494176 + 0.869362i \(0.335470\pi\)
\(464\) −0.00334042 + 0.0317820i −0.000155075 + 0.00147544i
\(465\) 2.43926 + 2.70907i 0.113118 + 0.125630i
\(466\) 9.32519 + 1.98213i 0.431981 + 0.0918204i
\(467\) −21.5508 + 15.6575i −0.997250 + 0.724545i −0.961497 0.274816i \(-0.911383\pi\)
−0.0357536 + 0.999361i \(0.511383\pi\)
\(468\) −3.30051 + 3.27942i −0.152566 + 0.151591i
\(469\) −2.71758 8.36385i −0.125486 0.386207i
\(470\) 0.766591 + 0.851385i 0.0353602 + 0.0392715i
\(471\) −4.60454 + 2.05007i −0.212166 + 0.0944624i
\(472\) −4.53489 7.85467i −0.208735 0.361540i
\(473\) −1.64346 9.46199i −0.0755665 0.435063i
\(474\) −0.762859 1.32131i −0.0350393 0.0606898i
\(475\) 0.00373213 0.0355088i 0.000171242 0.00162926i
\(476\) −12.5578 + 38.6489i −0.575585 + 1.77147i
\(477\) −3.64565 + 4.04891i −0.166923 + 0.185387i
\(478\) −0.0348411 0.331491i −0.00159360 0.0151621i
\(479\) −2.78294 26.4779i −0.127156 1.20981i −0.852987 0.521933i \(-0.825211\pi\)
0.725831 0.687873i \(-0.241455\pi\)
\(480\) −1.46317 4.50317i −0.0667842 0.205541i
\(481\) 6.51591 40.3034i 0.297100 1.83768i
\(482\) 2.32199 + 1.68703i 0.105764 + 0.0768420i
\(483\) −14.6809 + 25.4281i −0.668004 + 1.15702i
\(484\) −14.0666 + 1.90361i −0.639390 + 0.0865276i
\(485\) −4.93831 8.55340i −0.224237 0.388390i
\(486\) 0.681480 + 0.495124i 0.0309126 + 0.0224593i
\(487\) 19.7638 4.20093i 0.895584 0.190362i 0.262947 0.964810i \(-0.415306\pi\)
0.632637 + 0.774448i \(0.281972\pi\)
\(488\) 9.06460 10.0673i 0.410335 0.455723i
\(489\) −4.80529 + 3.49125i −0.217303 + 0.157880i
\(490\) −13.0697 5.81899i −0.590428 0.262875i
\(491\) −37.0835 7.88234i −1.67355 0.355725i −0.729110 0.684397i \(-0.760066\pi\)
−0.944444 + 0.328672i \(0.893399\pi\)
\(492\) 6.69333 + 7.43370i 0.301759 + 0.335137i
\(493\) −0.629415 0.457297i −0.0283474 0.0205956i
\(494\) −0.0157269 0.0195489i −0.000707588 0.000879547i
\(495\) −0.467313 2.69049i −0.0210042 0.120928i
\(496\) −0.544799 + 0.943620i −0.0244622 + 0.0423698i
\(497\) 50.6613 22.5559i 2.27247 1.01177i
\(498\) 8.51734 1.81042i 0.381671 0.0811267i
\(499\) −5.76827 17.7529i −0.258223 0.794729i −0.993177 0.116613i \(-0.962796\pi\)
0.734954 0.678117i \(-0.237204\pi\)
\(500\) 9.04832 + 4.02857i 0.404653 + 0.180163i
\(501\) 1.46275 + 0.651256i 0.0653507 + 0.0290960i
\(502\) −0.343339 1.05669i −0.0153240 0.0471623i
\(503\) −20.3336 + 4.32205i −0.906632 + 0.192711i −0.637552 0.770407i \(-0.720053\pi\)
−0.269080 + 0.963118i \(0.586720\pi\)
\(504\) 13.3092 5.92563i 0.592838 0.263949i
\(505\) 1.90311 3.29629i 0.0846875 0.146683i
\(506\) 6.87725 14.0094i 0.305731 0.622794i
\(507\) −9.60493 8.76044i −0.426570 0.389065i
\(508\) 3.77220 + 2.74066i 0.167364 + 0.121597i
\(509\) 3.91559 + 4.34870i 0.173555 + 0.192753i 0.823647 0.567103i \(-0.191936\pi\)
−0.650091 + 0.759856i \(0.725269\pi\)
\(510\) 4.06453 + 0.863942i 0.179980 + 0.0382560i
\(511\) −36.4483 16.2278i −1.61238 0.717877i
\(512\) 2.24864 1.63374i 0.0993769 0.0722016i
\(513\) 0.00552764 0.00613907i 0.000244051 0.000271046i
\(514\) 5.84376 1.24213i 0.257757 0.0547880i
\(515\) 5.74160 + 4.17152i 0.253005 + 0.183819i
\(516\) 1.86830 + 3.23599i 0.0822473 + 0.142457i
\(517\) −3.38396 + 4.30851i −0.148826 + 0.189488i
\(518\) −25.0675 + 43.4182i −1.10140 + 1.90769i
\(519\) 1.29759 + 0.942752i 0.0569577 + 0.0413822i
\(520\) 7.69118 2.92412i 0.337280 0.128231i
\(521\) −3.92709 12.0864i −0.172049 0.529513i 0.827437 0.561558i \(-0.189798\pi\)
−0.999486 + 0.0320454i \(0.989798\pi\)
\(522\) 0.0114337 + 0.108785i 0.000500441 + 0.00476138i
\(523\) −0.265724 2.52820i −0.0116193 0.110550i 0.987175 0.159642i \(-0.0510340\pi\)
−0.998794 + 0.0490917i \(0.984367\pi\)
\(524\) 16.6935 18.5400i 0.729257 0.809922i
\(525\) −7.02017 + 21.6059i −0.306385 + 0.942957i
\(526\) 2.01020 19.1257i 0.0876487 0.833922i
\(527\) −13.2632 22.9726i −0.577756 1.00070i
\(528\) 0.721653 0.381345i 0.0314059 0.0165959i
\(529\) −4.10240 7.10556i −0.178365 0.308937i
\(530\) 3.45206 1.53696i 0.149948 0.0667612i
\(531\) 2.18957 + 2.43176i 0.0950192 + 0.105530i
\(532\) −0.0173149 0.0532898i −0.000750696 0.00231041i
\(533\) −19.8262 + 19.6995i −0.858767 + 0.853281i
\(534\) 4.13117 3.00147i 0.178773 0.129886i
\(535\) 11.2737 + 2.39629i 0.487403 + 0.103601i
\(536\) −3.10304 3.44628i −0.134031 0.148857i
\(537\) 0.658756 6.26764i 0.0284274 0.270469i
\(538\) −9.89263 −0.426501
\(539\) 16.7206 66.3395i 0.720209 2.85745i
\(540\) 0.531245 + 0.920144i 0.0228612 + 0.0395967i
\(541\) 15.9410 + 11.5818i 0.685359 + 0.497943i 0.875131 0.483886i \(-0.160775\pi\)
−0.189772 + 0.981828i \(0.560775\pi\)
\(542\) −0.260954 + 0.0554675i −0.0112089 + 0.00238253i
\(543\) −17.7986 3.78322i −0.763813 0.162353i
\(544\) 3.60147 + 34.2657i 0.154412 + 1.46913i
\(545\) 1.32346 0.961548i 0.0566907 0.0411882i
\(546\) 7.20185 + 14.2471i 0.308211 + 0.609720i
\(547\) 2.91256 8.96395i 0.124532 0.383271i −0.869283 0.494314i \(-0.835419\pi\)
0.993816 + 0.111043i \(0.0354192\pi\)
\(548\) 21.5661 9.60186i 0.921260 0.410171i
\(549\) −2.44376 + 4.23272i −0.104297 + 0.180648i
\(550\) 2.95115 11.7088i 0.125837 0.499263i
\(551\) 0.00107272 4.56995e−5
\(552\) −1.61843 + 15.3984i −0.0688850 + 0.655397i
\(553\) 9.31226 1.97938i 0.395997 0.0841719i
\(554\) −0.848900 2.61265i −0.0360663 0.111001i
\(555\) −8.51710 3.79206i −0.361531 0.160964i
\(556\) 1.40797 + 13.3960i 0.0597114 + 0.568116i
\(557\) −18.1449 3.85681i −0.768822 0.163418i −0.193228 0.981154i \(-0.561896\pi\)
−0.575594 + 0.817736i \(0.695229\pi\)
\(558\) −1.15249 + 3.54699i −0.0487887 + 0.150156i
\(559\) −8.77413 + 5.65809i −0.371106 + 0.239312i
\(560\) 1.06505 0.0450065
\(561\) −0.744273 + 19.8570i −0.0314232 + 0.838362i
\(562\) 6.32719 10.9590i 0.266897 0.462278i
\(563\) 1.41971 13.5076i 0.0598335 0.569278i −0.923002 0.384795i \(-0.874272\pi\)
0.982836 0.184483i \(-0.0590611\pi\)
\(564\) 0.658700 2.02727i 0.0277363 0.0853634i
\(565\) 2.96742 3.29565i 0.124840 0.138649i
\(566\) 11.9495 + 5.32026i 0.502275 + 0.223627i
\(567\) −4.25236 + 3.08952i −0.178582 + 0.129748i
\(568\) 19.5674 21.7318i 0.821032 0.911848i
\(569\) 31.0720 + 34.5090i 1.30261 + 1.44669i 0.821702 + 0.569918i \(0.193025\pi\)
0.480905 + 0.876773i \(0.340308\pi\)
\(570\) −0.00523412 + 0.00233038i −0.000219233 + 9.76088e-5i
\(571\) 12.4864 0.522539 0.261269 0.965266i \(-0.415859\pi\)
0.261269 + 0.965266i \(0.415859\pi\)
\(572\) 7.87139 + 13.2728i 0.329119 + 0.554966i
\(573\) 20.2186 0.844643
\(574\) 31.3540 13.9597i 1.30869 0.582667i
\(575\) −16.1553 17.9423i −0.673722 0.748244i
\(576\) 2.91204 3.23415i 0.121335 0.134756i
\(577\) −17.1955 + 12.4933i −0.715859 + 0.520102i −0.885059 0.465480i \(-0.845882\pi\)
0.169199 + 0.985582i \(0.445882\pi\)
\(578\) −14.5409 6.47401i −0.604820 0.269283i
\(579\) −16.7529 + 18.6060i −0.696226 + 0.773237i
\(580\) −0.0426349 + 0.131217i −0.00177032 + 0.00544848i
\(581\) −5.67951 + 54.0369i −0.235626 + 2.24183i
\(582\) 5.05226 8.75077i 0.209423 0.362731i
\(583\) 10.0663 + 15.0066i 0.416905 + 0.621510i
\(584\) −21.0390 −0.870598
\(585\) −2.49489 + 1.60886i −0.103151 + 0.0665182i
\(586\) −2.68975 + 8.27821i −0.111113 + 0.341970i
\(587\) −32.3428 6.87468i −1.33493 0.283749i −0.515483 0.856900i \(-0.672387\pi\)
−0.819449 + 0.573151i \(0.805721\pi\)
\(588\) 2.78241 + 26.4729i 0.114745 + 1.09172i
\(589\) 0.0334131 + 0.0148765i 0.00137676 + 0.000612975i
\(590\) −0.701317 2.15843i −0.0288728 0.0888612i
\(591\) 2.77001 0.588784i 0.113943 0.0242193i
\(592\) 0.291284 2.77138i 0.0119717 0.113903i
\(593\) −18.6997 −0.767905 −0.383952 0.923353i \(-0.625437\pi\)
−0.383952 + 0.923353i \(0.625437\pi\)
\(594\) 2.14474 1.79033i 0.0879999 0.0734580i
\(595\) −12.9644 + 22.4550i −0.531488 + 0.920565i
\(596\) −1.60964 + 0.716659i −0.0659335 + 0.0293555i
\(597\) −0.713127 + 2.19478i −0.0291864 + 0.0898264i
\(598\) −16.9398 0.942222i −0.692718 0.0385303i
\(599\) 24.7896 18.0107i 1.01288 0.735898i 0.0480661 0.998844i \(-0.484694\pi\)
0.964810 + 0.262946i \(0.0846942\pi\)
\(600\) 1.25221 + 11.9140i 0.0511212 + 0.486386i
\(601\) 24.6197 + 5.23308i 1.00426 + 0.213462i 0.680555 0.732697i \(-0.261739\pi\)
0.323704 + 0.946159i \(0.395072\pi\)
\(602\) 12.5404 2.66555i 0.511110 0.108640i
\(603\) 1.35358 + 0.983437i 0.0551222 + 0.0400487i
\(604\) −10.5076 18.1997i −0.427548 0.740535i
\(605\) −9.03152 0.677986i −0.367184 0.0275640i
\(606\) 3.89406 0.158185
\(607\) −0.205020 + 1.95063i −0.00832149 + 0.0791737i −0.997894 0.0648588i \(-0.979340\pi\)
0.989573 + 0.144032i \(0.0460070\pi\)
\(608\) −0.0317880 0.0353042i −0.00128917 0.00143177i
\(609\) −0.667628 0.141909i −0.0270537 0.00575043i
\(610\) 2.74240 1.99247i 0.111036 0.0806727i
\(611\) 5.74789 + 1.55990i 0.232535 + 0.0631069i
\(612\) −2.38913 7.35300i −0.0965750 0.297227i
\(613\) 6.77731 + 7.52696i 0.273733 + 0.304011i 0.864299 0.502978i \(-0.167762\pi\)
−0.590566 + 0.806989i \(0.701096\pi\)
\(614\) −25.1429 + 11.1944i −1.01469 + 0.451767i
\(615\) 3.19120 + 5.52731i 0.128681 + 0.222883i
\(616\) −8.26877 47.6062i −0.333158 1.91811i
\(617\) 10.9655 + 18.9928i 0.441454 + 0.764621i 0.997798 0.0663313i \(-0.0211294\pi\)
−0.556343 + 0.830952i \(0.687796\pi\)
\(618\) −0.758957 + 7.22099i −0.0305297 + 0.290471i
\(619\) 7.67498 23.6212i 0.308483 0.949415i −0.669871 0.742478i \(-0.733651\pi\)
0.978354 0.206937i \(-0.0663495\pi\)
\(620\) −3.14770 + 3.49588i −0.126415 + 0.140398i
\(621\) −0.583909 5.55552i −0.0234315 0.222935i
\(622\) −1.50991 14.3658i −0.0605417 0.576016i
\(623\) 9.84633 + 30.3039i 0.394485 + 1.21410i
\(624\) −0.687784 0.560615i −0.0275334 0.0224426i
\(625\) −12.3705 8.98771i −0.494821 0.359508i
\(626\) 0.831585 1.44035i 0.0332368 0.0575678i
\(627\) −0.0152629 0.0227534i −0.000609540 0.000908684i
\(628\) −3.25209 5.63278i −0.129772 0.224773i
\(629\) 54.8849 + 39.8762i 2.18840 + 1.58997i
\(630\) 3.56583 0.757941i 0.142066 0.0301971i
\(631\) −20.0978 + 22.3209i −0.800081 + 0.888580i −0.995751 0.0920895i \(-0.970645\pi\)
0.195669 + 0.980670i \(0.437312\pi\)
\(632\) 4.06149 2.95084i 0.161557 0.117378i
\(633\) 9.89679 + 4.40634i 0.393362 + 0.175136i
\(634\) 8.75285 + 1.86048i 0.347620 + 0.0738889i
\(635\) 1.99067 + 2.21086i 0.0789974 + 0.0877355i
\(636\) −5.68799 4.13256i −0.225543 0.163867i
\(637\) −73.4954 + 11.3992i −2.91199 + 0.451653i
\(638\) 0.359125 + 0.0514087i 0.0142179 + 0.00203529i
\(639\) −5.27526 + 9.13702i −0.208686 + 0.361455i
\(640\) 5.89371 2.62405i 0.232970 0.103725i
\(641\) 16.6653 3.54233i 0.658241 0.139913i 0.133332 0.991071i \(-0.457432\pi\)
0.524910 + 0.851158i \(0.324099\pi\)
\(642\) 3.64377 + 11.2144i 0.143808 + 0.442596i
\(643\) 26.9116 + 11.9818i 1.06129 + 0.472516i 0.861728 0.507370i \(-0.169382\pi\)
0.199560 + 0.979886i \(0.436049\pi\)
\(644\) −34.6138 15.4111i −1.36398 0.607281i
\(645\) 0.736734 + 2.26744i 0.0290089 + 0.0892802i
\(646\) 0.0407803 0.00866813i 0.00160448 0.000341043i
\(647\) 32.9728 14.6804i 1.29630 0.577148i 0.361512 0.932367i \(-0.382260\pi\)
0.934783 + 0.355219i \(0.115594\pi\)
\(648\) −1.38586 + 2.40038i −0.0544417 + 0.0942958i
\(649\) 9.59551 5.07058i 0.376657 0.199038i
\(650\) −12.9717 + 2.01193i −0.508794 + 0.0789144i
\(651\) −18.8273 13.6788i −0.737900 0.536116i
\(652\) −5.12872 5.69603i −0.200856 0.223074i
\(653\) −11.5248 2.44967i −0.450999 0.0958628i −0.0231883 0.999731i \(-0.507382\pi\)
−0.427811 + 0.903868i \(0.640715\pi\)
\(654\) 1.52894 + 0.680727i 0.0597862 + 0.0266185i
\(655\) 12.8779 9.35634i 0.503181 0.365582i
\(656\) −1.27648 + 1.41768i −0.0498382 + 0.0553509i
\(657\) 7.42471 1.57817i 0.289665 0.0615703i
\(658\) −5.91690 4.29888i −0.230665 0.167588i
\(659\) −16.6223 28.7906i −0.647512 1.12152i −0.983715 0.179734i \(-0.942476\pi\)
0.336204 0.941789i \(-0.390857\pi\)
\(660\) 3.38985 0.962647i 0.131950 0.0374710i
\(661\) 16.5195 28.6127i 0.642536 1.11290i −0.342329 0.939580i \(-0.611216\pi\)
0.984865 0.173325i \(-0.0554510\pi\)
\(662\) 15.5366 + 11.2880i 0.603846 + 0.438720i
\(663\) 20.1919 7.67678i 0.784188 0.298141i
\(664\) 8.85391 + 27.2495i 0.343598 + 1.05749i
\(665\) −0.00373701 0.0355553i −0.000144915 0.00137877i
\(666\) −0.997019 9.48601i −0.0386337 0.367575i
\(667\) 0.485378 0.539066i 0.0187939 0.0208727i
\(668\) −0.638495 + 1.96509i −0.0247041 + 0.0760315i
\(669\) 0.876579 8.34009i 0.0338905 0.322447i
\(670\) −0.580206 1.00495i −0.0224153 0.0388244i
\(671\) 11.6317 + 11.2903i 0.449037 + 0.435855i
\(672\) 15.1135 + 26.1774i 0.583017 + 1.00982i
\(673\) −11.3737 + 5.06388i −0.438422 + 0.195198i −0.614064 0.789256i \(-0.710466\pi\)
0.175642 + 0.984454i \(0.443800\pi\)
\(674\) −11.0603 12.2837i −0.426027 0.473151i
\(675\) −1.33560 4.11054i −0.0514072 0.158215i
\(676\) 9.94728 13.5083i 0.382588 0.519551i
\(677\) −18.6831 + 13.5741i −0.718049 + 0.521693i −0.885760 0.464143i \(-0.846362\pi\)
0.167711 + 0.985836i \(0.446362\pi\)
\(678\) 4.43792 + 0.943309i 0.170437 + 0.0362276i
\(679\) 42.1894 + 46.8560i 1.61908 + 1.79817i
\(680\) −1.42920 + 13.5980i −0.0548074 + 0.521458i
\(681\) 28.1160 1.07741
\(682\) 10.4731 + 6.58161i 0.401035 + 0.252023i
\(683\) 23.9923 + 41.5559i 0.918039 + 1.59009i 0.802390 + 0.596800i \(0.203562\pi\)
0.115649 + 0.993290i \(0.463105\pi\)
\(684\) 0.00862429 + 0.00626591i 0.000329758 + 0.000239583i
\(685\) 14.7332 3.13165i 0.562928 0.119654i
\(686\) 59.0194 + 12.5450i 2.25337 + 0.478968i
\(687\) −2.41499 22.9771i −0.0921377 0.876632i
\(688\) −0.576509 + 0.418858i −0.0219792 + 0.0159688i
\(689\) 10.7518 16.4407i 0.409610 0.626341i
\(690\) −1.19723 + 3.68469i −0.0455777 + 0.140274i
\(691\) 35.5019 15.8065i 1.35056 0.601307i 0.401341 0.915929i \(-0.368544\pi\)
0.949217 + 0.314622i \(0.101878\pi\)
\(692\) −1.03487 + 1.79245i −0.0393398 + 0.0681386i
\(693\) 6.48910 + 16.1801i 0.246501 + 0.614632i
\(694\) 14.4132 0.547118
\(695\) −0.898352 + 8.54725i −0.0340764 + 0.324216i
\(696\) −0.352056 + 0.0748318i −0.0133446 + 0.00283649i
\(697\) −14.3516 44.1695i −0.543604 1.67304i
\(698\) 10.8499 + 4.83071i 0.410676 + 0.182845i
\(699\) −1.18302 11.2557i −0.0447459 0.425729i
\(700\) −28.6752 6.09510i −1.08382 0.230373i
\(701\) 14.2182 43.7592i 0.537015 1.65276i −0.202238 0.979336i \(-0.564822\pi\)
0.739254 0.673427i \(-0.235178\pi\)
\(702\) −2.70169 1.38751i −0.101969 0.0523681i
\(703\) −0.0935411 −0.00352797
\(704\) −8.04069 11.9868i −0.303045 0.451770i
\(705\) 0.680028 1.17784i 0.0256113 0.0443601i
\(706\) 0.612066 5.82342i 0.0230354 0.219167i
\(707\) −7.50864 + 23.1092i −0.282391 + 0.869111i
\(708\) −2.82550 + 3.13804i −0.106189 + 0.117935i
\(709\) 12.3044 + 5.47827i 0.462101 + 0.205741i 0.624563 0.780974i \(-0.285277\pi\)
−0.162462 + 0.986715i \(0.551944\pi\)
\(710\) 5.91992 4.30107i 0.222171 0.161416i
\(711\) −1.21196 + 1.34602i −0.0454521 + 0.0504797i
\(712\) 11.2429 + 12.4866i 0.421347 + 0.467953i
\(713\) 22.5943 10.0596i 0.846163 0.376736i
\(714\) −26.5271 −0.992751
\(715\) 3.15182 + 9.32782i 0.117871 + 0.348841i
\(716\) 8.13255 0.303927
\(717\) −0.361486 + 0.160944i −0.0135000 + 0.00601057i
\(718\) 9.04232 + 10.0425i 0.337456 + 0.374783i
\(719\) −9.58330 + 10.6433i −0.357397 + 0.396929i −0.894852 0.446363i \(-0.852719\pi\)
0.537455 + 0.843292i \(0.319386\pi\)
\(720\) −0.163928 + 0.119101i −0.00610925 + 0.00443863i
\(721\) −41.3894 18.4277i −1.54142 0.686285i
\(722\) 10.7092 11.8938i 0.398557 0.442642i
\(723\) 1.05291 3.24051i 0.0391580 0.120516i
\(724\) 2.45445 23.3525i 0.0912188 0.867889i
\(725\) 0.280622 0.486051i 0.0104220 0.0180515i
\(726\) −4.01926 8.34882i −0.149169 0.309854i
\(727\) −11.8168 −0.438261 −0.219130 0.975696i \(-0.570322\pi\)
−0.219130 + 0.975696i \(0.570322\pi\)
\(728\) −44.1454 + 28.4676i −1.63614 + 1.05508i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −5.14948 1.09456i −0.190591 0.0405113i
\(731\) −1.81341 17.2535i −0.0670714 0.638142i
\(732\) −5.76176 2.56530i −0.212961 0.0948163i
\(733\) 6.52394 + 20.0786i 0.240967 + 0.741621i 0.996274 + 0.0862490i \(0.0274881\pi\)
−0.755306 + 0.655372i \(0.772512\pi\)
\(734\) −23.6156 + 5.01965i −0.871668 + 0.185279i
\(735\) −1.77531 + 16.8909i −0.0654832 + 0.623031i
\(736\) −32.1244 −1.18412
\(737\) 4.25998 3.55602i 0.156918 0.130988i
\(738\) −3.26483 + 5.65485i −0.120180 + 0.208158i
\(739\) 29.9957 13.3549i 1.10341 0.491269i 0.227516 0.973774i \(-0.426940\pi\)
0.875893 + 0.482505i \(0.160273\pi\)
\(740\) 3.71775 11.4421i 0.136667 0.420619i
\(741\) −0.0163022 + 0.0249279i −0.000598875 + 0.000915748i
\(742\) −19.5160 + 14.1792i −0.716454 + 0.520534i
\(743\) 3.78103 + 35.9741i 0.138713 + 1.31976i 0.813420 + 0.581676i \(0.197603\pi\)
−0.674708 + 0.738085i \(0.735730\pi\)
\(744\) −12.0036 2.55144i −0.440073 0.0935405i
\(745\) −1.09965 + 0.233738i −0.0402882 + 0.00856351i
\(746\) 11.2033 + 8.13969i 0.410183 + 0.298015i
\(747\) −5.16861 8.95229i −0.189110 0.327547i
\(748\) −25.5842 + 1.72328i −0.935450 + 0.0630093i
\(749\) −73.5775 −2.68846
\(750\) −0.675821 + 6.43001i −0.0246775 + 0.234791i
\(751\) 19.7630 + 21.9490i 0.721161 + 0.800930i 0.986593 0.163199i \(-0.0521814\pi\)
−0.265432 + 0.964129i \(0.585515\pi\)
\(752\) 0.397632 + 0.0845193i 0.0145001 + 0.00308210i
\(753\) −1.06709 + 0.775288i −0.0388870 + 0.0282531i
\(754\) −0.100854 0.381276i −0.00367289 0.0138853i
\(755\) −4.14350 12.7524i −0.150798 0.464107i
\(756\) −4.53858 5.04060i −0.165066 0.183325i
\(757\) −0.790783 + 0.352079i −0.0287415 + 0.0127965i −0.421057 0.907034i \(-0.638341\pi\)
0.392316 + 0.919831i \(0.371674\pi\)
\(758\) −0.468644 0.811715i −0.0170219 0.0294828i
\(759\) −18.3401 2.62539i −0.665704 0.0952955i
\(760\) −0.00942620 0.0163267i −0.000341924 0.000592230i
\(761\) 0.759575 7.22688i 0.0275346 0.261974i −0.972091 0.234605i \(-0.924620\pi\)
0.999625 0.0273692i \(-0.00871297\pi\)
\(762\) −0.940542 + 2.89469i −0.0340723 + 0.104864i
\(763\) −6.98790 + 7.76085i −0.252979 + 0.280962i
\(764\) 2.72723 + 25.9479i 0.0986677 + 0.938761i
\(765\) −0.515638 4.90596i −0.0186429 0.177375i
\(766\) −3.46915 10.6769i −0.125345 0.385773i
\(767\) −9.14516 7.45426i −0.330213 0.269158i
\(768\) 12.3814 + 8.99563i 0.446776 + 0.324602i
\(769\) 10.8202 18.7411i 0.390185 0.675820i −0.602289 0.798278i \(-0.705744\pi\)
0.992474 + 0.122458i \(0.0390777\pi\)
\(770\) 0.452863 12.0823i 0.0163201 0.435414i
\(771\) −3.54619 6.14218i −0.127713 0.221205i
\(772\) −26.1380 18.9904i −0.940728 0.683479i
\(773\) 35.3428 7.51234i 1.27119 0.270200i 0.477560 0.878599i \(-0.341521\pi\)
0.793631 + 0.608399i \(0.208188\pi\)
\(774\) −1.63210 + 1.81263i −0.0586646 + 0.0651537i
\(775\) 15.4813 11.2479i 0.556106 0.404035i
\(776\) 30.3738 + 13.5233i 1.09036 + 0.485458i
\(777\) 58.2170 + 12.3744i 2.08852 + 0.443929i
\(778\) −14.4139 16.0083i −0.516764 0.573925i
\(779\) 0.0518062 + 0.0376394i 0.00185615 + 0.00134857i
\(780\) −2.40129 2.98485i −0.0859799 0.106875i
\(781\) 25.1090 + 24.3719i 0.898470 + 0.872094i
\(782\) 14.0961 24.4151i 0.504074 0.873082i
\(783\) 0.118628 0.0528167i 0.00423943 0.00188752i
\(784\) −4.96550 + 1.05545i −0.177339 + 0.0376946i
\(785\) −1.28241 3.94685i −0.0457712 0.140869i
\(786\) 14.8773 + 6.62381i 0.530656 + 0.236263i
\(787\) −12.5540 5.58939i −0.447501 0.199240i 0.170598 0.985341i \(-0.445430\pi\)
−0.618099 + 0.786100i \(0.712097\pi\)
\(788\) 1.12927 + 3.47552i 0.0402284 + 0.123810i
\(789\) −22.3312 + 4.74665i −0.795013 + 0.168985i
\(790\) 1.14761 0.510947i 0.0408300 0.0181787i
\(791\) −14.1554 + 24.5179i −0.503308 + 0.871755i
\(792\) 6.59636 + 6.40271i 0.234391 + 0.227511i
\(793\) 6.36793 16.4314i 0.226132 0.583497i
\(794\) 5.17707 + 3.76136i 0.183727 + 0.133486i
\(795\) −3.00168 3.33370i −0.106458 0.118234i
\(796\) −2.91290 0.619156i −0.103245 0.0219454i
\(797\) −17.4562 7.77200i −0.618330 0.275298i 0.0735715 0.997290i \(-0.476560\pi\)
−0.691902 + 0.721991i \(0.743227\pi\)
\(798\) 0.0295907 0.0214989i 0.00104750 0.000761052i
\(799\) −6.62218 + 7.35467i −0.234276 + 0.260190i
\(800\) −24.3120 + 5.16768i −0.859560 + 0.182705i
\(801\) −4.90431 3.56319i −0.173285 0.125899i
\(802\) 7.88902 + 13.6642i 0.278571 + 0.482499i
\(803\) 0.942944 25.1574i 0.0332758 0.887787i
\(804\) −1.07953 + 1.86980i −0.0380721 + 0.0659427i
\(805\) −19.5582 14.2099i −0.689336 0.500832i
\(806\) 2.14613 13.2746i 0.0755941 0.467579i
\(807\) 3.62909 + 11.1692i 0.127750 + 0.393175i
\(808\) 1.33934 + 12.7430i 0.0471178 + 0.448296i
\(809\) 4.68624 + 44.5866i 0.164759 + 1.56758i 0.694545 + 0.719449i \(0.255606\pi\)
−0.529786 + 0.848131i \(0.677728\pi\)
\(810\) −0.464082 + 0.515416i −0.0163062 + 0.0181099i
\(811\) 11.6817 35.9527i 0.410201 1.26247i −0.506273 0.862374i \(-0.668977\pi\)
0.916474 0.400095i \(-0.131023\pi\)
\(812\) 0.0920665 0.875954i 0.00323090 0.0307400i
\(813\) 0.158356 + 0.274280i 0.00555378 + 0.00961943i
\(814\) −31.3156 4.48282i −1.09761 0.157123i
\(815\) −2.44523 4.23527i −0.0856528 0.148355i
\(816\) 1.34698 0.599713i 0.0471536 0.0209941i
\(817\) 0.0160059 + 0.0177764i 0.000559976 + 0.000621916i
\(818\) −3.51065 10.8047i −0.122747 0.377776i
\(819\) 13.4436 13.3577i 0.469758 0.466757i
\(820\) −6.66312 + 4.84104i −0.232686 + 0.169056i
\(821\) 31.2498 + 6.64235i 1.09062 + 0.231819i 0.717917 0.696129i \(-0.245096\pi\)
0.372708 + 0.927949i \(0.378429\pi\)
\(822\) 10.3113 + 11.4518i 0.359647 + 0.399428i
\(823\) −3.86811 + 36.8027i −0.134834 + 1.28286i 0.692610 + 0.721312i \(0.256461\pi\)
−0.827444 + 0.561548i \(0.810206\pi\)
\(824\) −23.8911 −0.832285
\(825\) −14.3023 + 0.963364i −0.497943 + 0.0335400i
\(826\) 7.24412 + 12.5472i 0.252055 + 0.436573i
\(827\) 40.7590 + 29.6131i 1.41733 + 1.02975i 0.992205 + 0.124614i \(0.0397691\pi\)
0.425123 + 0.905136i \(0.360231\pi\)
\(828\) 7.05101 1.49874i 0.245040 0.0520848i
\(829\) 3.67632 + 0.781425i 0.127684 + 0.0271400i 0.271310 0.962492i \(-0.412543\pi\)
−0.143626 + 0.989632i \(0.545876\pi\)
\(830\) 0.749415 + 7.13021i 0.0260126 + 0.247493i
\(831\) −2.63837 + 1.91689i −0.0915241 + 0.0664962i
\(832\) −8.58821 + 13.1323i −0.297743 + 0.455282i
\(833\) 38.1904 117.538i 1.32322 4.07245i
\(834\) −8.03248 + 3.57629i −0.278142 + 0.123837i
\(835\) −0.659169 + 1.14172i −0.0228115 + 0.0395107i
\(836\) 0.0271422 0.0226570i 0.000938733 0.000783608i
\(837\) 4.42749 0.153037
\(838\) 2.52089 23.9847i 0.0870827 0.828536i
\(839\) −24.7498 + 5.26074i −0.854460 + 0.181621i −0.614261 0.789103i \(-0.710546\pi\)
−0.240198 + 0.970724i \(0.577213\pi\)
\(840\) 3.70674 + 11.4082i 0.127895 + 0.393619i
\(841\) −26.4774 11.7885i −0.913014 0.406500i
\(842\) 1.59274 + 15.1539i 0.0548895 + 0.522239i
\(843\) −14.6943 3.12338i −0.506100 0.107575i
\(844\) −4.31999 + 13.2956i −0.148700 + 0.457653i
\(845\) 8.00010 7.11101i 0.275212 0.244626i
\(846\) 1.39144 0.0478387
\(847\) 57.2960 7.75377i 1.96871 0.266423i
\(848\) 0.670414 1.16119i 0.0230221 0.0398754i
\(849\) 1.62315 15.4432i 0.0557064 0.530011i
\(850\) 6.74051 20.7452i 0.231198 0.711553i
\(851\) −42.3248 + 47.0064i −1.45088 + 1.61136i
\(852\) −12.4377 5.53763i −0.426109 0.189716i
\(853\) 21.9603 15.9551i 0.751908 0.546293i −0.144510 0.989503i \(-0.546161\pi\)
0.896418 + 0.443211i \(0.146161\pi\)
\(854\) −14.4800 + 16.0816i −0.495494 + 0.550302i
\(855\) 0.00455122 + 0.00505465i 0.000155649 + 0.000172865i
\(856\) −35.4447 + 15.7810i −1.21148 + 0.539384i
\(857\) 11.3399 0.387363 0.193682 0.981064i \(-0.437957\pi\)
0.193682 + 0.981064i \(0.437957\pi\)
\(858\) −6.65225 + 7.56407i −0.227104 + 0.258233i
\(859\) 45.6677 1.55816 0.779081 0.626923i \(-0.215686\pi\)
0.779081 + 0.626923i \(0.215686\pi\)
\(860\) −2.81058 + 1.25135i −0.0958398 + 0.0426706i
\(861\) −27.2633 30.2789i −0.929130 1.03190i
\(862\) −11.6322 + 12.9188i −0.396194 + 0.440018i
\(863\) 21.0212 15.2728i 0.715569 0.519891i −0.169397 0.985548i \(-0.554182\pi\)
0.884965 + 0.465657i \(0.154182\pi\)
\(864\) −5.25356 2.33904i −0.178730 0.0795756i
\(865\) −0.883646 + 0.981388i −0.0300449 + 0.0333682i
\(866\) 6.95287 21.3987i 0.236268 0.727158i
\(867\) −1.97514 + 18.7922i −0.0670794 + 0.638218i
\(868\) 15.0154 26.0074i 0.509656 0.882750i
\(869\) 3.34646 + 4.98880i 0.113521 + 0.169233i
\(870\) −0.0900622 −0.00305339
\(871\) −5.36622 2.75592i −0.181827 0.0933809i
\(872\) −1.70175 + 5.23744i −0.0576285 + 0.177362i
\(873\) −11.7334 2.49401i −0.397116 0.0844096i
\(874\) 0.00406322 + 0.0386589i 0.000137440 + 0.00130766i
\(875\) −36.8556 16.4092i −1.24595 0.554732i
\(876\) 3.02687 + 9.31575i 0.102269 + 0.314750i
\(877\) −38.8819 + 8.26461i −1.31295 + 0.279076i −0.810606 0.585592i \(-0.800862\pi\)
−0.502344 + 0.864668i \(0.667529\pi\)
\(878\) 2.52272 24.0021i 0.0851378 0.810032i
\(879\) 10.3332 0.348530
\(880\) 0.250155 + 0.623744i 0.00843272 + 0.0210264i
\(881\) 1.52820 2.64692i 0.0514864 0.0891771i −0.839134 0.543925i \(-0.816937\pi\)
0.890620 + 0.454748i \(0.150271\pi\)
\(882\) −15.8736 + 7.06740i −0.534493 + 0.237972i
\(883\) −10.1010 + 31.0876i −0.339925 + 1.04618i 0.624320 + 0.781168i \(0.285376\pi\)
−0.964245 + 0.265012i \(0.914624\pi\)
\(884\) 12.5758 + 24.8781i 0.422968 + 0.836741i
\(885\) −2.17969 + 1.58363i −0.0732693 + 0.0532333i
\(886\) −0.113429 1.07920i −0.00381072 0.0362566i
\(887\) 7.16287 + 1.52252i 0.240506 + 0.0511211i 0.326587 0.945167i \(-0.394101\pi\)
−0.0860817 + 0.996288i \(0.527435\pi\)
\(888\) 30.6992 6.52531i 1.03020 0.218975i
\(889\) −15.3649 11.1633i −0.515323 0.374404i
\(890\) 2.10220 + 3.64112i 0.0704659 + 0.122051i
\(891\) −2.80815 1.76473i −0.0940767 0.0591207i
\(892\) 10.8216 0.362335
\(893\) 0.00142637 0.0135710i 4.77316e−5 0.000454136i
\(894\) −0.769608 0.854736i −0.0257395 0.0285866i
\(895\) 5.07555 + 1.07884i 0.169657 + 0.0360617i
\(896\) −33.3196 + 24.2081i −1.11313 + 0.808737i
\(897\) 5.15052 + 19.4714i 0.171971 + 0.650130i
\(898\) −6.22880 19.1703i −0.207858 0.639721i
\(899\) 0.384704 + 0.427257i 0.0128306 + 0.0142498i
\(900\) 5.09518 2.26852i 0.169839 0.0756174i
\(901\) 16.3213 + 28.2694i 0.543743 + 0.941790i
\(902\) 15.5398 + 15.0836i 0.517419 + 0.502230i
\(903\) −7.60996 13.1808i −0.253244 0.438631i
\(904\) −1.56050 + 14.8472i −0.0519014 + 0.493809i
\(905\) 4.62971 14.2488i 0.153897 0.473645i
\(906\) 9.17917 10.1945i 0.304958 0.338690i
\(907\) −3.50710 33.3678i −0.116451 1.10796i −0.884167 0.467170i \(-0.845274\pi\)
0.767716 0.640790i \(-0.221393\pi\)
\(908\) 3.79249 + 36.0831i 0.125858 + 1.19746i
\(909\) −1.42853 4.39656i −0.0473813 0.145825i
\(910\) −12.2860 + 4.67104i −0.407278 + 0.154844i
\(911\) 2.19863 + 1.59740i 0.0728440 + 0.0529243i 0.623611 0.781735i \(-0.285665\pi\)
−0.550767 + 0.834659i \(0.685665\pi\)
\(912\) −0.00101650 + 0.00176063i −3.36597e−5 + 5.83003e-5i
\(913\) −32.9806 + 9.36582i −1.09150 + 0.309963i
\(914\) −6.09722 10.5607i −0.201678 0.349317i
\(915\) −3.25563 2.36535i −0.107628 0.0781961i
\(916\) 29.1623 6.19864i 0.963550 0.204809i
\(917\) −67.9958 + 75.5170i −2.24542 + 2.49379i
\(918\) 4.08296 2.96644i 0.134758 0.0979072i
\(919\) 10.8510 + 4.83118i 0.357942 + 0.159366i 0.577826 0.816160i \(-0.303901\pi\)
−0.219884 + 0.975526i \(0.570568\pi\)
\(920\) −12.4696 2.65050i −0.411111 0.0873843i
\(921\) 21.8626 + 24.2808i 0.720396 + 0.800080i
\(922\) −24.3007 17.6555i −0.800302 0.581453i
\(923\) 13.7462 35.4699i 0.452462 1.16751i
\(924\) −19.8897 + 10.5104i −0.654324 + 0.345767i
\(925\) −24.4701 + 42.3835i −0.804573 + 1.39356i
\(926\) −16.3655 + 7.28637i −0.537802 + 0.239445i
\(927\) 8.43123 1.79211i 0.276918 0.0588607i
\(928\) −0.230762 0.710212i −0.00757513 0.0233139i
\(929\) −48.1903 21.4557i −1.58107 0.703939i −0.586692 0.809810i \(-0.699570\pi\)
−0.994380 + 0.105871i \(0.966237\pi\)
\(930\) −2.80525 1.24898i −0.0919879 0.0409557i
\(931\) 0.0526577 + 0.162064i 0.00172579 + 0.00531142i
\(932\) 14.2856 3.03650i 0.467940 0.0994638i
\(933\) −15.6657 + 6.97482i −0.512872 + 0.228345i
\(934\) 11.2194 19.4326i 0.367111 0.635855i
\(935\) −16.1958 2.31842i −0.529658 0.0758205i
\(936\) 3.61126 9.31828i 0.118038 0.304578i
\(937\) −34.5140 25.0759i −1.12752 0.819195i −0.142192 0.989839i \(-0.545415\pi\)
−0.985333 + 0.170645i \(0.945415\pi\)
\(938\) 4.95686 + 5.50515i 0.161847 + 0.179750i
\(939\) −1.93128 0.410506i −0.0630249 0.0133964i
\(940\) 1.60333 + 0.713850i 0.0522949 + 0.0232832i
\(941\) 6.75052 4.90454i 0.220061 0.159883i −0.472293 0.881441i \(-0.656574\pi\)
0.692354 + 0.721558i \(0.256574\pi\)
\(942\) 2.84094 3.15519i 0.0925629 0.102802i
\(943\) 42.3555 9.00295i 1.37929 0.293176i
\(944\) −0.651499 0.473342i −0.0212045 0.0154060i
\(945\) −2.16387 3.74793i −0.0703906 0.121920i
\(946\) 4.50653 + 6.71821i 0.146520 + 0.218428i
\(947\) 4.98776 8.63905i 0.162080 0.280732i −0.773534 0.633755i \(-0.781513\pi\)
0.935615 + 0.353023i \(0.114846\pi\)
\(948\) −1.89092 1.37383i −0.0614141 0.0446200i
\(949\) −25.5817 + 9.72596i −0.830419 + 0.315718i
\(950\) 0.00929395 + 0.0286038i 0.000301535 + 0.000928031i
\(951\) −1.11041 10.5649i −0.0360076 0.342589i
\(952\) −9.12384 86.8075i −0.295705 2.81345i
\(953\) 5.68310 6.31172i 0.184094 0.204457i −0.644033 0.764998i \(-0.722740\pi\)
0.828127 + 0.560541i \(0.189407\pi\)
\(954\) 1.41822 4.36482i 0.0459165 0.141316i
\(955\) −1.74010 + 16.5559i −0.0563082 + 0.535737i
\(956\) −0.255310 0.442211i −0.00825733 0.0143021i
\(957\) −0.0737018 0.424327i −0.00238244 0.0137165i
\(958\) 11.2133 + 19.4221i 0.362286 + 0.627498i
\(959\) −87.8432 + 39.1103i −2.83660 + 1.26294i
\(960\) 2.39765 + 2.66286i 0.0773838 + 0.0859434i
\(961\) −3.52196 10.8395i −0.113612 0.349660i
\(962\) 8.79446 + 33.2472i 0.283545 + 1.07193i
\(963\) 11.3248 8.22794i 0.364936 0.265142i
\(964\) 4.30079 + 0.914162i 0.138519 + 0.0294432i
\(965\) −13.7936 15.3194i −0.444032 0.493148i
\(966\) 2.58531 24.5976i 0.0831811 0.791415i
\(967\) 13.2224 0.425205 0.212602 0.977139i \(-0.431806\pi\)
0.212602 + 0.977139i \(0.431806\pi\)
\(968\) 25.9384 16.0242i 0.833691 0.515037i
\(969\) −0.0247469 0.0428629i −0.000794984 0.00137695i
\(970\) 6.73072 + 4.89016i 0.216110 + 0.157013i
\(971\) 18.9467 4.02725i 0.608029 0.129241i 0.106400 0.994323i \(-0.466068\pi\)
0.501629 + 0.865083i \(0.332734\pi\)
\(972\) 1.26224 + 0.268297i 0.0404863 + 0.00860562i
\(973\) −5.73496 54.5645i −0.183854 1.74926i
\(974\) −13.7695 + 10.0042i −0.441205 + 0.320554i
\(975\) 7.03022 + 13.9076i 0.225147 + 0.445399i
\(976\) 0.371689 1.14394i 0.0118975 0.0366166i
\(977\) −30.1427 + 13.4204i −0.964349 + 0.429356i −0.827642 0.561256i \(-0.810318\pi\)
−0.136707 + 0.990612i \(0.543652\pi\)
\(978\) 2.50166 4.33300i 0.0799942 0.138554i
\(979\) −15.4348 + 12.8842i −0.493297 + 0.411780i
\(980\) −21.9167 −0.700104
\(981\) 0.207682 1.97596i 0.00663077 0.0630875i
\(982\) 31.2375 6.63973i 0.996828 0.211882i
\(983\) −0.584095 1.79766i −0.0186297 0.0573364i 0.941309 0.337545i \(-0.109596\pi\)
−0.959939 + 0.280208i \(0.909596\pi\)
\(984\) −19.6279 8.73892i −0.625715 0.278586i
\(985\) 0.243725 + 2.31889i 0.00776573 + 0.0738860i
\(986\) 0.641032 + 0.136256i 0.0204146 + 0.00433926i
\(987\) −2.68301 + 8.25747i −0.0854013 + 0.262838i
\(988\) −0.0341906 0.0175592i −0.00108775 0.000558633i
\(989\) 16.1752 0.514343
\(990\) 1.28142 + 1.91030i 0.0407261 + 0.0607134i
\(991\) 1.76363 3.05469i 0.0560235 0.0970356i −0.836654 0.547733i \(-0.815491\pi\)
0.892677 + 0.450697i \(0.148824\pi\)
\(992\) 2.66144 25.3219i 0.0845007 0.803971i
\(993\) 7.04505 21.6824i 0.223568 0.688071i
\(994\) −31.2574 + 34.7149i −0.991425 + 1.10109i
\(995\) −1.73581 0.772834i −0.0550290 0.0245005i
\(996\) 10.7919 7.84077i 0.341954 0.248444i
\(997\) 33.8185 37.5593i 1.07104 1.18951i 0.0899558 0.995946i \(-0.471327\pi\)
0.981087 0.193568i \(-0.0620059\pi\)
\(998\) 10.5213 + 11.6851i 0.333046 + 0.369885i
\(999\) −10.3444 + 4.60560i −0.327281 + 0.145715i
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 429.2.bg.b.334.6 yes 112
11.3 even 5 inner 429.2.bg.b.256.9 112
13.3 even 3 inner 429.2.bg.b.367.9 yes 112
143.3 even 15 inner 429.2.bg.b.289.6 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bg.b.256.9 112 11.3 even 5 inner
429.2.bg.b.289.6 yes 112 143.3 even 15 inner
429.2.bg.b.334.6 yes 112 1.1 even 1 trivial
429.2.bg.b.367.9 yes 112 13.3 even 3 inner