Properties

Label 539.2.f.e.295.2
Level $539$
Weight $2$
Character 539.295
Analytic conductor $4.304$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(148,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.f (of order \(5\), degree \(4\), 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: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 295.2
Root \(0.435488 - 1.34029i\) of defining polynomial
Character \(\chi\) \(=\) 539.295
Dual form 539.2.f.e.148.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.435488 + 1.34029i) q^{2} +(-1.75021 + 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(0.565930 + 1.74175i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} +O(q^{10})\) \(q+(-0.435488 + 1.34029i) q^{2} +(-1.75021 + 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(0.565930 + 1.74175i) q^{5} +(-0.942126 - 2.89957i) q^{6} +(-2.29616 + 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} -2.58091 q^{10} +(-2.26009 + 2.42734i) q^{11} -0.0302106 q^{12} +(1.43602 - 4.41961i) q^{13} +(-3.20531 - 2.32880i) q^{15} +(-1.22738 - 3.77748i) q^{16} +(1.69039 + 5.20248i) q^{17} +(1.91565 + 1.39180i) q^{18} +(-4.69325 + 3.40985i) q^{19} +(-0.00790293 + 0.0243227i) q^{20} +(-2.26911 - 4.08626i) q^{22} -0.719682 q^{23} +(1.89741 - 5.83962i) q^{24} +(1.33166 - 0.967509i) q^{25} +(5.29821 + 3.84937i) q^{26} +(-0.882303 - 2.71545i) q^{27} +(0.948551 + 0.689163i) q^{29} +(4.51715 - 3.28190i) q^{30} +(0.404153 - 1.24385i) q^{31} -0.0789938 q^{32} +(0.869026 - 7.12230i) q^{33} -7.70900 q^{34} +(0.0189823 - 0.0137915i) q^{36} +(-1.69468 - 1.23126i) q^{37} +(-2.52634 - 7.77528i) q^{38} +(3.10666 + 9.56131i) q^{39} +(-4.20516 - 3.05523i) q^{40} +(-0.741582 + 0.538791i) q^{41} +8.02379 q^{43} +(-0.0454574 + 0.00887181i) q^{44} +3.07713 q^{45} +(0.313413 - 0.964586i) q^{46} +(4.83455 - 3.51251i) q^{47} +(6.95163 + 5.05065i) q^{48} +(0.716823 + 2.20615i) q^{50} +(-9.57403 - 6.95594i) q^{51} +(0.0525003 - 0.0381437i) q^{52} +(3.13496 - 9.64840i) q^{53} +4.02373 q^{54} +(-5.50688 - 2.56282i) q^{55} +(3.87821 - 11.9359i) q^{57} +(-1.33676 + 0.971215i) q^{58} +(-6.21390 - 4.51466i) q^{59} +(-0.0170971 - 0.0526193i) q^{60} +(1.93943 + 5.96895i) q^{61} +(1.49113 + 1.08337i) q^{62} +(2.48916 - 7.66083i) q^{64} +8.51056 q^{65} +(9.16752 + 4.26643i) q^{66} -15.4673 q^{67} +(-0.0236055 + 0.0726501i) q^{68} +(1.25960 - 0.915151i) q^{69} +(4.29593 + 13.2215i) q^{71} +(1.47365 + 4.53542i) q^{72} +(4.86593 + 3.53531i) q^{73} +(2.38826 - 1.73517i) q^{74} +(-1.10040 + 3.38669i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(-4.83332 + 14.8754i) q^{79} +(5.88482 - 4.27557i) q^{80} +(9.07517 + 6.59349i) q^{81} +(-0.399188 - 1.22857i) q^{82} +(1.35217 + 4.16157i) q^{83} +(-8.10479 + 5.88848i) q^{85} +(-3.49426 + 10.7542i) q^{86} -2.53651 q^{87} +(1.14011 - 9.34400i) q^{88} -15.3437 q^{89} +(-1.34005 + 4.12425i) q^{90} +(-0.00813063 - 0.00590725i) q^{92} +(0.874336 + 2.69093i) q^{93} +(2.60240 + 8.00937i) q^{94} +(-8.59515 - 6.24474i) q^{95} +(0.138256 - 0.100449i) q^{96} +(-0.745114 + 2.29323i) q^{97} +(2.70537 + 4.87190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9} - 12 q^{10} - 3 q^{11} - 18 q^{12} + 7 q^{13} - 18 q^{15} + 17 q^{16} + 5 q^{17} + 11 q^{18} - 19 q^{19} - q^{20} - 33 q^{22} + 32 q^{23} + 35 q^{24} + 7 q^{25} + 27 q^{26} - 10 q^{27} + 3 q^{29} - 2 q^{30} + 7 q^{31} + 32 q^{32} + 26 q^{33} + 24 q^{34} + 52 q^{36} + 4 q^{37} + 5 q^{38} + 11 q^{39} + 10 q^{40} + 10 q^{41} - 8 q^{43} - 38 q^{44} - 70 q^{45} - 42 q^{46} + 23 q^{47} + 36 q^{48} + 52 q^{50} - 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 12 q^{55} - 11 q^{57} + 20 q^{58} - 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 7 q^{64} - 8 q^{65} - 8 q^{66} - 38 q^{67} + 2 q^{68} - 10 q^{69} - 14 q^{71} + 35 q^{73} - 29 q^{74} - 9 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 87 q^{80} - 14 q^{81} - 19 q^{82} - 5 q^{83} + 6 q^{85} - 52 q^{86} + 72 q^{87} + 55 q^{88} - 74 q^{89} + 14 q^{90} - 55 q^{92} + 32 q^{93} + 24 q^{94} + 32 q^{95} + 42 q^{96} - 20 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.435488 + 1.34029i −0.307936 + 0.947730i 0.670629 + 0.741793i \(0.266024\pi\)
−0.978565 + 0.205937i \(0.933976\pi\)
\(3\) −1.75021 + 1.27160i −1.01049 + 0.734161i −0.964311 0.264773i \(-0.914703\pi\)
−0.0461746 + 0.998933i \(0.514703\pi\)
\(4\) 0.0112975 + 0.00820814i 0.00564876 + 0.00410407i
\(5\) 0.565930 + 1.74175i 0.253091 + 0.778935i 0.994200 + 0.107550i \(0.0343005\pi\)
−0.741108 + 0.671385i \(0.765700\pi\)
\(6\) −0.942126 2.89957i −0.384621 1.18374i
\(7\) 0 0
\(8\) −2.29616 + 1.66826i −0.811817 + 0.589819i
\(9\) 0.519216 1.59798i 0.173072 0.532661i
\(10\) −2.58091 −0.816157
\(11\) −2.26009 + 2.42734i −0.681444 + 0.731871i
\(12\) −0.0302106 −0.00872104
\(13\) 1.43602 4.41961i 0.398280 1.22578i −0.528097 0.849184i \(-0.677094\pi\)
0.926377 0.376596i \(-0.122906\pi\)
\(14\) 0 0
\(15\) −3.20531 2.32880i −0.827609 0.601293i
\(16\) −1.22738 3.77748i −0.306844 0.944370i
\(17\) 1.69039 + 5.20248i 0.409980 + 1.26179i 0.916665 + 0.399656i \(0.130871\pi\)
−0.506685 + 0.862131i \(0.669129\pi\)
\(18\) 1.91565 + 1.39180i 0.451524 + 0.328051i
\(19\) −4.69325 + 3.40985i −1.07671 + 0.782272i −0.977106 0.212755i \(-0.931756\pi\)
−0.0995999 + 0.995028i \(0.531756\pi\)
\(20\) −0.00790293 + 0.0243227i −0.00176715 + 0.00543873i
\(21\) 0 0
\(22\) −2.26911 4.08626i −0.483775 0.871194i
\(23\) −0.719682 −0.150064 −0.0750321 0.997181i \(-0.523906\pi\)
−0.0750321 + 0.997181i \(0.523906\pi\)
\(24\) 1.89741 5.83962i 0.387307 1.19201i
\(25\) 1.33166 0.967509i 0.266332 0.193502i
\(26\) 5.29821 + 3.84937i 1.03906 + 0.754924i
\(27\) −0.882303 2.71545i −0.169799 0.522588i
\(28\) 0 0
\(29\) 0.948551 + 0.689163i 0.176142 + 0.127974i 0.672363 0.740222i \(-0.265280\pi\)
−0.496221 + 0.868196i \(0.665280\pi\)
\(30\) 4.51715 3.28190i 0.824714 0.599190i
\(31\) 0.404153 1.24385i 0.0725879 0.223403i −0.908180 0.418580i \(-0.862528\pi\)
0.980768 + 0.195177i \(0.0625281\pi\)
\(32\) −0.0789938 −0.0139643
\(33\) 0.869026 7.12230i 0.151278 1.23983i
\(34\) −7.70900 −1.32208
\(35\) 0 0
\(36\) 0.0189823 0.0137915i 0.00316372 0.00229858i
\(37\) −1.69468 1.23126i −0.278604 0.202417i 0.439705 0.898142i \(-0.355083\pi\)
−0.718308 + 0.695725i \(0.755083\pi\)
\(38\) −2.52634 7.77528i −0.409827 1.26132i
\(39\) 3.10666 + 9.56131i 0.497463 + 1.53103i
\(40\) −4.20516 3.05523i −0.664895 0.483074i
\(41\) −0.741582 + 0.538791i −0.115816 + 0.0841449i −0.644185 0.764869i \(-0.722803\pi\)
0.528370 + 0.849014i \(0.322803\pi\)
\(42\) 0 0
\(43\) 8.02379 1.22362 0.611808 0.791006i \(-0.290442\pi\)
0.611808 + 0.791006i \(0.290442\pi\)
\(44\) −0.0454574 + 0.00887181i −0.00685296 + 0.00133748i
\(45\) 3.07713 0.458711
\(46\) 0.313413 0.964586i 0.0462102 0.142220i
\(47\) 4.83455 3.51251i 0.705192 0.512352i −0.176427 0.984314i \(-0.556454\pi\)
0.881619 + 0.471962i \(0.156454\pi\)
\(48\) 6.95163 + 5.05065i 1.00338 + 0.728999i
\(49\) 0 0
\(50\) 0.716823 + 2.20615i 0.101374 + 0.311997i
\(51\) −9.57403 6.95594i −1.34063 0.974027i
\(52\) 0.0525003 0.0381437i 0.00728048 0.00528958i
\(53\) 3.13496 9.64840i 0.430619 1.32531i −0.466890 0.884315i \(-0.654626\pi\)
0.897510 0.440995i \(-0.145374\pi\)
\(54\) 4.02373 0.547560
\(55\) −5.50688 2.56282i −0.742547 0.345570i
\(56\) 0 0
\(57\) 3.87821 11.9359i 0.513682 1.58095i
\(58\) −1.33676 + 0.971215i −0.175526 + 0.127527i
\(59\) −6.21390 4.51466i −0.808981 0.587759i 0.104554 0.994519i \(-0.466659\pi\)
−0.913535 + 0.406760i \(0.866659\pi\)
\(60\) −0.0170971 0.0526193i −0.00220722 0.00679312i
\(61\) 1.93943 + 5.96895i 0.248318 + 0.764246i 0.995073 + 0.0991458i \(0.0316110\pi\)
−0.746754 + 0.665100i \(0.768389\pi\)
\(62\) 1.49113 + 1.08337i 0.189373 + 0.137588i
\(63\) 0 0
\(64\) 2.48916 7.66083i 0.311144 0.957604i
\(65\) 8.51056 1.05560
\(66\) 9.16752 + 4.26643i 1.12844 + 0.525161i
\(67\) −15.4673 −1.88963 −0.944814 0.327608i \(-0.893758\pi\)
−0.944814 + 0.327608i \(0.893758\pi\)
\(68\) −0.0236055 + 0.0726501i −0.00286258 + 0.00881012i
\(69\) 1.25960 0.915151i 0.151638 0.110171i
\(70\) 0 0
\(71\) 4.29593 + 13.2215i 0.509833 + 1.56910i 0.792491 + 0.609883i \(0.208784\pi\)
−0.282659 + 0.959221i \(0.591216\pi\)
\(72\) 1.47365 + 4.53542i 0.173671 + 0.534504i
\(73\) 4.86593 + 3.53531i 0.569514 + 0.413776i 0.834929 0.550358i \(-0.185509\pi\)
−0.265414 + 0.964134i \(0.585509\pi\)
\(74\) 2.38826 1.73517i 0.277629 0.201709i
\(75\) −1.10040 + 3.38669i −0.127064 + 0.391061i
\(76\) −0.0810106 −0.00929255
\(77\) 0 0
\(78\) −14.1679 −1.60420
\(79\) −4.83332 + 14.8754i −0.543791 + 1.67362i 0.180058 + 0.983656i \(0.442372\pi\)
−0.723848 + 0.689959i \(0.757628\pi\)
\(80\) 5.88482 4.27557i 0.657943 0.478024i
\(81\) 9.07517 + 6.59349i 1.00835 + 0.732610i
\(82\) −0.399188 1.22857i −0.0440829 0.135673i
\(83\) 1.35217 + 4.16157i 0.148420 + 0.456791i 0.997435 0.0715783i \(-0.0228036\pi\)
−0.849015 + 0.528370i \(0.822804\pi\)
\(84\) 0 0
\(85\) −8.10479 + 5.88848i −0.879088 + 0.638695i
\(86\) −3.49426 + 10.7542i −0.376796 + 1.15966i
\(87\) −2.53651 −0.271942
\(88\) 1.14011 9.34400i 0.121536 0.996073i
\(89\) −15.3437 −1.62643 −0.813215 0.581963i \(-0.802285\pi\)
−0.813215 + 0.581963i \(0.802285\pi\)
\(90\) −1.34005 + 4.12425i −0.141254 + 0.434735i
\(91\) 0 0
\(92\) −0.00813063 0.00590725i −0.000847677 0.000615873i
\(93\) 0.874336 + 2.69093i 0.0906644 + 0.279036i
\(94\) 2.60240 + 8.00937i 0.268417 + 0.826104i
\(95\) −8.59515 6.24474i −0.881844 0.640697i
\(96\) 0.138256 0.100449i 0.0141107 0.0102520i
\(97\) −0.745114 + 2.29323i −0.0756549 + 0.232842i −0.981731 0.190272i \(-0.939063\pi\)
0.906077 + 0.423114i \(0.139063\pi\)
\(98\) 0 0
\(99\) 2.70537 + 4.87190i 0.271900 + 0.489645i
\(100\) 0.0229859 0.00229859
\(101\) −3.67603 + 11.3136i −0.365778 + 1.12575i 0.583714 + 0.811959i \(0.301599\pi\)
−0.949492 + 0.313790i \(0.898401\pi\)
\(102\) 13.4924 9.80279i 1.33594 0.970620i
\(103\) 0.320625 + 0.232947i 0.0315921 + 0.0229530i 0.603469 0.797386i \(-0.293785\pi\)
−0.571877 + 0.820339i \(0.693785\pi\)
\(104\) 4.07573 + 12.5438i 0.399658 + 1.23002i
\(105\) 0 0
\(106\) 11.5665 + 8.40352i 1.12343 + 0.816222i
\(107\) 2.64496 1.92168i 0.255698 0.185776i −0.452550 0.891739i \(-0.649486\pi\)
0.708248 + 0.705963i \(0.249486\pi\)
\(108\) 0.0123209 0.0379199i 0.00118558 0.00364885i
\(109\) −2.84638 −0.272634 −0.136317 0.990665i \(-0.543527\pi\)
−0.136317 + 0.990665i \(0.543527\pi\)
\(110\) 5.83310 6.26476i 0.556165 0.597321i
\(111\) 4.53172 0.430132
\(112\) 0 0
\(113\) −11.7668 + 8.54906i −1.10692 + 0.804228i −0.982177 0.187961i \(-0.939812\pi\)
−0.124748 + 0.992188i \(0.539812\pi\)
\(114\) 14.3087 + 10.3959i 1.34013 + 0.973663i
\(115\) −0.407290 1.25351i −0.0379799 0.116890i
\(116\) 0.00505954 + 0.0155717i 0.000469767 + 0.00144579i
\(117\) −6.31686 4.58947i −0.583994 0.424296i
\(118\) 8.75705 6.36237i 0.806152 0.585704i
\(119\) 0 0
\(120\) 11.2450 1.02652
\(121\) −0.783964 10.9720i −0.0712695 0.997457i
\(122\) −8.84474 −0.800765
\(123\) 0.612797 1.88600i 0.0552541 0.170054i
\(124\) 0.0147756 0.0107351i 0.00132689 0.000964044i
\(125\) 9.84690 + 7.15419i 0.880734 + 0.639890i
\(126\) 0 0
\(127\) 1.55524 + 4.78655i 0.138006 + 0.424737i 0.996045 0.0888458i \(-0.0283178\pi\)
−0.858040 + 0.513583i \(0.828318\pi\)
\(128\) 9.05595 + 6.57953i 0.800440 + 0.581554i
\(129\) −14.0433 + 10.2031i −1.23645 + 0.898331i
\(130\) −3.70624 + 11.4066i −0.325059 + 1.00043i
\(131\) 0.180053 0.0157313 0.00786565 0.999969i \(-0.497496\pi\)
0.00786565 + 0.999969i \(0.497496\pi\)
\(132\) 0.0682787 0.0733313i 0.00594290 0.00638267i
\(133\) 0 0
\(134\) 6.73581 20.7307i 0.581885 1.79086i
\(135\) 4.23032 3.07350i 0.364088 0.264525i
\(136\) −12.5605 9.12574i −1.07705 0.782526i
\(137\) 2.57224 + 7.91655i 0.219762 + 0.676357i 0.998781 + 0.0493570i \(0.0157172\pi\)
−0.779020 + 0.627000i \(0.784283\pi\)
\(138\) 0.678031 + 2.08677i 0.0577179 + 0.177637i
\(139\) −5.63172 4.09169i −0.477677 0.347052i 0.322749 0.946485i \(-0.395393\pi\)
−0.800425 + 0.599432i \(0.795393\pi\)
\(140\) 0 0
\(141\) −3.99497 + 12.2953i −0.336438 + 1.03545i
\(142\) −19.5915 −1.64408
\(143\) 7.48237 + 13.4744i 0.625707 + 1.12679i
\(144\) −6.67362 −0.556135
\(145\) −0.663538 + 2.04216i −0.0551038 + 0.169592i
\(146\) −6.85740 + 4.98219i −0.567523 + 0.412329i
\(147\) 0 0
\(148\) −0.00903937 0.0278203i −0.000743031 0.00228682i
\(149\) −0.993277 3.05699i −0.0813724 0.250439i 0.902091 0.431546i \(-0.142032\pi\)
−0.983463 + 0.181108i \(0.942032\pi\)
\(150\) −4.05995 2.94972i −0.331493 0.240844i
\(151\) −18.0144 + 13.0882i −1.46599 + 1.06510i −0.484239 + 0.874936i \(0.660903\pi\)
−0.981752 + 0.190168i \(0.939097\pi\)
\(152\) 5.08796 15.6591i 0.412688 1.27012i
\(153\) 9.19115 0.743061
\(154\) 0 0
\(155\) 2.39521 0.192388
\(156\) −0.0433830 + 0.133519i −0.00347342 + 0.0106901i
\(157\) 10.7233 7.79096i 0.855816 0.621786i −0.0709277 0.997481i \(-0.522596\pi\)
0.926743 + 0.375695i \(0.122596\pi\)
\(158\) −17.8326 12.9561i −1.41868 1.03073i
\(159\) 6.78211 + 20.8732i 0.537856 + 1.65535i
\(160\) −0.0447049 0.137588i −0.00353423 0.0108773i
\(161\) 0 0
\(162\) −12.7893 + 9.29200i −1.00483 + 0.730048i
\(163\) 4.23920 13.0469i 0.332040 1.02191i −0.636122 0.771589i \(-0.719462\pi\)
0.968162 0.250325i \(-0.0805375\pi\)
\(164\) −0.0128005 −0.000999552
\(165\) 12.8971 2.51709i 1.00404 0.195955i
\(166\) −6.16657 −0.478619
\(167\) −2.87651 + 8.85300i −0.222591 + 0.685066i 0.775936 + 0.630812i \(0.217278\pi\)
−0.998527 + 0.0542539i \(0.982722\pi\)
\(168\) 0 0
\(169\) −6.95361 5.05209i −0.534893 0.388623i
\(170\) −4.36275 13.4272i −0.334608 1.02982i
\(171\) 3.01206 + 9.27018i 0.230338 + 0.708908i
\(172\) 0.0906490 + 0.0658604i 0.00691192 + 0.00502181i
\(173\) 8.49927 6.17508i 0.646188 0.469483i −0.215783 0.976441i \(-0.569230\pi\)
0.861970 + 0.506959i \(0.169230\pi\)
\(174\) 1.10462 3.39966i 0.0837409 0.257728i
\(175\) 0 0
\(176\) 11.9432 + 5.55819i 0.900254 + 0.418964i
\(177\) 16.6165 1.24897
\(178\) 6.68200 20.5651i 0.500837 1.54142i
\(179\) 6.73370 4.89232i 0.503300 0.365669i −0.306976 0.951717i \(-0.599317\pi\)
0.810276 + 0.586048i \(0.199317\pi\)
\(180\) 0.0347639 + 0.0252575i 0.00259115 + 0.00188258i
\(181\) 4.57437 + 14.0785i 0.340010 + 1.04644i 0.964201 + 0.265172i \(0.0854286\pi\)
−0.624191 + 0.781272i \(0.714571\pi\)
\(182\) 0 0
\(183\) −10.9845 7.98074i −0.812001 0.589953i
\(184\) 1.65251 1.20062i 0.121825 0.0885107i
\(185\) 1.18547 3.64852i 0.0871578 0.268244i
\(186\) −3.98740 −0.292370
\(187\) −16.4486 7.65494i −1.20284 0.559785i
\(188\) 0.0834496 0.00608619
\(189\) 0 0
\(190\) 12.1129 8.80052i 0.878760 0.638457i
\(191\) 7.77203 + 5.64671i 0.562364 + 0.408582i 0.832324 0.554290i \(-0.187010\pi\)
−0.269959 + 0.962872i \(0.587010\pi\)
\(192\) 5.38499 + 16.5733i 0.388628 + 1.19607i
\(193\) −0.459758 1.41499i −0.0330941 0.101853i 0.933145 0.359500i \(-0.117053\pi\)
−0.966239 + 0.257647i \(0.917053\pi\)
\(194\) −2.74911 1.99734i −0.197374 0.143401i
\(195\) −14.8953 + 10.8221i −1.06667 + 0.774983i
\(196\) 0 0
\(197\) −14.0434 −1.00055 −0.500274 0.865867i \(-0.666767\pi\)
−0.500274 + 0.865867i \(0.666767\pi\)
\(198\) −7.70793 + 1.50434i −0.547779 + 0.106909i
\(199\) 4.28729 0.303918 0.151959 0.988387i \(-0.451442\pi\)
0.151959 + 0.988387i \(0.451442\pi\)
\(200\) −1.44366 + 4.44312i −0.102082 + 0.314176i
\(201\) 27.0710 19.6682i 1.90944 1.38729i
\(202\) −13.5627 9.85391i −0.954271 0.693318i
\(203\) 0 0
\(204\) −0.0510676 0.157170i −0.00357545 0.0110041i
\(205\) −1.35812 0.986734i −0.0948554 0.0689165i
\(206\) −0.451846 + 0.328285i −0.0314816 + 0.0228727i
\(207\) −0.373671 + 1.15004i −0.0259719 + 0.0799333i
\(208\) −18.4575 −1.27980
\(209\) 2.33032 19.0987i 0.161192 1.32108i
\(210\) 0 0
\(211\) −0.449704 + 1.38405i −0.0309589 + 0.0952816i −0.965342 0.260988i \(-0.915952\pi\)
0.934383 + 0.356270i \(0.115952\pi\)
\(212\) 0.114613 0.0832710i 0.00787163 0.00571907i
\(213\) −24.3313 17.6777i −1.66715 1.21126i
\(214\) 1.42376 + 4.38189i 0.0973264 + 0.299540i
\(215\) 4.54090 + 13.9755i 0.309687 + 0.953118i
\(216\) 6.55599 + 4.76320i 0.446079 + 0.324095i
\(217\) 0 0
\(218\) 1.23957 3.81499i 0.0839540 0.258384i
\(219\) −13.0119 −0.879264
\(220\) −0.0411782 0.0741547i −0.00277623 0.00499951i
\(221\) 25.4204 1.70996
\(222\) −1.97351 + 6.07383i −0.132453 + 0.407649i
\(223\) −3.92893 + 2.85453i −0.263101 + 0.191154i −0.711513 0.702673i \(-0.751990\pi\)
0.448412 + 0.893827i \(0.351990\pi\)
\(224\) 0 0
\(225\) −0.854642 2.63032i −0.0569761 0.175354i
\(226\) −6.33396 19.4939i −0.421329 1.29672i
\(227\) 0.321296 + 0.233435i 0.0213252 + 0.0154936i 0.598397 0.801200i \(-0.295805\pi\)
−0.577072 + 0.816694i \(0.695805\pi\)
\(228\) 0.141786 0.103013i 0.00938999 0.00682223i
\(229\) −0.676634 + 2.08246i −0.0447132 + 0.137613i −0.970921 0.239401i \(-0.923049\pi\)
0.926208 + 0.377014i \(0.123049\pi\)
\(230\) 1.85744 0.122476
\(231\) 0 0
\(232\) −3.32773 −0.218476
\(233\) −0.389410 + 1.19848i −0.0255111 + 0.0785150i −0.963001 0.269496i \(-0.913143\pi\)
0.937490 + 0.348011i \(0.113143\pi\)
\(234\) 8.90215 6.46779i 0.581952 0.422813i
\(235\) 8.85393 + 6.43276i 0.577567 + 0.419627i
\(236\) −0.0331448 0.102009i −0.00215754 0.00664023i
\(237\) −10.4563 32.1812i −0.679210 2.09039i
\(238\) 0 0
\(239\) 9.02997 6.56066i 0.584100 0.424374i −0.256100 0.966650i \(-0.582438\pi\)
0.840200 + 0.542277i \(0.182438\pi\)
\(240\) −4.86285 + 14.9663i −0.313896 + 0.966072i
\(241\) 21.4843 1.38392 0.691962 0.721934i \(-0.256746\pi\)
0.691962 + 0.721934i \(0.256746\pi\)
\(242\) 15.0471 + 3.72744i 0.967267 + 0.239609i
\(243\) −15.7022 −1.00730
\(244\) −0.0270832 + 0.0833535i −0.00173382 + 0.00533616i
\(245\) 0 0
\(246\) 2.26092 + 1.64266i 0.144151 + 0.104732i
\(247\) 8.33060 + 25.6390i 0.530063 + 1.63137i
\(248\) 1.14707 + 3.53032i 0.0728391 + 0.224176i
\(249\) −7.65846 5.56419i −0.485335 0.352616i
\(250\) −13.8769 + 10.0822i −0.877653 + 0.637652i
\(251\) 0.130968 0.403077i 0.00826660 0.0254420i −0.946838 0.321710i \(-0.895742\pi\)
0.955105 + 0.296268i \(0.0957423\pi\)
\(252\) 0 0
\(253\) 1.62655 1.74691i 0.102260 0.109828i
\(254\) −7.09267 −0.445033
\(255\) 6.69730 20.6122i 0.419401 1.29078i
\(256\) 0.271127 0.196986i 0.0169455 0.0123116i
\(257\) 14.1093 + 10.2510i 0.880115 + 0.639441i 0.933282 0.359145i \(-0.116932\pi\)
−0.0531672 + 0.998586i \(0.516932\pi\)
\(258\) −7.55942 23.2655i −0.470629 1.44845i
\(259\) 0 0
\(260\) 0.0961483 + 0.0698558i 0.00596286 + 0.00433227i
\(261\) 1.59377 1.15794i 0.0986521 0.0716749i
\(262\) −0.0784109 + 0.241324i −0.00484424 + 0.0149090i
\(263\) 1.51519 0.0934307 0.0467153 0.998908i \(-0.485125\pi\)
0.0467153 + 0.998908i \(0.485125\pi\)
\(264\) 9.88643 + 17.8037i 0.608468 + 1.09574i
\(265\) 18.5793 1.14132
\(266\) 0 0
\(267\) 26.8548 19.5111i 1.64348 1.19406i
\(268\) −0.174742 0.126957i −0.0106741 0.00775516i
\(269\) 0.627622 + 1.93162i 0.0382668 + 0.117773i 0.968365 0.249538i \(-0.0802786\pi\)
−0.930098 + 0.367311i \(0.880279\pi\)
\(270\) 2.27715 + 7.00834i 0.138583 + 0.426514i
\(271\) 6.15212 + 4.46978i 0.373715 + 0.271520i 0.758750 0.651382i \(-0.225811\pi\)
−0.385035 + 0.922902i \(0.625811\pi\)
\(272\) 17.5775 12.7708i 1.06579 0.774344i
\(273\) 0 0
\(274\) −11.7307 −0.708676
\(275\) −0.661205 + 5.41905i −0.0398722 + 0.326781i
\(276\) 0.0217420 0.00130872
\(277\) 4.45813 13.7207i 0.267863 0.824398i −0.723157 0.690684i \(-0.757310\pi\)
0.991020 0.133714i \(-0.0426903\pi\)
\(278\) 7.93661 5.76628i 0.476006 0.345839i
\(279\) −1.77781 1.29166i −0.106435 0.0773295i
\(280\) 0 0
\(281\) 5.48494 + 16.8809i 0.327204 + 1.00703i 0.970436 + 0.241359i \(0.0775933\pi\)
−0.643232 + 0.765672i \(0.722407\pi\)
\(282\) −14.7395 10.7089i −0.877725 0.637704i
\(283\) −25.1897 + 18.3014i −1.49737 + 1.08790i −0.525956 + 0.850512i \(0.676292\pi\)
−0.971414 + 0.237392i \(0.923708\pi\)
\(284\) −0.0599905 + 0.184632i −0.00355978 + 0.0109559i
\(285\) 22.9842 1.36147
\(286\) −21.3182 + 4.16062i −1.26057 + 0.246022i
\(287\) 0 0
\(288\) −0.0410148 + 0.126231i −0.00241682 + 0.00743821i
\(289\) −10.4551 + 7.59609i −0.615007 + 0.446829i
\(290\) −2.44813 1.77867i −0.143759 0.104447i
\(291\) −1.61197 4.96112i −0.0944951 0.290826i
\(292\) 0.0259547 + 0.0798805i 0.00151889 + 0.00467465i
\(293\) −19.4409 14.1247i −1.13575 0.825171i −0.149229 0.988803i \(-0.547679\pi\)
−0.986522 + 0.163632i \(0.947679\pi\)
\(294\) 0 0
\(295\) 4.34679 13.3781i 0.253080 0.778901i
\(296\) 5.94532 0.345565
\(297\) 8.58540 + 3.99552i 0.498176 + 0.231843i
\(298\) 4.52983 0.262406
\(299\) −1.03348 + 3.18072i −0.0597676 + 0.183946i
\(300\) −0.0402302 + 0.0292290i −0.00232269 + 0.00168754i
\(301\) 0 0
\(302\) −9.69701 29.8443i −0.558000 1.71735i
\(303\) −7.95265 24.4757i −0.456868 1.40609i
\(304\) 18.6410 + 13.5435i 1.06914 + 0.776772i
\(305\) −9.29885 + 6.75601i −0.532450 + 0.386848i
\(306\) −4.00263 + 12.3188i −0.228815 + 0.704221i
\(307\) 5.46298 0.311789 0.155894 0.987774i \(-0.450174\pi\)
0.155894 + 0.987774i \(0.450174\pi\)
\(308\) 0 0
\(309\) −0.857378 −0.0487745
\(310\) −1.04308 + 3.21028i −0.0592431 + 0.182332i
\(311\) 11.2360 8.16342i 0.637134 0.462905i −0.221730 0.975108i \(-0.571170\pi\)
0.858864 + 0.512203i \(0.171170\pi\)
\(312\) −23.0842 16.7716i −1.30688 0.949506i
\(313\) −8.48207 26.1051i −0.479435 1.47555i −0.839882 0.542770i \(-0.817376\pi\)
0.360447 0.932780i \(-0.382624\pi\)
\(314\) 5.77229 + 17.7653i 0.325749 + 1.00255i
\(315\) 0 0
\(316\) −0.176704 + 0.128383i −0.00994038 + 0.00722211i
\(317\) 2.41828 7.44269i 0.135824 0.418023i −0.859893 0.510474i \(-0.829470\pi\)
0.995717 + 0.0924507i \(0.0294701\pi\)
\(318\) −30.9297 −1.73445
\(319\) −3.81665 + 0.744885i −0.213691 + 0.0417056i
\(320\) 14.7520 0.824659
\(321\) −2.18563 + 6.72669i −0.121990 + 0.375447i
\(322\) 0 0
\(323\) −25.6731 18.6526i −1.42849 1.03786i
\(324\) 0.0484067 + 0.148980i 0.00268926 + 0.00827669i
\(325\) −2.36372 7.27479i −0.131116 0.403533i
\(326\) 15.6406 + 11.3635i 0.866252 + 0.629369i
\(327\) 4.98178 3.61947i 0.275493 0.200157i
\(328\) 0.803950 2.47430i 0.0443907 0.136621i
\(329\) 0 0
\(330\) −2.24288 + 18.3820i −0.123467 + 1.01190i
\(331\) −28.1462 −1.54705 −0.773527 0.633764i \(-0.781509\pi\)
−0.773527 + 0.633764i \(0.781509\pi\)
\(332\) −0.0188825 + 0.0581143i −0.00103631 + 0.00318943i
\(333\) −2.84743 + 2.06878i −0.156038 + 0.113368i
\(334\) −10.6129 7.71075i −0.580714 0.421913i
\(335\) −8.75338 26.9401i −0.478248 1.47190i
\(336\) 0 0
\(337\) 20.2084 + 14.6823i 1.10082 + 0.799793i 0.981194 0.193025i \(-0.0618300\pi\)
0.119628 + 0.992819i \(0.461830\pi\)
\(338\) 9.79950 7.11975i 0.533022 0.387263i
\(339\) 9.72333 29.9253i 0.528099 1.62532i
\(340\) −0.139898 −0.00758701
\(341\) 2.10583 + 3.79224i 0.114037 + 0.205361i
\(342\) −13.7365 −0.742783
\(343\) 0 0
\(344\) −18.4239 + 13.3858i −0.993352 + 0.721713i
\(345\) 2.30681 + 1.67599i 0.124194 + 0.0902325i
\(346\) 4.57509 + 14.0807i 0.245959 + 0.756983i
\(347\) 6.38096 + 19.6386i 0.342548 + 1.05425i 0.962883 + 0.269918i \(0.0869965\pi\)
−0.620335 + 0.784337i \(0.713003\pi\)
\(348\) −0.0286563 0.0208200i −0.00153614 0.00111607i
\(349\) −4.85185 + 3.52507i −0.259713 + 0.188693i −0.710021 0.704181i \(-0.751314\pi\)
0.450307 + 0.892874i \(0.351314\pi\)
\(350\) 0 0
\(351\) −13.2682 −0.708206
\(352\) 0.178533 0.191745i 0.00951585 0.0102200i
\(353\) −24.0382 −1.27942 −0.639712 0.768615i \(-0.720946\pi\)
−0.639712 + 0.768615i \(0.720946\pi\)
\(354\) −7.23629 + 22.2710i −0.384604 + 1.18369i
\(355\) −20.5974 + 14.9649i −1.09320 + 0.794253i
\(356\) −0.173346 0.125943i −0.00918732 0.00667498i
\(357\) 0 0
\(358\) 3.62470 + 11.1557i 0.191571 + 0.589596i
\(359\) 8.85883 + 6.43632i 0.467551 + 0.339696i 0.796486 0.604657i \(-0.206690\pi\)
−0.328935 + 0.944353i \(0.606690\pi\)
\(360\) −7.06559 + 5.13345i −0.372389 + 0.270557i
\(361\) 4.52822 13.9364i 0.238328 0.733497i
\(362\) −20.8613 −1.09645
\(363\) 15.3242 + 18.2065i 0.804311 + 0.955593i
\(364\) 0 0
\(365\) −3.40385 + 10.4760i −0.178166 + 0.548338i
\(366\) 15.4802 11.2470i 0.809161 0.587890i
\(367\) 8.58995 + 6.24096i 0.448392 + 0.325776i 0.788960 0.614444i \(-0.210620\pi\)
−0.340569 + 0.940220i \(0.610620\pi\)
\(368\) 0.883322 + 2.71859i 0.0460463 + 0.141716i
\(369\) 0.475937 + 1.46478i 0.0247763 + 0.0762535i
\(370\) 4.37382 + 3.17777i 0.227384 + 0.165204i
\(371\) 0 0
\(372\) −0.0122097 + 0.0375775i −0.000633042 + 0.00194830i
\(373\) 36.6036 1.89526 0.947631 0.319367i \(-0.103470\pi\)
0.947631 + 0.319367i \(0.103470\pi\)
\(374\) 17.4230 18.7124i 0.900924 0.967593i
\(375\) −26.3315 −1.35975
\(376\) −5.24115 + 16.1306i −0.270292 + 0.831872i
\(377\) 4.40797 3.20258i 0.227022 0.164941i
\(378\) 0 0
\(379\) −3.91147 12.0383i −0.200919 0.618364i −0.999856 0.0169501i \(-0.994604\pi\)
0.798938 0.601414i \(-0.205396\pi\)
\(380\) −0.0458463 0.141100i −0.00235187 0.00723830i
\(381\) −8.80860 6.39982i −0.451278 0.327873i
\(382\) −10.9529 + 7.95773i −0.560398 + 0.407153i
\(383\) 4.77984 14.7108i 0.244238 0.751688i −0.751522 0.659708i \(-0.770680\pi\)
0.995761 0.0919809i \(-0.0293199\pi\)
\(384\) −24.2164 −1.23579
\(385\) 0 0
\(386\) 2.09672 0.106720
\(387\) 4.16608 12.8219i 0.211774 0.651773i
\(388\) −0.0272411 + 0.0197918i −0.00138296 + 0.00100478i
\(389\) 10.2850 + 7.47249i 0.521470 + 0.378870i 0.817157 0.576415i \(-0.195549\pi\)
−0.295687 + 0.955285i \(0.595549\pi\)
\(390\) −8.01801 24.6769i −0.406008 1.24956i
\(391\) −1.21654 3.74414i −0.0615232 0.189349i
\(392\) 0 0
\(393\) −0.315131 + 0.228956i −0.0158963 + 0.0115493i
\(394\) 6.11571 18.8222i 0.308105 0.948250i
\(395\) −28.6446 −1.44127
\(396\) −0.00942522 + 0.0772465i −0.000473635 + 0.00388178i
\(397\) 18.9574 0.951445 0.475722 0.879596i \(-0.342187\pi\)
0.475722 + 0.879596i \(0.342187\pi\)
\(398\) −1.86706 + 5.74622i −0.0935873 + 0.288032i
\(399\) 0 0
\(400\) −5.28919 3.84282i −0.264460 0.192141i
\(401\) −2.68291 8.25715i −0.133978 0.412343i 0.861451 0.507840i \(-0.169556\pi\)
−0.995430 + 0.0954974i \(0.969556\pi\)
\(402\) 14.5721 + 44.8484i 0.726791 + 2.23683i
\(403\) −4.91698 3.57240i −0.244932 0.177954i
\(404\) −0.134394 + 0.0976429i −0.00668635 + 0.00485792i
\(405\) −6.34833 + 19.5381i −0.315451 + 0.970858i
\(406\) 0 0
\(407\) 6.81881 1.33081i 0.337996 0.0659658i
\(408\) 33.5879 1.66285
\(409\) −1.76574 + 5.43440i −0.0873104 + 0.268714i −0.985173 0.171561i \(-0.945119\pi\)
0.897863 + 0.440275i \(0.145119\pi\)
\(410\) 1.91396 1.39057i 0.0945237 0.0686755i
\(411\) −14.5687 10.5848i −0.718620 0.522108i
\(412\) 0.00171020 + 0.00526346i 8.42556e−5 + 0.000259312i
\(413\) 0 0
\(414\) −1.37866 1.00166i −0.0677575 0.0492287i
\(415\) −6.48318 + 4.71031i −0.318247 + 0.231220i
\(416\) −0.113437 + 0.349122i −0.00556169 + 0.0171171i
\(417\) 15.0597 0.737477
\(418\) 24.5830 + 11.4406i 1.20239 + 0.559576i
\(419\) 27.1909 1.32836 0.664181 0.747571i \(-0.268780\pi\)
0.664181 + 0.747571i \(0.268780\pi\)
\(420\) 0 0
\(421\) 19.3881 14.0863i 0.944921 0.686525i −0.00467947 0.999989i \(-0.501490\pi\)
0.949600 + 0.313464i \(0.101490\pi\)
\(422\) −1.65919 1.20547i −0.0807679 0.0586813i
\(423\) −3.10275 9.54928i −0.150861 0.464302i
\(424\) 8.89768 + 27.3842i 0.432110 + 1.32990i
\(425\) 7.28447 + 5.29248i 0.353349 + 0.256723i
\(426\) 34.2893 24.9126i 1.66132 1.20702i
\(427\) 0 0
\(428\) 0.0456549 0.00220681
\(429\) −30.2299 14.0685i −1.45951 0.679235i
\(430\) −20.7087 −0.998663
\(431\) 5.09049 15.6669i 0.245200 0.754649i −0.750403 0.660980i \(-0.770141\pi\)
0.995603 0.0936683i \(-0.0298593\pi\)
\(432\) −9.17463 + 6.66576i −0.441415 + 0.320706i
\(433\) 16.2539 + 11.8092i 0.781113 + 0.567512i 0.905313 0.424745i \(-0.139636\pi\)
−0.124200 + 0.992257i \(0.539636\pi\)
\(434\) 0 0
\(435\) −1.43548 4.41797i −0.0688262 0.211825i
\(436\) −0.0321571 0.0233635i −0.00154005 0.00111891i
\(437\) 3.37765 2.45401i 0.161575 0.117391i
\(438\) 5.66653 17.4398i 0.270757 0.833306i
\(439\) −26.7682 −1.27758 −0.638788 0.769383i \(-0.720564\pi\)
−0.638788 + 0.769383i \(0.720564\pi\)
\(440\) 16.9201 3.30226i 0.806636 0.157429i
\(441\) 0 0
\(442\) −11.0703 + 34.0708i −0.526559 + 1.62058i
\(443\) −21.2086 + 15.4090i −1.00765 + 0.732103i −0.963716 0.266931i \(-0.913990\pi\)
−0.0439378 + 0.999034i \(0.513990\pi\)
\(444\) 0.0511972 + 0.0371970i 0.00242971 + 0.00176529i
\(445\) −8.68346 26.7249i −0.411635 1.26688i
\(446\) −2.11491 6.50903i −0.100144 0.308212i
\(447\) 5.62573 + 4.08733i 0.266088 + 0.193324i
\(448\) 0 0
\(449\) 3.01211 9.27033i 0.142150 0.437494i −0.854483 0.519479i \(-0.826126\pi\)
0.996634 + 0.0819851i \(0.0261260\pi\)
\(450\) 3.89758 0.183734
\(451\) 0.368215 3.01779i 0.0173386 0.142102i
\(452\) −0.203107 −0.00955336
\(453\) 14.8860 45.8143i 0.699404 2.15254i
\(454\) −0.452792 + 0.328973i −0.0212506 + 0.0154395i
\(455\) 0 0
\(456\) 11.0072 + 33.8767i 0.515459 + 1.58642i
\(457\) 3.67276 + 11.3036i 0.171805 + 0.528760i 0.999473 0.0324572i \(-0.0103333\pi\)
−0.827669 + 0.561217i \(0.810333\pi\)
\(458\) −2.49645 1.81378i −0.116651 0.0847522i
\(459\) 12.6356 9.18033i 0.589781 0.428501i
\(460\) 0.00568760 0.0175046i 0.000265186 0.000816158i
\(461\) −9.14737 −0.426035 −0.213018 0.977048i \(-0.568329\pi\)
−0.213018 + 0.977048i \(0.568329\pi\)
\(462\) 0 0
\(463\) 38.9342 1.80943 0.904713 0.426021i \(-0.140085\pi\)
0.904713 + 0.426021i \(0.140085\pi\)
\(464\) 1.43907 4.42899i 0.0668070 0.205611i
\(465\) −4.19212 + 3.04575i −0.194405 + 0.141243i
\(466\) −1.43673 1.04385i −0.0665553 0.0483552i
\(467\) 6.42243 + 19.7662i 0.297195 + 0.914671i 0.982475 + 0.186392i \(0.0596795\pi\)
−0.685281 + 0.728279i \(0.740320\pi\)
\(468\) −0.0336939 0.103699i −0.00155750 0.00479350i
\(469\) 0 0
\(470\) −12.4776 + 9.06548i −0.575547 + 0.418159i
\(471\) −8.86110 + 27.2717i −0.408298 + 1.25661i
\(472\) 21.7998 1.00342
\(473\) −18.1345 + 19.4765i −0.833826 + 0.895529i
\(474\) 47.6858 2.19028
\(475\) −2.95076 + 9.08152i −0.135390 + 0.416689i
\(476\) 0 0
\(477\) −13.7903 10.0192i −0.631413 0.458748i
\(478\) 4.86076 + 14.9599i 0.222326 + 0.684249i
\(479\) 7.58214 + 23.3354i 0.346437 + 1.06622i 0.960810 + 0.277207i \(0.0894088\pi\)
−0.614374 + 0.789015i \(0.710591\pi\)
\(480\) 0.253200 + 0.183960i 0.0115569 + 0.00839661i
\(481\) −7.87527 + 5.72172i −0.359081 + 0.260888i
\(482\) −9.35614 + 28.7952i −0.426161 + 1.31159i
\(483\) 0 0
\(484\) 0.0812030 0.130392i 0.00369105 0.00592690i
\(485\) −4.41591 −0.200516
\(486\) 6.83811 21.0456i 0.310183 0.954646i
\(487\) 10.0086 7.27168i 0.453533 0.329511i −0.337456 0.941341i \(-0.609566\pi\)
0.790989 + 0.611830i \(0.209566\pi\)
\(488\) −14.4110 10.4702i −0.652356 0.473964i
\(489\) 9.17101 + 28.2255i 0.414727 + 1.27640i
\(490\) 0 0
\(491\) −13.3691 9.71320i −0.603338 0.438350i 0.243724 0.969845i \(-0.421631\pi\)
−0.847062 + 0.531494i \(0.821631\pi\)
\(492\) 0.0224036 0.0162772i 0.00101003 0.000733831i
\(493\) −1.98194 + 6.09977i −0.0892620 + 0.274720i
\(494\) −37.9916 −1.70932
\(495\) −6.95459 + 7.46924i −0.312586 + 0.335717i
\(496\) −5.19468 −0.233248
\(497\) 0 0
\(498\) 10.7928 7.84144i 0.483638 0.351383i
\(499\) 11.1167 + 8.07673i 0.497650 + 0.361564i 0.808119 0.589020i \(-0.200486\pi\)
−0.310469 + 0.950584i \(0.600486\pi\)
\(500\) 0.0525231 + 0.161649i 0.00234890 + 0.00722918i
\(501\) −6.22300 19.1524i −0.278023 0.855667i
\(502\) 0.483206 + 0.351070i 0.0215665 + 0.0156690i
\(503\) −18.2812 + 13.2820i −0.815117 + 0.592217i −0.915310 0.402751i \(-0.868054\pi\)
0.100193 + 0.994968i \(0.468054\pi\)
\(504\) 0 0
\(505\) −21.7859 −0.969461
\(506\) 1.63304 + 2.94081i 0.0725973 + 0.130735i
\(507\) 18.5946 0.825813
\(508\) −0.0217182 + 0.0668418i −0.000963590 + 0.00296563i
\(509\) −17.3644 + 12.6160i −0.769664 + 0.559194i −0.901859 0.432030i \(-0.857798\pi\)
0.132195 + 0.991224i \(0.457798\pi\)
\(510\) 24.7098 + 17.9527i 1.09417 + 0.794958i
\(511\) 0 0
\(512\) 7.06408 + 21.7410i 0.312191 + 0.960825i
\(513\) 13.4001 + 9.73576i 0.591630 + 0.429844i
\(514\) −19.8838 + 14.4464i −0.877037 + 0.637204i
\(515\) −0.224286 + 0.690280i −0.00988321 + 0.0304174i
\(516\) −0.242403 −0.0106712
\(517\) −2.40048 + 19.6737i −0.105573 + 0.865248i
\(518\) 0 0
\(519\) −7.02327 + 21.6154i −0.308287 + 0.948811i
\(520\) −19.5416 + 14.1978i −0.856957 + 0.622616i
\(521\) 28.0822 + 20.4029i 1.23031 + 0.893869i 0.996913 0.0785132i \(-0.0250173\pi\)
0.233393 + 0.972383i \(0.425017\pi\)
\(522\) 0.857916 + 2.64039i 0.0375500 + 0.115567i
\(523\) −6.09633 18.7626i −0.266574 0.820430i −0.991327 0.131421i \(-0.958046\pi\)
0.724753 0.689009i \(-0.241954\pi\)
\(524\) 0.00203415 + 0.00147790i 8.88624e−5 + 6.45623e-5i
\(525\) 0 0
\(526\) −0.659847 + 2.03080i −0.0287707 + 0.0885471i
\(527\) 7.15430 0.311646
\(528\) −27.9710 + 5.45902i −1.21728 + 0.237573i
\(529\) −22.4821 −0.977481
\(530\) −8.09105 + 24.9017i −0.351453 + 1.08166i
\(531\) −10.4407 + 7.58562i −0.453088 + 0.329188i
\(532\) 0 0
\(533\) 1.31632 + 4.05122i 0.0570162 + 0.175478i
\(534\) 14.4557 + 44.4901i 0.625560 + 1.92527i
\(535\) 4.84395 + 3.51933i 0.209422 + 0.152154i
\(536\) 35.5154 25.8034i 1.53403 1.11454i
\(537\) −5.56431 + 17.1252i −0.240118 + 0.739006i
\(538\) −2.86226 −0.123401
\(539\) 0 0
\(540\) 0.0730199 0.00314227
\(541\) −1.71487 + 5.27782i −0.0737279 + 0.226911i −0.981129 0.193355i \(-0.938063\pi\)
0.907401 + 0.420266i \(0.138063\pi\)
\(542\) −8.66998 + 6.29911i −0.372408 + 0.270570i
\(543\) −25.9083 18.8235i −1.11183 0.807794i
\(544\) −0.133530 0.410964i −0.00572506 0.0176199i
\(545\) −1.61085 4.95770i −0.0690014 0.212364i
\(546\) 0 0
\(547\) 6.83353 4.96485i 0.292181 0.212282i −0.432032 0.901858i \(-0.642203\pi\)
0.724213 + 0.689576i \(0.242203\pi\)
\(548\) −0.0359201 + 0.110551i −0.00153443 + 0.00472250i
\(549\) 10.5453 0.450061
\(550\) −6.97518 3.24614i −0.297422 0.138416i
\(551\) −6.80173 −0.289763
\(552\) −1.36553 + 4.20267i −0.0581209 + 0.178878i
\(553\) 0 0
\(554\) 16.4483 + 11.9504i 0.698822 + 0.507724i
\(555\) 2.56463 + 7.89313i 0.108863 + 0.335045i
\(556\) −0.0300394 0.0924519i −0.00127396 0.00392083i
\(557\) 9.85665 + 7.16128i 0.417640 + 0.303433i 0.776687 0.629886i \(-0.216898\pi\)
−0.359048 + 0.933319i \(0.616898\pi\)
\(558\) 2.50542 1.82029i 0.106063 0.0770591i
\(559\) 11.5223 35.4620i 0.487342 1.49988i
\(560\) 0 0
\(561\) 38.5226 7.51837i 1.62643 0.317426i
\(562\) −25.0140 −1.05515
\(563\) 8.45270 26.0147i 0.356239 1.09639i −0.599049 0.800713i \(-0.704454\pi\)
0.955288 0.295678i \(-0.0955456\pi\)
\(564\) −0.146055 + 0.106115i −0.00615001 + 0.00446824i
\(565\) −21.5495 15.6566i −0.906594 0.658679i
\(566\) −13.5594 41.7316i −0.569944 1.75411i
\(567\) 0 0
\(568\) −31.9211 23.1920i −1.33938 0.973115i
\(569\) −5.77253 + 4.19399i −0.241997 + 0.175821i −0.702173 0.712007i \(-0.747786\pi\)
0.460176 + 0.887828i \(0.347786\pi\)
\(570\) −10.0093 + 30.8055i −0.419245 + 1.29030i
\(571\) 32.4839 1.35941 0.679705 0.733486i \(-0.262108\pi\)
0.679705 + 0.733486i \(0.262108\pi\)
\(572\) −0.0260678 + 0.213644i −0.00108995 + 0.00893291i
\(573\) −20.7831 −0.868226
\(574\) 0 0
\(575\) −0.958373 + 0.696299i −0.0399669 + 0.0290377i
\(576\) −10.9495 7.95525i −0.456228 0.331469i
\(577\) −10.7482 33.0795i −0.447453 1.37712i −0.879771 0.475398i \(-0.842304\pi\)
0.432317 0.901721i \(-0.357696\pi\)
\(578\) −5.62791 17.3209i −0.234090 0.720456i
\(579\) 2.60398 + 1.89190i 0.108218 + 0.0786248i
\(580\) −0.0242587 + 0.0176249i −0.00100729 + 0.000731836i
\(581\) 0 0
\(582\) 7.35135 0.304723
\(583\) 16.3347 + 29.4159i 0.676513 + 1.21828i
\(584\) −17.0708 −0.706395
\(585\) 4.41882 13.5997i 0.182696 0.562279i
\(586\) 27.3975 19.9054i 1.13178 0.822285i
\(587\) −11.7105 8.50816i −0.483343 0.351169i 0.319276 0.947662i \(-0.396560\pi\)
−0.802618 + 0.596493i \(0.796560\pi\)
\(588\) 0 0
\(589\) 2.34456 + 7.21581i 0.0966059 + 0.297322i
\(590\) 16.0375 + 11.6520i 0.660255 + 0.479704i
\(591\) 24.5789 17.8576i 1.01104 0.734563i
\(592\) −2.57103 + 7.91283i −0.105669 + 0.325215i
\(593\) 15.0291 0.617169 0.308585 0.951197i \(-0.400145\pi\)
0.308585 + 0.951197i \(0.400145\pi\)
\(594\) −9.09400 + 9.76696i −0.373131 + 0.400743i
\(595\) 0 0
\(596\) 0.0138706 0.0426894i 0.000568163 0.00174863i
\(597\) −7.50366 + 5.45173i −0.307104 + 0.223124i
\(598\) −3.81303 2.77033i −0.155926 0.113287i
\(599\) 0.544010 + 1.67429i 0.0222276 + 0.0684097i 0.961555 0.274612i \(-0.0885495\pi\)
−0.939327 + 0.343022i \(0.888549\pi\)
\(600\) −3.12318 9.61216i −0.127503 0.392415i
\(601\) 18.9605 + 13.7756i 0.773415 + 0.561919i 0.902995 0.429650i \(-0.141363\pi\)
−0.129581 + 0.991569i \(0.541363\pi\)
\(602\) 0 0
\(603\) −8.03085 + 24.7164i −0.327042 + 1.00653i
\(604\) −0.310948 −0.0126523
\(605\) 18.6669 7.57487i 0.758917 0.307962i
\(606\) 36.2679 1.47328
\(607\) 7.81149 24.0413i 0.317059 0.975806i −0.657840 0.753158i \(-0.728530\pi\)
0.974899 0.222649i \(-0.0714703\pi\)
\(608\) 0.370738 0.269357i 0.0150354 0.0109239i
\(609\) 0 0
\(610\) −5.00550 15.4053i −0.202667 0.623744i
\(611\) −8.58142 26.4109i −0.347167 1.06847i
\(612\) 0.103837 + 0.0754422i 0.00419737 + 0.00304957i
\(613\) −0.939222 + 0.682385i −0.0379348 + 0.0275613i −0.606591 0.795014i \(-0.707463\pi\)
0.568656 + 0.822575i \(0.307463\pi\)
\(614\) −2.37906 + 7.32199i −0.0960110 + 0.295492i
\(615\) 3.63174 0.146446
\(616\) 0 0
\(617\) 12.9711 0.522197 0.261098 0.965312i \(-0.415915\pi\)
0.261098 + 0.965312i \(0.415915\pi\)
\(618\) 0.373377 1.14914i 0.0150194 0.0462251i
\(619\) 37.0465 26.9158i 1.48902 1.08184i 0.514517 0.857480i \(-0.327971\pi\)
0.974507 0.224358i \(-0.0720286\pi\)
\(620\) 0.0270599 + 0.0196602i 0.00108675 + 0.000789572i
\(621\) 0.634978 + 1.95426i 0.0254808 + 0.0784218i
\(622\) 6.04824 + 18.6146i 0.242512 + 0.746377i
\(623\) 0 0
\(624\) 32.3046 23.4707i 1.29322 0.939578i
\(625\) −4.34493 + 13.3723i −0.173797 + 0.534893i
\(626\) 38.6824 1.54606
\(627\) 20.2074 + 36.3900i 0.807006 + 1.45328i
\(628\) 0.185097 0.00738615
\(629\) 3.54092 10.8978i 0.141186 0.434525i
\(630\) 0 0
\(631\) 10.2103 + 7.41824i 0.406467 + 0.295316i 0.772170 0.635416i \(-0.219171\pi\)
−0.365703 + 0.930732i \(0.619171\pi\)
\(632\) −13.7180 42.2196i −0.545672 1.67941i
\(633\) −0.972881 2.99422i −0.0386685 0.119009i
\(634\) 8.92225 + 6.48240i 0.354348 + 0.257449i
\(635\) −7.45682 + 5.41770i −0.295915 + 0.214995i
\(636\) −0.0947088 + 0.291484i −0.00375545 + 0.0115581i
\(637\) 0 0
\(638\) 0.663738 5.43981i 0.0262776 0.215364i
\(639\) 23.3582 0.924038
\(640\) −6.33488 + 19.4968i −0.250408 + 0.770678i
\(641\) −22.6175 + 16.4326i −0.893336 + 0.649047i −0.936746 0.350011i \(-0.886178\pi\)
0.0434095 + 0.999057i \(0.486178\pi\)
\(642\) −8.06392 5.85878i −0.318257 0.231228i
\(643\) 15.3575 + 47.2657i 0.605642 + 1.86398i 0.492313 + 0.870418i \(0.336152\pi\)
0.113330 + 0.993557i \(0.463848\pi\)
\(644\) 0 0
\(645\) −25.7188 18.6858i −1.01268 0.735752i
\(646\) 36.1802 26.2865i 1.42349 1.03423i
\(647\) 3.40125 10.4680i 0.133717 0.411539i −0.861671 0.507467i \(-0.830582\pi\)
0.995388 + 0.0959281i \(0.0305819\pi\)
\(648\) −31.8377 −1.25070
\(649\) 25.0026 4.87970i 0.981439 0.191545i
\(650\) 10.7797 0.422816
\(651\) 0 0
\(652\) 0.154983 0.112602i 0.00606962 0.00440984i
\(653\) −23.4100 17.0084i −0.916106 0.665590i 0.0264458 0.999650i \(-0.491581\pi\)
−0.942552 + 0.334060i \(0.891581\pi\)
\(654\) 2.68165 + 8.25328i 0.104861 + 0.322729i
\(655\) 0.101897 + 0.313608i 0.00398146 + 0.0122537i
\(656\) 2.94547 + 2.14001i 0.115001 + 0.0835533i
\(657\) 8.17583 5.94009i 0.318969 0.231745i
\(658\) 0 0
\(659\) 10.8405 0.422288 0.211144 0.977455i \(-0.432281\pi\)
0.211144 + 0.977455i \(0.432281\pi\)
\(660\) 0.166366 + 0.0774241i 0.00647578 + 0.00301373i
\(661\) −20.3444 −0.791305 −0.395652 0.918400i \(-0.629481\pi\)
−0.395652 + 0.918400i \(0.629481\pi\)
\(662\) 12.2573 37.7241i 0.476394 1.46619i
\(663\) −44.4911 + 32.3247i −1.72789 + 1.25539i
\(664\) −10.0474 7.29986i −0.389915 0.283289i
\(665\) 0 0
\(666\) −1.53275 4.71732i −0.0593929 0.182792i
\(667\) −0.682656 0.495978i −0.0264325 0.0192044i
\(668\) −0.105164 + 0.0764062i −0.00406892 + 0.00295625i
\(669\) 3.24662 9.99208i 0.125522 0.386316i
\(670\) 39.9197 1.54223
\(671\) −18.8720 8.78272i −0.728544 0.339053i
\(672\) 0 0
\(673\) −3.73255 + 11.4876i −0.143879 + 0.442815i −0.996865 0.0791188i \(-0.974789\pi\)
0.852986 + 0.521934i \(0.174789\pi\)
\(674\) −28.4790 + 20.6912i −1.09697 + 0.796996i
\(675\) −3.80215 2.76242i −0.146345 0.106326i
\(676\) −0.0370903 0.114152i −0.00142655 0.00439047i
\(677\) −1.04951 3.23007i −0.0403361 0.124142i 0.928861 0.370429i \(-0.120789\pi\)
−0.969197 + 0.246287i \(0.920789\pi\)
\(678\) 35.8743 + 26.0642i 1.37775 + 1.00099i
\(679\) 0 0
\(680\) 8.78642 27.0418i 0.336944 1.03701i
\(681\) −0.859173 −0.0329236
\(682\) −5.99978 + 1.17096i −0.229743 + 0.0448384i
\(683\) −4.75643 −0.182000 −0.0909999 0.995851i \(-0.529006\pi\)
−0.0909999 + 0.995851i \(0.529006\pi\)
\(684\) −0.0420620 + 0.129454i −0.00160828 + 0.00494978i
\(685\) −12.3330 + 8.96042i −0.471218 + 0.342360i
\(686\) 0 0
\(687\) −1.46382 4.50516i −0.0558481 0.171883i
\(688\) −9.84822 30.3097i −0.375460 1.15555i
\(689\) −38.1404 27.7106i −1.45303 1.05569i
\(690\) −3.25091 + 2.36193i −0.123760 + 0.0899170i
\(691\) −2.04998 + 6.30920i −0.0779850 + 0.240013i −0.982447 0.186540i \(-0.940272\pi\)
0.904462 + 0.426554i \(0.140272\pi\)
\(692\) 0.146707 0.00557695
\(693\) 0 0
\(694\) −29.1003 −1.10463
\(695\) 3.93955 12.1247i 0.149435 0.459915i
\(696\) 5.82424 4.23156i 0.220767 0.160397i
\(697\) −4.05661 2.94730i −0.153655 0.111637i
\(698\) −2.61171 8.03802i −0.0988547 0.304244i
\(699\) −0.842441 2.59277i −0.0318641 0.0980675i
\(700\) 0 0
\(701\) −2.45134 + 1.78101i −0.0925860 + 0.0672677i −0.633115 0.774058i \(-0.718224\pi\)
0.540529 + 0.841325i \(0.318224\pi\)
\(702\) 5.77815 17.7833i 0.218082 0.671188i
\(703\) 12.1519 0.458319
\(704\) 12.9697 + 23.3562i 0.488815 + 0.880270i
\(705\) −23.6762 −0.891697
\(706\) 10.4683 32.2182i 0.393981 1.21255i
\(707\) 0 0
\(708\) 0.187726 + 0.136391i 0.00705516 + 0.00512587i
\(709\) −4.22026 12.9886i −0.158495 0.487798i 0.840003 0.542582i \(-0.182553\pi\)
−0.998498 + 0.0547836i \(0.982553\pi\)
\(710\) −11.0874 34.1236i −0.416103 1.28063i
\(711\) 21.2611 + 15.4471i 0.797354 + 0.579312i
\(712\) 35.2317 25.5973i 1.32036 0.959300i
\(713\) −0.290862 + 0.895180i −0.0108928 + 0.0335247i
\(714\) 0 0
\(715\) −19.2346 + 20.6580i −0.719335 + 0.772566i
\(716\) 0.116231 0.00434376
\(717\) −7.46181 + 22.9651i −0.278666 + 0.857647i
\(718\) −12.4845 + 9.07050i −0.465916 + 0.338508i
\(719\) −1.53737 1.11696i −0.0573341 0.0416557i 0.558749 0.829337i \(-0.311281\pi\)
−0.616083 + 0.787681i \(0.711281\pi\)
\(720\) −3.77680 11.6238i −0.140753 0.433193i
\(721\) 0 0
\(722\) 16.7069 + 12.1383i 0.621768 + 0.451741i
\(723\) −37.6021 + 27.3195i −1.39844 + 1.01602i
\(724\) −0.0638788 + 0.196599i −0.00237404 + 0.00730654i
\(725\) 1.92992 0.0716754
\(726\) −31.0755 + 12.6102i −1.15332 + 0.468008i
\(727\) 13.8211 0.512595 0.256298 0.966598i \(-0.417497\pi\)
0.256298 + 0.966598i \(0.417497\pi\)
\(728\) 0 0
\(729\) 0.256684 0.186492i 0.00950682 0.00690711i
\(730\) −12.5586 9.12432i −0.464813 0.337706i
\(731\) 13.5633 + 41.7436i 0.501658 + 1.54394i
\(732\) −0.0585912 0.180325i −0.00216559 0.00666502i
\(733\) 39.1357 + 28.4337i 1.44551 + 1.05022i 0.986855 + 0.161610i \(0.0516685\pi\)
0.458655 + 0.888615i \(0.348331\pi\)
\(734\) −12.1055 + 8.79519i −0.446824 + 0.324636i
\(735\) 0 0
\(736\) 0.0568504 0.00209553
\(737\) 34.9575 37.5443i 1.28767 1.38296i
\(738\) −2.17050 −0.0798973
\(739\) 7.17170 22.0722i 0.263815 0.811939i −0.728149 0.685419i \(-0.759619\pi\)
0.991964 0.126520i \(-0.0403809\pi\)
\(740\) 0.0433404 0.0314887i 0.00159323 0.00115755i
\(741\) −47.1829 34.2804i −1.73331 1.25932i
\(742\) 0 0
\(743\) −13.8536 42.6369i −0.508238 1.56420i −0.795257 0.606272i \(-0.792664\pi\)
0.287019 0.957925i \(-0.407336\pi\)
\(744\) −6.49679 4.72020i −0.238184 0.173051i
\(745\) 4.76240 3.46009i 0.174481 0.126768i
\(746\) −15.9404 + 49.0596i −0.583620 + 1.79620i
\(747\) 7.35218 0.269002
\(748\) −0.122996 0.221495i −0.00449718 0.00809864i
\(749\) 0 0
\(750\) 11.4670 35.2919i 0.418717 1.28868i
\(751\) 33.3199 24.2083i 1.21586 0.883373i 0.220109 0.975475i \(-0.429359\pi\)
0.995750 + 0.0921022i \(0.0293587\pi\)
\(752\) −19.2022 13.9512i −0.700234 0.508750i
\(753\) 0.283333 + 0.872008i 0.0103252 + 0.0317777i
\(754\) 2.37278 + 7.30266i 0.0864115 + 0.265947i
\(755\) −32.9913 23.9696i −1.20068 0.872343i
\(756\) 0 0
\(757\) −6.76401 + 20.8175i −0.245842 + 0.756624i 0.749655 + 0.661829i \(0.230219\pi\)
−0.995497 + 0.0947948i \(0.969781\pi\)
\(758\) 17.8382 0.647912
\(759\) −0.625423 + 5.12580i −0.0227014 + 0.186055i
\(760\) 30.1537 1.09379
\(761\) 11.0367 33.9673i 0.400078 1.23131i −0.524857 0.851190i \(-0.675881\pi\)
0.924935 0.380124i \(-0.124119\pi\)
\(762\) 12.4137 9.01906i 0.449700 0.326726i
\(763\) 0 0
\(764\) 0.0414558 + 0.127588i 0.00149982 + 0.00461596i
\(765\) 5.20154 + 16.0087i 0.188062 + 0.578796i
\(766\) 17.6353 + 12.8128i 0.637188 + 0.462944i
\(767\) −28.8764 + 20.9799i −1.04266 + 0.757540i
\(768\) −0.224043 + 0.689533i −0.00808445 + 0.0248814i
\(769\) −5.30246 −0.191212 −0.0956058 0.995419i \(-0.530479\pi\)
−0.0956058 + 0.995419i \(0.530479\pi\)
\(770\) 0 0
\(771\) −37.7295 −1.35880
\(772\) 0.00642030 0.0197596i 0.000231072 0.000711165i
\(773\) −40.3628 + 29.3253i −1.45175 + 1.05476i −0.466332 + 0.884610i \(0.654425\pi\)
−0.985418 + 0.170149i \(0.945575\pi\)
\(774\) 15.3708 + 11.1675i 0.552492 + 0.401409i
\(775\) −0.665245 2.04741i −0.0238963 0.0735452i
\(776\) −2.11479 6.50867i −0.0759167 0.233648i
\(777\) 0 0
\(778\) −14.4943 + 10.5307i −0.519646 + 0.377545i
\(779\) 1.64324 5.05736i 0.0588750 0.181199i
\(780\) −0.257109 −0.00920597
\(781\) −41.8023 19.4541i −1.49580 0.696124i
\(782\) 5.54803 0.198397
\(783\) 1.03448 3.18379i 0.0369692 0.113779i
\(784\) 0 0
\(785\) 19.6386 + 14.2683i 0.700931 + 0.509256i
\(786\) −0.169633 0.522075i −0.00605059 0.0186218i
\(787\) −11.0804 34.1020i −0.394974 1.21560i −0.928982 0.370125i \(-0.879315\pi\)
0.534008 0.845479i \(-0.320685\pi\)
\(788\) −0.158655 0.115270i −0.00565186 0.00410632i
\(789\) −2.65191 + 1.92672i −0.0944103 + 0.0685931i
\(790\) 12.4744 38.3922i 0.443818 1.36593i
\(791\) 0 0
\(792\) −14.3396 6.67342i −0.509535 0.237130i
\(793\) 29.1655 1.03570
\(794\) −8.25571 + 25.4085i −0.292984 + 0.901713i
\(795\) −32.5177 + 23.6255i −1.15328 + 0.837910i
\(796\) 0.0484357 + 0.0351906i 0.00171676 + 0.00124730i
\(797\) −4.55530 14.0198i −0.161357 0.496606i 0.837392 0.546602i \(-0.184079\pi\)
−0.998749 + 0.0499962i \(0.984079\pi\)
\(798\) 0 0
\(799\) 26.4460 + 19.2142i 0.935593 + 0.679748i
\(800\) −0.105193 + 0.0764272i −0.00371913 + 0.00270211i
\(801\) −7.96670 + 24.5190i −0.281489 + 0.866336i
\(802\) 12.2354 0.432046
\(803\) −19.5789 + 3.82116i −0.690923 + 0.134846i
\(804\) 0.467275 0.0164795
\(805\) 0 0
\(806\) 6.92934 5.03446i 0.244076 0.177331i
\(807\) −3.55473 2.58266i −0.125132 0.0909140i
\(808\) −10.4334 32.1106i −0.367044 1.12965i
\(809\) −8.33599 25.6556i −0.293078 0.902001i −0.983860 0.178938i \(-0.942734\pi\)
0.690782 0.723063i \(-0.257266\pi\)
\(810\) −23.4222 17.0172i −0.822973 0.597925i
\(811\) 1.18472 0.860750i 0.0416012 0.0302250i −0.566790 0.823862i \(-0.691815\pi\)
0.608392 + 0.793637i \(0.291815\pi\)
\(812\) 0 0
\(813\) −16.4513 −0.576972
\(814\) −1.18583 + 9.71876i −0.0415634 + 0.340642i
\(815\) 25.1236 0.880041
\(816\) −14.5250 + 44.7033i −0.508476 + 1.56493i
\(817\) −37.6577 + 27.3599i −1.31747 + 0.957201i
\(818\) −6.51473 4.73323i −0.227782 0.165493i
\(819\) 0 0
\(820\) −0.00724418 0.0222953i −0.000252978 0.000778586i
\(821\) −24.7791 18.0031i −0.864797 0.628312i 0.0643886 0.997925i \(-0.479490\pi\)
−0.929186 + 0.369613i \(0.879490\pi\)
\(822\) 20.5312 14.9168i 0.716107 0.520282i
\(823\) −7.58137 + 23.3330i −0.264270 + 0.813339i 0.727591 + 0.686011i \(0.240640\pi\)
−0.991861 + 0.127328i \(0.959360\pi\)
\(824\) −1.12482 −0.0391851
\(825\) −5.73364 10.3253i −0.199620 0.359480i
\(826\) 0 0
\(827\) −2.02927 + 6.24545i −0.0705646 + 0.217176i −0.980119 0.198408i \(-0.936423\pi\)
0.909555 + 0.415584i \(0.136423\pi\)
\(828\) −0.0136612 + 0.00992547i −0.000474761 + 0.000344934i
\(829\) −16.0543 11.6642i −0.557590 0.405113i 0.272986 0.962018i \(-0.411989\pi\)
−0.830576 + 0.556905i \(0.811989\pi\)
\(830\) −3.48985 10.7406i −0.121134 0.372813i
\(831\) 9.64463 + 29.6831i 0.334569 + 1.02970i
\(832\) −30.2834 22.0022i −1.04989 0.762789i
\(833\) 0 0
\(834\) −6.55832 + 20.1844i −0.227096 + 0.698930i
\(835\) −17.0476 −0.589958
\(836\) 0.183091 0.196640i 0.00633235 0.00680095i
\(837\) −3.73421 −0.129073
\(838\) −11.8413 + 36.4438i −0.409051 + 1.25893i
\(839\) −6.44019 + 4.67907i −0.222340 + 0.161539i −0.693379 0.720573i \(-0.743879\pi\)
0.471039 + 0.882112i \(0.343879\pi\)
\(840\) 0 0
\(841\) −8.53669 26.2732i −0.294369 0.905973i
\(842\) 10.4365 + 32.1202i 0.359665 + 1.10694i
\(843\) −31.0656 22.5705i −1.06996 0.777370i
\(844\) −0.0164410 + 0.0119451i −0.000565922 + 0.000411166i
\(845\) 4.86424 14.9706i 0.167335 0.515004i
\(846\) 14.1500 0.486489
\(847\) 0 0
\(848\) −40.2944 −1.38372
\(849\) 20.8152 64.0625i 0.714375 2.19862i
\(850\) −10.2658 + 7.45852i −0.352113 + 0.255825i
\(851\) 1.21963 + 0.886114i 0.0418084 + 0.0303756i
\(852\) −0.129782 0.399429i −0.00444627 0.0136842i
\(853\) −10.5292 32.4055i −0.360513 1.10954i −0.952744 0.303776i \(-0.901753\pi\)
0.592231 0.805768i \(-0.298247\pi\)
\(854\) 0 0
\(855\) −14.4417 + 10.4925i −0.493897 + 0.358837i
\(856\) −2.86741 + 8.82497i −0.0980060 + 0.301631i
\(857\) −24.8539 −0.848992 −0.424496 0.905430i \(-0.639549\pi\)
−0.424496 + 0.905430i \(0.639549\pi\)
\(858\) 32.0207 34.3902i 1.09317 1.17406i
\(859\) −2.05654 −0.0701683 −0.0350841 0.999384i \(-0.511170\pi\)
−0.0350841 + 0.999384i \(0.511170\pi\)
\(860\) −0.0634115 + 0.195160i −0.00216231 + 0.00665491i
\(861\) 0 0
\(862\) 18.7814 + 13.6455i 0.639697 + 0.464767i
\(863\) −0.0801824 0.246776i −0.00272944 0.00840035i 0.949683 0.313214i \(-0.101406\pi\)
−0.952412 + 0.304814i \(0.901406\pi\)
\(864\) 0.0696964 + 0.214504i 0.00237112 + 0.00729756i
\(865\) 15.5655 + 11.3090i 0.529241 + 0.384516i
\(866\) −22.9061 + 16.6423i −0.778381 + 0.565527i
\(867\) 8.63946 26.5895i 0.293412 0.903028i
\(868\) 0 0
\(869\) −25.1840 45.3519i −0.854307 1.53846i
\(870\) 6.54651 0.221947
\(871\) −22.2113 + 68.3593i −0.752601 + 2.31627i
\(872\) 6.53577 4.74851i 0.221329 0.160805i
\(873\) 3.27766 + 2.38136i 0.110932 + 0.0805968i
\(874\) 1.81816 + 5.59573i 0.0615003 + 0.189278i
\(875\) 0 0
\(876\) −0.147003 0.106804i −0.00496676 0.00360856i
\(877\) −15.0420 + 10.9287i −0.507934 + 0.369035i −0.812039 0.583603i \(-0.801642\pi\)
0.304106 + 0.952638i \(0.401642\pi\)
\(878\) 11.6572 35.8772i 0.393412 1.21080i
\(879\) 51.9867 1.75347
\(880\) −2.92197 + 23.9477i −0.0984996 + 0.807275i
\(881\) −6.45292 −0.217404 −0.108702 0.994074i \(-0.534670\pi\)
−0.108702 + 0.994074i \(0.534670\pi\)
\(882\) 0 0
\(883\) 0.225301 0.163691i 0.00758198 0.00550863i −0.583988 0.811762i \(-0.698508\pi\)
0.591570 + 0.806254i \(0.298508\pi\)
\(884\) 0.287188 + 0.208654i 0.00965917 + 0.00701779i
\(885\) 9.40377 + 28.9418i 0.316104 + 0.972869i
\(886\) −11.4165 35.1362i −0.383543 1.18042i
\(887\) 24.7211 + 17.9609i 0.830054 + 0.603069i 0.919575 0.392916i \(-0.128534\pi\)
−0.0895209 + 0.995985i \(0.528534\pi\)
\(888\) −10.4056 + 7.56009i −0.349188 + 0.253700i
\(889\) 0 0
\(890\) 39.6008 1.32742
\(891\) −36.5154 + 7.12661i −1.22331 + 0.238750i
\(892\) −0.0678176 −0.00227070
\(893\) −10.7127 + 32.9702i −0.358485 + 1.10330i
\(894\) −7.92816 + 5.76014i −0.265157 + 0.192648i
\(895\) 12.3320 + 8.95972i 0.412213 + 0.299491i
\(896\) 0 0
\(897\) −2.23581 6.88111i −0.0746514 0.229753i
\(898\) 11.1132 + 8.07423i 0.370853 + 0.269441i
\(899\) 1.24058 0.901332i 0.0413756 0.0300611i
\(900\) 0.0119347 0.0367311i 0.000397822 0.00122437i
\(901\) 55.4949 1.84880
\(902\) 3.88437 + 1.80773i 0.129335 + 0.0601907i
\(903\) 0 0
\(904\) 12.7564 39.2601i 0.424271 1.30577i
\(905\) −21.9324 + 15.9348i −0.729058 + 0.529692i
\(906\) 54.9220 + 39.9031i 1.82466 + 1.32569i
\(907\) 9.86836 + 30.3717i 0.327674 + 1.00848i 0.970219 + 0.242228i \(0.0778782\pi\)
−0.642546 + 0.766247i \(0.722122\pi\)
\(908\) 0.00171378 + 0.00527448i 5.68739e−5 + 0.000175040i
\(909\) 16.1704 + 11.7484i 0.536337 + 0.389671i
\(910\) 0 0
\(911\) 0.865378 2.66336i 0.0286713 0.0882411i −0.935697 0.352805i \(-0.885228\pi\)
0.964368 + 0.264564i \(0.0852280\pi\)
\(912\) −49.8477 −1.65062
\(913\) −13.1576 6.12334i −0.435452 0.202653i
\(914\) −16.7496 −0.554027
\(915\) 7.68399 23.6489i 0.254025 0.781808i
\(916\) −0.0247374 + 0.0179728i −0.000817348 + 0.000593838i
\(917\) 0 0
\(918\) 6.80167 + 20.9334i 0.224488 + 0.690904i
\(919\) −4.89293 15.0589i −0.161403 0.496747i 0.837350 0.546667i \(-0.184104\pi\)
−0.998753 + 0.0499194i \(0.984104\pi\)
\(920\) 3.02638 + 2.19880i 0.0997769 + 0.0724922i
\(921\) −9.56137 + 6.94674i −0.315058 + 0.228903i
\(922\) 3.98356 12.2602i 0.131192 0.403767i
\(923\) 64.6030 2.12643
\(924\) 0 0
\(925\) −3.44799 −0.113369
\(926\) −16.9554 + 52.1833i −0.557188 + 1.71485i
\(927\) 0.538719 0.391402i 0.0176939 0.0128553i
\(928\) −0.0749296 0.0544396i −0.00245969 0.00178707i
\(929\) 8.49282 + 26.1382i 0.278640 + 0.857567i 0.988233 + 0.152955i \(0.0488790\pi\)
−0.709593 + 0.704612i \(0.751121\pi\)
\(930\) −2.25659 6.94506i −0.0739964 0.227737i
\(931\) 0 0
\(932\) −0.0142366 + 0.0103435i −0.000466337 + 0.000338814i
\(933\) −9.28472 + 28.5754i −0.303968 + 0.935517i
\(934\) −29.2894 −0.958379
\(935\) 4.02424 32.9816i 0.131607 1.07861i
\(936\) 22.1610 0.724354
\(937\) 3.80357 11.7062i 0.124257 0.382425i −0.869508 0.493919i \(-0.835564\pi\)
0.993765 + 0.111495i \(0.0355638\pi\)
\(938\) 0 0
\(939\) 48.0408 + 34.9037i 1.56775 + 1.13904i
\(940\) 0.0472266 + 0.145349i 0.00154036 + 0.00474075i
\(941\) −0.451208 1.38867i −0.0147089 0.0452695i 0.943433 0.331564i \(-0.107576\pi\)
−0.958142 + 0.286295i \(0.907576\pi\)
\(942\) −32.6931 23.7530i −1.06520 0.773913i
\(943\) 0.533703 0.387758i 0.0173798 0.0126271i
\(944\) −9.42725 + 29.0141i −0.306831 + 0.944328i
\(945\) 0 0
\(946\) −18.2068 32.7873i −0.591955 1.06601i
\(947\) 11.0714 0.359771 0.179885 0.983688i \(-0.442427\pi\)
0.179885 + 0.983688i \(0.442427\pi\)
\(948\) 0.146017 0.449395i 0.00474242 0.0145957i
\(949\) 22.6123 16.4288i 0.734025 0.533301i
\(950\) −10.8869 7.90978i −0.353217 0.256627i
\(951\) 5.23165 + 16.1014i 0.169648 + 0.522123i
\(952\) 0 0
\(953\) 11.9924 + 8.71296i 0.388471 + 0.282240i 0.764828 0.644234i \(-0.222824\pi\)
−0.376358 + 0.926474i \(0.622824\pi\)
\(954\) 19.4342 14.1197i 0.629204 0.457144i
\(955\) −5.43675 + 16.7326i −0.175929 + 0.541454i
\(956\) 0.155867 0.00504110
\(957\) 5.73274 6.15697i 0.185313 0.199027i
\(958\) −34.5782 −1.11717
\(959\) 0 0
\(960\) −25.8191 + 18.7586i −0.833306 + 0.605432i
\(961\) 23.6957 + 17.2159i 0.764377 + 0.555353i
\(962\) −4.23920 13.0469i −0.136677 0.420649i
\(963\) −1.69750 5.22437i −0.0547012 0.168353i
\(964\) 0.242719 + 0.176346i 0.00781746 + 0.00567972i
\(965\) 2.20437 1.60157i 0.0709612 0.0515563i
\(966\) 0 0
\(967\) 16.5193 0.531224 0.265612 0.964080i \(-0.414426\pi\)
0.265612 + 0.964080i \(0.414426\pi\)
\(968\) 20.1043 + 23.8857i 0.646177 + 0.767716i
\(969\) 68.6520 2.20542
\(970\) 1.92308 5.91862i 0.0617462 0.190035i
\(971\) 33.0073 23.9812i 1.05926 0.769595i 0.0853055 0.996355i \(-0.472813\pi\)
0.973951 + 0.226760i \(0.0728134\pi\)
\(972\) −0.177396 0.128886i −0.00568998 0.00413401i
\(973\) 0 0
\(974\) 5.38755 + 16.5812i 0.172628 + 0.531296i
\(975\) 13.3877 + 9.72671i 0.428748 + 0.311504i
\(976\) 20.1672 14.6523i 0.645535 0.469009i
\(977\) 15.1772 46.7107i 0.485562 1.49441i −0.345603 0.938381i \(-0.612326\pi\)
0.831165 0.556025i \(-0.187674\pi\)
\(978\) −41.8243 −1.33739
\(979\) 34.6782 37.2444i 1.10832 1.19034i
\(980\) 0 0
\(981\) −1.47789 + 4.54847i −0.0471853 + 0.145222i
\(982\) 18.8406 13.6885i 0.601228 0.436817i
\(983\) 0.895411 + 0.650554i 0.0285592 + 0.0207495i 0.601973 0.798516i \(-0.294381\pi\)
−0.573414 + 0.819266i \(0.694381\pi\)
\(984\) 1.73925 + 5.35286i 0.0554453 + 0.170643i
\(985\) −7.94756 24.4601i −0.253230 0.779362i
\(986\) −7.31238 5.31275i −0.232874 0.169193i
\(987\) 0 0
\(988\) −0.116333 + 0.358036i −0.00370104 + 0.0113906i
\(989\) −5.77458 −0.183621
\(990\) −6.98233 12.5740i −0.221913 0.399627i
\(991\) 41.7851 1.32735 0.663674 0.748022i \(-0.268996\pi\)
0.663674 + 0.748022i \(0.268996\pi\)
\(992\) −0.0319255 + 0.0982567i −0.00101364 + 0.00311965i
\(993\) 49.2618 35.7908i 1.56328 1.13579i
\(994\) 0 0
\(995\) 2.42630 + 7.46739i 0.0769189 + 0.236732i
\(996\) −0.0408500 0.125723i −0.00129438 0.00398369i
\(997\) 35.7541 + 25.9769i 1.13234 + 0.822695i 0.986034 0.166543i \(-0.0532606\pi\)
0.146309 + 0.989239i \(0.453261\pi\)
\(998\) −15.6664 + 11.3823i −0.495910 + 0.360300i
\(999\) −1.84819 + 5.68816i −0.0584743 + 0.179965i
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 539.2.f.e.295.2 16
7.2 even 3 539.2.q.f.361.3 32
7.3 odd 6 539.2.q.g.471.2 32
7.4 even 3 539.2.q.f.471.2 32
7.5 odd 6 539.2.q.g.361.3 32
7.6 odd 2 77.2.f.b.64.2 16
11.4 even 5 5929.2.a.bt.1.3 8
11.5 even 5 inner 539.2.f.e.148.2 16
11.7 odd 10 5929.2.a.bs.1.6 8
21.20 even 2 693.2.m.i.64.3 16
77.5 odd 30 539.2.q.g.214.2 32
77.6 even 10 847.2.f.x.148.3 16
77.13 even 10 847.2.f.v.729.2 16
77.16 even 15 539.2.q.f.214.2 32
77.20 odd 10 847.2.f.w.729.3 16
77.27 odd 10 77.2.f.b.71.2 yes 16
77.38 odd 30 539.2.q.g.324.3 32
77.41 even 10 847.2.f.v.323.2 16
77.48 odd 10 847.2.a.p.1.3 8
77.60 even 15 539.2.q.f.324.3 32
77.62 even 10 847.2.a.o.1.6 8
77.69 odd 10 847.2.f.w.323.3 16
77.76 even 2 847.2.f.x.372.3 16
231.62 odd 10 7623.2.a.cw.1.3 8
231.104 even 10 693.2.m.i.379.3 16
231.125 even 10 7623.2.a.ct.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.64.2 16 7.6 odd 2
77.2.f.b.71.2 yes 16 77.27 odd 10
539.2.f.e.148.2 16 11.5 even 5 inner
539.2.f.e.295.2 16 1.1 even 1 trivial
539.2.q.f.214.2 32 77.16 even 15
539.2.q.f.324.3 32 77.60 even 15
539.2.q.f.361.3 32 7.2 even 3
539.2.q.f.471.2 32 7.4 even 3
539.2.q.g.214.2 32 77.5 odd 30
539.2.q.g.324.3 32 77.38 odd 30
539.2.q.g.361.3 32 7.5 odd 6
539.2.q.g.471.2 32 7.3 odd 6
693.2.m.i.64.3 16 21.20 even 2
693.2.m.i.379.3 16 231.104 even 10
847.2.a.o.1.6 8 77.62 even 10
847.2.a.p.1.3 8 77.48 odd 10
847.2.f.v.323.2 16 77.41 even 10
847.2.f.v.729.2 16 77.13 even 10
847.2.f.w.323.3 16 77.69 odd 10
847.2.f.w.729.3 16 77.20 odd 10
847.2.f.x.148.3 16 77.6 even 10
847.2.f.x.372.3 16 77.76 even 2
5929.2.a.bs.1.6 8 11.7 odd 10
5929.2.a.bt.1.3 8 11.4 even 5
7623.2.a.ct.1.6 8 231.125 even 10
7623.2.a.cw.1.3 8 231.62 odd 10