Properties

Label 471.2.q.b.19.12
Level $471$
Weight $2$
Character 471.19
Analytic conductor $3.761$
Analytic rank $0$
Dimension $336$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [471,2,Mod(19,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([0, 62]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.q (of order \(39\), degree \(24\), 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: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(14\) over \(\Q(\zeta_{39})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label 19.12
Character \(\chi\) \(=\) 471.19
Dual form 471.2.q.b.124.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.97256 + 0.486192i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.88370 + 0.988640i) q^{4} +(2.48102 - 1.86436i) q^{5} +(-1.40733 - 1.46519i) q^{6} +(1.36867 - 0.718334i) q^{7} +(0.193693 + 0.171597i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\) \(q+(1.97256 + 0.486192i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.88370 + 0.988640i) q^{4} +(2.48102 - 1.86436i) q^{5} +(-1.40733 - 1.46519i) q^{6} +(1.36867 - 0.718334i) q^{7} +(0.193693 + 0.171597i) q^{8} +(0.428693 + 0.903450i) q^{9} +(5.80039 - 2.47132i) q^{10} +(-2.02107 - 2.10416i) q^{11} +(-1.06369 - 1.84236i) q^{12} +(-2.62302 + 4.54320i) q^{13} +(3.04903 - 0.751519i) q^{14} +(-3.09337 + 0.249723i) q^{15} +(-2.11833 - 3.06893i) q^{16} +(5.45492 - 4.09911i) q^{17} +(0.406371 + 1.99054i) q^{18} +(-0.471643 + 2.31026i) q^{19} +(6.51667 - 1.05906i) q^{20} +(-1.54071 - 0.124379i) q^{21} +(-2.96366 - 5.13321i) q^{22} +(2.01878 + 2.92471i) q^{23} +(-0.0719946 - 0.248554i) q^{24} +(1.28851 - 4.44845i) q^{25} +(-7.38292 + 7.68644i) q^{26} +(0.120537 - 0.992709i) q^{27} +3.28833 q^{28} +(-0.504426 + 4.15432i) q^{29} +(-6.22327 - 1.01138i) q^{30} +(2.64319 + 3.23732i) q^{31} +(-2.86996 - 7.56747i) q^{32} +(0.583589 + 2.85861i) q^{33} +(12.7531 - 5.43359i) q^{34} +(2.05646 - 4.33390i) q^{35} +(-0.0856607 + 2.12565i) q^{36} +(5.47005 + 4.11047i) q^{37} +(-2.05357 + 4.32782i) q^{38} +(4.64513 - 2.43795i) q^{39} +(0.800474 + 0.0646210i) q^{40} +(-6.31796 + 9.15314i) q^{41} +(-2.97867 - 0.994428i) q^{42} +(-1.87651 + 1.18664i) q^{43} +(-1.72683 - 5.96171i) q^{44} +(2.74795 + 1.44224i) q^{45} +(2.56020 + 6.75069i) q^{46} +(-7.18090 - 3.05950i) q^{47} +(0.150153 + 3.72601i) q^{48} +(-2.61920 + 3.79456i) q^{49} +(4.70446 - 8.14836i) q^{50} +(-6.80128 + 0.549056i) q^{51} +(-9.43255 + 5.96478i) q^{52} +(5.59251 - 1.86705i) q^{53} +(0.720413 - 1.89957i) q^{54} +(-8.93723 - 1.45244i) q^{55} +(0.388366 + 0.0957236i) q^{56} +(1.63338 - 1.70053i) q^{57} +(-3.01481 + 7.94939i) q^{58} +(-4.15848 + 3.68410i) q^{59} +(-6.07385 - 2.58783i) q^{60} +(2.13863 - 10.4757i) q^{61} +(3.63989 + 7.67091i) q^{62} +(1.23572 + 0.928582i) q^{63} +(-1.08296 - 8.91897i) q^{64} +(1.96242 + 16.1620i) q^{65} +(-0.238669 + 5.92251i) q^{66} +(-7.92816 - 7.02374i) q^{67} +(14.3280 - 2.32852i) q^{68} +(-0.143097 - 3.55091i) q^{69} +(6.16360 - 7.54904i) q^{70} +(9.71557 - 3.24353i) q^{71} +(-0.0719946 + 0.248554i) q^{72} +(-0.780396 - 0.493492i) q^{73} +(8.79151 + 10.7676i) q^{74} +(-3.46658 + 3.07112i) q^{75} +(-3.17245 + 3.88554i) q^{76} +(-4.27767 - 1.42810i) q^{77} +(10.3481 - 2.55058i) q^{78} +(-14.1027 + 3.47601i) q^{79} +(-10.9772 - 3.66473i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-16.9127 + 14.9834i) q^{82} +(-8.17297 - 10.0101i) q^{83} +(-2.77927 - 1.75750i) q^{84} +(5.89153 - 20.3399i) q^{85} +(-4.27847 + 1.42836i) q^{86} +(2.64668 - 3.24159i) q^{87} +(-0.0304001 - 0.754370i) q^{88} +(2.80827 - 0.456388i) q^{89} +(4.71930 + 4.18093i) q^{90} +(-0.326513 + 8.10235i) q^{91} +(0.911286 + 7.50512i) q^{92} +(-0.503761 - 4.14885i) q^{93} +(-12.6772 - 9.52633i) q^{94} +(3.13701 + 6.61111i) q^{95} +(-1.61889 + 7.92985i) q^{96} +(-7.31869 - 3.11820i) q^{97} +(-7.01141 + 6.21156i) q^{98} +(1.03458 - 2.72797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(1\) \(e\left(\frac{31}{39}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.97256 + 0.486192i 1.39481 + 0.343790i 0.863911 0.503645i \(-0.168008\pi\)
0.530899 + 0.847435i \(0.321854\pi\)
\(3\) −0.845190 0.534466i −0.487971 0.308574i
\(4\) 1.88370 + 0.988640i 0.941848 + 0.494320i
\(5\) 2.48102 1.86436i 1.10954 0.833769i 0.122223 0.992503i \(-0.460998\pi\)
0.987321 + 0.158734i \(0.0507412\pi\)
\(6\) −1.40733 1.46519i −0.574542 0.598161i
\(7\) 1.36867 0.718334i 0.517309 0.271505i −0.185799 0.982588i \(-0.559487\pi\)
0.703108 + 0.711083i \(0.251795\pi\)
\(8\) 0.193693 + 0.171597i 0.0684808 + 0.0606687i
\(9\) 0.428693 + 0.903450i 0.142898 + 0.301150i
\(10\) 5.80039 2.47132i 1.83425 0.781499i
\(11\) −2.02107 2.10416i −0.609376 0.634428i 0.343007 0.939333i \(-0.388555\pi\)
−0.952383 + 0.304905i \(0.901375\pi\)
\(12\) −1.06369 1.84236i −0.307060 0.531843i
\(13\) −2.62302 + 4.54320i −0.727494 + 1.26006i 0.230446 + 0.973085i \(0.425982\pi\)
−0.957939 + 0.286971i \(0.907352\pi\)
\(14\) 3.04903 0.751519i 0.814889 0.200852i
\(15\) −3.09337 + 0.249723i −0.798705 + 0.0644781i
\(16\) −2.11833 3.06893i −0.529583 0.767233i
\(17\) 5.45492 4.09911i 1.32301 0.994180i 0.324174 0.945997i \(-0.394914\pi\)
0.998839 0.0481823i \(-0.0153429\pi\)
\(18\) 0.406371 + 1.99054i 0.0957826 + 0.469174i
\(19\) −0.471643 + 2.31026i −0.108202 + 0.530010i 0.889171 + 0.457575i \(0.151282\pi\)
−0.997373 + 0.0724347i \(0.976923\pi\)
\(20\) 6.51667 1.05906i 1.45717 0.236813i
\(21\) −1.54071 0.124379i −0.336211 0.0271418i
\(22\) −2.96366 5.13321i −0.631854 1.09440i
\(23\) 2.01878 + 2.92471i 0.420945 + 0.609845i 0.974884 0.222713i \(-0.0714912\pi\)
−0.553939 + 0.832557i \(0.686876\pi\)
\(24\) −0.0719946 0.248554i −0.0146958 0.0507359i
\(25\) 1.28851 4.44845i 0.257702 0.889689i
\(26\) −7.38292 + 7.68644i −1.44791 + 1.50743i
\(27\) 0.120537 0.992709i 0.0231973 0.191047i
\(28\) 3.28833 0.621437
\(29\) −0.504426 + 4.15432i −0.0936695 + 0.771438i 0.867874 + 0.496785i \(0.165486\pi\)
−0.961543 + 0.274653i \(0.911437\pi\)
\(30\) −6.22327 1.01138i −1.13621 0.184652i
\(31\) 2.64319 + 3.23732i 0.474731 + 0.581440i 0.955345 0.295492i \(-0.0954837\pi\)
−0.480614 + 0.876932i \(0.659586\pi\)
\(32\) −2.86996 7.56747i −0.507343 1.33775i
\(33\) 0.583589 + 2.85861i 0.101590 + 0.497620i
\(34\) 12.7531 5.43359i 2.18714 0.931854i
\(35\) 2.05646 4.33390i 0.347605 0.732563i
\(36\) −0.0856607 + 2.12565i −0.0142768 + 0.354275i
\(37\) 5.47005 + 4.11047i 0.899270 + 0.675758i 0.946353 0.323133i \(-0.104736\pi\)
−0.0470832 + 0.998891i \(0.514993\pi\)
\(38\) −2.05357 + 4.32782i −0.333134 + 0.702064i
\(39\) 4.64513 2.43795i 0.743816 0.390385i
\(40\) 0.800474 + 0.0646210i 0.126566 + 0.0102175i
\(41\) −6.31796 + 9.15314i −0.986699 + 1.42948i −0.0853684 + 0.996349i \(0.527207\pi\)
−0.901331 + 0.433131i \(0.857409\pi\)
\(42\) −2.97867 0.994428i −0.459619 0.153444i
\(43\) −1.87651 + 1.18664i −0.286166 + 0.180960i −0.669834 0.742511i \(-0.733635\pi\)
0.383669 + 0.923471i \(0.374661\pi\)
\(44\) −1.72683 5.96171i −0.260329 0.898761i
\(45\) 2.74795 + 1.44224i 0.409641 + 0.214996i
\(46\) 2.56020 + 6.75069i 0.377481 + 0.995334i
\(47\) −7.18090 3.05950i −1.04744 0.446273i −0.201467 0.979495i \(-0.564571\pi\)
−0.845975 + 0.533222i \(0.820981\pi\)
\(48\) 0.150153 + 3.72601i 0.0216727 + 0.537802i
\(49\) −2.61920 + 3.79456i −0.374171 + 0.542080i
\(50\) 4.70446 8.14836i 0.665311 1.15235i
\(51\) −6.80128 + 0.549056i −0.952370 + 0.0768832i
\(52\) −9.43255 + 5.96478i −1.30806 + 0.827167i
\(53\) 5.59251 1.86705i 0.768190 0.256459i 0.0945508 0.995520i \(-0.469859\pi\)
0.673639 + 0.739061i \(0.264730\pi\)
\(54\) 0.720413 1.89957i 0.0980358 0.258499i
\(55\) −8.93723 1.45244i −1.20510 0.195847i
\(56\) 0.388366 + 0.0957236i 0.0518976 + 0.0127916i
\(57\) 1.63338 1.70053i 0.216347 0.225241i
\(58\) −3.01481 + 7.94939i −0.395864 + 1.04381i
\(59\) −4.15848 + 3.68410i −0.541389 + 0.479628i −0.888934 0.458035i \(-0.848554\pi\)
0.347546 + 0.937663i \(0.387015\pi\)
\(60\) −6.07385 2.58783i −0.784131 0.334087i
\(61\) 2.13863 10.4757i 0.273824 1.34128i −0.577395 0.816465i \(-0.695931\pi\)
0.851218 0.524812i \(-0.175864\pi\)
\(62\) 3.63989 + 7.67091i 0.462266 + 0.974206i
\(63\) 1.23572 + 0.928582i 0.155686 + 0.116990i
\(64\) −1.08296 8.91897i −0.135370 1.11487i
\(65\) 1.96242 + 16.1620i 0.243409 + 2.00465i
\(66\) −0.238669 + 5.92251i −0.0293781 + 0.729011i
\(67\) −7.92816 7.02374i −0.968579 0.858086i 0.0213329 0.999772i \(-0.493209\pi\)
−0.989912 + 0.141687i \(0.954747\pi\)
\(68\) 14.3280 2.32852i 1.73752 0.282374i
\(69\) −0.143097 3.55091i −0.0172268 0.427479i
\(70\) 6.16360 7.54904i 0.736691 0.902283i
\(71\) 9.71557 3.24353i 1.15303 0.384937i 0.325048 0.945697i \(-0.394619\pi\)
0.827978 + 0.560761i \(0.189491\pi\)
\(72\) −0.0719946 + 0.248554i −0.00848465 + 0.0292924i
\(73\) −0.780396 0.493492i −0.0913384 0.0577589i 0.488016 0.872835i \(-0.337721\pi\)
−0.579354 + 0.815076i \(0.696695\pi\)
\(74\) 8.79151 + 10.7676i 1.02199 + 1.25171i
\(75\) −3.46658 + 3.07112i −0.400286 + 0.354622i
\(76\) −3.17245 + 3.88554i −0.363905 + 0.445702i
\(77\) −4.27767 1.42810i −0.487486 0.162747i
\(78\) 10.3481 2.55058i 1.17169 0.288796i
\(79\) −14.1027 + 3.47601i −1.58668 + 0.391082i −0.931311 0.364225i \(-0.881334\pi\)
−0.655371 + 0.755307i \(0.727488\pi\)
\(80\) −10.9772 3.66473i −1.22729 0.409730i
\(81\) −0.632445 + 0.774605i −0.0702717 + 0.0860672i
\(82\) −16.9127 + 14.9834i −1.86770 + 1.65464i
\(83\) −8.17297 10.0101i −0.897100 1.09875i −0.994628 0.103515i \(-0.966991\pi\)
0.0975284 0.995233i \(-0.468906\pi\)
\(84\) −2.77927 1.75750i −0.303243 0.191759i
\(85\) 5.89153 20.3399i 0.639026 2.20617i
\(86\) −4.27847 + 1.42836i −0.461359 + 0.154024i
\(87\) 2.64668 3.24159i 0.283754 0.347535i
\(88\) −0.0304001 0.754370i −0.00324066 0.0804161i
\(89\) 2.80827 0.456388i 0.297676 0.0483770i −0.00973915 0.999953i \(-0.503100\pi\)
0.307415 + 0.951576i \(0.400536\pi\)
\(90\) 4.71930 + 4.18093i 0.497458 + 0.440709i
\(91\) −0.326513 + 8.10235i −0.0342279 + 0.849357i
\(92\) 0.911286 + 7.50512i 0.0950082 + 0.782463i
\(93\) −0.503761 4.14885i −0.0522376 0.430215i
\(94\) −12.6772 9.52633i −1.30756 0.982566i
\(95\) 3.13701 + 6.61111i 0.321850 + 0.678286i
\(96\) −1.61889 + 7.92985i −0.165227 + 0.809337i
\(97\) −7.31869 3.11820i −0.743100 0.316605i −0.0129721 0.999916i \(-0.504129\pi\)
−0.730128 + 0.683311i \(0.760540\pi\)
\(98\) −7.01141 + 6.21156i −0.708259 + 0.627463i
\(99\) 1.03458 2.72797i 0.103980 0.274172i
\(100\) 6.82507 7.10565i 0.682507 0.710565i
\(101\) 10.4984 + 2.58763i 1.04463 + 0.257479i 0.724055 0.689743i \(-0.242276\pi\)
0.320579 + 0.947222i \(0.396122\pi\)
\(102\) −13.6829 2.22368i −1.35481 0.220177i
\(103\) −2.47791 + 6.53371i −0.244156 + 0.643786i −0.999939 0.0110360i \(-0.996487\pi\)
0.755783 + 0.654822i \(0.227256\pi\)
\(104\) −1.28766 + 0.429883i −0.126265 + 0.0421535i
\(105\) −4.05442 + 2.56386i −0.395671 + 0.250207i
\(106\) 11.9393 0.963840i 1.15965 0.0936164i
\(107\) −6.69845 + 11.6021i −0.647564 + 1.12161i 0.336139 + 0.941812i \(0.390879\pi\)
−0.983703 + 0.179801i \(0.942455\pi\)
\(108\) 1.20849 1.75079i 0.116287 0.168470i
\(109\) 0.175142 + 4.34609i 0.0167755 + 0.416280i 0.985658 + 0.168757i \(0.0539755\pi\)
−0.968882 + 0.247523i \(0.920384\pi\)
\(110\) −16.9231 7.21024i −1.61355 0.687469i
\(111\) −2.42632 6.39769i −0.230296 0.607241i
\(112\) −5.10382 2.67869i −0.482265 0.253112i
\(113\) 3.27460 + 11.3052i 0.308048 + 1.06351i 0.953920 + 0.300060i \(0.0970066\pi\)
−0.645872 + 0.763445i \(0.723506\pi\)
\(114\) 4.04873 2.56026i 0.379198 0.239791i
\(115\) 10.4614 + 3.49252i 0.975527 + 0.325679i
\(116\) −5.05731 + 7.32678i −0.469559 + 0.680274i
\(117\) −5.22902 0.422130i −0.483423 0.0390260i
\(118\) −9.99404 + 5.24527i −0.920026 + 0.482867i
\(119\) 4.52147 9.52879i 0.414482 0.873503i
\(120\) −0.642015 0.482443i −0.0586077 0.0440408i
\(121\) 0.100173 2.48577i 0.00910665 0.225979i
\(122\) 9.31179 19.6242i 0.843049 1.77669i
\(123\) 10.2319 4.35941i 0.922581 0.393075i
\(124\) 1.77842 + 8.71129i 0.159707 + 0.782297i
\(125\) 0.405753 + 1.06988i 0.0362916 + 0.0956932i
\(126\) 1.98606 + 2.43248i 0.176932 + 0.216703i
\(127\) 6.62377 + 1.07647i 0.587764 + 0.0955210i 0.447018 0.894525i \(-0.352486\pi\)
0.140746 + 0.990046i \(0.455050\pi\)
\(128\) 0.249025 2.05091i 0.0220109 0.181276i
\(129\) 2.22023 0.195480
\(130\) −3.98685 + 32.8346i −0.349670 + 2.87979i
\(131\) 9.22784 9.60720i 0.806240 0.839385i −0.183387 0.983041i \(-0.558706\pi\)
0.989628 + 0.143656i \(0.0458857\pi\)
\(132\) −1.72683 + 5.96171i −0.150301 + 0.518900i
\(133\) 1.01401 + 3.50078i 0.0879262 + 0.303556i
\(134\) −12.2239 17.7093i −1.05598 1.52985i
\(135\) −1.55172 2.68765i −0.133551 0.231316i
\(136\) 1.75997 + 0.142080i 0.150916 + 0.0121832i
\(137\) 8.05644 1.30930i 0.688308 0.111861i 0.193809 0.981039i \(-0.437916\pi\)
0.494499 + 0.869178i \(0.335352\pi\)
\(138\) 1.44416 7.07395i 0.122935 0.602175i
\(139\) −2.48630 12.1787i −0.210886 1.03299i −0.938044 0.346516i \(-0.887365\pi\)
0.727159 0.686470i \(-0.240840\pi\)
\(140\) 8.15841 6.13065i 0.689512 0.518134i
\(141\) 4.43403 + 6.42380i 0.373413 + 0.540982i
\(142\) 20.7415 1.67443i 1.74059 0.140515i
\(143\) 14.8609 3.66289i 1.24273 0.306306i
\(144\) 1.86451 3.22943i 0.155376 0.269120i
\(145\) 6.49367 + 11.2474i 0.539270 + 0.934043i
\(146\) −1.29944 1.35287i −0.107543 0.111964i
\(147\) 4.24178 1.80725i 0.349856 0.149060i
\(148\) 6.24013 + 13.1508i 0.512935 + 1.08099i
\(149\) 9.08287 + 8.04672i 0.744097 + 0.659213i 0.947454 0.319892i \(-0.103647\pi\)
−0.203357 + 0.979105i \(0.565185\pi\)
\(150\) −8.33118 + 4.37254i −0.680238 + 0.357017i
\(151\) 5.45086 + 5.67494i 0.443584 + 0.461820i 0.905030 0.425348i \(-0.139848\pi\)
−0.461445 + 0.887169i \(0.652669\pi\)
\(152\) −0.487787 + 0.366548i −0.0395648 + 0.0297310i
\(153\) 6.04183 + 3.17099i 0.488453 + 0.256360i
\(154\) −7.74363 4.89678i −0.624000 0.394593i
\(155\) 12.5933 + 3.10398i 1.01152 + 0.249318i
\(156\) 11.1603 0.893537
\(157\) 6.09269 10.9489i 0.486250 0.873820i
\(158\) −29.5085 −2.34757
\(159\) −5.72461 1.41099i −0.453991 0.111899i
\(160\) −21.2290 13.4244i −1.67830 1.06129i
\(161\) 4.86397 + 2.55281i 0.383335 + 0.201190i
\(162\) −1.62414 + 1.22046i −0.127605 + 0.0958887i
\(163\) −4.11920 4.28854i −0.322641 0.335905i 0.540053 0.841631i \(-0.318404\pi\)
−0.862694 + 0.505726i \(0.831225\pi\)
\(164\) −20.9503 + 10.9955i −1.63594 + 0.858608i
\(165\) 6.77738 + 6.00423i 0.527618 + 0.467429i
\(166\) −11.2548 23.7191i −0.873545 1.84096i
\(167\) 14.8231 6.31554i 1.14705 0.488711i 0.267046 0.963684i \(-0.413952\pi\)
0.880000 + 0.474973i \(0.157542\pi\)
\(168\) −0.277082 0.288473i −0.0213773 0.0222562i
\(169\) −7.26043 12.5754i −0.558494 0.967341i
\(170\) 21.5105 37.2573i 1.64978 2.85750i
\(171\) −2.28940 + 0.564285i −0.175074 + 0.0431520i
\(172\) −4.70794 + 0.380064i −0.358977 + 0.0289796i
\(173\) −1.38047 1.99996i −0.104955 0.152054i 0.766987 0.641663i \(-0.221755\pi\)
−0.871942 + 0.489608i \(0.837140\pi\)
\(174\) 6.79677 5.10744i 0.515261 0.387194i
\(175\) −1.43193 7.01404i −0.108243 0.530212i
\(176\) −2.17622 + 10.6598i −0.164039 + 0.803515i
\(177\) 5.48373 0.891193i 0.412183 0.0669862i
\(178\) 5.76137 + 0.465106i 0.431833 + 0.0348612i
\(179\) −1.98917 3.44534i −0.148677 0.257517i 0.782061 0.623201i \(-0.214168\pi\)
−0.930739 + 0.365684i \(0.880835\pi\)
\(180\) 3.75046 + 5.43347i 0.279542 + 0.404987i
\(181\) −4.90013 16.9172i −0.364223 1.25745i −0.908268 0.418389i \(-0.862595\pi\)
0.544045 0.839056i \(-0.316892\pi\)
\(182\) −4.58336 + 15.8236i −0.339742 + 1.17292i
\(183\) −7.40646 + 7.71094i −0.547501 + 0.570009i
\(184\) −0.110848 + 0.912913i −0.00817180 + 0.0673008i
\(185\) 21.2347 1.56121
\(186\) 1.02344 8.42877i 0.0750421 0.618027i
\(187\) −19.6500 3.19343i −1.43695 0.233527i
\(188\) −10.5019 12.8625i −0.765929 0.938093i
\(189\) −0.548122 1.44528i −0.0398700 0.105128i
\(190\) 2.97367 + 14.5660i 0.215733 + 1.05673i
\(191\) 15.3784 6.55214i 1.11274 0.474096i 0.244209 0.969723i \(-0.421472\pi\)
0.868536 + 0.495626i \(0.165061\pi\)
\(192\) −3.85158 + 8.11703i −0.277964 + 0.585796i
\(193\) −0.888026 + 22.0361i −0.0639215 + 1.58620i 0.575801 + 0.817590i \(0.304690\pi\)
−0.639722 + 0.768606i \(0.720951\pi\)
\(194\) −12.9205 9.70912i −0.927638 0.697074i
\(195\) 6.97942 14.7088i 0.499807 1.05332i
\(196\) −8.68522 + 4.55836i −0.620373 + 0.325597i
\(197\) −20.1102 1.62346i −1.43279 0.115667i −0.660447 0.750873i \(-0.729633\pi\)
−0.772342 + 0.635206i \(0.780915\pi\)
\(198\) 3.36710 4.87809i 0.239289 0.346670i
\(199\) −11.3091 3.77554i −0.801682 0.267641i −0.113838 0.993499i \(-0.536314\pi\)
−0.687844 + 0.725859i \(0.741443\pi\)
\(200\) 1.01291 0.640528i 0.0716239 0.0452922i
\(201\) 2.94685 + 10.1737i 0.207855 + 0.717599i
\(202\) 19.4507 + 10.2085i 1.36855 + 0.718269i
\(203\) 2.29380 + 6.04824i 0.160993 + 0.424504i
\(204\) −13.3544 5.68976i −0.934992 0.398363i
\(205\) 1.38982 + 34.4881i 0.0970694 + 2.40875i
\(206\) −8.06446 + 11.6834i −0.561878 + 0.814020i
\(207\) −1.77690 + 3.07767i −0.123503 + 0.213913i
\(208\) 19.4992 1.57414i 1.35202 0.109147i
\(209\) 5.81438 3.67679i 0.402189 0.254329i
\(210\) −9.24412 + 3.08614i −0.637905 + 0.212964i
\(211\) 5.85113 15.4282i 0.402808 1.06212i −0.568162 0.822917i \(-0.692345\pi\)
0.970970 0.239201i \(-0.0768856\pi\)
\(212\) 12.3804 + 2.01201i 0.850291 + 0.138186i
\(213\) −9.94506 2.45124i −0.681424 0.167956i
\(214\) −18.8539 + 19.6290i −1.28883 + 1.34181i
\(215\) −2.44334 + 6.44257i −0.166635 + 0.439380i
\(216\) 0.193693 0.171597i 0.0131791 0.0116757i
\(217\) 5.94314 + 2.53213i 0.403446 + 0.171892i
\(218\) −1.76756 + 8.65808i −0.119714 + 0.586399i
\(219\) 0.395828 + 0.834190i 0.0267476 + 0.0563693i
\(220\) −15.3991 11.5717i −1.03821 0.780161i
\(221\) 4.31471 + 35.5348i 0.290239 + 2.39033i
\(222\) −1.67556 13.7995i −0.112456 0.926160i
\(223\) 0.0378825 0.940045i 0.00253680 0.0629501i −0.997425 0.0717210i \(-0.977151\pi\)
0.999962 + 0.00877091i \(0.00279190\pi\)
\(224\) −9.36401 8.29579i −0.625659 0.554286i
\(225\) 4.57132 0.742913i 0.304755 0.0495275i
\(226\) 0.962826 + 23.8923i 0.0640463 + 1.58929i
\(227\) 0.854165 1.04616i 0.0566929 0.0694362i −0.745480 0.666528i \(-0.767780\pi\)
0.802173 + 0.597092i \(0.203677\pi\)
\(228\) 4.75801 1.58846i 0.315107 0.105198i
\(229\) −3.40583 + 11.7583i −0.225064 + 0.777010i 0.765909 + 0.642948i \(0.222289\pi\)
−0.990973 + 0.134061i \(0.957198\pi\)
\(230\) 18.9376 + 11.9754i 1.24871 + 0.789636i
\(231\) 2.85218 + 3.49328i 0.187659 + 0.229841i
\(232\) −0.810572 + 0.718104i −0.0532167 + 0.0471459i
\(233\) 16.6465 20.3883i 1.09055 1.33568i 0.152846 0.988250i \(-0.451156\pi\)
0.937705 0.347432i \(-0.112946\pi\)
\(234\) −10.1093 3.37499i −0.660867 0.220630i
\(235\) −23.5200 + 5.79715i −1.53427 + 0.378164i
\(236\) −11.4756 + 2.82847i −0.746995 + 0.184118i
\(237\) 13.7773 + 4.59954i 0.894932 + 0.298772i
\(238\) 13.5517 16.5978i 0.878425 1.07588i
\(239\) −2.93899 + 2.60372i −0.190108 + 0.168421i −0.752808 0.658240i \(-0.771301\pi\)
0.562700 + 0.826661i \(0.309763\pi\)
\(240\) 7.31916 + 8.96434i 0.472450 + 0.578646i
\(241\) −12.4467 7.87079i −0.801759 0.507002i 0.0696424 0.997572i \(-0.477814\pi\)
−0.871402 + 0.490570i \(0.836789\pi\)
\(242\) 1.40616 4.85463i 0.0903913 0.312067i
\(243\) 0.948536 0.316668i 0.0608486 0.0203143i
\(244\) 14.3852 17.6187i 0.920920 1.12792i
\(245\) 0.576170 + 14.2975i 0.0368101 + 0.913434i
\(246\) 22.3026 3.62452i 1.42196 0.231091i
\(247\) −9.25884 8.20262i −0.589126 0.521920i
\(248\) −0.0435471 + 1.08061i −0.00276524 + 0.0686187i
\(249\) 1.55767 + 12.8286i 0.0987134 + 0.812978i
\(250\) 0.280203 + 2.30768i 0.0177216 + 0.145950i
\(251\) −24.1892 18.1770i −1.52681 1.14732i −0.941743 0.336335i \(-0.890813\pi\)
−0.585065 0.810987i \(-0.698931\pi\)
\(252\) 1.40968 + 2.97085i 0.0888018 + 0.187146i
\(253\) 2.07395 10.1589i 0.130388 0.638684i
\(254\) 12.5424 + 5.34382i 0.786981 + 0.335301i
\(255\) −15.8505 + 14.0423i −0.992594 + 0.879361i
\(256\) −4.88352 + 12.8768i −0.305220 + 0.804800i
\(257\) 5.85121 6.09176i 0.364989 0.379993i −0.513231 0.858250i \(-0.671552\pi\)
0.878220 + 0.478257i \(0.158731\pi\)
\(258\) 4.37953 + 1.07946i 0.272658 + 0.0672041i
\(259\) 10.4394 + 1.69657i 0.648672 + 0.105419i
\(260\) −12.2818 + 32.3844i −0.761685 + 2.00840i
\(261\) −3.96947 + 1.32520i −0.245704 + 0.0820280i
\(262\) 22.8734 14.4643i 1.41312 0.893606i
\(263\) −4.76272 + 0.384487i −0.293682 + 0.0237085i −0.226430 0.974028i \(-0.572705\pi\)
−0.0672525 + 0.997736i \(0.521423\pi\)
\(264\) −0.377491 + 0.653834i −0.0232330 + 0.0402407i
\(265\) 10.3942 15.0587i 0.638513 0.925046i
\(266\) 0.298150 + 7.39851i 0.0182807 + 0.453632i
\(267\) −2.61744 1.11519i −0.160185 0.0682485i
\(268\) −7.99029 21.0687i −0.488085 1.28697i
\(269\) −25.9575 13.6235i −1.58266 0.830642i −0.999837 0.0180388i \(-0.994258\pi\)
−0.582818 0.812603i \(-0.698050\pi\)
\(270\) −1.75414 6.05599i −0.106753 0.368556i
\(271\) 3.97403 2.51303i 0.241405 0.152655i −0.408285 0.912855i \(-0.633873\pi\)
0.649690 + 0.760199i \(0.274899\pi\)
\(272\) −24.1352 8.05752i −1.46341 0.488559i
\(273\) 4.60639 6.67351i 0.278792 0.403899i
\(274\) 16.5284 + 1.33431i 0.998516 + 0.0806086i
\(275\) −11.9644 + 6.27940i −0.721481 + 0.378662i
\(276\) 3.24102 6.83030i 0.195086 0.411136i
\(277\) −10.3017 7.74125i −0.618971 0.465127i 0.244415 0.969671i \(-0.421404\pi\)
−0.863386 + 0.504544i \(0.831661\pi\)
\(278\) 1.01682 25.2321i 0.0609847 1.51332i
\(279\) −1.79164 + 3.77581i −0.107263 + 0.226052i
\(280\) 1.14201 0.486563i 0.0682479 0.0290777i
\(281\) 0.0297816 + 0.145880i 0.00177662 + 0.00870247i 0.980669 0.195672i \(-0.0626890\pi\)
−0.978893 + 0.204375i \(0.934484\pi\)
\(282\) 5.62318 + 14.8271i 0.334856 + 0.882942i
\(283\) 3.52468 + 4.31694i 0.209520 + 0.256616i 0.868665 0.495401i \(-0.164979\pi\)
−0.659144 + 0.752017i \(0.729081\pi\)
\(284\) 21.5079 + 3.49537i 1.27626 + 0.207412i
\(285\) 0.882042 7.26427i 0.0522477 0.430298i
\(286\) 31.0949 1.83868
\(287\) −2.07219 + 17.0660i −0.122318 + 1.00738i
\(288\) 5.60651 5.83699i 0.330367 0.343948i
\(289\) 8.22379 28.3918i 0.483752 1.67011i
\(290\) 7.34077 + 25.3433i 0.431065 + 1.48821i
\(291\) 4.51911 + 6.54706i 0.264915 + 0.383795i
\(292\) −0.982142 1.70112i −0.0574755 0.0995505i
\(293\) −17.9475 1.44887i −1.04850 0.0846438i −0.455813 0.890076i \(-0.650651\pi\)
−0.592688 + 0.805432i \(0.701933\pi\)
\(294\) 9.24584 1.50260i 0.539228 0.0876331i
\(295\) −3.44878 + 16.8932i −0.200796 + 0.983562i
\(296\) 0.354165 + 1.73481i 0.0205854 + 0.100834i
\(297\) −2.33243 + 1.75271i −0.135341 + 0.101702i
\(298\) 14.0042 + 20.2886i 0.811244 + 1.17529i
\(299\) −18.5828 + 1.50016i −1.07467 + 0.0867566i
\(300\) −9.56621 + 2.35786i −0.552305 + 0.136131i
\(301\) −1.71593 + 2.97208i −0.0989046 + 0.171308i
\(302\) 7.99302 + 13.8443i 0.459947 + 0.796651i
\(303\) −7.49018 7.79810i −0.430299 0.447989i
\(304\) 8.08912 3.44645i 0.463943 0.197668i
\(305\) −14.2245 29.9776i −0.814495 1.71651i
\(306\) 10.3761 + 9.19246i 0.593165 + 0.525498i
\(307\) −7.12898 + 3.74158i −0.406873 + 0.213543i −0.655728 0.754998i \(-0.727638\pi\)
0.248855 + 0.968541i \(0.419946\pi\)
\(308\) −6.64596 6.91917i −0.378689 0.394257i
\(309\) 5.58635 4.19787i 0.317796 0.238808i
\(310\) 23.3320 + 12.2456i 1.32517 + 0.695502i
\(311\) 9.21851 + 5.82943i 0.522734 + 0.330557i 0.769635 0.638484i \(-0.220438\pi\)
−0.246901 + 0.969041i \(0.579412\pi\)
\(312\) 1.31807 + 0.324876i 0.0746212 + 0.0183925i
\(313\) 27.7166 1.56664 0.783318 0.621621i \(-0.213525\pi\)
0.783318 + 0.621621i \(0.213525\pi\)
\(314\) 17.3415 18.6352i 0.978636 1.05165i
\(315\) 4.79705 0.270283
\(316\) −30.0018 7.39478i −1.68773 0.415989i
\(317\) 20.2689 + 12.8173i 1.13841 + 0.719889i 0.964294 0.264836i \(-0.0853177\pi\)
0.174119 + 0.984725i \(0.444292\pi\)
\(318\) −10.6061 5.56652i −0.594761 0.312155i
\(319\) 9.76083 7.33479i 0.546501 0.410669i
\(320\) −19.3150 20.1091i −1.07974 1.12413i
\(321\) 11.8624 6.22585i 0.662093 0.347493i
\(322\) 8.35332 + 7.40039i 0.465512 + 0.412408i
\(323\) 6.89723 + 14.5356i 0.383772 + 0.808783i
\(324\) −1.95714 + 0.833859i −0.108730 + 0.0463255i
\(325\) 16.8304 + 17.5223i 0.933582 + 0.971962i
\(326\) −6.04031 10.4621i −0.334542 0.579444i
\(327\) 2.17481 3.76688i 0.120267 0.208309i
\(328\) −2.79439 + 0.688756i −0.154295 + 0.0380302i
\(329\) −12.0260 + 0.970842i −0.663017 + 0.0535242i
\(330\) 10.4496 + 15.1388i 0.575230 + 0.833364i
\(331\) −0.264442 + 0.198715i −0.0145350 + 0.0109224i −0.607985 0.793949i \(-0.708022\pi\)
0.593450 + 0.804871i \(0.297766\pi\)
\(332\) −5.49903 26.9360i −0.301799 1.47831i
\(333\) −1.36864 + 6.70405i −0.0750011 + 0.367379i
\(334\) 32.3100 5.25089i 1.76793 0.287316i
\(335\) −32.7647 2.64504i −1.79013 0.144514i
\(336\) 2.88203 + 4.99182i 0.157227 + 0.272326i
\(337\) −9.41837 13.6449i −0.513051 0.743283i 0.477767 0.878487i \(-0.341446\pi\)
−0.990818 + 0.135204i \(0.956831\pi\)
\(338\) −8.20755 28.3357i −0.446432 1.54126i
\(339\) 3.27460 11.3052i 0.177852 0.614015i
\(340\) 31.2067 32.4896i 1.69242 1.76200i
\(341\) 1.46976 12.1045i 0.0795919 0.655498i
\(342\) −4.79032 −0.259031
\(343\) −2.16327 + 17.8161i −0.116806 + 0.961982i
\(344\) −0.567090 0.0921612i −0.0305755 0.00496900i
\(345\) −6.97521 8.54308i −0.375533 0.459944i
\(346\) −1.75070 4.61622i −0.0941183 0.248169i
\(347\) 6.74319 + 33.0303i 0.361993 + 1.77316i 0.598089 + 0.801430i \(0.295927\pi\)
−0.236095 + 0.971730i \(0.575868\pi\)
\(348\) 8.19030 3.48956i 0.439046 0.187060i
\(349\) 10.7962 22.7525i 0.577908 1.21792i −0.378424 0.925632i \(-0.623534\pi\)
0.956332 0.292283i \(-0.0944149\pi\)
\(350\) 0.585612 14.5318i 0.0313023 0.776758i
\(351\) 4.19390 + 3.15151i 0.223854 + 0.168215i
\(352\) −10.1228 + 21.3333i −0.539545 + 1.13707i
\(353\) 16.3189 8.56482i 0.868567 0.455859i 0.0292952 0.999571i \(-0.490674\pi\)
0.839272 + 0.543711i \(0.182981\pi\)
\(354\) 11.2503 + 0.908216i 0.597946 + 0.0482712i
\(355\) 18.0574 26.1606i 0.958386 1.38846i
\(356\) 5.74113 + 1.91667i 0.304279 + 0.101583i
\(357\) −8.91431 + 5.63707i −0.471795 + 0.298345i
\(358\) −2.24866 7.76326i −0.118845 0.410301i
\(359\) −0.630804 0.331072i −0.0332926 0.0174733i 0.447995 0.894036i \(-0.352138\pi\)
−0.481287 + 0.876563i \(0.659831\pi\)
\(360\) 0.284776 + 0.750891i 0.0150090 + 0.0395755i
\(361\) 12.3648 + 5.26813i 0.650777 + 0.277270i
\(362\) −1.44078 35.7526i −0.0757257 1.87911i
\(363\) −1.41322 + 2.04741i −0.0741750 + 0.107461i
\(364\) −8.62535 + 14.9395i −0.452091 + 0.783045i
\(365\) −2.85622 + 0.230578i −0.149502 + 0.0120690i
\(366\) −18.3587 + 11.6093i −0.959623 + 0.606829i
\(367\) −2.65318 + 0.885762i −0.138495 + 0.0462364i −0.385070 0.922887i \(-0.625823\pi\)
0.246576 + 0.969124i \(0.420695\pi\)
\(368\) 4.69929 12.3910i 0.244967 0.645926i
\(369\) −10.9779 1.78408i −0.571485 0.0928754i
\(370\) 41.8867 + 10.3241i 2.17759 + 0.536727i
\(371\) 6.31313 6.57267i 0.327762 0.341236i
\(372\) 3.15278 8.31320i 0.163464 0.431019i
\(373\) −16.5105 + 14.6270i −0.854880 + 0.757358i −0.971806 0.235783i \(-0.924235\pi\)
0.116925 + 0.993141i \(0.462696\pi\)
\(374\) −37.2081 15.8529i −1.92398 0.819733i
\(375\) 0.228877 1.12111i 0.0118192 0.0578941i
\(376\) −0.865889 1.82482i −0.0446548 0.0941080i
\(377\) −17.5508 13.1886i −0.903911 0.679245i
\(378\) −0.378520 3.11739i −0.0194689 0.160341i
\(379\) −2.80377 23.0911i −0.144020 1.18611i −0.868098 0.496393i \(-0.834658\pi\)
0.724078 0.689718i \(-0.242266\pi\)
\(380\) −0.626833 + 15.5547i −0.0321558 + 0.797939i
\(381\) −5.02301 4.45000i −0.257337 0.227980i
\(382\) 33.5205 5.44761i 1.71506 0.278724i
\(383\) 0.285859 + 7.09351i 0.0146067 + 0.362462i 0.989919 + 0.141633i \(0.0452352\pi\)
−0.975313 + 0.220829i \(0.929124\pi\)
\(384\) −1.30661 + 1.60031i −0.0666778 + 0.0816655i
\(385\) −13.2755 + 4.43200i −0.676581 + 0.225876i
\(386\) −12.4655 + 43.0358i −0.634476 + 2.19047i
\(387\) −1.87651 1.18664i −0.0953886 0.0603201i
\(388\) −10.7034 13.1093i −0.543383 0.665523i
\(389\) 19.7462 17.4936i 1.00117 0.886960i 0.00757682 0.999971i \(-0.497588\pi\)
0.993594 + 0.113012i \(0.0360497\pi\)
\(390\) 20.9186 25.6207i 1.05926 1.29735i
\(391\) 23.0010 + 7.67887i 1.16321 + 0.388337i
\(392\) −1.15845 + 0.285533i −0.0585108 + 0.0144216i
\(393\) −12.9340 + 3.18795i −0.652434 + 0.160811i
\(394\) −38.8792 12.9798i −1.95870 0.653911i
\(395\) −28.5086 + 34.9167i −1.43442 + 1.75685i
\(396\) 4.64583 4.11584i 0.233462 0.206829i
\(397\) 20.8874 + 25.5824i 1.04831 + 1.28394i 0.957611 + 0.288066i \(0.0930122\pi\)
0.0906973 + 0.995879i \(0.471090\pi\)
\(398\) −20.4723 12.9459i −1.02618 0.648918i
\(399\) 1.01401 3.50078i 0.0507642 0.175258i
\(400\) −16.3815 + 5.46894i −0.819073 + 0.273447i
\(401\) 1.41015 1.72712i 0.0704197 0.0862485i −0.738194 0.674589i \(-0.764321\pi\)
0.808613 + 0.588340i \(0.200218\pi\)
\(402\) 0.866461 + 21.5010i 0.0432151 + 1.07237i
\(403\) −21.6409 + 3.51699i −1.07801 + 0.175194i
\(404\) 17.2176 + 15.2535i 0.856609 + 0.758889i
\(405\) −0.124963 + 3.10092i −0.00620944 + 0.154086i
\(406\) 1.58404 + 13.0457i 0.0786146 + 0.647450i
\(407\) −2.40627 19.8174i −0.119274 0.982312i
\(408\) −1.41158 1.06073i −0.0698834 0.0525140i
\(409\) −4.99390 10.5244i −0.246933 0.520400i 0.741703 0.670728i \(-0.234018\pi\)
−0.988636 + 0.150328i \(0.951967\pi\)
\(410\) −14.0263 + 68.7055i −0.692711 + 3.39312i
\(411\) −7.50900 3.19929i −0.370392 0.157809i
\(412\) −11.1271 + 9.85776i −0.548194 + 0.485657i
\(413\) −3.04519 + 8.02950i −0.149844 + 0.395106i
\(414\) −5.00137 + 5.20698i −0.245804 + 0.255909i
\(415\) −38.9397 9.59777i −1.91147 0.471136i
\(416\) 41.9085 + 6.81079i 2.05473 + 0.333927i
\(417\) −4.40771 + 11.6222i −0.215847 + 0.569140i
\(418\) 13.2568 4.42578i 0.648413 0.216472i
\(419\) −24.7698 + 15.6634i −1.21008 + 0.765209i −0.978226 0.207541i \(-0.933454\pi\)
−0.231855 + 0.972750i \(0.574480\pi\)
\(420\) −10.1720 + 0.821171i −0.496344 + 0.0400691i
\(421\) −12.7396 + 22.0657i −0.620891 + 1.07542i 0.368429 + 0.929656i \(0.379896\pi\)
−0.989320 + 0.145759i \(0.953438\pi\)
\(422\) 19.0428 27.5882i 0.926987 1.34297i
\(423\) −0.314296 7.79917i −0.0152816 0.379209i
\(424\) 1.40361 + 0.598022i 0.0681653 + 0.0290425i
\(425\) −11.2060 29.5477i −0.543568 1.43327i
\(426\) −18.4255 9.67042i −0.892716 0.468534i
\(427\) −4.59798 15.8741i −0.222512 0.768199i
\(428\) −24.0881 + 15.2324i −1.16434 + 0.736286i
\(429\) −14.5180 4.84681i −0.700935 0.234006i
\(430\) −7.95197 + 11.5204i −0.383478 + 0.555564i
\(431\) −15.8795 1.28192i −0.764887 0.0617481i −0.308136 0.951342i \(-0.599705\pi\)
−0.456751 + 0.889594i \(0.650987\pi\)
\(432\) −3.30189 + 1.73297i −0.158862 + 0.0833774i
\(433\) −11.4446 + 24.1189i −0.549991 + 1.15908i 0.418081 + 0.908410i \(0.362703\pi\)
−0.968072 + 0.250672i \(0.919349\pi\)
\(434\) 10.4921 + 7.88429i 0.503636 + 0.378458i
\(435\) 0.522948 12.9768i 0.0250734 0.622191i
\(436\) −3.96681 + 8.35987i −0.189976 + 0.400365i
\(437\) −7.70899 + 3.28449i −0.368771 + 0.157119i
\(438\) 0.375218 + 1.83794i 0.0179286 + 0.0878200i
\(439\) −7.84903 20.6962i −0.374614 0.987776i −0.981240 0.192789i \(-0.938247\pi\)
0.606626 0.794987i \(-0.292522\pi\)
\(440\) −1.48184 1.81493i −0.0706441 0.0865233i
\(441\) −4.55103 0.739614i −0.216716 0.0352197i
\(442\) −8.76573 + 72.1923i −0.416943 + 3.43384i
\(443\) 27.4110 1.30234 0.651168 0.758933i \(-0.274279\pi\)
0.651168 + 0.758933i \(0.274279\pi\)
\(444\) 1.75455 14.4500i 0.0832674 0.685769i
\(445\) 6.11649 6.36794i 0.289949 0.301869i
\(446\) 0.531768 1.83588i 0.0251800 0.0869313i
\(447\) −3.37605 11.6555i −0.159682 0.551286i
\(448\) −7.88901 11.4292i −0.372721 0.539979i
\(449\) 6.56693 + 11.3743i 0.309913 + 0.536784i 0.978343 0.206990i \(-0.0663669\pi\)
−0.668430 + 0.743775i \(0.733034\pi\)
\(450\) 9.37841 + 0.757103i 0.442102 + 0.0356902i
\(451\) 32.0287 5.20517i 1.50817 0.245102i
\(452\) −5.00844 + 24.5330i −0.235577 + 1.15393i
\(453\) −1.57395 7.70970i −0.0739505 0.362233i
\(454\) 2.19353 1.64833i 0.102947 0.0773599i
\(455\) 14.2956 + 20.7108i 0.670190 + 0.970937i
\(456\) 0.608181 0.0490974i 0.0284807 0.00229920i
\(457\) 12.3945 3.05497i 0.579790 0.142905i 0.0614951 0.998107i \(-0.480413\pi\)
0.518295 + 0.855202i \(0.326567\pi\)
\(458\) −12.4350 + 21.5380i −0.581049 + 1.00641i
\(459\) −3.41170 5.90924i −0.159245 0.275820i
\(460\) 16.2532 + 16.9214i 0.757809 + 0.788962i
\(461\) −11.8254 + 5.03834i −0.550765 + 0.234659i −0.649377 0.760467i \(-0.724970\pi\)
0.0986117 + 0.995126i \(0.468560\pi\)
\(462\) 3.92768 + 8.27741i 0.182732 + 0.385100i
\(463\) 12.7720 + 11.3150i 0.593564 + 0.525852i 0.905553 0.424234i \(-0.139457\pi\)
−0.311988 + 0.950086i \(0.600995\pi\)
\(464\) 13.8179 7.25217i 0.641478 0.336674i
\(465\) −8.98480 9.35417i −0.416660 0.433789i
\(466\) 42.7489 32.1237i 1.98031 1.48810i
\(467\) −17.9757 9.43439i −0.831817 0.436571i −0.00564155 0.999984i \(-0.501796\pi\)
−0.826176 + 0.563413i \(0.809488\pi\)
\(468\) −9.43255 5.96478i −0.436020 0.275722i
\(469\) −15.8964 3.91812i −0.734029 0.180922i
\(470\) −49.2130 −2.27003
\(471\) −11.0013 + 5.99759i −0.506914 + 0.276355i
\(472\) −1.43765 −0.0661731
\(473\) 6.28944 + 1.55021i 0.289189 + 0.0712786i
\(474\) 24.9403 + 15.7713i 1.14555 + 0.724399i
\(475\) 9.66935 + 5.07487i 0.443660 + 0.232851i
\(476\) 17.9376 13.4792i 0.822169 0.617820i
\(477\) 4.08426 + 4.25216i 0.187005 + 0.194693i
\(478\) −7.06325 + 3.70708i −0.323065 + 0.169558i
\(479\) 22.5024 + 19.9354i 1.02816 + 0.910869i 0.996066 0.0886155i \(-0.0282442\pi\)
0.0320931 + 0.999485i \(0.489783\pi\)
\(480\) 10.7676 + 22.6923i 0.491473 + 1.03576i
\(481\) −33.0227 + 14.0697i −1.50571 + 0.641521i
\(482\) −20.7250 21.5771i −0.944000 0.982808i
\(483\) −2.74659 4.75724i −0.124974 0.216462i
\(484\) 2.64623 4.58340i 0.120283 0.208336i
\(485\) −23.9712 + 5.90838i −1.08848 + 0.268286i
\(486\) 2.02501 0.163475i 0.0918561 0.00741539i
\(487\) −0.288953 0.418621i −0.0130937 0.0189695i 0.816382 0.577512i \(-0.195976\pi\)
−0.829476 + 0.558542i \(0.811361\pi\)
\(488\) 2.21184 1.66209i 0.100125 0.0752392i
\(489\) 1.18943 + 5.82621i 0.0537878 + 0.263470i
\(490\) −5.81481 + 28.4828i −0.262686 + 1.28672i
\(491\) −19.1279 + 3.10859i −0.863232 + 0.140289i −0.575878 0.817536i \(-0.695340\pi\)
−0.287354 + 0.957824i \(0.592776\pi\)
\(492\) 23.5837 + 1.90387i 1.06324 + 0.0858332i
\(493\) 14.2774 + 24.7292i 0.643022 + 1.11375i
\(494\) −14.2756 20.6817i −0.642288 0.930515i
\(495\) −2.51912 8.69699i −0.113226 0.390901i
\(496\) 4.33596 14.9695i 0.194690 0.672150i
\(497\) 10.9675 11.4184i 0.491959 0.512183i
\(498\) −3.16456 + 26.0625i −0.141807 + 1.16789i
\(499\) −6.40420 −0.286691 −0.143346 0.989673i \(-0.545786\pi\)
−0.143346 + 0.989673i \(0.545786\pi\)
\(500\) −0.293413 + 2.41648i −0.0131218 + 0.108068i
\(501\) −15.9038 2.58462i −0.710529 0.115472i
\(502\) −38.8771 47.6158i −1.73517 2.12520i
\(503\) −1.82881 4.82219i −0.0815428 0.215011i 0.888044 0.459759i \(-0.152064\pi\)
−0.969587 + 0.244748i \(0.921295\pi\)
\(504\) 0.0800080 + 0.391905i 0.00356384 + 0.0174568i
\(505\) 30.8711 13.1529i 1.37375 0.585299i
\(506\) 9.03017 19.0307i 0.401440 0.846017i
\(507\) −0.584696 + 14.5091i −0.0259673 + 0.644371i
\(508\) 11.4129 + 8.57626i 0.506367 + 0.380510i
\(509\) 6.17985 13.0238i 0.273917 0.577268i −0.719145 0.694860i \(-0.755466\pi\)
0.993062 + 0.117592i \(0.0375176\pi\)
\(510\) −38.0932 + 19.9929i −1.68680 + 0.885298i
\(511\) −1.42260 0.114844i −0.0629320 0.00508040i
\(512\) −18.2408 + 26.4264i −0.806139 + 1.16789i
\(513\) 2.23657 + 0.746675i 0.0987468 + 0.0329665i
\(514\) 14.5036 9.17154i 0.639728 0.404539i
\(515\) 6.03348 + 20.8300i 0.265867 + 0.917878i
\(516\) 4.18223 + 2.19500i 0.184113 + 0.0966297i
\(517\) 8.07545 + 21.2932i 0.355158 + 0.936474i
\(518\) 19.7675 + 8.42213i 0.868532 + 0.370047i
\(519\) 0.0978517 + 2.42816i 0.00429521 + 0.106585i
\(520\) −2.39324 + 3.46721i −0.104951 + 0.152047i
\(521\) −16.7432 + 29.0000i −0.733531 + 1.27051i 0.221834 + 0.975084i \(0.428796\pi\)
−0.955365 + 0.295428i \(0.904538\pi\)
\(522\) −8.47431 + 0.684117i −0.370910 + 0.0299430i
\(523\) −30.8344 + 19.4985i −1.34829 + 0.852609i −0.996510 0.0834720i \(-0.973399\pi\)
−0.351784 + 0.936081i \(0.614425\pi\)
\(524\) 26.8805 8.97403i 1.17428 0.392032i
\(525\) −2.53851 + 6.69351i −0.110790 + 0.292129i
\(526\) −9.58169 1.55718i −0.417782 0.0678961i
\(527\) 27.6885 + 6.82461i 1.20613 + 0.297285i
\(528\) 7.53663 7.84647i 0.327990 0.341474i
\(529\) 3.67746 9.69665i 0.159889 0.421594i
\(530\) 27.8247 24.6505i 1.20863 1.07075i
\(531\) −5.11111 2.17764i −0.221803 0.0945015i
\(532\) −1.55092 + 7.59691i −0.0672409 + 0.329368i
\(533\) −25.0124 52.7126i −1.08341 2.28323i
\(534\) −4.62087 3.47236i −0.199965 0.150264i
\(535\) 5.01148 + 41.2733i 0.216665 + 1.78440i
\(536\) −0.330376 2.72089i −0.0142701 0.117525i
\(537\) −0.160191 + 3.97511i −0.00691277 + 0.171539i
\(538\) −44.5790 39.4936i −1.92194 1.70269i
\(539\) 13.2779 2.15788i 0.571921 0.0929463i
\(540\) −0.265842 6.59681i −0.0114400 0.283881i
\(541\) −8.16024 + 9.99448i −0.350836 + 0.429696i −0.919631 0.392783i \(-0.871512\pi\)
0.568795 + 0.822479i \(0.307410\pi\)
\(542\) 9.06083 3.02495i 0.389196 0.129933i
\(543\) −4.90013 + 16.9172i −0.210285 + 0.725986i
\(544\) −46.6753 29.5157i −2.00119 1.26547i
\(545\) 8.53723 + 10.4562i 0.365695 + 0.447895i
\(546\) 12.3310 10.9243i 0.527718 0.467517i
\(547\) 5.44011 6.66292i 0.232602 0.284886i −0.645094 0.764103i \(-0.723182\pi\)
0.877696 + 0.479217i \(0.159079\pi\)
\(548\) 16.4703 + 5.49860i 0.703577 + 0.234888i
\(549\) 10.3811 2.55871i 0.443055 0.109203i
\(550\) −26.6535 + 6.56950i −1.13651 + 0.280124i
\(551\) −9.35965 3.12471i −0.398735 0.133117i
\(552\) 0.581608 0.712341i 0.0247549 0.0303192i
\(553\) −16.8051 + 14.8880i −0.714625 + 0.633102i
\(554\) −16.5571 20.2787i −0.703442 0.861560i
\(555\) −17.9474 11.3492i −0.761823 0.481748i
\(556\) 7.35693 25.3991i 0.312003 1.07716i
\(557\) −26.9100 + 8.98386i −1.14021 + 0.380659i −0.823193 0.567761i \(-0.807810\pi\)
−0.317018 + 0.948420i \(0.602682\pi\)
\(558\) −5.36989 + 6.57692i −0.227326 + 0.278423i
\(559\) −0.468993 11.6379i −0.0198363 0.492232i
\(560\) −17.6567 + 2.86949i −0.746132 + 0.121258i
\(561\) 14.9012 + 13.2013i 0.629128 + 0.557359i
\(562\) −0.0121797 + 0.302236i −0.000513770 + 0.0127491i
\(563\) −3.15644 25.9956i −0.133028 1.09559i −0.894399 0.447269i \(-0.852397\pi\)
0.761371 0.648316i \(-0.224527\pi\)
\(564\) 2.00154 + 16.4841i 0.0842799 + 0.694108i
\(565\) 29.2014 + 21.9434i 1.22851 + 0.923166i
\(566\) 4.85377 + 10.2291i 0.204019 + 0.429961i
\(567\) −0.309185 + 1.51449i −0.0129845 + 0.0636025i
\(568\) 2.43842 + 1.03891i 0.102314 + 0.0435918i
\(569\) 6.16104 5.45820i 0.258284 0.228820i −0.524036 0.851696i \(-0.675574\pi\)
0.782320 + 0.622876i \(0.214036\pi\)
\(570\) 5.27171 13.9004i 0.220808 0.582222i
\(571\) −24.3487 + 25.3497i −1.01896 + 1.06085i −0.0208293 + 0.999783i \(0.506631\pi\)
−0.998134 + 0.0610696i \(0.980549\pi\)
\(572\) 31.6147 + 7.79232i 1.32188 + 0.325813i
\(573\) −16.4996 2.68145i −0.689281 0.112019i
\(574\) −12.3849 + 32.6563i −0.516936 + 1.36305i
\(575\) 15.6116 5.21193i 0.651051 0.217353i
\(576\) 7.59359 4.80189i 0.316399 0.200079i
\(577\) −23.7731 + 1.91916i −0.989685 + 0.0798956i −0.564693 0.825301i \(-0.691005\pi\)
−0.424992 + 0.905197i \(0.639723\pi\)
\(578\) 30.0258 52.0062i 1.24891 2.16317i
\(579\) 12.5281 18.1501i 0.520651 0.754293i
\(580\) 1.11251 + 27.6065i 0.0461943 + 1.14630i
\(581\) −18.3767 7.82957i −0.762393 0.324825i
\(582\) 5.73108 + 15.1116i 0.237561 + 0.626397i
\(583\) −15.2314 7.99407i −0.630821 0.331081i
\(584\) −0.0664753 0.229499i −0.00275077 0.00949675i
\(585\) −13.7603 + 8.70148i −0.568918 + 0.359762i
\(586\) −34.6980 11.5839i −1.43336 0.478526i
\(587\) −20.8797 + 30.2495i −0.861798 + 1.24853i 0.105381 + 0.994432i \(0.466394\pi\)
−0.967179 + 0.254098i \(0.918221\pi\)
\(588\) 9.77695 + 0.789277i 0.403195 + 0.0325492i
\(589\) −8.72569 + 4.57960i −0.359536 + 0.188699i
\(590\) −15.0163 + 31.6461i −0.618210 + 1.30285i
\(591\) 16.1292 + 12.1203i 0.663467 + 0.498563i
\(592\) 1.02739 25.4945i 0.0422257 1.04782i
\(593\) −9.08173 + 19.1393i −0.372942 + 0.785959i 0.627034 + 0.778992i \(0.284269\pi\)
−0.999976 + 0.00696664i \(0.997782\pi\)
\(594\) −5.45301 + 2.32331i −0.223740 + 0.0953266i
\(595\) −6.54729 32.0707i −0.268413 1.31477i
\(596\) 9.15405 + 24.1372i 0.374965 + 0.988700i
\(597\) 7.54045 + 9.23538i 0.308610 + 0.377979i
\(598\) −37.3851 6.07568i −1.52879 0.248453i
\(599\) 3.18320 26.2160i 0.130062 1.07116i −0.770808 0.637068i \(-0.780147\pi\)
0.900870 0.434089i \(-0.142930\pi\)
\(600\) −1.19845 −0.0489263
\(601\) 4.94226 40.7032i 0.201599 1.66032i −0.443541 0.896254i \(-0.646278\pi\)
0.645140 0.764064i \(-0.276799\pi\)
\(602\) −4.82978 + 5.02833i −0.196847 + 0.204939i
\(603\) 2.94685 10.1737i 0.120005 0.414306i
\(604\) 4.65728 + 16.0788i 0.189502 + 0.654237i
\(605\) −4.38585 6.35400i −0.178310 0.258327i
\(606\) −10.9834 19.0239i −0.446172 0.772792i
\(607\) 10.5107 + 0.848513i 0.426617 + 0.0344401i 0.291911 0.956446i \(-0.405709\pi\)
0.134706 + 0.990886i \(0.456991\pi\)
\(608\) 18.8364 3.06122i 0.763918 0.124149i
\(609\) 1.29389 6.33787i 0.0524309 0.256824i
\(610\) −13.4839 66.0485i −0.545947 2.67422i
\(611\) 32.7355 24.5991i 1.32434 0.995175i
\(612\) 8.24599 + 11.9464i 0.333324 + 0.482904i
\(613\) −17.0995 + 1.38041i −0.690642 + 0.0557544i −0.420804 0.907151i \(-0.638252\pi\)
−0.269838 + 0.962906i \(0.586970\pi\)
\(614\) −15.8815 + 3.91443i −0.640924 + 0.157974i
\(615\) 17.2580 29.8918i 0.695911 1.20535i
\(616\) −0.583497 1.01065i −0.0235098 0.0407201i
\(617\) 24.4516 + 25.4568i 0.984383 + 1.02485i 0.999688 + 0.0249680i \(0.00794840\pi\)
−0.0153056 + 0.999883i \(0.504872\pi\)
\(618\) 13.0604 5.56451i 0.525365 0.223837i
\(619\) −5.35934 11.2946i −0.215410 0.453967i 0.766767 0.641926i \(-0.221864\pi\)
−0.982177 + 0.187958i \(0.939813\pi\)
\(620\) 20.6533 + 18.2972i 0.829457 + 0.734835i
\(621\) 3.14673 1.65153i 0.126274 0.0662736i
\(622\) 15.3498 + 15.9809i 0.615472 + 0.640775i
\(623\) 3.51576 2.64192i 0.140856 0.105846i
\(624\) −17.3218 9.09120i −0.693428 0.363939i
\(625\) 22.5730 + 14.2743i 0.902919 + 0.570971i
\(626\) 54.6727 + 13.4756i 2.18516 + 0.538594i
\(627\) −6.87937 −0.274736
\(628\) 22.3013 14.6010i 0.889920 0.582643i
\(629\) 46.6880 1.86157
\(630\) 9.46247 + 2.33229i 0.376994 + 0.0929207i
\(631\) 24.3408 + 15.3922i 0.968991 + 0.612753i 0.922431 0.386163i \(-0.126200\pi\)
0.0465602 + 0.998915i \(0.485174\pi\)
\(632\) −3.32807 1.74671i −0.132384 0.0694803i
\(633\) −13.1911 + 9.91250i −0.524301 + 0.393986i
\(634\) 33.7499 + 35.1374i 1.34038 + 1.39548i
\(635\) 18.4406 9.67838i 0.731793 0.384075i
\(636\) −9.38846 8.31745i −0.372277 0.329808i
\(637\) −10.3692 21.8527i −0.410844 0.865836i
\(638\) 22.8199 9.72266i 0.903450 0.384924i
\(639\) 7.09536 + 7.38706i 0.280688 + 0.292227i
\(640\) −3.20580 5.55261i −0.126720 0.219486i
\(641\) 4.61591 7.99499i 0.182318 0.315783i −0.760352 0.649511i \(-0.774973\pi\)
0.942669 + 0.333728i \(0.108307\pi\)
\(642\) 26.4262 6.51347i 1.04296 0.257066i
\(643\) 12.4135 1.00212i 0.489539 0.0395197i 0.166767 0.985996i \(-0.446667\pi\)
0.322772 + 0.946477i \(0.395385\pi\)
\(644\) 6.63843 + 9.61743i 0.261591 + 0.378980i
\(645\) 5.50842 4.13931i 0.216894 0.162985i
\(646\) 6.53810 + 32.0257i 0.257238 + 1.26004i
\(647\) 7.38659 36.1819i 0.290397 1.42246i −0.528703 0.848807i \(-0.677321\pi\)
0.819100 0.573651i \(-0.194474\pi\)
\(648\) −0.255420 + 0.0415098i −0.0100338 + 0.00163066i
\(649\) 16.1565 + 1.30429i 0.634199 + 0.0511978i
\(650\) 24.6797 + 42.7466i 0.968019 + 1.67666i
\(651\) −3.66974 5.31654i −0.143828 0.208372i
\(652\) −3.51950 12.1507i −0.137834 0.475859i
\(653\) 5.56932 19.2275i 0.217944 0.752431i −0.774802 0.632204i \(-0.782151\pi\)
0.992746 0.120227i \(-0.0383623\pi\)
\(654\) 6.12137 6.37302i 0.239365 0.249205i
\(655\) 4.98312 41.0397i 0.194707 1.60355i
\(656\) 41.4739 1.61928
\(657\) 0.111296 0.916605i 0.00434207 0.0357602i
\(658\) −24.1941 3.93192i −0.943183 0.153282i
\(659\) 7.60660 + 9.31639i 0.296311 + 0.362915i 0.901207 0.433390i \(-0.142683\pi\)
−0.604896 + 0.796305i \(0.706785\pi\)
\(660\) 6.83049 + 18.0105i 0.265877 + 0.701059i
\(661\) −9.45663 46.3216i −0.367820 1.80170i −0.569211 0.822191i \(-0.692751\pi\)
0.201391 0.979511i \(-0.435454\pi\)
\(662\) −0.618241 + 0.263408i −0.0240286 + 0.0102376i
\(663\) 15.3454 32.3397i 0.595966 1.25597i
\(664\) 0.134651 3.34133i 0.00522548 0.129669i
\(665\) 9.04252 + 6.79501i 0.350654 + 0.263499i
\(666\) −5.95918 + 12.5587i −0.230914 + 0.486640i
\(667\) −13.1685 + 6.91137i −0.509887 + 0.267609i
\(668\) 34.1660 + 2.75817i 1.32192 + 0.106717i
\(669\) −0.534440 + 0.774270i −0.0206626 + 0.0299350i
\(670\) −63.3443 21.1474i −2.44720 0.816997i
\(671\) −26.3649 + 16.6721i −1.01780 + 0.643621i
\(672\) 3.48055 + 12.0163i 0.134265 + 0.463538i
\(673\) −3.87196 2.03216i −0.149253 0.0783341i 0.388443 0.921473i \(-0.373013\pi\)
−0.537696 + 0.843139i \(0.680705\pi\)
\(674\) −11.9443 31.4944i −0.460076 1.21312i
\(675\) −4.26070 1.81531i −0.163994 0.0698715i
\(676\) −1.24387 30.8662i −0.0478410 1.18716i
\(677\) 5.61767 8.13860i 0.215905 0.312792i −0.700034 0.714109i \(-0.746832\pi\)
0.915939 + 0.401317i \(0.131447\pi\)
\(678\) 11.9558 20.7081i 0.459161 0.795291i
\(679\) −12.2568 + 0.989470i −0.470372 + 0.0379724i
\(680\) 4.63141 2.92873i 0.177607 0.112312i
\(681\) −1.28107 + 0.427684i −0.0490907 + 0.0163889i
\(682\) 8.78432 23.1624i 0.336369 0.886932i
\(683\) −7.37920 1.19924i −0.282357 0.0458875i 0.0175833 0.999845i \(-0.494403\pi\)
−0.299941 + 0.953958i \(0.596967\pi\)
\(684\) −4.87040 1.20045i −0.186224 0.0459002i
\(685\) 17.5472 18.2685i 0.670443 0.698005i
\(686\) −12.9293 + 34.0916i −0.493641 + 1.30162i
\(687\) 9.16298 8.11769i 0.349589 0.309709i
\(688\) 7.61678 + 3.24521i 0.290387 + 0.123722i
\(689\) −6.18684 + 30.3052i −0.235700 + 1.15453i
\(690\) −9.60544 20.2430i −0.365673 0.770639i
\(691\) −5.93562 4.46033i −0.225801 0.169679i 0.481821 0.876270i \(-0.339976\pi\)
−0.707622 + 0.706591i \(0.750232\pi\)
\(692\) −0.623151 5.13211i −0.0236886 0.195094i
\(693\) −0.543591 4.47688i −0.0206493 0.170063i
\(694\) −2.75774 + 68.4327i −0.104683 + 2.59767i
\(695\) −28.8741 25.5802i −1.09526 0.970314i
\(696\) 1.06889 0.173711i 0.0405162 0.00658452i
\(697\) 3.05575 + 75.8277i 0.115745 + 2.87218i
\(698\) 32.3583 39.6317i 1.22478 1.50008i
\(699\) −24.9663 + 8.33499i −0.944314 + 0.315258i
\(700\) 4.23705 14.6280i 0.160145 0.552886i
\(701\) 20.2521 + 12.8066i 0.764910 + 0.483700i 0.859071 0.511857i \(-0.171042\pi\)
−0.0941604 + 0.995557i \(0.530017\pi\)
\(702\) 6.74048 + 8.25559i 0.254403 + 0.311587i
\(703\) −12.0762 + 10.6986i −0.455462 + 0.403504i
\(704\) −16.5782 + 20.3046i −0.624814 + 0.765258i
\(705\) 22.9772 + 7.67092i 0.865372 + 0.288903i
\(706\) 36.3542 8.96049i 1.36821 0.337233i
\(707\) 16.2277 3.99977i 0.610305 0.150427i
\(708\) 11.2108 + 3.74270i 0.421326 + 0.140659i
\(709\) −0.448827 + 0.549713i −0.0168560 + 0.0206449i −0.782964 0.622067i \(-0.786293\pi\)
0.766108 + 0.642712i \(0.222191\pi\)
\(710\) 48.3383 42.8240i 1.81411 1.60716i
\(711\) −9.18615 11.2510i −0.344507 0.421945i
\(712\) 0.622256 + 0.393491i 0.0233200 + 0.0147467i
\(713\) −4.13220 + 14.2660i −0.154752 + 0.534267i
\(714\) −20.3247 + 6.78538i −0.760633 + 0.253937i
\(715\) 30.0412 36.7938i 1.12348 1.37601i
\(716\) −0.340787 8.45655i −0.0127358 0.316036i
\(717\) 3.87561 0.629847i 0.144737 0.0235221i
\(718\) −1.08333 0.959751i −0.0404297 0.0358176i
\(719\) −0.750610 + 18.6262i −0.0279930 + 0.694640i 0.922885 + 0.385075i \(0.125824\pi\)
−0.950878 + 0.309565i \(0.899817\pi\)
\(720\) −1.39495 11.4884i −0.0519866 0.428148i
\(721\) 1.30194 + 10.7225i 0.0484869 + 0.399326i
\(722\) 21.8289 + 16.4033i 0.812387 + 0.610469i
\(723\) 6.31312 + 13.3046i 0.234787 + 0.494804i
\(724\) 7.49467 36.7113i 0.278537 1.36436i
\(725\) 17.8303 + 7.59679i 0.662201 + 0.282138i
\(726\) −3.78310 + 3.35154i −0.140404 + 0.124387i
\(727\) −4.65621 + 12.2774i −0.172689 + 0.455344i −0.993219 0.116260i \(-0.962909\pi\)
0.820530 + 0.571604i \(0.193679\pi\)
\(728\) −1.45358 + 1.51334i −0.0538733 + 0.0560880i
\(729\) −0.970942 0.239316i −0.0359608 0.00886354i
\(730\) −5.74618 0.933845i −0.212676 0.0345631i
\(731\) −5.37209 + 14.1650i −0.198694 + 0.523913i
\(732\) −21.5749 + 7.20274i −0.797430 + 0.266221i
\(733\) −1.51176 + 0.955980i −0.0558382 + 0.0353099i −0.562093 0.827074i \(-0.690004\pi\)
0.506255 + 0.862384i \(0.331029\pi\)
\(734\) −5.66421 + 0.457262i −0.209070 + 0.0168779i
\(735\) 7.15455 12.3921i 0.263900 0.457088i
\(736\) 16.3388 23.6709i 0.602258 0.872521i
\(737\) 1.24432 + 30.8776i 0.0458352 + 1.13739i
\(738\) −20.7871 8.85656i −0.765184 0.326014i
\(739\) 6.10395 + 16.0948i 0.224537 + 0.592056i 0.999186 0.0403354i \(-0.0128426\pi\)
−0.774649 + 0.632392i \(0.782073\pi\)
\(740\) 39.9997 + 20.9935i 1.47042 + 0.771735i
\(741\) 3.44146 + 11.8813i 0.126425 + 0.436471i
\(742\) 15.6486 9.89558i 0.574479 0.363278i
\(743\) 33.5232 + 11.1917i 1.22985 + 0.410583i 0.856033 0.516921i \(-0.172922\pi\)
0.373813 + 0.927504i \(0.378050\pi\)
\(744\) 0.614354 0.890046i 0.0225233 0.0326307i
\(745\) 37.5368 + 3.03028i 1.37524 + 0.111021i
\(746\) −39.6795 + 20.8254i −1.45277 + 0.762471i
\(747\) 5.53991 11.6751i 0.202695 0.427170i
\(748\) −33.8574 25.4422i −1.23795 0.930258i
\(749\) −0.833824 + 20.6911i −0.0304673 + 0.756038i
\(750\) 0.996551 2.10019i 0.0363889 0.0766880i
\(751\) −26.1102 + 11.1245i −0.952775 + 0.405940i −0.811710 0.584061i \(-0.801463\pi\)
−0.141065 + 0.990000i \(0.545053\pi\)
\(752\) 5.82214 + 28.5187i 0.212311 + 1.03997i
\(753\) 10.7295 + 28.2913i 0.391004 + 1.03099i
\(754\) −28.2078 34.5483i −1.02727 1.25817i
\(755\) 24.1038 + 3.91725i 0.877228 + 0.142563i
\(756\) 0.396365 3.26436i 0.0144156 0.118724i
\(757\) −3.60954 −0.131191 −0.0655954 0.997846i \(-0.520895\pi\)
−0.0655954 + 0.997846i \(0.520895\pi\)
\(758\) 5.69612 46.9118i 0.206892 1.70391i
\(759\) −7.18247 + 7.47774i −0.260707 + 0.271425i
\(760\) −0.526829 + 1.81883i −0.0191101 + 0.0659758i
\(761\) −10.9839 37.9209i −0.398167 1.37463i −0.870046 0.492970i \(-0.835911\pi\)
0.471879 0.881663i \(-0.343576\pi\)
\(762\) −7.74463 11.2200i −0.280558 0.406459i
\(763\) 3.36166 + 5.82256i 0.121700 + 0.210791i
\(764\) 35.4460 + 2.86150i 1.28239 + 0.103525i
\(765\) 20.9018 3.39687i 0.755705 0.122814i
\(766\) −2.88494 + 14.1314i −0.104237 + 0.510587i
\(767\) −5.82980 28.5563i −0.210502 1.03111i
\(768\) 11.0097 8.27326i 0.397279 0.298536i
\(769\) 24.9105 + 36.0892i 0.898297 + 1.30141i 0.953020 + 0.302907i \(0.0979570\pi\)
−0.0547231 + 0.998502i \(0.517428\pi\)
\(770\) −28.3415 + 2.28796i −1.02136 + 0.0824523i
\(771\) −8.20122 + 2.02142i −0.295360 + 0.0727997i
\(772\) −23.4586 + 40.6314i −0.844293 + 1.46236i
\(773\) −22.6072 39.1569i −0.813125 1.40837i −0.910666 0.413143i \(-0.864431\pi\)
0.0975410 0.995232i \(-0.468902\pi\)
\(774\) −3.12460 3.25306i −0.112312 0.116929i
\(775\) 17.8068 7.58678i 0.639640 0.272525i
\(776\) −0.882504 1.85984i −0.0316800 0.0667643i
\(777\) −7.91651 7.01342i −0.284003 0.251605i
\(778\) 47.4557 24.9067i 1.70137 0.892948i
\(779\) −18.1663 18.9131i −0.650876 0.677634i
\(780\) 27.6888 20.8068i 0.991419 0.745003i
\(781\) −26.4608 13.8877i −0.946841 0.496940i
\(782\) 41.6375 + 26.3299i 1.48895 + 0.941557i
\(783\) 4.06323 + 1.00150i 0.145208 + 0.0357905i
\(784\) 17.1936 0.614056
\(785\) −5.29672 38.5235i −0.189048 1.37496i
\(786\) −27.0630 −0.965307
\(787\) 24.4472 + 6.02569i 0.871448 + 0.214793i 0.649589 0.760286i \(-0.274941\pi\)
0.221860 + 0.975079i \(0.428787\pi\)
\(788\) −36.2764 22.9398i −1.29229 0.817197i
\(789\) 4.23090 + 2.22055i 0.150624 + 0.0790536i
\(790\) −73.2111 + 55.0146i −2.60473 + 1.95733i
\(791\) 12.6028 + 13.1209i 0.448103 + 0.466524i
\(792\) 0.668504 0.350858i 0.0237542 0.0124672i
\(793\) 41.9835 + 37.1942i 1.49088 + 1.32080i
\(794\) 28.7636 + 60.6181i 1.02078 + 2.15126i
\(795\) −16.8334 + 7.17206i −0.597021 + 0.254367i
\(796\) −17.5703 18.2926i −0.622762 0.648364i
\(797\) −27.0994 46.9375i −0.959909 1.66261i −0.722712 0.691149i \(-0.757105\pi\)
−0.237197 0.971462i \(-0.576229\pi\)
\(798\) 3.70226 6.41250i 0.131059 0.227000i
\(799\) −51.7125 + 12.7460i −1.82946 + 0.450920i
\(800\) −37.3615 + 3.01613i −1.32093 + 0.106636i
\(801\) 1.61621 + 2.34148i 0.0571059 + 0.0827322i
\(802\) 3.62133 2.72125i 0.127873 0.0960907i
\(803\) 0.538850 + 2.63946i 0.0190156 + 0.0931445i
\(804\) −4.50717 + 22.0776i −0.158956 + 0.778616i
\(805\) 16.8270 2.73465i 0.593072 0.0963837i
\(806\) −44.3979 3.58417i −1.56385 0.126247i
\(807\) 14.6577 + 25.3879i 0.515975 + 0.893695i
\(808\) 1.58944 + 2.30271i 0.0559164 + 0.0810089i
\(809\) −8.44991 29.1725i −0.297083 1.02565i −0.960703 0.277580i \(-0.910468\pi\)
0.663620 0.748070i \(-0.269019\pi\)
\(810\) −1.75414 + 6.05599i −0.0616341 + 0.212786i
\(811\) 19.6952 20.5048i 0.691591 0.720022i −0.279125 0.960255i \(-0.590044\pi\)
0.970715 + 0.240233i \(0.0772237\pi\)
\(812\) −1.65872 + 13.6608i −0.0582097 + 0.479400i
\(813\) −4.70194 −0.164904
\(814\) 4.88856 40.2609i 0.171344 1.41114i
\(815\) −18.2152 2.96026i −0.638051 0.103693i
\(816\) 16.0924 + 19.7096i 0.563346 + 0.689973i
\(817\) −1.85639 4.89490i −0.0649469 0.171251i
\(818\) −4.73388 23.1881i −0.165516 0.810752i
\(819\) −7.46004 + 3.17843i −0.260675 + 0.111063i
\(820\) −31.4783 + 66.3391i −1.09927 + 2.31666i
\(821\) 0.973237 24.1506i 0.0339662 0.842862i −0.888983 0.457940i \(-0.848587\pi\)
0.922949 0.384922i \(-0.125772\pi\)
\(822\) −13.2565 9.96160i −0.462373 0.347451i
\(823\) −17.7869 + 37.4850i −0.620011 + 1.30665i 0.314007 + 0.949421i \(0.398328\pi\)
−0.934018 + 0.357225i \(0.883723\pi\)
\(824\) −1.60112 + 0.840331i −0.0557776 + 0.0292743i
\(825\) 13.4683 + 1.08728i 0.468907 + 0.0378541i
\(826\) −9.91069 + 14.3581i −0.344837 + 0.499583i
\(827\) 36.4984 + 12.1850i 1.26917 + 0.423713i 0.869950 0.493141i \(-0.164151\pi\)
0.399224 + 0.916853i \(0.369279\pi\)
\(828\) −6.38984 + 4.04069i −0.222062 + 0.140424i
\(829\) 4.26185 + 14.7136i 0.148020 + 0.511024i 0.999920 0.0126808i \(-0.00403654\pi\)
−0.851900 + 0.523705i \(0.824549\pi\)
\(830\) −72.1445 37.8643i −2.50417 1.31429i
\(831\) 4.56949 + 12.0488i 0.158514 + 0.417967i
\(832\) 43.3612 + 18.4745i 1.50328 + 0.640488i
\(833\) 1.26680 + 31.4354i 0.0438921 + 1.08917i
\(834\) −14.3451 + 20.7824i −0.496730 + 0.719637i
\(835\) 25.0019 43.3046i 0.865228 1.49862i
\(836\) 14.5875 1.17763i 0.504521 0.0407291i
\(837\) 3.53232 2.23370i 0.122095 0.0772081i
\(838\) −56.4752 + 18.8542i −1.95091 + 0.651308i
\(839\) 18.6401 49.1499i 0.643527 1.69684i −0.0712210 0.997461i \(-0.522690\pi\)
0.714748 0.699382i \(-0.246541\pi\)
\(840\) −1.22526 0.199125i −0.0422756 0.00687045i
\(841\) 11.1534 + 2.74906i 0.384599 + 0.0947953i
\(842\) −35.8578 + 37.3319i −1.23574 + 1.28654i
\(843\) 0.0527967 0.139214i 0.00181842 0.00479477i
\(844\) 26.2746 23.2773i 0.904410 0.801238i
\(845\) −41.4584 17.6638i −1.42621 0.607653i
\(846\) 3.17193 15.5371i 0.109053 0.534178i
\(847\) −1.64851 3.47416i −0.0566434 0.119374i
\(848\) −17.5766 13.2080i −0.603584 0.453564i
\(849\) −0.671762 5.53246i −0.0230548 0.189873i
\(850\) −7.73856 63.7328i −0.265430 2.18602i
\(851\) −0.979114 + 24.2965i −0.0335636 + 0.832872i
\(852\) −16.3101 14.4495i −0.558774 0.495031i
\(853\) −33.8145 + 5.49539i −1.15779 + 0.188158i −0.708819 0.705390i \(-0.750772\pi\)
−0.448966 + 0.893549i \(0.648208\pi\)
\(854\) −1.35194 33.5480i −0.0462624 1.14799i
\(855\) −4.62800 + 5.66827i −0.158274 + 0.193851i
\(856\) −3.28832 + 1.09780i −0.112392 + 0.0375221i
\(857\) −5.51323 + 19.0339i −0.188328 + 0.650185i 0.809666 + 0.586890i \(0.199648\pi\)
−0.997995 + 0.0632947i \(0.979839\pi\)
\(858\) −26.2811 16.6192i −0.897222 0.567369i
\(859\) 31.6103 + 38.7156i 1.07853 + 1.32096i 0.943962 + 0.330053i \(0.107067\pi\)
0.134566 + 0.990905i \(0.457036\pi\)
\(860\) −10.9719 + 9.72025i −0.374139 + 0.331458i
\(861\) 10.8726 13.3165i 0.370538 0.453826i
\(862\) −30.6999 10.2491i −1.04564 0.349087i
\(863\) −10.0749 + 2.48323i −0.342953 + 0.0845302i −0.407030 0.913415i \(-0.633436\pi\)
0.0640776 + 0.997945i \(0.479589\pi\)
\(864\) −7.85823 + 1.93688i −0.267343 + 0.0658940i
\(865\) −7.15363 2.38823i −0.243231 0.0812024i
\(866\) −34.3015 + 42.0117i −1.16561 + 1.42762i
\(867\) −22.1251 + 19.6011i −0.751409 + 0.665690i
\(868\) 8.69169 + 10.6454i 0.295015 + 0.361328i
\(869\) 35.8167 + 22.6491i 1.21500 + 0.768319i
\(870\) 7.34077 25.3433i 0.248875 0.859218i
\(871\) 52.7059 17.5958i 1.78587 0.596211i
\(872\) −0.711852 + 0.871861i −0.0241064 + 0.0295249i
\(873\) −0.320326 7.94882i −0.0108414 0.269027i
\(874\) −16.8033 + 2.73081i −0.568381 + 0.0923710i
\(875\) 1.32387 + 1.17285i 0.0447551 + 0.0396496i
\(876\) −0.0790937 + 1.96269i −0.00267233 + 0.0663132i
\(877\) 3.13463 + 25.8160i 0.105849 + 0.871744i 0.944825 + 0.327575i \(0.106232\pi\)
−0.838976 + 0.544168i \(0.816845\pi\)
\(878\) −5.42035 44.6406i −0.182928 1.50655i
\(879\) 14.3946 + 10.8169i 0.485519 + 0.364844i
\(880\) 14.4746 + 30.5045i 0.487937 + 1.02831i
\(881\) −0.939063 + 4.59983i −0.0316378 + 0.154972i −0.992541 0.121913i \(-0.961097\pi\)
0.960903 + 0.276885i \(0.0893022\pi\)
\(882\) −8.61758 3.67161i −0.290169 0.123629i
\(883\) 34.9589 30.9709i 1.17646 1.04225i 0.178158 0.984002i \(-0.442986\pi\)
0.998302 0.0582503i \(-0.0185522\pi\)
\(884\) −27.0035 + 71.2025i −0.908227 + 2.39480i
\(885\) 11.9437 12.4347i 0.401484 0.417989i
\(886\) 54.0698 + 13.3270i 1.81651 + 0.447730i
\(887\) 6.24733 + 1.01529i 0.209765 + 0.0340901i 0.264385 0.964417i \(-0.414831\pi\)
−0.0546208 + 0.998507i \(0.517395\pi\)
\(888\) 0.627862 1.65554i 0.0210697 0.0555561i
\(889\) 9.83903 3.28475i 0.329990 0.110167i
\(890\) 15.1612 9.58735i 0.508204 0.321369i
\(891\) 2.90811 0.234767i 0.0974253 0.00786498i
\(892\) 1.00073 1.73331i 0.0335068 0.0580354i
\(893\) 10.4551 15.1468i 0.349865 0.506867i
\(894\) −0.992658 24.6326i −0.0331994 0.823836i
\(895\) −11.3585 4.83942i −0.379674 0.161764i
\(896\) −1.13240 2.98590i −0.0378309 0.0997519i
\(897\) 16.5078 + 8.66397i 0.551180 + 0.289282i
\(898\) 7.42359 + 25.6292i 0.247728 + 0.855257i
\(899\) −14.7822 + 9.34767i −0.493013 + 0.311762i
\(900\) 9.34546 + 3.11997i 0.311515 + 0.103999i
\(901\) 22.8534 33.1089i 0.761358 1.10302i
\(902\) 65.7092 + 5.30460i 2.18788 + 0.176624i
\(903\) 3.03876 1.59487i 0.101124 0.0530738i
\(904\) −1.30567 + 2.75165i −0.0434261 + 0.0915185i
\(905\) −43.6971 32.8362i −1.45254 1.09151i
\(906\) 0.643693 15.9731i 0.0213853 0.530670i
\(907\) 4.61208 9.71974i 0.153141 0.322739i −0.812351 0.583168i \(-0.801813\pi\)
0.965493 + 0.260429i \(0.0838641\pi\)
\(908\) 2.64326 1.12619i 0.0877198 0.0373739i
\(909\) 2.16281 + 10.5941i 0.0717357 + 0.351385i
\(910\) 18.1296 + 47.8037i 0.600989 + 1.58468i
\(911\) −4.12656 5.05412i −0.136719 0.167451i 0.701707 0.712465i \(-0.252421\pi\)
−0.838426 + 0.545015i \(0.816524\pi\)
\(912\) −8.67886 1.41045i −0.287386 0.0467047i
\(913\) −4.54462 + 37.4283i −0.150405 + 1.23870i
\(914\) 25.9342 0.857826
\(915\) −3.99956 + 32.9393i −0.132221 + 1.08894i
\(916\) −18.0403 + 18.7819i −0.596067 + 0.620571i
\(917\) 5.72870 19.7778i 0.189178 0.653120i
\(918\) −3.85676 13.3151i −0.127292 0.439463i
\(919\) −8.95100 12.9678i −0.295266 0.427767i 0.647072 0.762429i \(-0.275993\pi\)
−0.942338 + 0.334662i \(0.891378\pi\)
\(920\) 1.42699 + 2.47161i 0.0470464 + 0.0814867i
\(921\) 8.02509 + 0.647852i 0.264436 + 0.0213475i
\(922\) −25.7760 + 4.18900i −0.848886 + 0.137957i
\(923\) −10.7481 + 52.6476i −0.353777 + 1.73292i
\(924\) 1.91904 + 9.40006i 0.0631316 + 0.309239i
\(925\) 25.3334 19.0368i 0.832958 0.625927i
\(926\) 19.6922 + 28.5291i 0.647127 + 0.937525i
\(927\) −6.96515 + 0.562285i −0.228765 + 0.0184679i
\(928\) 32.8854 8.10552i 1.07952 0.266077i
\(929\) 16.4190 28.4386i 0.538690 0.933039i −0.460285 0.887771i \(-0.652253\pi\)
0.998975 0.0452675i \(-0.0144140\pi\)
\(930\) −13.1751 22.8200i −0.432029 0.748297i
\(931\) −7.53110 7.84070i −0.246822 0.256969i
\(932\) 51.5137 21.9479i 1.68739 0.718928i
\(933\) −4.67576 9.85396i −0.153078 0.322604i
\(934\) −30.8712 27.3495i −1.01014 0.894904i
\(935\) −54.7056 + 28.7117i −1.78906 + 0.938974i
\(936\) −0.940388 0.979047i −0.0307375 0.0320012i
\(937\) −25.9964 + 19.5350i −0.849265 + 0.638182i −0.933624 0.358254i \(-0.883372\pi\)
0.0843588 + 0.996435i \(0.473116\pi\)
\(938\) −29.4517 15.4574i −0.961632 0.504703i
\(939\) −23.4258 14.8136i −0.764473 0.483423i
\(940\) −50.0357 12.3327i −1.63199 0.402248i
\(941\) −37.0618 −1.20818 −0.604090 0.796916i \(-0.706463\pi\)
−0.604090 + 0.796916i \(0.706463\pi\)
\(942\) −24.6167 + 6.48186i −0.802056 + 0.211190i
\(943\) −39.5249 −1.28711
\(944\) 20.1153 + 4.95797i 0.654696 + 0.161368i
\(945\) −4.05442 2.56386i −0.131890 0.0834024i
\(946\) 11.6526 + 6.11575i 0.378858 + 0.198840i
\(947\) 35.5891 26.7435i 1.15649 0.869046i 0.163419 0.986557i \(-0.447748\pi\)
0.993072 + 0.117510i \(0.0374913\pi\)
\(948\) 21.4050 + 22.2849i 0.695201 + 0.723781i
\(949\) 4.28902 2.25105i 0.139228 0.0730723i
\(950\) 16.6060 + 14.7116i 0.538770 + 0.477309i
\(951\) −10.2807 21.6660i −0.333373 0.702569i
\(952\) 2.51089 1.06979i 0.0813783 0.0346720i
\(953\) −21.0773 21.9438i −0.682762 0.710830i 0.286164 0.958181i \(-0.407620\pi\)
−0.968926 + 0.247350i \(0.920440\pi\)
\(954\) 5.98907 + 10.3734i 0.193903 + 0.335850i
\(955\) 25.9386 44.9270i 0.839353 1.45380i
\(956\) −8.11031 + 1.99901i −0.262306 + 0.0646527i
\(957\) −12.1699 + 0.982460i −0.393399 + 0.0317584i
\(958\) 34.6948 + 50.2641i 1.12094 + 1.62396i
\(959\) 10.0861 7.57922i 0.325697 0.244746i
\(960\) 5.57726 + 27.3192i 0.180005 + 0.881724i
\(961\) 2.70701 13.2598i 0.0873228 0.427736i
\(962\) −71.9798 + 11.6979i −2.32072 + 0.377154i
\(963\) −13.3535 1.07800i −0.430309 0.0347382i
\(964\) −15.6643 27.1314i −0.504514 0.873844i
\(965\) 38.8802 + 56.3277i 1.25160 + 1.81325i
\(966\) −3.10488 10.7193i −0.0998980 0.344888i
\(967\) 12.2419 42.2640i 0.393673 1.35912i −0.481983 0.876181i \(-0.660083\pi\)
0.875656 0.482936i \(-0.160430\pi\)
\(968\) 0.445953 0.464286i 0.0143335 0.0149227i
\(969\) 1.93931 15.9717i 0.0622997 0.513084i
\(970\) −50.1573 −1.61045
\(971\) −5.14095 + 42.3395i −0.164981 + 1.35874i 0.641338 + 0.767259i \(0.278380\pi\)
−0.806319 + 0.591481i \(0.798543\pi\)
\(972\) 2.09982 + 0.341255i 0.0673519 + 0.0109457i
\(973\) −12.1513 14.8827i −0.389553 0.477116i
\(974\) −0.366447 0.966242i −0.0117417 0.0309604i
\(975\) −4.85981 23.8049i −0.155639 0.762368i
\(976\) −36.6796 + 15.6277i −1.17408 + 0.500230i
\(977\) −22.8465 + 48.1480i −0.730924 + 1.54039i 0.106791 + 0.994282i \(0.465943\pi\)
−0.837715 + 0.546108i \(0.816109\pi\)
\(978\) −0.486438 + 12.0708i −0.0155546 + 0.385982i
\(979\) −6.63602 4.98665i −0.212088 0.159374i
\(980\) −13.0498 + 27.5018i −0.416859 + 0.878512i
\(981\) −3.85140 + 2.02137i −0.122966 + 0.0645373i
\(982\) −39.2424 3.16797i −1.25227 0.101094i
\(983\) 0.918913 1.33128i 0.0293088 0.0424611i −0.808056 0.589106i \(-0.799480\pi\)
0.837364 + 0.546645i \(0.184095\pi\)
\(984\) 2.72991 + 0.911378i 0.0870264 + 0.0290537i
\(985\) −52.9204 + 33.4648i −1.68618 + 1.06628i
\(986\) 16.1399 + 55.7214i 0.513999 + 1.77453i
\(987\) 10.6832 + 5.60696i 0.340049 + 0.178471i
\(988\) −9.33140 24.6049i −0.296872 0.782786i
\(989\) −7.25884 3.09270i −0.230818 0.0983423i
\(990\) −0.740693 18.3801i −0.0235408 0.584158i
\(991\) −23.7420 + 34.3962i −0.754188 + 1.09263i 0.238407 + 0.971165i \(0.423375\pi\)
−0.992596 + 0.121465i \(0.961241\pi\)
\(992\) 16.9125 29.2933i 0.536972 0.930062i
\(993\) 0.329710 0.0266169i 0.0104630 0.000844663i
\(994\) 27.1855 17.1911i 0.862272 0.545268i
\(995\) −35.0971 + 11.7171i −1.11265 + 0.371458i
\(996\) −9.74866 + 25.7051i −0.308898 + 0.814498i
\(997\) 4.47780 + 0.727714i 0.141813 + 0.0230469i 0.230904 0.972977i \(-0.425832\pi\)
−0.0890901 + 0.996024i \(0.528396\pi\)
\(998\) −12.6327 3.11367i −0.399880 0.0985616i
\(999\) 4.73985 4.93470i 0.149962 0.156127i
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 471.2.q.b.19.12 336
157.124 even 39 inner 471.2.q.b.124.12 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.q.b.19.12 336 1.1 even 1 trivial
471.2.q.b.124.12 yes 336 157.124 even 39 inner