Properties

Label 360.2.bk.a.229.18
Level $360$
Weight $2$
Character 360.229
Analytic conductor $2.875$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(229,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.229");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bk (of order \(6\), degree \(2\), 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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(68\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 229.18
Character \(\chi\) \(=\) 360.229
Dual form 360.2.bk.a.349.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.954059 + 1.04392i) q^{2} +(-1.07030 + 1.36178i) q^{3} +(-0.179543 - 1.99192i) q^{4} +(1.96832 - 1.06099i) q^{5} +(-0.400461 - 2.41653i) q^{6} +(-1.60442 + 0.926310i) q^{7} +(2.25071 + 1.71299i) q^{8} +(-0.708903 - 2.91504i) q^{9} +O(q^{10})\) \(q+(-0.954059 + 1.04392i) q^{2} +(-1.07030 + 1.36178i) q^{3} +(-0.179543 - 1.99192i) q^{4} +(1.96832 - 1.06099i) q^{5} +(-0.400461 - 2.41653i) q^{6} +(-1.60442 + 0.926310i) q^{7} +(2.25071 + 1.71299i) q^{8} +(-0.708903 - 2.91504i) q^{9} +(-0.770302 + 3.06702i) q^{10} +(-2.88736 + 1.66702i) q^{11} +(2.90473 + 1.88746i) q^{12} +(-3.23243 + 5.59873i) q^{13} +(0.563713 - 2.55864i) q^{14} +(-0.661859 + 3.81601i) q^{15} +(-3.93553 + 0.715271i) q^{16} -0.590749i q^{17} +(3.71941 + 2.04108i) q^{18} +4.73221i q^{19} +(-2.46682 - 3.73026i) q^{20} +(0.455778 - 3.17630i) q^{21} +(1.01448 - 4.60462i) q^{22} +(-7.05625 - 4.07393i) q^{23} +(-4.74165 + 1.23156i) q^{24} +(2.74859 - 4.17675i) q^{25} +(-2.76071 - 8.71592i) q^{26} +(4.72839 + 2.15460i) q^{27} +(2.13320 + 3.02956i) q^{28} +(0.135659 - 0.0783230i) q^{29} +(-3.35216 - 4.33163i) q^{30} +(-2.77492 + 4.80630i) q^{31} +(3.00804 - 4.79079i) q^{32} +(0.820235 - 5.71618i) q^{33} +(0.616695 + 0.563609i) q^{34} +(-2.17520 + 3.52555i) q^{35} +(-5.67926 + 1.93546i) q^{36} -3.21991 q^{37} +(-4.94005 - 4.51480i) q^{38} +(-4.16458 - 10.3942i) q^{39} +(6.24758 + 0.983722i) q^{40} +(-0.929101 + 1.60925i) q^{41} +(2.88096 + 3.50617i) q^{42} +(-1.08597 - 1.88095i) q^{43} +(3.83898 + 5.45211i) q^{44} +(-4.48819 - 4.98560i) q^{45} +(10.9849 - 3.47940i) q^{46} +(8.32731 - 4.80777i) q^{47} +(3.23816 - 6.12489i) q^{48} +(-1.78390 + 3.08981i) q^{49} +(1.73789 + 6.85418i) q^{50} +(0.804471 + 0.632280i) q^{51} +(11.7326 + 5.43354i) q^{52} -6.40212 q^{53} +(-6.76040 + 2.88045i) q^{54} +(-3.91456 + 6.34471i) q^{55} +(-5.19782 - 0.663489i) q^{56} +(-6.44424 - 5.06489i) q^{57} +(-0.0476640 + 0.216342i) q^{58} +(1.67616 + 0.967729i) q^{59} +(7.72004 + 0.633235i) q^{60} +(2.78455 - 1.60766i) q^{61} +(-2.36996 - 7.48229i) q^{62} +(3.83760 + 4.02027i) q^{63} +(2.13136 + 7.71086i) q^{64} +(-0.422244 + 14.4497i) q^{65} +(5.18469 + 6.30983i) q^{66} +(-3.33522 + 5.77678i) q^{67} +(-1.17673 + 0.106065i) q^{68} +(13.1001 - 5.24874i) q^{69} +(-1.60513 - 5.63432i) q^{70} +2.20166 q^{71} +(3.39789 - 7.77524i) q^{72} +15.2968i q^{73} +(3.07198 - 3.36133i) q^{74} +(2.74601 + 8.21337i) q^{75} +(9.42620 - 0.849633i) q^{76} +(3.08835 - 5.34919i) q^{77} +(14.8240 + 5.56919i) q^{78} +(-0.603265 - 1.04489i) q^{79} +(-6.98749 + 5.58346i) q^{80} +(-7.99491 + 4.13296i) q^{81} +(-0.793513 - 2.50523i) q^{82} +(2.12097 + 3.67362i) q^{83} +(-6.40878 - 0.337595i) q^{84} +(-0.626781 - 1.16278i) q^{85} +(2.99964 + 0.660873i) q^{86} +(-0.0385378 + 0.268568i) q^{87} +(-9.35419 - 1.19404i) q^{88} +12.3193 q^{89} +(9.48657 + 0.0712379i) q^{90} -11.9769i q^{91} +(-6.84806 + 14.7870i) q^{92} +(-3.57513 - 8.92303i) q^{93} +(-2.92581 + 13.2800i) q^{94} +(5.02084 + 9.31451i) q^{95} +(3.30450 + 9.22390i) q^{96} +(12.0457 - 6.95457i) q^{97} +(-1.52357 - 4.81011i) q^{98} +(6.90629 + 7.23502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.954059 + 1.04392i −0.674622 + 0.738164i
\(3\) −1.07030 + 1.36178i −0.617940 + 0.786225i
\(4\) −0.179543 1.99192i −0.0897714 0.995962i
\(5\) 1.96832 1.06099i 0.880260 0.474491i
\(6\) −0.400461 2.41653i −0.163488 0.986545i
\(7\) −1.60442 + 0.926310i −0.606412 + 0.350112i −0.771560 0.636157i \(-0.780523\pi\)
0.165148 + 0.986269i \(0.447190\pi\)
\(8\) 2.25071 + 1.71299i 0.795745 + 0.605632i
\(9\) −0.708903 2.91504i −0.236301 0.971680i
\(10\) −0.770302 + 3.06702i −0.243591 + 0.969878i
\(11\) −2.88736 + 1.66702i −0.870573 + 0.502625i −0.867539 0.497370i \(-0.834299\pi\)
−0.00303427 + 0.999995i \(0.500966\pi\)
\(12\) 2.90473 + 1.88746i 0.838524 + 0.544864i
\(13\) −3.23243 + 5.59873i −0.896514 + 1.55281i −0.0645952 + 0.997912i \(0.520576\pi\)
−0.831919 + 0.554897i \(0.812758\pi\)
\(14\) 0.563713 2.55864i 0.150659 0.683825i
\(15\) −0.661859 + 3.81601i −0.170891 + 0.985290i
\(16\) −3.93553 + 0.715271i −0.983882 + 0.178818i
\(17\) 0.590749i 0.143278i −0.997431 0.0716388i \(-0.977177\pi\)
0.997431 0.0716388i \(-0.0228229\pi\)
\(18\) 3.71941 + 2.04108i 0.876673 + 0.481087i
\(19\) 4.73221i 1.08564i 0.839848 + 0.542821i \(0.182644\pi\)
−0.839848 + 0.542821i \(0.817356\pi\)
\(20\) −2.46682 3.73026i −0.551597 0.834111i
\(21\) 0.455778 3.17630i 0.0994590 0.693125i
\(22\) 1.01448 4.60462i 0.216287 0.981707i
\(23\) −7.05625 4.07393i −1.47133 0.849473i −0.471848 0.881680i \(-0.656413\pi\)
−0.999481 + 0.0322071i \(0.989746\pi\)
\(24\) −4.74165 + 1.23156i −0.967886 + 0.251391i
\(25\) 2.74859 4.17675i 0.549717 0.835351i
\(26\) −2.76071 8.71592i −0.541419 1.70933i
\(27\) 4.72839 + 2.15460i 0.909979 + 0.414654i
\(28\) 2.13320 + 3.02956i 0.403137 + 0.572534i
\(29\) 0.135659 0.0783230i 0.0251913 0.0145442i −0.487351 0.873206i \(-0.662037\pi\)
0.512543 + 0.858662i \(0.328704\pi\)
\(30\) −3.35216 4.33163i −0.612018 0.790844i
\(31\) −2.77492 + 4.80630i −0.498390 + 0.863236i −0.999998 0.00185828i \(-0.999408\pi\)
0.501608 + 0.865095i \(0.332742\pi\)
\(32\) 3.00804 4.79079i 0.531751 0.846901i
\(33\) 0.820235 5.71618i 0.142785 0.995059i
\(34\) 0.616695 + 0.563609i 0.105762 + 0.0966582i
\(35\) −2.17520 + 3.52555i −0.367676 + 0.595927i
\(36\) −5.67926 + 1.93546i −0.946544 + 0.322576i
\(37\) −3.21991 −0.529350 −0.264675 0.964338i \(-0.585265\pi\)
−0.264675 + 0.964338i \(0.585265\pi\)
\(38\) −4.94005 4.51480i −0.801382 0.732398i
\(39\) −4.16458 10.3942i −0.666866 1.66440i
\(40\) 6.24758 + 0.983722i 0.987830 + 0.155540i
\(41\) −0.929101 + 1.60925i −0.145101 + 0.251323i −0.929411 0.369047i \(-0.879684\pi\)
0.784309 + 0.620370i \(0.213017\pi\)
\(42\) 2.88096 + 3.50617i 0.444542 + 0.541014i
\(43\) −1.08597 1.88095i −0.165608 0.286842i 0.771263 0.636517i \(-0.219625\pi\)
−0.936871 + 0.349675i \(0.886292\pi\)
\(44\) 3.83898 + 5.45211i 0.578749 + 0.821936i
\(45\) −4.48819 4.98560i −0.669060 0.743209i
\(46\) 10.9849 3.47940i 1.61964 0.513010i
\(47\) 8.32731 4.80777i 1.21466 0.701286i 0.250891 0.968015i \(-0.419276\pi\)
0.963771 + 0.266729i \(0.0859430\pi\)
\(48\) 3.23816 6.12489i 0.467389 0.884052i
\(49\) −1.78390 + 3.08981i −0.254843 + 0.441401i
\(50\) 1.73789 + 6.85418i 0.245775 + 0.969327i
\(51\) 0.804471 + 0.632280i 0.112649 + 0.0885369i
\(52\) 11.7326 + 5.43354i 1.62702 + 0.753497i
\(53\) −6.40212 −0.879398 −0.439699 0.898145i \(-0.644915\pi\)
−0.439699 + 0.898145i \(0.644915\pi\)
\(54\) −6.76040 + 2.88045i −0.919974 + 0.391979i
\(55\) −3.91456 + 6.34471i −0.527840 + 0.855520i
\(56\) −5.19782 0.663489i −0.694588 0.0886624i
\(57\) −6.44424 5.06489i −0.853560 0.670862i
\(58\) −0.0476640 + 0.216342i −0.00625859 + 0.0284072i
\(59\) 1.67616 + 0.967729i 0.218217 + 0.125988i 0.605124 0.796131i \(-0.293123\pi\)
−0.386907 + 0.922119i \(0.626457\pi\)
\(60\) 7.72004 + 0.633235i 0.996653 + 0.0817503i
\(61\) 2.78455 1.60766i 0.356526 0.205840i −0.311030 0.950400i \(-0.600674\pi\)
0.667556 + 0.744560i \(0.267341\pi\)
\(62\) −2.36996 7.48229i −0.300985 0.950251i
\(63\) 3.83760 + 4.02027i 0.483493 + 0.506507i
\(64\) 2.13136 + 7.71086i 0.266420 + 0.963857i
\(65\) −0.422244 + 14.4497i −0.0523729 + 1.79226i
\(66\) 5.18469 + 6.30983i 0.638191 + 0.776687i
\(67\) −3.33522 + 5.77678i −0.407462 + 0.705745i −0.994605 0.103738i \(-0.966920\pi\)
0.587142 + 0.809484i \(0.300253\pi\)
\(68\) −1.17673 + 0.106065i −0.142699 + 0.0128622i
\(69\) 13.1001 5.24874i 1.57707 0.631874i
\(70\) −1.60513 5.63432i −0.191850 0.673430i
\(71\) 2.20166 0.261289 0.130644 0.991429i \(-0.458295\pi\)
0.130644 + 0.991429i \(0.458295\pi\)
\(72\) 3.39789 7.77524i 0.400445 0.916321i
\(73\) 15.2968i 1.79035i 0.445710 + 0.895177i \(0.352951\pi\)
−0.445710 + 0.895177i \(0.647049\pi\)
\(74\) 3.07198 3.36133i 0.357111 0.390747i
\(75\) 2.74601 + 8.21337i 0.317082 + 0.948398i
\(76\) 9.42620 0.849633i 1.08126 0.0974596i
\(77\) 3.08835 5.34919i 0.351951 0.609596i
\(78\) 14.8240 + 5.56919i 1.67848 + 0.630587i
\(79\) −0.603265 1.04489i −0.0678727 0.117559i 0.830092 0.557626i \(-0.188288\pi\)
−0.897965 + 0.440068i \(0.854954\pi\)
\(80\) −6.98749 + 5.58346i −0.781225 + 0.624249i
\(81\) −7.99491 + 4.13296i −0.888324 + 0.459218i
\(82\) −0.793513 2.50523i −0.0876289 0.276656i
\(83\) 2.12097 + 3.67362i 0.232806 + 0.403232i 0.958633 0.284645i \(-0.0918759\pi\)
−0.725827 + 0.687878i \(0.758543\pi\)
\(84\) −6.40878 0.337595i −0.699255 0.0368346i
\(85\) −0.626781 1.16278i −0.0679839 0.126122i
\(86\) 2.99964 + 0.660873i 0.323459 + 0.0712638i
\(87\) −0.0385378 + 0.268568i −0.00413168 + 0.0287935i
\(88\) −9.35419 1.19404i −0.997160 0.127285i
\(89\) 12.3193 1.30584 0.652921 0.757426i \(-0.273543\pi\)
0.652921 + 0.757426i \(0.273543\pi\)
\(90\) 9.48657 + 0.0712379i 0.999972 + 0.00750913i
\(91\) 11.9769i 1.25552i
\(92\) −6.84806 + 14.7870i −0.713959 + 1.54165i
\(93\) −3.57513 8.92303i −0.370724 0.925275i
\(94\) −2.92581 + 13.2800i −0.301774 + 1.36972i
\(95\) 5.02084 + 9.31451i 0.515127 + 0.955648i
\(96\) 3.30450 + 9.22390i 0.337265 + 0.941410i
\(97\) 12.0457 6.95457i 1.22305 0.706130i 0.257485 0.966282i \(-0.417106\pi\)
0.965568 + 0.260152i \(0.0837727\pi\)
\(98\) −1.52357 4.81011i −0.153904 0.485894i
\(99\) 6.90629 + 7.23502i 0.694108 + 0.727147i
\(100\) −8.81327 4.72507i −0.881327 0.472507i
\(101\) −12.4676 + 7.19817i −1.24057 + 0.716245i −0.969211 0.246233i \(-0.920807\pi\)
−0.271362 + 0.962477i \(0.587474\pi\)
\(102\) −1.42756 + 0.236572i −0.141350 + 0.0234241i
\(103\) −7.10860 4.10415i −0.700431 0.404394i 0.107077 0.994251i \(-0.465851\pi\)
−0.807508 + 0.589857i \(0.799184\pi\)
\(104\) −16.8658 + 7.06400i −1.65383 + 0.692682i
\(105\) −2.47291 6.73555i −0.241332 0.657323i
\(106\) 6.10800 6.68331i 0.593261 0.649140i
\(107\) 17.4628 1.68819 0.844094 0.536195i \(-0.180139\pi\)
0.844094 + 0.536195i \(0.180139\pi\)
\(108\) 3.44286 9.80544i 0.331289 0.943529i
\(109\) 16.1089i 1.54295i −0.636259 0.771476i \(-0.719519\pi\)
0.636259 0.771476i \(-0.280481\pi\)
\(110\) −2.88865 10.1397i −0.275422 0.966784i
\(111\) 3.44628 4.38481i 0.327106 0.416188i
\(112\) 5.65166 4.79311i 0.534032 0.452906i
\(113\) 3.62139 + 2.09081i 0.340671 + 0.196687i 0.660569 0.750765i \(-0.270315\pi\)
−0.319898 + 0.947452i \(0.603649\pi\)
\(114\) 11.4355 1.89507i 1.07104 0.177489i
\(115\) −18.2114 0.532167i −1.69822 0.0496248i
\(116\) −0.180370 0.256161i −0.0167469 0.0237839i
\(117\) 18.6120 + 5.45370i 1.72068 + 0.504195i
\(118\) −2.60938 + 0.826504i −0.240213 + 0.0760858i
\(119\) 0.547216 + 0.947806i 0.0501632 + 0.0868853i
\(120\) −8.02642 + 7.45497i −0.732709 + 0.680542i
\(121\) 0.0579116 0.100306i 0.00526469 0.00911872i
\(122\) −0.978355 + 4.44066i −0.0885761 + 0.402038i
\(123\) −1.19703 2.98762i −0.107933 0.269385i
\(124\) 10.0720 + 4.66449i 0.904492 + 0.418884i
\(125\) 0.978591 11.1374i 0.0875278 0.996162i
\(126\) −7.85815 + 0.170581i −0.700059 + 0.0151966i
\(127\) 1.18401i 0.105064i 0.998619 + 0.0525322i \(0.0167292\pi\)
−0.998619 + 0.0525322i \(0.983271\pi\)
\(128\) −10.0830 5.13164i −0.891217 0.453577i
\(129\) 3.72376 + 0.534335i 0.327858 + 0.0470456i
\(130\) −14.6815 14.2266i −1.28765 1.24776i
\(131\) −6.15679 3.55462i −0.537921 0.310569i 0.206315 0.978486i \(-0.433853\pi\)
−0.744236 + 0.667917i \(0.767186\pi\)
\(132\) −11.5335 0.607548i −1.00386 0.0528803i
\(133\) −4.38349 7.59243i −0.380097 0.658347i
\(134\) −2.84850 8.99309i −0.246073 0.776885i
\(135\) 11.5930 0.775838i 0.997768 0.0667735i
\(136\) 1.01194 1.32960i 0.0867735 0.114012i
\(137\) −3.36728 + 1.94410i −0.287686 + 0.166096i −0.636898 0.770948i \(-0.719783\pi\)
0.349212 + 0.937044i \(0.386449\pi\)
\(138\) −7.01902 + 18.6831i −0.597499 + 1.59041i
\(139\) 2.71801 + 1.56924i 0.230538 + 0.133101i 0.610820 0.791769i \(-0.290840\pi\)
−0.380282 + 0.924871i \(0.624173\pi\)
\(140\) 7.41317 + 3.69984i 0.626527 + 0.312694i
\(141\) −2.36560 + 16.4858i −0.199219 + 1.38835i
\(142\) −2.10051 + 2.29836i −0.176271 + 0.192874i
\(143\) 21.5541i 1.80244i
\(144\) 4.87495 + 10.9652i 0.406246 + 0.913764i
\(145\) 0.183921 0.298099i 0.0152738 0.0247557i
\(146\) −15.9686 14.5940i −1.32157 1.20781i
\(147\) −2.29833 5.73631i −0.189563 0.473123i
\(148\) 0.578111 + 6.41382i 0.0475204 + 0.527212i
\(149\) 6.27214 + 3.62122i 0.513834 + 0.296662i 0.734408 0.678708i \(-0.237460\pi\)
−0.220574 + 0.975370i \(0.570793\pi\)
\(150\) −11.1940 4.96942i −0.913984 0.405751i
\(151\) 6.77715 + 11.7384i 0.551517 + 0.955255i 0.998165 + 0.0605455i \(0.0192840\pi\)
−0.446649 + 0.894709i \(0.647383\pi\)
\(152\) −8.10620 + 10.6508i −0.657500 + 0.863895i
\(153\) −1.72206 + 0.418784i −0.139220 + 0.0338567i
\(154\) 2.63766 + 8.32744i 0.212548 + 0.671044i
\(155\) −0.362480 + 12.4045i −0.0291151 + 0.996354i
\(156\) −19.9567 + 10.1617i −1.59782 + 0.813589i
\(157\) −1.59282 + 2.75885i −0.127121 + 0.220180i −0.922560 0.385854i \(-0.873907\pi\)
0.795439 + 0.606034i \(0.207240\pi\)
\(158\) 1.66633 + 0.367122i 0.132566 + 0.0292066i
\(159\) 6.85221 8.71829i 0.543415 0.691405i
\(160\) 0.837791 12.6213i 0.0662332 0.997804i
\(161\) 15.0949 1.18964
\(162\) 3.31313 12.2891i 0.260304 0.965527i
\(163\) 14.4380 1.13087 0.565435 0.824793i \(-0.308708\pi\)
0.565435 + 0.824793i \(0.308708\pi\)
\(164\) 3.37232 + 1.56177i 0.263334 + 0.121954i
\(165\) −4.45034 12.1215i −0.346459 0.943661i
\(166\) −5.85850 1.29073i −0.454708 0.100180i
\(167\) 10.4193 + 6.01557i 0.806268 + 0.465499i 0.845658 0.533725i \(-0.179208\pi\)
−0.0393901 + 0.999224i \(0.512542\pi\)
\(168\) 6.46677 6.36817i 0.498922 0.491315i
\(169\) −14.3972 24.9367i −1.10748 1.91820i
\(170\) 1.81184 + 0.455055i 0.138962 + 0.0349011i
\(171\) 13.7946 3.35468i 1.05490 0.256539i
\(172\) −3.55173 + 2.50087i −0.270817 + 0.190690i
\(173\) 5.44736 + 9.43511i 0.414155 + 0.717338i 0.995339 0.0964340i \(-0.0307437\pi\)
−0.581184 + 0.813772i \(0.697410\pi\)
\(174\) −0.243596 0.296460i −0.0184670 0.0224746i
\(175\) −0.540904 + 9.24729i −0.0408885 + 0.699029i
\(176\) 10.1709 8.62585i 0.766663 0.650198i
\(177\) −3.11183 + 1.24680i −0.233899 + 0.0937149i
\(178\) −11.7533 + 12.8604i −0.880949 + 0.963925i
\(179\) 0.363546i 0.0271727i −0.999908 0.0135863i \(-0.995675\pi\)
0.999908 0.0135863i \(-0.00432480\pi\)
\(180\) −9.12511 + 9.83526i −0.680146 + 0.733077i
\(181\) 3.06981i 0.228177i 0.993471 + 0.114089i \(0.0363948\pi\)
−0.993471 + 0.114089i \(0.963605\pi\)
\(182\) 12.5030 + 11.4267i 0.926781 + 0.847002i
\(183\) −0.791029 + 5.51264i −0.0584746 + 0.407506i
\(184\) −8.90297 21.2565i −0.656336 1.56705i
\(185\) −6.33782 + 3.41630i −0.465966 + 0.251172i
\(186\) 12.7258 + 4.78094i 0.933103 + 0.350556i
\(187\) 0.984790 + 1.70571i 0.0720150 + 0.124734i
\(188\) −11.0718 15.7242i −0.807496 1.14680i
\(189\) −9.58213 + 0.923075i −0.696998 + 0.0671438i
\(190\) −14.5138 3.64523i −1.05294 0.264453i
\(191\) −9.10363 15.7680i −0.658716 1.14093i −0.980948 0.194269i \(-0.937767\pi\)
0.322233 0.946661i \(-0.395567\pi\)
\(192\) −12.7817 5.35050i −0.922441 0.386139i
\(193\) 19.6102 + 11.3220i 1.41158 + 0.814974i 0.995537 0.0943730i \(-0.0300846\pi\)
0.416039 + 0.909347i \(0.363418\pi\)
\(194\) −4.23226 + 19.2098i −0.303858 + 1.37918i
\(195\) −19.2254 16.0406i −1.37676 1.14869i
\(196\) 6.47495 + 2.99864i 0.462496 + 0.214189i
\(197\) −12.2075 −0.869747 −0.434873 0.900492i \(-0.643207\pi\)
−0.434873 + 0.900492i \(0.643207\pi\)
\(198\) −14.1418 + 0.306984i −1.00501 + 0.0218164i
\(199\) −14.9325 −1.05854 −0.529269 0.848454i \(-0.677534\pi\)
−0.529269 + 0.848454i \(0.677534\pi\)
\(200\) 13.3410 4.69236i 0.943350 0.331800i
\(201\) −4.29701 10.7247i −0.303088 0.756465i
\(202\) 4.38050 19.8827i 0.308211 1.39894i
\(203\) −0.145103 + 0.251325i −0.0101842 + 0.0176396i
\(204\) 1.11502 1.71597i 0.0780668 0.120142i
\(205\) −0.121366 + 4.15329i −0.00847657 + 0.290079i
\(206\) 11.0664 3.50521i 0.771035 0.244220i
\(207\) −6.87346 + 23.4573i −0.477739 + 1.63039i
\(208\) 8.71670 24.3460i 0.604395 1.68809i
\(209\) −7.88868 13.6636i −0.545672 0.945131i
\(210\) 9.39069 + 3.84459i 0.648019 + 0.265302i
\(211\) −5.55973 3.20991i −0.382748 0.220980i 0.296265 0.955106i \(-0.404259\pi\)
−0.679013 + 0.734126i \(0.737592\pi\)
\(212\) 1.14945 + 12.7525i 0.0789448 + 0.875848i
\(213\) −2.35644 + 2.99818i −0.161461 + 0.205432i
\(214\) −16.6605 + 18.2297i −1.13889 + 1.24616i
\(215\) −4.13321 2.55011i −0.281882 0.173916i
\(216\) 6.95142 + 12.9490i 0.472984 + 0.881071i
\(217\) 10.2817i 0.697969i
\(218\) 16.8164 + 15.3688i 1.13895 + 1.04091i
\(219\) −20.8309 16.3722i −1.40762 1.10633i
\(220\) 13.3410 + 6.65837i 0.899451 + 0.448907i
\(221\) 3.30744 + 1.90955i 0.222483 + 0.128450i
\(222\) 1.28945 + 7.78101i 0.0865421 + 0.522227i
\(223\) −20.2535 + 11.6934i −1.35628 + 0.783046i −0.989120 0.147113i \(-0.953002\pi\)
−0.367156 + 0.930159i \(0.619668\pi\)
\(224\) −0.388388 + 10.4728i −0.0259503 + 0.699743i
\(225\) −14.1239 5.05132i −0.941592 0.336755i
\(226\) −5.63765 + 1.78569i −0.375011 + 0.118782i
\(227\) −11.6127 20.1137i −0.770760 1.33500i −0.937147 0.348935i \(-0.886543\pi\)
0.166387 0.986061i \(-0.446790\pi\)
\(228\) −8.93187 + 13.7458i −0.591528 + 0.910338i
\(229\) 6.49252 + 3.74846i 0.429038 + 0.247705i 0.698937 0.715184i \(-0.253657\pi\)
−0.269899 + 0.962889i \(0.586990\pi\)
\(230\) 17.9303 18.5035i 1.18229 1.22009i
\(231\) 3.97895 + 9.93092i 0.261796 + 0.653406i
\(232\) 0.439496 + 0.0561005i 0.0288543 + 0.00368318i
\(233\) 19.5735i 1.28230i 0.767414 + 0.641152i \(0.221543\pi\)
−0.767414 + 0.641152i \(0.778457\pi\)
\(234\) −23.4502 + 14.2263i −1.53299 + 0.930003i
\(235\) 11.2898 18.2985i 0.736466 1.19366i
\(236\) 1.62670 3.51252i 0.105889 0.228646i
\(237\) 2.06858 + 0.296829i 0.134369 + 0.0192811i
\(238\) −1.51151 0.333013i −0.0979768 0.0215860i
\(239\) 2.50305 4.33540i 0.161909 0.280434i −0.773645 0.633620i \(-0.781568\pi\)
0.935553 + 0.353186i \(0.114902\pi\)
\(240\) −0.124720 15.4914i −0.00805064 0.999968i
\(241\) 5.73015 + 9.92490i 0.369111 + 0.639319i 0.989427 0.145033i \(-0.0463288\pi\)
−0.620316 + 0.784352i \(0.712995\pi\)
\(242\) 0.0494603 + 0.156153i 0.00317943 + 0.0100379i
\(243\) 2.92878 15.3109i 0.187882 0.982192i
\(244\) −3.70229 5.25798i −0.237015 0.336608i
\(245\) −0.233026 + 7.97444i −0.0148875 + 0.509468i
\(246\) 4.26088 + 1.60076i 0.271664 + 0.102061i
\(247\) −26.4943 15.2965i −1.68580 0.973294i
\(248\) −14.4786 + 6.06417i −0.919395 + 0.385075i
\(249\) −7.27275 1.04359i −0.460892 0.0661350i
\(250\) 10.6930 + 11.6473i 0.676283 + 0.736642i
\(251\) 5.20608i 0.328605i 0.986410 + 0.164303i \(0.0525373\pi\)
−0.986410 + 0.164303i \(0.947463\pi\)
\(252\) 7.31906 8.36603i 0.461058 0.527010i
\(253\) 27.1653 1.70787
\(254\) −1.23602 1.12962i −0.0775547 0.0708786i
\(255\) 2.25430 + 0.390992i 0.141170 + 0.0244849i
\(256\) 14.9768 5.62994i 0.936048 0.351871i
\(257\) 8.63681 + 4.98647i 0.538750 + 0.311047i 0.744572 0.667542i \(-0.232654\pi\)
−0.205822 + 0.978589i \(0.565987\pi\)
\(258\) −4.11049 + 3.37752i −0.255908 + 0.210275i
\(259\) 5.16607 2.98263i 0.321004 0.185332i
\(260\) 28.8585 1.75326i 1.78973 0.108733i
\(261\) −0.324484 0.339929i −0.0200851 0.0210411i
\(262\) 9.58468 3.03588i 0.592144 0.187557i
\(263\) 10.2358 5.90965i 0.631167 0.364404i −0.150037 0.988680i \(-0.547939\pi\)
0.781204 + 0.624276i \(0.214606\pi\)
\(264\) 11.6378 11.4604i 0.716259 0.705338i
\(265\) −12.6014 + 6.79261i −0.774100 + 0.417266i
\(266\) 12.1080 + 2.66761i 0.742389 + 0.163561i
\(267\) −13.1854 + 16.7762i −0.806932 + 1.02669i
\(268\) 12.1057 + 5.60634i 0.739474 + 0.342461i
\(269\) 16.1799i 0.986508i 0.869885 + 0.493254i \(0.164193\pi\)
−0.869885 + 0.493254i \(0.835807\pi\)
\(270\) −10.2505 + 12.8424i −0.623826 + 0.781563i
\(271\) 20.1093 1.22155 0.610776 0.791803i \(-0.290857\pi\)
0.610776 + 0.791803i \(0.290857\pi\)
\(272\) 0.422546 + 2.32491i 0.0256206 + 0.140968i
\(273\) 16.3100 + 12.8189i 0.987124 + 0.775837i
\(274\) 1.18310 5.36997i 0.0714736 0.324412i
\(275\) −0.973430 + 16.6418i −0.0587000 + 1.00354i
\(276\) −12.8071 25.1521i −0.770899 1.51398i
\(277\) 1.26920 + 2.19832i 0.0762588 + 0.132084i 0.901633 0.432502i \(-0.142369\pi\)
−0.825374 + 0.564586i \(0.809036\pi\)
\(278\) −4.23130 + 1.34023i −0.253777 + 0.0803819i
\(279\) 15.9777 + 4.68179i 0.956560 + 0.280292i
\(280\) −10.9349 + 4.20890i −0.653488 + 0.251530i
\(281\) −3.84074 6.65235i −0.229119 0.396846i 0.728428 0.685122i \(-0.240251\pi\)
−0.957547 + 0.288276i \(0.906918\pi\)
\(282\) −14.9529 18.1979i −0.890433 1.08367i
\(283\) 1.95480 3.38581i 0.116201 0.201266i −0.802058 0.597246i \(-0.796262\pi\)
0.918259 + 0.395980i \(0.129595\pi\)
\(284\) −0.395292 4.38554i −0.0234563 0.260234i
\(285\) −18.0582 3.13205i −1.06967 0.185527i
\(286\) 22.5008 + 20.5639i 1.33050 + 1.21597i
\(287\) 3.44254i 0.203207i
\(288\) −16.0978 5.37235i −0.948570 0.316569i
\(289\) 16.6510 0.979472
\(290\) 0.135720 + 0.476403i 0.00796974 + 0.0279753i
\(291\) −3.42190 + 23.8471i −0.200596 + 1.39794i
\(292\) 30.4701 2.74643i 1.78313 0.160723i
\(293\) −0.689283 + 1.19387i −0.0402683 + 0.0697468i −0.885457 0.464721i \(-0.846155\pi\)
0.845189 + 0.534468i \(0.179488\pi\)
\(294\) 8.18100 + 3.07351i 0.477126 + 0.179251i
\(295\) 4.32597 + 0.126412i 0.251868 + 0.00735998i
\(296\) −7.24707 5.51566i −0.421227 0.320591i
\(297\) −17.2444 + 1.66120i −1.00062 + 0.0963925i
\(298\) −9.76426 + 3.09276i −0.565629 + 0.179159i
\(299\) 45.6176 26.3374i 2.63814 1.52313i
\(300\) 15.8674 6.94450i 0.916104 0.400941i
\(301\) 3.48468 + 2.01188i 0.200854 + 0.115963i
\(302\) −18.7197 4.12429i −1.07720 0.237326i
\(303\) 3.54176 24.6824i 0.203469 1.41797i
\(304\) −3.38481 18.6237i −0.194132 1.06814i
\(305\) 3.77518 6.11879i 0.216166 0.350361i
\(306\) 1.20577 2.19724i 0.0689291 0.125608i
\(307\) −27.3968 −1.56362 −0.781808 0.623519i \(-0.785702\pi\)
−0.781808 + 0.623519i \(0.785702\pi\)
\(308\) −11.2097 5.19136i −0.638730 0.295805i
\(309\) 13.1973 5.28768i 0.750769 0.300805i
\(310\) −12.6035 12.2130i −0.715831 0.693654i
\(311\) 2.27190 3.93505i 0.128828 0.223136i −0.794395 0.607402i \(-0.792212\pi\)
0.923223 + 0.384265i \(0.125545\pi\)
\(312\) 8.43188 30.5282i 0.477361 1.72832i
\(313\) 15.7733 9.10673i 0.891561 0.514743i 0.0171079 0.999854i \(-0.494554\pi\)
0.874453 + 0.485111i \(0.161221\pi\)
\(314\) −1.36037 4.29488i −0.0767704 0.242374i
\(315\) 11.8191 + 3.84151i 0.665932 + 0.216445i
\(316\) −1.97302 + 1.38926i −0.110991 + 0.0781520i
\(317\) −3.94082 6.82570i −0.221338 0.383369i 0.733876 0.679283i \(-0.237709\pi\)
−0.955215 + 0.295914i \(0.904376\pi\)
\(318\) 2.56380 + 15.4709i 0.143771 + 0.867566i
\(319\) −0.261132 + 0.452294i −0.0146206 + 0.0253236i
\(320\) 12.3764 + 12.9161i 0.691860 + 0.722031i
\(321\) −18.6904 + 23.7805i −1.04320 + 1.32730i
\(322\) −14.4014 + 15.7579i −0.802559 + 0.878151i
\(323\) 2.79555 0.155548
\(324\) 9.66798 + 15.1832i 0.537110 + 0.843512i
\(325\) 14.4999 + 28.8896i 0.804311 + 1.60251i
\(326\) −13.7747 + 15.0721i −0.762910 + 0.834768i
\(327\) 21.9368 + 17.2414i 1.21311 + 0.953451i
\(328\) −4.84776 + 2.03041i −0.267673 + 0.112111i
\(329\) −8.90697 + 15.4273i −0.491057 + 0.850536i
\(330\) 16.8998 + 6.91886i 0.930305 + 0.380871i
\(331\) 3.80014 2.19401i 0.208874 0.120594i −0.391914 0.920002i \(-0.628187\pi\)
0.600788 + 0.799408i \(0.294854\pi\)
\(332\) 6.93677 4.88438i 0.380705 0.268065i
\(333\) 2.28260 + 9.38616i 0.125086 + 0.514358i
\(334\) −16.2204 + 5.13769i −0.887540 + 0.281122i
\(335\) −0.435671 + 14.9092i −0.0238033 + 0.814577i
\(336\) 0.478186 + 12.8264i 0.0260872 + 0.699738i
\(337\) −9.50739 5.48909i −0.517900 0.299010i 0.218175 0.975910i \(-0.429990\pi\)
−0.736075 + 0.676900i \(0.763323\pi\)
\(338\) 39.7677 + 8.76152i 2.16308 + 0.476564i
\(339\) −6.72320 + 2.69374i −0.365154 + 0.146304i
\(340\) −2.20364 + 1.45727i −0.119509 + 0.0790315i
\(341\) 18.5034i 1.00201i
\(342\) −9.65882 + 17.6010i −0.522289 + 0.951753i
\(343\) 19.5781i 1.05712i
\(344\) 0.777846 6.09371i 0.0419386 0.328551i
\(345\) 20.2164 24.2304i 1.08841 1.30452i
\(346\) −15.0466 3.31503i −0.808911 0.178217i
\(347\) −1.19627 + 2.07199i −0.0642189 + 0.111230i −0.896347 0.443353i \(-0.853789\pi\)
0.832128 + 0.554583i \(0.187122\pi\)
\(348\) 0.541886 + 0.0285449i 0.0290481 + 0.00153017i
\(349\) −17.7287 + 10.2357i −0.948995 + 0.547903i −0.892769 0.450515i \(-0.851240\pi\)
−0.0562266 + 0.998418i \(0.517907\pi\)
\(350\) −9.13739 9.38712i −0.488414 0.501763i
\(351\) −27.3472 + 19.5084i −1.45969 + 1.04128i
\(352\) −0.698957 + 18.8472i −0.0372545 + 1.00456i
\(353\) −22.2359 + 12.8379i −1.18350 + 0.683293i −0.956821 0.290677i \(-0.906119\pi\)
−0.226677 + 0.973970i \(0.572786\pi\)
\(354\) 1.66731 4.43802i 0.0886167 0.235878i
\(355\) 4.33357 2.33595i 0.230002 0.123979i
\(356\) −2.21184 24.5391i −0.117227 1.30057i
\(357\) −1.87639 0.269250i −0.0993093 0.0142502i
\(358\) 0.379513 + 0.346844i 0.0200579 + 0.0183313i
\(359\) −13.8514 −0.731051 −0.365525 0.930801i \(-0.619111\pi\)
−0.365525 + 0.930801i \(0.619111\pi\)
\(360\) −1.56134 18.9093i −0.0822900 0.996608i
\(361\) −3.39378 −0.178620
\(362\) −3.20464 2.92878i −0.168432 0.153933i
\(363\) 0.0746118 + 0.186221i 0.00391611 + 0.00977406i
\(364\) −23.8571 + 2.15037i −1.25045 + 0.112710i
\(365\) 16.2298 + 30.1090i 0.849507 + 1.57598i
\(366\) −5.00008 6.08516i −0.261358 0.318076i
\(367\) 16.1398 9.31834i 0.842493 0.486414i −0.0156178 0.999878i \(-0.504972\pi\)
0.858111 + 0.513464i \(0.171638\pi\)
\(368\) 30.6840 + 10.9859i 1.59952 + 0.572681i
\(369\) 5.34967 + 1.56756i 0.278493 + 0.0816041i
\(370\) 2.48030 9.87554i 0.128945 0.513405i
\(371\) 10.2717 5.93034i 0.533278 0.307888i
\(372\) −17.1321 + 8.72345i −0.888259 + 0.452290i
\(373\) −10.8701 + 18.8276i −0.562834 + 0.974858i 0.434413 + 0.900714i \(0.356956\pi\)
−0.997248 + 0.0741441i \(0.976378\pi\)
\(374\) −2.72017 0.599301i −0.140657 0.0309891i
\(375\) 14.1194 + 13.2531i 0.729121 + 0.684385i
\(376\) 26.9780 + 3.44367i 1.39128 + 0.177594i
\(377\) 1.01269i 0.0521564i
\(378\) 8.17830 10.8837i 0.420647 0.559795i
\(379\) 26.5083i 1.36164i 0.732450 + 0.680821i \(0.238377\pi\)
−0.732450 + 0.680821i \(0.761623\pi\)
\(380\) 17.6523 11.6735i 0.905546 0.598837i
\(381\) −1.61237 1.26725i −0.0826042 0.0649234i
\(382\) 25.1459 + 5.54008i 1.28658 + 0.283455i
\(383\) −9.17444 5.29687i −0.468792 0.270657i 0.246942 0.969030i \(-0.420574\pi\)
−0.715734 + 0.698373i \(0.753908\pi\)
\(384\) 17.7800 8.23841i 0.907332 0.420414i
\(385\) 0.403424 13.8056i 0.0205604 0.703601i
\(386\) −30.5286 + 9.66971i −1.55386 + 0.492175i
\(387\) −4.71319 + 4.49904i −0.239585 + 0.228699i
\(388\) −16.0157 22.7454i −0.813074 1.15472i
\(389\) −28.8599 + 16.6623i −1.46326 + 0.844811i −0.999160 0.0409742i \(-0.986954\pi\)
−0.464095 + 0.885785i \(0.653621\pi\)
\(390\) 35.0872 4.76618i 1.77671 0.241345i
\(391\) −2.40667 + 4.16847i −0.121710 + 0.210809i
\(392\) −9.30783 + 3.89845i −0.470116 + 0.196902i
\(393\) 11.4303 4.57968i 0.576580 0.231014i
\(394\) 11.6467 12.7436i 0.586750 0.642016i
\(395\) −2.29604 1.41661i −0.115526 0.0712775i
\(396\) 13.1716 15.0558i 0.661900 0.756583i
\(397\) −20.1614 −1.01187 −0.505936 0.862571i \(-0.668853\pi\)
−0.505936 + 0.862571i \(0.668853\pi\)
\(398\) 14.2465 15.5884i 0.714113 0.781375i
\(399\) 15.0309 + 2.15684i 0.752486 + 0.107977i
\(400\) −7.82962 + 18.4037i −0.391481 + 0.920186i
\(401\) 1.93691 3.35482i 0.0967246 0.167532i −0.813602 0.581422i \(-0.802497\pi\)
0.910327 + 0.413890i \(0.135830\pi\)
\(402\) 15.2954 + 5.74630i 0.762865 + 0.286599i
\(403\) −17.9394 31.0720i −0.893627 1.54781i
\(404\) 16.5767 + 23.5421i 0.824721 + 1.17127i
\(405\) −11.3515 + 16.6176i −0.564061 + 0.825733i
\(406\) −0.123927 0.391255i −0.00615040 0.0194176i
\(407\) 9.29705 5.36765i 0.460837 0.266065i
\(408\) 0.727542 + 2.80112i 0.0360187 + 0.138676i
\(409\) 15.0600 26.0847i 0.744671 1.28981i −0.205678 0.978620i \(-0.565940\pi\)
0.950348 0.311188i \(-0.100727\pi\)
\(410\) −4.21992 4.08918i −0.208407 0.201950i
\(411\) 0.956569 6.66629i 0.0471841 0.328824i
\(412\) −6.89886 + 14.8967i −0.339882 + 0.733906i
\(413\) −3.58567 −0.176439
\(414\) −17.9298 29.5550i −0.881204 1.45255i
\(415\) 8.07243 + 4.98054i 0.396260 + 0.244485i
\(416\) 17.0991 + 32.3271i 0.838352 + 1.58497i
\(417\) −5.04605 + 2.02177i −0.247106 + 0.0990064i
\(418\) 21.7900 + 4.80072i 1.06578 + 0.234811i
\(419\) −23.7922 13.7364i −1.16232 0.671067i −0.210463 0.977602i \(-0.567497\pi\)
−0.951860 + 0.306534i \(0.900831\pi\)
\(420\) −12.9727 + 6.13518i −0.633004 + 0.299366i
\(421\) 0.0412004 0.0237870i 0.00200798 0.00115931i −0.498996 0.866604i \(-0.666298\pi\)
0.501004 + 0.865445i \(0.332964\pi\)
\(422\) 8.65521 2.74148i 0.421329 0.133453i
\(423\) −19.9181 20.8662i −0.968451 1.01455i
\(424\) −14.4093 10.9667i −0.699777 0.532592i
\(425\) −2.46741 1.62372i −0.119687 0.0787621i
\(426\) −0.881679 5.32038i −0.0427175 0.257773i
\(427\) −2.97839 + 5.15872i −0.144134 + 0.249648i
\(428\) −3.13531 34.7845i −0.151551 1.68137i
\(429\) 29.3520 + 23.0694i 1.41713 + 1.11380i
\(430\) 6.60544 1.88179i 0.318542 0.0907478i
\(431\) −6.98377 −0.336396 −0.168198 0.985753i \(-0.553795\pi\)
−0.168198 + 0.985753i \(0.553795\pi\)
\(432\) −20.1498 5.09742i −0.969460 0.245250i
\(433\) 13.4813i 0.647869i −0.946080 0.323934i \(-0.894994\pi\)
0.946080 0.323934i \(-0.105006\pi\)
\(434\) 10.7333 + 9.80938i 0.515216 + 0.470865i
\(435\) 0.209094 + 0.569516i 0.0100253 + 0.0273062i
\(436\) −32.0877 + 2.89223i −1.53672 + 0.138513i
\(437\) 19.2787 33.3916i 0.922224 1.59734i
\(438\) 36.9652 6.12578i 1.76627 0.292701i
\(439\) 2.35018 + 4.07064i 0.112168 + 0.194281i 0.916644 0.399704i \(-0.130887\pi\)
−0.804476 + 0.593985i \(0.797554\pi\)
\(440\) −19.6789 + 7.57448i −0.938156 + 0.361099i
\(441\) 10.2715 + 3.00977i 0.489120 + 0.143322i
\(442\) −5.14892 + 1.63088i −0.244909 + 0.0775732i
\(443\) 4.10464 + 7.10944i 0.195017 + 0.337780i 0.946906 0.321510i \(-0.104190\pi\)
−0.751889 + 0.659290i \(0.770857\pi\)
\(444\) −9.35298 6.07746i −0.443873 0.288424i
\(445\) 24.2483 13.0707i 1.14948 0.619610i
\(446\) 7.11609 32.2992i 0.336957 1.52941i
\(447\) −11.6444 + 4.66549i −0.550762 + 0.220670i
\(448\) −10.5622 10.3971i −0.499019 0.491217i
\(449\) −35.1881 −1.66063 −0.830314 0.557297i \(-0.811839\pi\)
−0.830314 + 0.557297i \(0.811839\pi\)
\(450\) 18.7482 9.92497i 0.883799 0.467867i
\(451\) 6.19532i 0.291726i
\(452\) 3.51454 7.58892i 0.165310 0.356953i
\(453\) −23.2387 3.33461i −1.09185 0.156673i
\(454\) 32.0763 + 7.06698i 1.50542 + 0.331670i
\(455\) −12.7074 23.5744i −0.595734 1.10519i
\(456\) −5.82800 22.4385i −0.272921 1.05078i
\(457\) −30.6355 + 17.6874i −1.43307 + 0.827383i −0.997354 0.0727007i \(-0.976838\pi\)
−0.435716 + 0.900084i \(0.643505\pi\)
\(458\) −10.1073 + 3.20143i −0.472285 + 0.149593i
\(459\) 1.27283 2.79329i 0.0594106 0.130380i
\(460\) 2.20969 + 36.3713i 0.103027 + 1.69582i
\(461\) 13.7003 7.90989i 0.638088 0.368400i −0.145790 0.989316i \(-0.546572\pi\)
0.783878 + 0.620915i \(0.213239\pi\)
\(462\) −14.1632 5.32097i −0.658934 0.247554i
\(463\) −5.52455 3.18960i −0.256748 0.148233i 0.366102 0.930575i \(-0.380692\pi\)
−0.622850 + 0.782341i \(0.714025\pi\)
\(464\) −0.477869 + 0.405276i −0.0221845 + 0.0188144i
\(465\) −16.5043 13.7702i −0.765368 0.638578i
\(466\) −20.4332 18.6743i −0.946550 0.865070i
\(467\) −24.9649 −1.15524 −0.577618 0.816307i \(-0.696018\pi\)
−0.577618 + 0.816307i \(0.696018\pi\)
\(468\) 7.52171 38.0529i 0.347691 1.75899i
\(469\) 12.3578i 0.570630i
\(470\) 8.33101 + 29.2435i 0.384281 + 1.34890i
\(471\) −2.05215 5.12188i −0.0945581 0.236004i
\(472\) 2.11483 + 5.04930i 0.0973429 + 0.232413i
\(473\) 6.27116 + 3.62065i 0.288348 + 0.166478i
\(474\) −2.28342 + 1.87625i −0.104881 + 0.0861789i
\(475\) 19.7653 + 13.0069i 0.906893 + 0.596796i
\(476\) 1.78971 1.26019i 0.0820312 0.0577605i
\(477\) 4.53848 + 18.6624i 0.207803 + 0.854494i
\(478\) 2.13776 + 6.74921i 0.0977791 + 0.308702i
\(479\) −1.38572 2.40013i −0.0633150 0.109665i 0.832630 0.553829i \(-0.186834\pi\)
−0.895945 + 0.444164i \(0.853501\pi\)
\(480\) 16.2908 + 14.6495i 0.743571 + 0.668657i
\(481\) 10.4081 18.0274i 0.474570 0.821979i
\(482\) −15.8277 3.48712i −0.720933 0.158834i
\(483\) −16.1561 + 20.5559i −0.735127 + 0.935327i
\(484\) −0.210199 0.0973464i −0.00955452 0.00442484i
\(485\) 16.3310 26.4692i 0.741553 1.20191i
\(486\) 13.1891 + 17.6649i 0.598269 + 0.801295i
\(487\) 20.8545i 0.945008i 0.881329 + 0.472504i \(0.156650\pi\)
−0.881329 + 0.472504i \(0.843350\pi\)
\(488\) 9.02112 + 1.15152i 0.408367 + 0.0521270i
\(489\) −15.4530 + 19.6614i −0.698810 + 0.889119i
\(490\) −8.10237 7.85135i −0.366028 0.354688i
\(491\) −32.5679 18.8031i −1.46977 0.848571i −0.470343 0.882484i \(-0.655870\pi\)
−0.999425 + 0.0339131i \(0.989203\pi\)
\(492\) −5.73620 + 2.92080i −0.258608 + 0.131680i
\(493\) −0.0462692 0.0801406i −0.00208386 0.00360935i
\(494\) 41.2455 13.0642i 1.85572 0.587787i
\(495\) 21.2701 + 6.91333i 0.956021 + 0.310731i
\(496\) 7.48296 20.9001i 0.335995 0.938444i
\(497\) −3.53238 + 2.03942i −0.158449 + 0.0914804i
\(498\) 8.02806 6.59653i 0.359746 0.295597i
\(499\) 26.4715 + 15.2833i 1.18503 + 0.684175i 0.957172 0.289520i \(-0.0934958\pi\)
0.227854 + 0.973695i \(0.426829\pi\)
\(500\) −22.3606 + 0.0503652i −0.999997 + 0.00225240i
\(501\) −19.3437 + 7.75031i −0.864212 + 0.346258i
\(502\) −5.43474 4.96691i −0.242564 0.221684i
\(503\) 20.6381i 0.920208i 0.887865 + 0.460104i \(0.152188\pi\)
−0.887865 + 0.460104i \(0.847812\pi\)
\(504\) 1.75066 + 15.6222i 0.0779805 + 0.695869i
\(505\) −16.9030 + 27.3964i −0.752175 + 1.21912i
\(506\) −25.9173 + 28.3584i −1.15216 + 1.26068i
\(507\) 49.3677 + 7.08394i 2.19249 + 0.314609i
\(508\) 2.35847 0.212581i 0.104640 0.00943177i
\(509\) 1.15035 + 0.664155i 0.0509884 + 0.0294381i 0.525277 0.850931i \(-0.323962\pi\)
−0.474289 + 0.880369i \(0.657295\pi\)
\(510\) −2.55890 + 1.98029i −0.113310 + 0.0876885i
\(511\) −14.1696 24.5424i −0.626825 1.08569i
\(512\) −8.41151 + 21.0059i −0.371740 + 0.928337i
\(513\) −10.1960 + 22.3757i −0.450166 + 0.987912i
\(514\) −13.4455 + 4.25877i −0.593056 + 0.187846i
\(515\) −18.3465 0.536114i −0.808443 0.0236240i
\(516\) 0.395782 7.51338i 0.0174233 0.330758i
\(517\) −16.0293 + 27.7636i −0.704968 + 1.22104i
\(518\) −1.81510 + 8.23858i −0.0797511 + 0.361982i
\(519\) −18.6789 2.68030i −0.819913 0.117652i
\(520\) −25.7025 + 31.7987i −1.12713 + 1.39447i
\(521\) 0.811244 0.0355412 0.0177706 0.999842i \(-0.494343\pi\)
0.0177706 + 0.999842i \(0.494343\pi\)
\(522\) 0.664436 0.0144233i 0.0290816 0.000631289i
\(523\) 30.4237 1.33034 0.665169 0.746693i \(-0.268360\pi\)
0.665169 + 0.746693i \(0.268360\pi\)
\(524\) −5.97513 + 12.9021i −0.261025 + 0.563629i
\(525\) −12.0139 10.6340i −0.524328 0.464106i
\(526\) −3.59636 + 16.3235i −0.156809 + 0.711740i
\(527\) 2.83931 + 1.63928i 0.123682 + 0.0714081i
\(528\) 0.860560 + 23.0829i 0.0374511 + 1.00455i
\(529\) 21.6938 + 37.5747i 0.943207 + 1.63368i
\(530\) 4.93156 19.6354i 0.214213 0.852909i
\(531\) 1.63274 5.57209i 0.0708547 0.241808i
\(532\) −14.3365 + 10.0947i −0.621567 + 0.437663i
\(533\) −6.00651 10.4036i −0.260171 0.450629i
\(534\) −4.93340 29.7700i −0.213489 1.28827i
\(535\) 34.3723 18.5279i 1.48605 0.801030i
\(536\) −17.4021 + 7.28864i −0.751658 + 0.314821i
\(537\) 0.495070 + 0.389104i 0.0213639 + 0.0167911i
\(538\) −16.8906 15.4366i −0.728205 0.665520i
\(539\) 11.8952i 0.512362i
\(540\) −3.62685 22.9531i −0.156075 0.987745i
\(541\) 11.9797i 0.515048i −0.966272 0.257524i \(-0.917093\pi\)
0.966272 0.257524i \(-0.0829067\pi\)
\(542\) −19.1855 + 20.9925i −0.824086 + 0.901706i
\(543\) −4.18041 3.28563i −0.179399 0.141000i
\(544\) −2.83015 1.77700i −0.121342 0.0761881i
\(545\) −17.0914 31.7075i −0.732116 1.35820i
\(546\) −28.9426 + 4.79629i −1.23863 + 0.205262i
\(547\) −4.69681 8.13511i −0.200821 0.347832i 0.747972 0.663730i \(-0.231028\pi\)
−0.948793 + 0.315898i \(0.897694\pi\)
\(548\) 4.47708 + 6.35833i 0.191251 + 0.271614i
\(549\) −6.66038 6.97741i −0.284258 0.297789i
\(550\) −16.4440 16.8934i −0.701173 0.720337i
\(551\) 0.370640 + 0.641968i 0.0157898 + 0.0273488i
\(552\) 38.4756 + 10.6270i 1.63763 + 0.452313i
\(553\) 1.93578 + 1.11762i 0.0823176 + 0.0475261i
\(554\) −3.50576 0.772381i −0.148946 0.0328153i
\(555\) 2.13112 12.2872i 0.0904612 0.521563i
\(556\) 2.63781 5.69581i 0.111868 0.241556i
\(557\) −8.56289 −0.362821 −0.181411 0.983407i \(-0.558066\pi\)
−0.181411 + 0.983407i \(0.558066\pi\)
\(558\) −20.1311 + 12.2127i −0.852217 + 0.517007i
\(559\) 14.0412 0.593881
\(560\) 6.03883 15.4308i 0.255187 0.652069i
\(561\) −3.37682 0.484553i −0.142570 0.0204578i
\(562\) 10.6088 + 2.33731i 0.447506 + 0.0985935i
\(563\) −5.86483 + 10.1582i −0.247173 + 0.428116i −0.962740 0.270427i \(-0.912835\pi\)
0.715567 + 0.698544i \(0.246168\pi\)
\(564\) 33.2631 + 1.75220i 1.40063 + 0.0737809i
\(565\) 9.34639 + 0.273117i 0.393205 + 0.0114901i
\(566\) 1.66953 + 5.27092i 0.0701755 + 0.221553i
\(567\) 8.99876 14.0368i 0.377912 0.589488i
\(568\) 4.95529 + 3.77141i 0.207919 + 0.158245i
\(569\) 19.7153 + 34.1479i 0.826509 + 1.43156i 0.900761 + 0.434316i \(0.143010\pi\)
−0.0742514 + 0.997240i \(0.523657\pi\)
\(570\) 20.4982 15.8631i 0.858573 0.664433i
\(571\) 7.92266 + 4.57415i 0.331553 + 0.191422i 0.656530 0.754300i \(-0.272023\pi\)
−0.324977 + 0.945722i \(0.605357\pi\)
\(572\) −42.9341 + 3.86988i −1.79517 + 0.161808i
\(573\) 31.2162 + 4.47932i 1.30407 + 0.187126i
\(574\) 3.59374 + 3.28439i 0.150000 + 0.137088i
\(575\) −36.4105 + 18.2747i −1.51842 + 0.762107i
\(576\) 20.9665 11.6793i 0.873605 0.486636i
\(577\) 20.4943i 0.853190i −0.904443 0.426595i \(-0.859713\pi\)
0.904443 0.426595i \(-0.140287\pi\)
\(578\) −15.8861 + 17.3823i −0.660773 + 0.723010i
\(579\) −36.4070 + 14.5869i −1.51302 + 0.606212i
\(580\) −0.626812 0.312836i −0.0260269 0.0129898i
\(581\) −6.80582 3.92934i −0.282353 0.163017i
\(582\) −21.6298 26.3237i −0.896583 1.09115i
\(583\) 18.4852 10.6725i 0.765580 0.442008i
\(584\) −26.2032 + 34.4286i −1.08430 + 1.42467i
\(585\) 42.4208 9.01257i 1.75388 0.372624i
\(586\) −0.588693 1.85858i −0.0243187 0.0767773i
\(587\) −12.1463 21.0379i −0.501330 0.868329i −0.999999 0.00153627i \(-0.999511\pi\)
0.498669 0.866793i \(-0.333822\pi\)
\(588\) −11.0137 + 5.60801i −0.454196 + 0.231271i
\(589\) −22.7444 13.1315i −0.937166 0.541073i
\(590\) −4.25919 + 4.39537i −0.175348 + 0.180954i
\(591\) 13.0657 16.6239i 0.537451 0.683817i
\(592\) 12.6720 2.30311i 0.520818 0.0946572i
\(593\) 6.89686i 0.283220i 0.989923 + 0.141610i \(0.0452279\pi\)
−0.989923 + 0.141610i \(0.954772\pi\)
\(594\) 14.7180 19.5866i 0.603886 0.803649i
\(595\) 2.08271 + 1.28500i 0.0853830 + 0.0526797i
\(596\) 6.08709 13.1438i 0.249337 0.538391i
\(597\) 15.9823 20.3349i 0.654113 0.832250i
\(598\) −16.0278 + 72.7486i −0.655425 + 2.97491i
\(599\) −1.81418 + 3.14225i −0.0741254 + 0.128389i −0.900706 0.434430i \(-0.856950\pi\)
0.826580 + 0.562819i \(0.190283\pi\)
\(600\) −7.88891 + 23.1898i −0.322063 + 0.946718i
\(601\) 0.432510 + 0.749129i 0.0176424 + 0.0305576i 0.874712 0.484643i \(-0.161051\pi\)
−0.857069 + 0.515201i \(0.827717\pi\)
\(602\) −5.42484 + 1.71828i −0.221100 + 0.0700318i
\(603\) 19.2039 + 5.62713i 0.782042 + 0.229155i
\(604\) 22.1652 15.6071i 0.901888 0.635044i
\(605\) 0.00756485 0.258878i 0.000307555 0.0105249i
\(606\) 22.3874 + 27.2458i 0.909426 + 1.10678i
\(607\) −2.81348 1.62436i −0.114196 0.0659309i 0.441814 0.897107i \(-0.354335\pi\)
−0.556010 + 0.831176i \(0.687668\pi\)
\(608\) 22.6710 + 14.2347i 0.919431 + 0.577292i
\(609\) −0.186946 0.466592i −0.00757545 0.0189073i
\(610\) 2.78579 + 9.77868i 0.112793 + 0.395927i
\(611\) 62.1631i 2.51485i
\(612\) 1.14337 + 3.35502i 0.0462179 + 0.135619i
\(613\) −13.7010 −0.553380 −0.276690 0.960959i \(-0.589238\pi\)
−0.276690 + 0.960959i \(0.589238\pi\)
\(614\) 26.1381 28.6001i 1.05485 1.15420i
\(615\) −5.52598 4.61056i −0.222829 0.185916i
\(616\) 16.1141 6.74914i 0.649254 0.271931i
\(617\) 13.1108 + 7.56954i 0.527822 + 0.304738i 0.740129 0.672465i \(-0.234764\pi\)
−0.212307 + 0.977203i \(0.568098\pi\)
\(618\) −7.07109 + 18.8217i −0.284441 + 0.757120i
\(619\) −7.93920 + 4.58370i −0.319103 + 0.184234i −0.650993 0.759084i \(-0.725647\pi\)
0.331889 + 0.943318i \(0.392314\pi\)
\(620\) 24.7739 1.50511i 0.994945 0.0604465i
\(621\) −24.5870 34.4665i −0.986643 1.38309i
\(622\) 1.94035 + 6.12596i 0.0778011 + 0.245629i
\(623\) −19.7653 + 11.4115i −0.791878 + 0.457191i
\(624\) 23.8245 + 37.9279i 0.953743 + 1.51833i
\(625\) −9.89056 22.9603i −0.395622 0.918413i
\(626\) −5.54197 + 25.1545i −0.221502 + 1.00537i
\(627\) 27.0501 + 3.88152i 1.08028 + 0.155013i
\(628\) 5.78140 + 2.67745i 0.230703 + 0.106842i
\(629\) 1.90216i 0.0758440i
\(630\) −15.2864 + 8.67320i −0.609024 + 0.345549i
\(631\) 26.2470 1.04488 0.522439 0.852677i \(-0.325022\pi\)
0.522439 + 0.852677i \(0.325022\pi\)
\(632\) 0.432101 3.38512i 0.0171881 0.134653i
\(633\) 10.3218 4.13557i 0.410255 0.164374i
\(634\) 10.8853 + 2.39822i 0.432309 + 0.0952453i
\(635\) 1.25623 + 2.33052i 0.0498520 + 0.0924840i
\(636\) −18.5964 12.0838i −0.737397 0.479153i
\(637\) −11.5327 19.9752i −0.456941 0.791445i
\(638\) −0.223024 0.704116i −0.00882960 0.0278762i
\(639\) −1.56076 6.41792i −0.0617428 0.253889i
\(640\) −25.2912 + 0.597252i −0.999721 + 0.0236085i
\(641\) −20.3809 35.3008i −0.804998 1.39430i −0.916292 0.400510i \(-0.868833\pi\)
0.111294 0.993788i \(-0.464500\pi\)
\(642\) −6.99316 42.1993i −0.275998 1.66547i
\(643\) −15.9839 + 27.6850i −0.630345 + 1.09179i 0.357137 + 0.934052i \(0.383753\pi\)
−0.987481 + 0.157737i \(0.949580\pi\)
\(644\) −2.71018 30.0679i −0.106796 1.18484i
\(645\) 7.89648 2.89914i 0.310923 0.114153i
\(646\) −2.66712 + 2.91833i −0.104936 + 0.114820i
\(647\) 31.4488i 1.23638i 0.786029 + 0.618190i \(0.212134\pi\)
−0.786029 + 0.618190i \(0.787866\pi\)
\(648\) −25.0739 4.39308i −0.984996 0.172577i
\(649\) −6.45289 −0.253298
\(650\) −43.9923 12.4257i −1.72552 0.487374i
\(651\) 14.0015 + 11.0046i 0.548761 + 0.431303i
\(652\) −2.59224 28.7594i −0.101520 1.12630i
\(653\) −4.85136 + 8.40281i −0.189849 + 0.328827i −0.945200 0.326493i \(-0.894133\pi\)
0.755351 + 0.655320i \(0.227466\pi\)
\(654\) −38.9276 + 6.45099i −1.52219 + 0.252253i
\(655\) −15.8900 0.464331i −0.620873 0.0181429i
\(656\) 2.50545 6.99781i 0.0978215 0.273219i
\(657\) 44.5908 10.8439i 1.73965 0.423063i
\(658\) −7.60714 24.0168i −0.296557 0.936271i
\(659\) 17.1787 9.91816i 0.669189 0.386356i −0.126580 0.991956i \(-0.540400\pi\)
0.795769 + 0.605600i \(0.207067\pi\)
\(660\) −23.3462 + 11.0411i −0.908749 + 0.429773i
\(661\) 34.2332 + 19.7646i 1.33152 + 0.768753i 0.985532 0.169487i \(-0.0542110\pi\)
0.345986 + 0.938240i \(0.387544\pi\)
\(662\) −1.33518 + 6.06026i −0.0518933 + 0.235539i
\(663\) −6.14036 + 2.46022i −0.238472 + 0.0955469i
\(664\) −1.51919 + 11.9014i −0.0589559 + 0.461865i
\(665\) −16.6836 10.2935i −0.646964 0.399164i
\(666\) −11.9761 6.57209i −0.464066 0.254663i
\(667\) −1.27633 −0.0494196
\(668\) 10.1119 21.8345i 0.391240 0.844801i
\(669\) 5.75357 40.0963i 0.222446 1.55021i
\(670\) −15.1484 14.6791i −0.585233 0.567102i
\(671\) −5.36001 + 9.28381i −0.206921 + 0.358398i
\(672\) −13.8460 11.7380i −0.534120 0.452802i
\(673\) −13.7903 + 7.96182i −0.531576 + 0.306905i −0.741658 0.670778i \(-0.765960\pi\)
0.210082 + 0.977684i \(0.432627\pi\)
\(674\) 14.8008 4.68804i 0.570105 0.180577i
\(675\) 21.9956 13.8272i 0.846612 0.532210i
\(676\) −47.0870 + 33.1553i −1.81104 + 1.27520i
\(677\) 2.57113 + 4.45333i 0.0988166 + 0.171155i 0.911195 0.411975i \(-0.135161\pi\)
−0.812379 + 0.583130i \(0.801828\pi\)
\(678\) 3.60228 9.58848i 0.138345 0.368243i
\(679\) −12.8842 + 22.3161i −0.494449 + 0.856411i
\(680\) 0.581132 3.69075i 0.0222854 0.141534i
\(681\) 39.8196 + 5.71386i 1.52589 + 0.218956i
\(682\) 19.3161 + 17.6533i 0.739650 + 0.675980i
\(683\) 32.5301 1.24473 0.622364 0.782728i \(-0.286172\pi\)
0.622364 + 0.782728i \(0.286172\pi\)
\(684\) −9.15898 26.8754i −0.350202 1.02761i
\(685\) −4.56522 + 7.39929i −0.174428 + 0.282712i
\(686\) 20.4380 + 18.6787i 0.780327 + 0.713155i
\(687\) −12.0535 + 4.82941i −0.459871 + 0.184254i
\(688\) 5.61924 + 6.62577i 0.214231 + 0.252605i
\(689\) 20.6944 35.8437i 0.788393 1.36554i
\(690\) 6.00696 + 44.2215i 0.228681 + 1.68348i
\(691\) −21.0875 + 12.1749i −0.802207 + 0.463154i −0.844242 0.535962i \(-0.819949\pi\)
0.0420353 + 0.999116i \(0.486616\pi\)
\(692\) 17.8160 12.5447i 0.677263 0.476880i
\(693\) −17.7824 5.21062i −0.675499 0.197935i
\(694\) −1.02169 3.22561i −0.0387828 0.122442i
\(695\) 7.01486 + 0.204986i 0.266089 + 0.00777556i
\(696\) −0.546790 + 0.538453i −0.0207260 + 0.0204100i
\(697\) 0.950663 + 0.548865i 0.0360089 + 0.0207898i
\(698\) 6.22899 28.2728i 0.235771 1.07014i
\(699\) −26.6549 20.9496i −1.00818 0.792386i
\(700\) 18.5170 0.582844i 0.699878 0.0220294i
\(701\) 29.3780i 1.10959i −0.831987 0.554796i \(-0.812796\pi\)
0.831987 0.554796i \(-0.187204\pi\)
\(702\) 5.72566 47.1605i 0.216101 1.77996i
\(703\) 15.2373i 0.574685i
\(704\) −19.0082 18.7110i −0.716397 0.705198i
\(705\) 12.8350 + 34.9592i 0.483395 + 1.31664i
\(706\) 7.81261 35.4607i 0.294031 1.33458i
\(707\) 13.3355 23.0977i 0.501532 0.868679i
\(708\) 3.04223 + 5.97468i 0.114334 + 0.224542i
\(709\) 12.2117 7.05045i 0.458622 0.264785i −0.252843 0.967507i \(-0.581366\pi\)
0.711464 + 0.702722i \(0.248032\pi\)
\(710\) −1.69594 + 6.75254i −0.0636476 + 0.253418i
\(711\) −2.61823 + 2.49927i −0.0981912 + 0.0937298i
\(712\) 27.7271 + 21.1028i 1.03912 + 0.790859i
\(713\) 39.1610 22.6096i 1.46659 0.846737i
\(714\) 2.07127 1.70193i 0.0775152 0.0636930i
\(715\) −22.8688 42.4254i −0.855243 1.58662i
\(716\) −0.724156 + 0.0652720i −0.0270630 + 0.00243933i
\(717\) 3.22486 + 8.04880i 0.120435 + 0.300588i
\(718\) 13.2151 14.4598i 0.493183 0.539635i
\(719\) 45.4953 1.69669 0.848345 0.529444i \(-0.177600\pi\)
0.848345 + 0.529444i \(0.177600\pi\)
\(720\) 21.2294 + 16.4107i 0.791175 + 0.611590i
\(721\) 15.2069 0.566333
\(722\) 3.23787 3.54284i 0.120501 0.131851i
\(723\) −19.6486 2.81944i −0.730738 0.104856i
\(724\) 6.11483 0.551162i 0.227256 0.0204838i
\(725\) 0.0457355 0.781893i 0.00169857 0.0290388i
\(726\) −0.265584 0.0997767i −0.00985674 0.00370306i
\(727\) 13.8164 7.97688i 0.512420 0.295846i −0.221408 0.975181i \(-0.571065\pi\)
0.733828 + 0.679335i \(0.237732\pi\)
\(728\) 20.5163 26.9565i 0.760384 0.999076i
\(729\) 17.7154 + 20.3756i 0.656125 + 0.754653i
\(730\) −46.9156 11.7832i −1.73643 0.436114i
\(731\) −1.11117 + 0.641533i −0.0410980 + 0.0237280i
\(732\) 11.1228 + 0.585915i 0.411110 + 0.0216561i
\(733\) 17.2293 29.8421i 0.636380 1.10224i −0.349841 0.936809i \(-0.613764\pi\)
0.986221 0.165434i \(-0.0529023\pi\)
\(734\) −5.67075 + 25.7390i −0.209311 + 0.950043i
\(735\) −10.6100 8.85240i −0.391357 0.326526i
\(736\) −40.7428 + 21.5505i −1.50180 + 0.794362i
\(737\) 22.2395i 0.819204i
\(738\) −6.74032 + 4.08909i −0.248114 + 0.150521i
\(739\) 16.8961i 0.621532i 0.950487 + 0.310766i \(0.100585\pi\)
−0.950487 + 0.310766i \(0.899415\pi\)
\(740\) 7.94293 + 12.0111i 0.291988 + 0.441536i
\(741\) 49.1875 19.7076i 1.80695 0.723978i
\(742\) −3.60896 + 16.3807i −0.132489 + 0.601354i
\(743\) −17.4220 10.0586i −0.639152 0.369015i 0.145136 0.989412i \(-0.453638\pi\)
−0.784288 + 0.620397i \(0.786971\pi\)
\(744\) 7.23845 26.2073i 0.265374 0.960805i
\(745\) 16.1877 + 0.473031i 0.593071 + 0.0173305i
\(746\) −9.28381 29.3102i −0.339904 1.07312i
\(747\) 9.20519 8.78694i 0.336800 0.321497i
\(748\) 3.22083 2.26787i 0.117765 0.0829217i
\(749\) −28.0175 + 16.1759i −1.02374 + 0.591055i
\(750\) −27.3059 + 2.09531i −0.997069 + 0.0765100i
\(751\) −4.26382 + 7.38515i −0.155589 + 0.269488i −0.933273 0.359167i \(-0.883061\pi\)
0.777684 + 0.628655i \(0.216394\pi\)
\(752\) −29.3335 + 24.8774i −1.06968 + 0.907186i
\(753\) −7.08955 5.57209i −0.258358 0.203058i
\(754\) −1.05717 0.966169i −0.0384999 0.0351858i
\(755\) 25.7940 + 15.9144i 0.938738 + 0.579184i
\(756\) 3.55910 + 18.9212i 0.129443 + 0.688156i
\(757\) 30.3158 1.10185 0.550924 0.834556i \(-0.314276\pi\)
0.550924 + 0.834556i \(0.314276\pi\)
\(758\) −27.6726 25.2905i −1.00511 0.918593i
\(759\) −29.0751 + 36.9932i −1.05536 + 1.34277i
\(760\) −4.65517 + 29.5649i −0.168861 + 1.07243i
\(761\) −20.0870 + 34.7918i −0.728154 + 1.26120i 0.229508 + 0.973307i \(0.426288\pi\)
−0.957662 + 0.287894i \(0.907045\pi\)
\(762\) 2.86121 0.474152i 0.103651 0.0171767i
\(763\) 14.9218 + 25.8453i 0.540206 + 0.935664i
\(764\) −29.7741 + 20.9648i −1.07719 + 0.758479i
\(765\) −2.94523 + 2.65139i −0.106485 + 0.0958613i
\(766\) 14.2825 4.52387i 0.516047 0.163454i
\(767\) −10.8361 + 6.25623i −0.391269 + 0.225899i
\(768\) −8.36293 + 26.4209i −0.301771 + 0.953380i
\(769\) −18.9297 + 32.7872i −0.682623 + 1.18234i 0.291554 + 0.956554i \(0.405828\pi\)
−0.974177 + 0.225784i \(0.927506\pi\)
\(770\) 14.0271 + 13.5925i 0.505502 + 0.489841i
\(771\) −16.0345 + 6.42443i −0.577468 + 0.231370i
\(772\) 19.0317 41.0949i 0.684964 1.47904i
\(773\) −11.8902 −0.427662 −0.213831 0.976871i \(-0.568594\pi\)
−0.213831 + 0.976871i \(0.568594\pi\)
\(774\) −0.199982 9.21256i −0.00718820 0.331139i
\(775\) 12.4476 + 24.8007i 0.447132 + 0.890866i
\(776\) 39.0244 + 4.98136i 1.40089 + 0.178820i
\(777\) −1.46756 + 10.2274i −0.0526486 + 0.366905i
\(778\) 10.1400 46.0243i 0.363535 1.65005i
\(779\) −7.61531 4.39670i −0.272847 0.157528i
\(780\) −28.4998 + 41.1755i −1.02046 + 1.47432i
\(781\) −6.35699 + 3.67021i −0.227471 + 0.131330i
\(782\) −2.05545 6.48934i −0.0735028 0.232058i
\(783\) 0.810206 0.0780495i 0.0289544 0.00278926i
\(784\) 4.81054 13.4360i 0.171805 0.479857i
\(785\) −0.208066 + 7.12028i −0.00742620 + 0.254134i
\(786\) −6.12431 + 16.3016i −0.218447 + 0.581458i
\(787\) −3.21964 + 5.57658i −0.114768 + 0.198784i −0.917687 0.397304i \(-0.869946\pi\)
0.802919 + 0.596088i \(0.203279\pi\)
\(788\) 2.19176 + 24.3164i 0.0780784 + 0.866235i
\(789\) −2.90776 + 20.2641i −0.103519 + 0.721419i
\(790\) 3.66939 1.04535i 0.130551 0.0371919i
\(791\) −7.74694 −0.275450
\(792\) 3.15055 + 28.1143i 0.111950 + 0.998998i
\(793\) 20.7866i 0.738155i
\(794\) 19.2352 21.0469i 0.682630 0.746927i
\(795\) 4.23730 24.4306i 0.150281 0.866462i
\(796\) 2.68103 + 29.7445i 0.0950265 + 1.05426i
\(797\) 15.1379 26.2197i 0.536213 0.928748i −0.462891 0.886415i \(-0.653188\pi\)
0.999104 0.0423326i \(-0.0134789\pi\)
\(798\) −16.5919 + 13.6333i −0.587348 + 0.482614i
\(799\) −2.84019 4.91935i −0.100479 0.174034i
\(800\) −11.7421 25.7317i −0.415146 0.909755i
\(801\) −8.73318 35.9112i −0.308572 1.26886i
\(802\) 1.65425 + 5.22268i 0.0584135 + 0.184419i
\(803\) −25.5001 44.1674i −0.899878 1.55863i
\(804\) −20.5914 + 10.4849i −0.726202 + 0.369773i
\(805\) 29.7116 16.0156i 1.04720 0.564475i
\(806\) 49.5520 + 10.9172i 1.74540 + 0.384541i
\(807\) −22.0336 17.3174i −0.775618 0.609603i
\(808\) −40.3913 5.15584i −1.42096 0.181382i
\(809\) 3.79502 0.133426 0.0667130 0.997772i \(-0.478749\pi\)
0.0667130 + 0.997772i \(0.478749\pi\)
\(810\) −6.51739 27.7042i −0.228998 0.973427i
\(811\) 25.9465i 0.911105i 0.890209 + 0.455552i \(0.150558\pi\)
−0.890209 + 0.455552i \(0.849442\pi\)
\(812\) 0.526673 + 0.243910i 0.0184826 + 0.00855956i
\(813\) −21.5230 + 27.3845i −0.754846 + 0.960416i
\(814\) −3.26653 + 14.8264i −0.114492 + 0.519666i
\(815\) 28.4186 15.3186i 0.995461 0.536588i
\(816\) −3.61827 1.91294i −0.126665 0.0669663i
\(817\) 8.90104 5.13902i 0.311408 0.179791i
\(818\) 12.8623 + 40.6079i 0.449718 + 1.41982i
\(819\) −34.9132 + 8.49048i −1.21997 + 0.296681i
\(820\) 8.29484 0.503942i 0.289668 0.0175984i
\(821\) 39.0578 22.5500i 1.36313 0.787002i 0.373089 0.927796i \(-0.378299\pi\)
0.990039 + 0.140794i \(0.0449654\pi\)
\(822\) 6.04645 + 7.35861i 0.210894 + 0.256661i
\(823\) 36.8115 + 21.2532i 1.28317 + 0.740838i 0.977427 0.211276i \(-0.0677617\pi\)
0.305743 + 0.952114i \(0.401095\pi\)
\(824\) −8.96902 21.4142i −0.312450 0.745997i
\(825\) −21.6206 19.1373i −0.752732 0.666276i
\(826\) 3.42094 3.74315i 0.119030 0.130241i
\(827\) 26.0006 0.904131 0.452065 0.891985i \(-0.350687\pi\)
0.452065 + 0.891985i \(0.350687\pi\)
\(828\) 47.9592 + 9.47984i 1.66670 + 0.329447i
\(829\) 31.5003i 1.09405i −0.837116 0.547025i \(-0.815760\pi\)
0.837116 0.547025i \(-0.184240\pi\)
\(830\) −12.9009 + 3.67526i −0.447796 + 0.127570i
\(831\) −4.35206 0.624493i −0.150971 0.0216634i
\(832\) −50.0605 12.9919i −1.73553 0.450412i
\(833\) 1.82530 + 1.05384i 0.0632429 + 0.0365133i
\(834\) 2.70367 7.19657i 0.0936203 0.249197i
\(835\) 26.8910 + 0.785799i 0.930601 + 0.0271937i
\(836\) −25.8005 + 18.1669i −0.892329 + 0.628314i
\(837\) −23.4766 + 16.7472i −0.811469 + 0.578868i
\(838\) 37.0388 11.7318i 1.27949 0.405268i
\(839\) 28.7717 + 49.8341i 0.993310 + 1.72046i 0.596661 + 0.802493i \(0.296494\pi\)
0.396649 + 0.917971i \(0.370173\pi\)
\(840\) 5.97210 19.3958i 0.206057 0.669219i
\(841\) −14.4877 + 25.0935i −0.499577 + 0.865293i
\(842\) −0.0144758 + 0.0657042i −0.000498868 + 0.00226432i
\(843\) 13.1698 + 1.88978i 0.453592 + 0.0650876i
\(844\) −5.39570 + 11.6509i −0.185728 + 0.401040i
\(845\) −54.7959 33.8081i −1.88504 1.16303i
\(846\) 40.7857 0.885357i 1.40224 0.0304392i
\(847\) 0.214576i 0.00737293i
\(848\) 25.1957 4.57925i 0.865224 0.157252i
\(849\) 2.51851 + 6.28586i 0.0864351 + 0.215730i
\(850\) 4.04910 1.02666i 0.138883 0.0352140i
\(851\) 22.7205 + 13.1177i 0.778848 + 0.449668i
\(852\) 6.39523 + 4.15555i 0.219097 + 0.142367i
\(853\) −21.6573 37.5115i −0.741532 1.28437i −0.951798 0.306726i \(-0.900766\pi\)
0.210266 0.977644i \(-0.432567\pi\)
\(854\) −2.54374 8.03092i −0.0870449 0.274813i
\(855\) 23.5929 21.2390i 0.806859 0.726360i
\(856\) 39.3036 + 29.9135i 1.34337 + 1.02242i
\(857\) 46.1891 26.6673i 1.57779 0.910938i 0.582624 0.812742i \(-0.302026\pi\)
0.995167 0.0981959i \(-0.0313072\pi\)
\(858\) −52.0862 + 8.63158i −1.77819 + 0.294677i
\(859\) 14.2097 + 8.20399i 0.484830 + 0.279916i 0.722427 0.691447i \(-0.243027\pi\)
−0.237597 + 0.971364i \(0.576360\pi\)
\(860\) −4.33754 + 8.69089i −0.147909 + 0.296357i
\(861\) 4.68799 + 3.68456i 0.159766 + 0.125570i
\(862\) 6.66293 7.29051i 0.226940 0.248316i
\(863\) 29.1271i 0.991499i 0.868466 + 0.495750i \(0.165107\pi\)
−0.868466 + 0.495750i \(0.834893\pi\)
\(864\) 24.5454 16.1716i 0.835053 0.550169i
\(865\) 20.7328 + 12.7917i 0.704935 + 0.434932i
\(866\) 14.0734 + 12.8619i 0.478233 + 0.437066i
\(867\) −17.8216 + 22.6751i −0.605254 + 0.770085i
\(868\) −20.4804 + 1.84601i −0.695151 + 0.0626577i
\(869\) 3.48369 + 2.01131i 0.118176 + 0.0682290i
\(870\) −0.794018 0.325075i −0.0269197 0.0110211i
\(871\) −21.5617 37.3460i −0.730592 1.26542i
\(872\) 27.5943 36.2564i 0.934460 1.22780i
\(873\) −28.8121 30.1835i −0.975141 1.02156i
\(874\) 16.4652 + 51.9830i 0.556945 + 1.75835i
\(875\) 8.74664 + 18.7755i 0.295691 + 0.634729i
\(876\) −28.8722 + 44.4331i −0.975500 + 1.50126i
\(877\) −8.30152 + 14.3786i −0.280322 + 0.485532i −0.971464 0.237187i \(-0.923775\pi\)
0.691142 + 0.722719i \(0.257108\pi\)
\(878\) −6.49164 1.43022i −0.219082 0.0482676i
\(879\) −0.888054 2.21646i −0.0299533 0.0747593i
\(880\) 10.8677 27.7698i 0.366350 0.936118i
\(881\) 22.4187 0.755305 0.377652 0.925947i \(-0.376731\pi\)
0.377652 + 0.925947i \(0.376731\pi\)
\(882\) −12.9416 + 7.85116i −0.435766 + 0.264362i
\(883\) −1.09932 −0.0369951 −0.0184976 0.999829i \(-0.505888\pi\)
−0.0184976 + 0.999829i \(0.505888\pi\)
\(884\) 3.20986 6.93102i 0.107959 0.233116i
\(885\) −4.80224 + 5.75573i −0.161426 + 0.193477i
\(886\) −11.3378 2.49791i −0.380900 0.0839189i
\(887\) −2.99508 1.72921i −0.100565 0.0580612i 0.448874 0.893595i \(-0.351825\pi\)
−0.549439 + 0.835534i \(0.685159\pi\)
\(888\) 15.2677 3.96551i 0.512350 0.133074i
\(889\) −1.09676 1.89965i −0.0367843 0.0637123i
\(890\) −9.48957 + 37.7835i −0.318091 + 1.26651i
\(891\) 16.1945 25.2610i 0.542536 0.846277i
\(892\) 26.9287 + 38.2440i 0.901639 + 1.28050i
\(893\) 22.7514 + 39.4065i 0.761346 + 1.31869i
\(894\) 6.23905 16.6070i 0.208665 0.555421i
\(895\) −0.385720 0.715575i −0.0128932 0.0239191i
\(896\) 20.9308 1.10668i 0.699248 0.0369714i
\(897\) −12.9589 + 90.3103i −0.432687 + 3.01537i
\(898\) 33.5715 36.7336i 1.12029 1.22581i
\(899\) 0.869359i 0.0289947i
\(900\) −7.52601 + 29.0406i −0.250867 + 0.968022i
\(901\) 3.78204i 0.125998i
\(902\) 6.46743 + 5.91070i 0.215342 + 0.196805i
\(903\) −6.46941 + 2.59206i −0.215289 + 0.0862582i
\(904\) 4.56915 + 10.9092i 0.151968 + 0.362834i
\(905\) 3.25705 + 6.04238i 0.108268 + 0.200855i
\(906\) 25.6522 21.0780i 0.852236 0.700269i
\(907\) 16.7205 + 28.9607i 0.555194 + 0.961625i 0.997888 + 0.0649519i \(0.0206894\pi\)
−0.442694 + 0.896673i \(0.645977\pi\)
\(908\) −37.9801 + 26.7429i −1.26041 + 0.887493i
\(909\) 29.8213 + 31.2407i 0.989109 + 1.03619i
\(910\) 36.7335 + 9.22584i 1.21770 + 0.305834i
\(911\) 4.97939 + 8.62456i 0.164975 + 0.285745i 0.936646 0.350277i \(-0.113912\pi\)
−0.771672 + 0.636021i \(0.780579\pi\)
\(912\) 28.9843 + 15.3237i 0.959764 + 0.507417i
\(913\) −12.2480 7.07139i −0.405350 0.234029i
\(914\) 10.7638 48.8559i 0.356036 1.61601i
\(915\) 4.29188 + 11.6899i 0.141885 + 0.386457i
\(916\) 6.30096 13.6056i 0.208190 0.449542i
\(917\) 13.1707 0.434936
\(918\) 1.70162 + 3.99370i 0.0561619 + 0.131812i
\(919\) −26.5683 −0.876408 −0.438204 0.898875i \(-0.644385\pi\)
−0.438204 + 0.898875i \(0.644385\pi\)
\(920\) −40.0769 32.3936i −1.32130 1.06798i
\(921\) 29.3228 37.3084i 0.966221 1.22936i
\(922\) −4.81362 + 21.8486i −0.158528 + 0.719544i
\(923\) −7.11671 + 12.3265i −0.234249 + 0.405732i
\(924\) 19.0672 9.70880i 0.627266 0.319396i
\(925\) −8.85019 + 13.4488i −0.290993 + 0.442193i
\(926\) 8.60044 2.72413i 0.282628 0.0895204i
\(927\) −6.92445 + 23.6313i −0.227429 + 0.776153i
\(928\) 0.0328397 0.885515i 0.00107801 0.0290684i
\(929\) −29.4711 51.0454i −0.966915 1.67475i −0.704378 0.709825i \(-0.748774\pi\)
−0.262537 0.964922i \(-0.584559\pi\)
\(930\) 30.1211 4.09158i 0.987709 0.134168i
\(931\) −14.6216 8.44179i −0.479204 0.276668i
\(932\) 38.9890 3.51428i 1.27713 0.115114i
\(933\) 2.92706 + 7.30554i 0.0958276 + 0.239173i
\(934\) 23.8180 26.0614i 0.779348 0.852754i
\(935\) 3.74813 + 2.31252i 0.122577 + 0.0756276i
\(936\) 32.5480 + 44.1568i 1.06387 + 1.44331i
\(937\) 35.6730i 1.16538i −0.812693 0.582692i \(-0.801999\pi\)
0.812693 0.582692i \(-0.198001\pi\)
\(938\) 12.9006 + 11.7901i 0.421218 + 0.384959i
\(939\) −4.48084 + 31.2268i −0.146227 + 1.01905i
\(940\) −38.4762 19.2031i −1.25495 0.626336i
\(941\) 18.8543 + 10.8855i 0.614632 + 0.354858i 0.774776 0.632236i \(-0.217863\pi\)
−0.160144 + 0.987094i \(0.551196\pi\)
\(942\) 7.30471 + 2.74429i 0.238000 + 0.0894139i
\(943\) 13.1119 7.57018i 0.426983 0.246519i
\(944\) −7.28875 2.60962i −0.237228 0.0849358i
\(945\) −17.8814 + 11.9835i −0.581680 + 0.389823i
\(946\) −9.76273 + 3.09228i −0.317414 + 0.100539i
\(947\) 16.9667 + 29.3872i 0.551344 + 0.954955i 0.998178 + 0.0603385i \(0.0192180\pi\)
−0.446834 + 0.894617i \(0.647449\pi\)
\(948\) 0.219861 4.17376i 0.00714075 0.135557i
\(949\) −85.6426 49.4458i −2.78008 1.60508i
\(950\) −32.4354 + 8.22406i −1.05234 + 0.266824i
\(951\) 13.5130 + 1.93903i 0.438189 + 0.0628773i
\(952\) −0.391955 + 3.07061i −0.0127033 + 0.0995190i
\(953\) 29.8028i 0.965408i −0.875783 0.482704i \(-0.839655\pi\)
0.875783 0.482704i \(-0.160345\pi\)
\(954\) −23.8121 13.0672i −0.770945 0.423067i
\(955\) −34.6486 21.3775i −1.12120 0.691760i
\(956\) −9.08520 4.20749i −0.293836 0.136080i
\(957\) −0.336435 0.839696i −0.0108754 0.0271435i
\(958\) 3.82760 + 0.843288i 0.123664 + 0.0272454i
\(959\) 3.60168 6.23829i 0.116304 0.201445i
\(960\) −30.8354 + 3.02981i −0.995207 + 0.0977866i
\(961\) 0.0996707 + 0.172635i 0.00321518 + 0.00556886i
\(962\) 8.88922 + 28.0645i 0.286600 + 0.904835i
\(963\) −12.3794 50.9046i −0.398921 1.64038i
\(964\) 18.7409 13.1960i 0.603602 0.425013i
\(965\) 50.6118 + 1.47896i 1.62925 + 0.0476094i
\(966\) −6.04491 36.4773i −0.194492 1.17364i
\(967\) −8.50028 4.90764i −0.273351 0.157819i 0.357059 0.934082i \(-0.383780\pi\)
−0.630409 + 0.776263i \(0.717113\pi\)
\(968\) 0.302165 0.126557i 0.00971194 0.00406771i
\(969\) −2.99208 + 3.80692i −0.0961195 + 0.122296i
\(970\) 12.0510 + 42.3015i 0.386935 + 1.35822i
\(971\) 16.8674i 0.541300i 0.962678 + 0.270650i \(0.0872386\pi\)
−0.962678 + 0.270650i \(0.912761\pi\)
\(972\) −31.0239 3.08496i −0.995092 0.0989503i
\(973\) −5.81441 −0.186402
\(974\) −21.7705 19.8964i −0.697570 0.637523i
\(975\) −54.8607 11.1749i −1.75695 0.357884i
\(976\) −9.80878 + 8.31872i −0.313971 + 0.266276i
\(977\) −24.3616 14.0652i −0.779396 0.449984i 0.0568205 0.998384i \(-0.481904\pi\)
−0.836216 + 0.548400i \(0.815237\pi\)
\(978\) −5.78186 34.8899i −0.184883 1.11566i
\(979\) −35.5703 + 20.5365i −1.13683 + 0.656349i
\(980\) 15.9263 0.967582i 0.508748 0.0309083i
\(981\) −46.9580 + 11.4196i −1.49925 + 0.364601i
\(982\) 50.7006 16.0591i 1.61792 0.512465i
\(983\) −15.1286 + 8.73451i −0.482528 + 0.278588i −0.721469 0.692446i \(-0.756533\pi\)
0.238941 + 0.971034i \(0.423200\pi\)
\(984\) 2.42359 8.77475i 0.0772611 0.279729i
\(985\) −24.0283 + 12.9521i −0.765604 + 0.412687i
\(986\) 0.127804 + 0.0281575i 0.00407011 + 0.000896717i
\(987\) −11.4755 28.6413i −0.365269 0.911662i
\(988\) −25.7126 + 55.5211i −0.818028 + 1.76636i
\(989\) 17.6966i 0.562719i
\(990\) −27.5099 + 15.6086i −0.874323 + 0.496074i
\(991\) −55.1709 −1.75256 −0.876280 0.481801i \(-0.839983\pi\)
−0.876280 + 0.481801i \(0.839983\pi\)
\(992\) 14.6789 + 27.7516i 0.466056 + 0.881114i
\(993\) −1.07953 + 7.52322i −0.0342580 + 0.238742i
\(994\) 1.24110 5.63325i 0.0393654 0.178676i
\(995\) −29.3920 + 15.8433i −0.931790 + 0.502267i
\(996\) −0.772989 + 14.6741i −0.0244931 + 0.464968i
\(997\) 12.3131 + 21.3268i 0.389959 + 0.675428i 0.992444 0.122702i \(-0.0391560\pi\)
−0.602485 + 0.798130i \(0.705823\pi\)
\(998\) −41.2099 + 13.0529i −1.30448 + 0.413184i
\(999\) −15.2250 6.93763i −0.481697 0.219497i
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 360.2.bk.a.229.18 yes 136
5.4 even 2 inner 360.2.bk.a.229.51 yes 136
8.5 even 2 inner 360.2.bk.a.229.5 136
9.7 even 3 inner 360.2.bk.a.349.64 yes 136
40.29 even 2 inner 360.2.bk.a.229.64 yes 136
45.34 even 6 inner 360.2.bk.a.349.5 yes 136
72.61 even 6 inner 360.2.bk.a.349.51 yes 136
360.349 even 6 inner 360.2.bk.a.349.18 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bk.a.229.5 136 8.5 even 2 inner
360.2.bk.a.229.18 yes 136 1.1 even 1 trivial
360.2.bk.a.229.51 yes 136 5.4 even 2 inner
360.2.bk.a.229.64 yes 136 40.29 even 2 inner
360.2.bk.a.349.5 yes 136 45.34 even 6 inner
360.2.bk.a.349.18 yes 136 360.349 even 6 inner
360.2.bk.a.349.51 yes 136 72.61 even 6 inner
360.2.bk.a.349.64 yes 136 9.7 even 3 inner