Properties

Label 110.2.k.a.57.1
Level $110$
Weight $2$
Character 110.57
Analytic conductor $0.878$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [110,2,Mod(7,110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(110, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([5, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("110.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 110.k (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.878354422234\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(6\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 57.1
Character \(\chi\) \(=\) 110.57
Dual form 110.2.k.a.83.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.453990 - 0.891007i) q^{2} +(-0.348671 + 2.20142i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.49719 + 1.66085i) q^{5} +(2.11978 - 0.688757i) q^{6} +(-3.91761 + 0.620489i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-1.87153 - 0.608097i) q^{9} +O(q^{10})\) \(q+(-0.453990 - 0.891007i) q^{2} +(-0.348671 + 2.20142i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.49719 + 1.66085i) q^{5} +(2.11978 - 0.688757i) q^{6} +(-3.91761 + 0.620489i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-1.87153 - 0.608097i) q^{9} +(2.15954 + 0.579997i) q^{10} +(2.83922 + 1.71431i) q^{11} +(-1.57605 - 1.57605i) q^{12} +(2.65534 - 1.35296i) q^{13} +(2.33142 + 3.20892i) q^{14} +(-3.13421 - 3.87504i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(4.15761 + 2.11841i) q^{17} +(0.307838 + 1.94362i) q^{18} +(2.59693 - 1.88678i) q^{19} +(-0.463629 - 2.18748i) q^{20} -8.84068i q^{21} +(0.238480 - 3.30804i) q^{22} +(-5.14200 + 5.14200i) q^{23} +(-0.688757 + 2.11978i) q^{24} +(-0.516841 - 4.97322i) q^{25} +(-2.41100 - 1.75169i) q^{26} +(-1.04442 + 2.04980i) q^{27} +(1.80073 - 3.53413i) q^{28} +(0.0660203 + 0.0479665i) q^{29} +(-2.02979 + 4.55183i) q^{30} +(-0.600717 + 1.84882i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.76387 + 5.65259i) q^{33} -4.66620i q^{34} +(4.83487 - 7.43555i) q^{35} +(1.59202 - 1.15667i) q^{36} +(-0.916611 - 5.78725i) q^{37} +(-2.86011 - 1.45730i) q^{38} +(2.05261 + 6.31728i) q^{39} +(-1.73857 + 1.40619i) q^{40} +(1.64181 + 2.25975i) q^{41} +(-7.87710 + 4.01358i) q^{42} +(-2.07213 - 2.07213i) q^{43} +(-3.05575 + 1.28933i) q^{44} +(3.81199 - 2.19789i) q^{45} +(6.91597 + 2.24713i) q^{46} +(12.1843 + 1.92981i) q^{47} +(2.20142 - 0.348671i) q^{48} +(8.30529 - 2.69855i) q^{49} +(-4.19653 + 2.71830i) q^{50} +(-6.11316 + 8.41404i) q^{51} +(-0.466200 + 2.94347i) q^{52} +(1.67555 + 3.28846i) q^{53} +2.30054 q^{54} +(-7.09805 + 2.14887i) q^{55} -3.96645 q^{56} +(3.24812 + 6.37480i) q^{57} +(0.0127659 - 0.0806009i) q^{58} +(-1.48475 + 2.04358i) q^{59} +(4.97722 - 0.257934i) q^{60} +(1.70602 - 0.554319i) q^{61} +(1.92003 - 0.304102i) q^{62} +(7.70925 + 1.22102i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-1.72848 + 6.43577i) q^{65} +(7.19925 + 1.67841i) q^{66} +(2.34748 + 2.34748i) q^{67} +(-4.15761 + 2.11841i) q^{68} +(-9.52685 - 13.1126i) q^{69} +(-8.82012 - 0.932234i) q^{70} +(-1.98584 - 6.11179i) q^{71} +(-1.75336 - 0.893382i) q^{72} +(-1.22279 - 7.72040i) q^{73} +(-4.74035 + 3.44406i) q^{74} +(11.1284 + 0.596233i) q^{75} +3.20998i q^{76} +(-12.1867 - 4.95428i) q^{77} +(4.69687 - 4.69687i) q^{78} +(-3.80642 + 11.7150i) q^{79} +(2.04222 + 0.910682i) q^{80} +(-8.92437 - 6.48393i) q^{81} +(1.26809 - 2.48877i) q^{82} +(6.86376 - 13.4709i) q^{83} +(7.15226 + 5.19642i) q^{84} +(-9.74309 + 3.73350i) q^{85} +(-0.905554 + 2.78701i) q^{86} +(-0.128614 + 0.128614i) q^{87} +(2.53609 + 2.13735i) q^{88} +5.99094i q^{89} +(-3.68895 - 2.39869i) q^{90} +(-9.56310 + 6.94800i) q^{91} +(-1.13757 - 7.18235i) q^{92} +(-3.86058 - 1.96706i) q^{93} +(-3.81210 - 11.7324i) q^{94} +(-0.754441 + 7.13797i) q^{95} +(-1.31009 - 1.80319i) q^{96} +(9.78069 - 4.98351i) q^{97} +(-6.17495 - 6.17495i) q^{98} +(-4.27122 - 4.93489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/110\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(101\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.453990 0.891007i −0.321020 0.630037i
\(3\) −0.348671 + 2.20142i −0.201306 + 1.27099i 0.655437 + 0.755250i \(0.272484\pi\)
−0.856743 + 0.515744i \(0.827516\pi\)
\(4\) −0.587785 + 0.809017i −0.293893 + 0.404508i
\(5\) −1.49719 + 1.66085i −0.669564 + 0.742754i
\(6\) 2.11978 0.688757i 0.865396 0.281184i
\(7\) −3.91761 + 0.620489i −1.48072 + 0.234523i −0.843904 0.536494i \(-0.819748\pi\)
−0.636815 + 0.771017i \(0.719748\pi\)
\(8\) 0.987688 + 0.156434i 0.349201 + 0.0553079i
\(9\) −1.87153 0.608097i −0.623843 0.202699i
\(10\) 2.15954 + 0.579997i 0.682906 + 0.183411i
\(11\) 2.83922 + 1.71431i 0.856056 + 0.516883i
\(12\) −1.57605 1.57605i −0.454965 0.454965i
\(13\) 2.65534 1.35296i 0.736460 0.375245i −0.0451771 0.998979i \(-0.514385\pi\)
0.781637 + 0.623734i \(0.214385\pi\)
\(14\) 2.33142 + 3.20892i 0.623098 + 0.857621i
\(15\) −3.13421 3.87504i −0.809249 1.00053i
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) 4.15761 + 2.11841i 1.00837 + 0.513790i 0.878500 0.477742i \(-0.158544\pi\)
0.129869 + 0.991531i \(0.458544\pi\)
\(18\) 0.307838 + 1.94362i 0.0725582 + 0.458115i
\(19\) 2.59693 1.88678i 0.595776 0.432856i −0.248601 0.968606i \(-0.579971\pi\)
0.844377 + 0.535750i \(0.179971\pi\)
\(20\) −0.463629 2.18748i −0.103671 0.489134i
\(21\) 8.84068i 1.92919i
\(22\) 0.238480 3.30804i 0.0508440 0.705276i
\(23\) −5.14200 + 5.14200i −1.07218 + 1.07218i −0.0749964 + 0.997184i \(0.523895\pi\)
−0.997184 + 0.0749964i \(0.976105\pi\)
\(24\) −0.688757 + 2.11978i −0.140592 + 0.432698i
\(25\) −0.516841 4.97322i −0.103368 0.994643i
\(26\) −2.41100 1.75169i −0.472836 0.343536i
\(27\) −1.04442 + 2.04980i −0.200999 + 0.394483i
\(28\) 1.80073 3.53413i 0.340306 0.667888i
\(29\) 0.0660203 + 0.0479665i 0.0122597 + 0.00890716i 0.593898 0.804540i \(-0.297588\pi\)
−0.581639 + 0.813447i \(0.697588\pi\)
\(30\) −2.02979 + 4.55183i −0.370587 + 0.831047i
\(31\) −0.600717 + 1.84882i −0.107892 + 0.332057i −0.990398 0.138243i \(-0.955854\pi\)
0.882506 + 0.470300i \(0.155854\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −4.76387 + 5.65259i −0.829283 + 0.983990i
\(34\) 4.66620i 0.800246i
\(35\) 4.83487 7.43555i 0.817243 1.25684i
\(36\) 1.59202 1.15667i 0.265336 0.192778i
\(37\) −0.916611 5.78725i −0.150690 0.951419i −0.940925 0.338615i \(-0.890042\pi\)
0.790235 0.612804i \(-0.209958\pi\)
\(38\) −2.86011 1.45730i −0.463971 0.236405i
\(39\) 2.05261 + 6.31728i 0.328680 + 1.01157i
\(40\) −1.73857 + 1.40619i −0.274892 + 0.222338i
\(41\) 1.64181 + 2.25975i 0.256407 + 0.352914i 0.917742 0.397177i \(-0.130010\pi\)
−0.661335 + 0.750090i \(0.730010\pi\)
\(42\) −7.87710 + 4.01358i −1.21546 + 0.619309i
\(43\) −2.07213 2.07213i −0.315997 0.315997i 0.531231 0.847227i \(-0.321730\pi\)
−0.847227 + 0.531231i \(0.821730\pi\)
\(44\) −3.05575 + 1.28933i −0.460672 + 0.194374i
\(45\) 3.81199 2.19789i 0.568259 0.327642i
\(46\) 6.91597 + 2.24713i 1.01970 + 0.331322i
\(47\) 12.1843 + 1.92981i 1.77727 + 0.281492i 0.956915 0.290367i \(-0.0937772\pi\)
0.820352 + 0.571858i \(0.193777\pi\)
\(48\) 2.20142 0.348671i 0.317748 0.0503264i
\(49\) 8.30529 2.69855i 1.18647 0.385507i
\(50\) −4.19653 + 2.71830i −0.593479 + 0.384426i
\(51\) −6.11316 + 8.41404i −0.856013 + 1.17820i
\(52\) −0.466200 + 2.94347i −0.0646503 + 0.408186i
\(53\) 1.67555 + 3.28846i 0.230155 + 0.451704i 0.976984 0.213311i \(-0.0684249\pi\)
−0.746830 + 0.665016i \(0.768425\pi\)
\(54\) 2.30054 0.313064
\(55\) −7.09805 + 2.14887i −0.957101 + 0.289754i
\(56\) −3.96645 −0.530039
\(57\) 3.24812 + 6.37480i 0.430225 + 0.844363i
\(58\) 0.0127659 0.0806009i 0.00167625 0.0105834i
\(59\) −1.48475 + 2.04358i −0.193298 + 0.266052i −0.894654 0.446759i \(-0.852578\pi\)
0.701356 + 0.712811i \(0.252578\pi\)
\(60\) 4.97722 0.257934i 0.642556 0.0332991i
\(61\) 1.70602 0.554319i 0.218433 0.0709733i −0.197756 0.980251i \(-0.563365\pi\)
0.416189 + 0.909278i \(0.363365\pi\)
\(62\) 1.92003 0.304102i 0.243844 0.0386210i
\(63\) 7.70925 + 1.22102i 0.971274 + 0.153835i
\(64\) 0.951057 + 0.309017i 0.118882 + 0.0386271i
\(65\) −1.72848 + 6.43577i −0.214392 + 0.798259i
\(66\) 7.19925 + 1.67841i 0.886166 + 0.206599i
\(67\) 2.34748 + 2.34748i 0.286790 + 0.286790i 0.835809 0.549020i \(-0.184999\pi\)
−0.549020 + 0.835809i \(0.684999\pi\)
\(68\) −4.15761 + 2.11841i −0.504184 + 0.256895i
\(69\) −9.52685 13.1126i −1.14690 1.57857i
\(70\) −8.82012 0.932234i −1.05421 0.111423i
\(71\) −1.98584 6.11179i −0.235676 0.725336i −0.997031 0.0770011i \(-0.975466\pi\)
0.761355 0.648335i \(-0.224534\pi\)
\(72\) −1.75336 0.893382i −0.206636 0.105286i
\(73\) −1.22279 7.72040i −0.143117 0.903604i −0.949854 0.312694i \(-0.898769\pi\)
0.806737 0.590911i \(-0.201231\pi\)
\(74\) −4.74035 + 3.44406i −0.551054 + 0.400364i
\(75\) 11.1284 + 0.596233i 1.28499 + 0.0688470i
\(76\) 3.20998i 0.368210i
\(77\) −12.1867 4.95428i −1.38880 0.564593i
\(78\) 4.69687 4.69687i 0.531816 0.531816i
\(79\) −3.80642 + 11.7150i −0.428256 + 1.31803i 0.471587 + 0.881820i \(0.343681\pi\)
−0.899842 + 0.436215i \(0.856319\pi\)
\(80\) 2.04222 + 0.910682i 0.228327 + 0.101817i
\(81\) −8.92437 6.48393i −0.991596 0.720437i
\(82\) 1.26809 2.48877i 0.140037 0.274838i
\(83\) 6.86376 13.4709i 0.753396 1.47862i −0.120606 0.992700i \(-0.538484\pi\)
0.874002 0.485922i \(-0.161516\pi\)
\(84\) 7.15226 + 5.19642i 0.780375 + 0.566976i
\(85\) −9.74309 + 3.73350i −1.05679 + 0.404955i
\(86\) −0.905554 + 2.78701i −0.0976484 + 0.300531i
\(87\) −0.128614 + 0.128614i −0.0137889 + 0.0137889i
\(88\) 2.53609 + 2.13735i 0.270348 + 0.227842i
\(89\) 5.99094i 0.635038i 0.948252 + 0.317519i \(0.102850\pi\)
−0.948252 + 0.317519i \(0.897150\pi\)
\(90\) −3.68895 2.39869i −0.388849 0.252844i
\(91\) −9.56310 + 6.94800i −1.00249 + 0.728349i
\(92\) −1.13757 7.18235i −0.118600 0.748812i
\(93\) −3.86058 1.96706i −0.400323 0.203975i
\(94\) −3.81210 11.7324i −0.393188 1.21011i
\(95\) −0.754441 + 7.13797i −0.0774040 + 0.732340i
\(96\) −1.31009 1.80319i −0.133711 0.184037i
\(97\) 9.78069 4.98351i 0.993078 0.505999i 0.119579 0.992825i \(-0.461845\pi\)
0.873499 + 0.486826i \(0.161845\pi\)
\(98\) −6.17495 6.17495i −0.623764 0.623764i
\(99\) −4.27122 4.93489i −0.429273 0.495976i
\(100\) 4.32721 + 2.50505i 0.432721 + 0.250505i
\(101\) −7.31649 2.37727i −0.728018 0.236547i −0.0785218 0.996912i \(-0.525020\pi\)
−0.649496 + 0.760365i \(0.725020\pi\)
\(102\) 10.2723 + 1.62697i 1.01711 + 0.161094i
\(103\) 5.63036 0.891762i 0.554776 0.0878679i 0.127250 0.991871i \(-0.459385\pi\)
0.427526 + 0.904003i \(0.359385\pi\)
\(104\) 2.83430 0.920920i 0.277926 0.0903037i
\(105\) 14.6830 + 13.2362i 1.43292 + 1.29172i
\(106\) 2.16935 2.98586i 0.210706 0.290012i
\(107\) 1.97017 12.4391i 0.190463 1.20254i −0.688353 0.725376i \(-0.741666\pi\)
0.878816 0.477161i \(-0.158334\pi\)
\(108\) −1.04442 2.04980i −0.100500 0.197242i
\(109\) 13.0770 1.25255 0.626273 0.779604i \(-0.284580\pi\)
0.626273 + 0.779604i \(0.284580\pi\)
\(110\) 5.13711 + 5.34885i 0.489804 + 0.509992i
\(111\) 13.0598 1.23958
\(112\) 1.80073 + 3.53413i 0.170153 + 0.333944i
\(113\) −0.0655098 + 0.413613i −0.00616264 + 0.0389094i −0.990578 0.136949i \(-0.956270\pi\)
0.984415 + 0.175859i \(0.0562702\pi\)
\(114\) 4.20537 5.78820i 0.393869 0.542115i
\(115\) −0.841532 16.2386i −0.0784733 1.51426i
\(116\) −0.0776115 + 0.0252175i −0.00720605 + 0.00234139i
\(117\) −5.79229 + 0.917408i −0.535497 + 0.0848144i
\(118\) 2.49491 + 0.395154i 0.229675 + 0.0363769i
\(119\) −17.6024 5.71935i −1.61361 0.524292i
\(120\) −2.48943 4.31763i −0.227253 0.394144i
\(121\) 5.12231 + 9.73457i 0.465665 + 0.884961i
\(122\) −1.26842 1.26842i −0.114837 0.114837i
\(123\) −5.54712 + 2.82640i −0.500167 + 0.254848i
\(124\) −1.14263 1.57270i −0.102611 0.141232i
\(125\) 9.03357 + 6.58746i 0.807987 + 0.589200i
\(126\) −2.41198 7.42332i −0.214877 0.661322i
\(127\) −7.73399 3.94067i −0.686281 0.349678i 0.0758331 0.997121i \(-0.475838\pi\)
−0.762114 + 0.647443i \(0.775838\pi\)
\(128\) −0.156434 0.987688i −0.0138270 0.0873001i
\(129\) 5.28413 3.83915i 0.465242 0.338018i
\(130\) 6.51903 1.38169i 0.571757 0.121182i
\(131\) 1.31996i 0.115326i 0.998336 + 0.0576628i \(0.0183648\pi\)
−0.998336 + 0.0576628i \(0.981635\pi\)
\(132\) −1.77291 7.17656i −0.154312 0.624640i
\(133\) −9.00303 + 9.00303i −0.780661 + 0.780661i
\(134\) 1.02588 3.15735i 0.0886229 0.272753i
\(135\) −1.84070 4.80356i −0.158422 0.413425i
\(136\) 3.77503 + 2.74272i 0.323706 + 0.235186i
\(137\) −8.13766 + 15.9711i −0.695248 + 1.36450i 0.225462 + 0.974252i \(0.427611\pi\)
−0.920710 + 0.390248i \(0.872389\pi\)
\(138\) −7.35830 + 14.4415i −0.626380 + 1.22934i
\(139\) −2.00508 1.45677i −0.170068 0.123562i 0.499495 0.866317i \(-0.333519\pi\)
−0.669564 + 0.742755i \(0.733519\pi\)
\(140\) 3.17362 + 8.28201i 0.268220 + 0.699957i
\(141\) −8.49666 + 26.1500i −0.715548 + 2.20223i
\(142\) −4.54409 + 4.54409i −0.381332 + 0.381332i
\(143\) 9.85849 + 0.710708i 0.824408 + 0.0594324i
\(144\) 1.96784i 0.163987i
\(145\) −0.178510 + 0.0378347i −0.0148245 + 0.00314200i
\(146\) −6.32379 + 4.59450i −0.523361 + 0.380244i
\(147\) 3.04484 + 19.2244i 0.251134 + 1.58560i
\(148\) 5.22076 + 2.66011i 0.429144 + 0.218660i
\(149\) −3.39237 10.4406i −0.277914 0.855331i −0.988434 0.151654i \(-0.951540\pi\)
0.710520 0.703677i \(-0.248460\pi\)
\(150\) −4.52093 10.1861i −0.369132 0.831694i
\(151\) −7.30350 10.0524i −0.594350 0.818053i 0.400826 0.916154i \(-0.368723\pi\)
−0.995176 + 0.0981010i \(0.968723\pi\)
\(152\) 2.86011 1.45730i 0.231986 0.118203i
\(153\) −6.49290 6.49290i −0.524920 0.524920i
\(154\) 1.11833 + 13.1076i 0.0901177 + 1.05624i
\(155\) −2.17122 3.76573i −0.174396 0.302471i
\(156\) −6.31728 2.05261i −0.505787 0.164340i
\(157\) 5.61637 + 0.889545i 0.448235 + 0.0709934i 0.376471 0.926428i \(-0.377137\pi\)
0.0717635 + 0.997422i \(0.477137\pi\)
\(158\) 12.1662 1.92693i 0.967889 0.153299i
\(159\) −7.82350 + 2.54201i −0.620444 + 0.201595i
\(160\) −0.115724 2.23307i −0.00914880 0.176540i
\(161\) 16.9538 23.3349i 1.33615 1.83905i
\(162\) −1.72565 + 10.8953i −0.135580 + 0.856017i
\(163\) −5.50237 10.7990i −0.430979 0.845843i −0.999728 0.0233320i \(-0.992573\pi\)
0.568749 0.822511i \(-0.307427\pi\)
\(164\) −2.79321 −0.218113
\(165\) −2.25569 16.3751i −0.175605 1.27480i
\(166\) −15.1187 −1.17344
\(167\) −1.86387 3.65804i −0.144230 0.283068i 0.807578 0.589760i \(-0.200778\pi\)
−0.951809 + 0.306692i \(0.900778\pi\)
\(168\) 1.38299 8.73183i 0.106700 0.673676i
\(169\) −2.42088 + 3.33205i −0.186221 + 0.256312i
\(170\) 7.74985 + 6.98619i 0.594386 + 0.535816i
\(171\) −6.00757 + 1.95198i −0.459410 + 0.149271i
\(172\) 2.89436 0.458421i 0.220693 0.0349543i
\(173\) 12.8231 + 2.03097i 0.974919 + 0.154412i 0.623515 0.781812i \(-0.285704\pi\)
0.351405 + 0.936224i \(0.385704\pi\)
\(174\) 0.172986 + 0.0562064i 0.0131140 + 0.00426100i
\(175\) 5.11061 + 19.1624i 0.386326 + 1.44854i
\(176\) 0.753035 3.23001i 0.0567622 0.243471i
\(177\) −3.98110 3.98110i −0.299238 0.299238i
\(178\) 5.33796 2.71983i 0.400097 0.203860i
\(179\) 4.78324 + 6.58357i 0.357516 + 0.492079i 0.949455 0.313904i \(-0.101637\pi\)
−0.591938 + 0.805983i \(0.701637\pi\)
\(180\) −0.462502 + 4.37586i −0.0344729 + 0.326157i
\(181\) 5.23127 + 16.1002i 0.388837 + 1.19672i 0.933658 + 0.358165i \(0.116598\pi\)
−0.544821 + 0.838552i \(0.683402\pi\)
\(182\) 10.5323 + 5.36646i 0.780704 + 0.397789i
\(183\) 0.625452 + 3.94895i 0.0462348 + 0.291915i
\(184\) −5.88307 + 4.27430i −0.433706 + 0.315106i
\(185\) 10.9841 + 7.14227i 0.807567 + 0.525110i
\(186\) 4.33283i 0.317698i
\(187\) 8.17276 + 13.1420i 0.597652 + 0.961041i
\(188\) −8.72302 + 8.72302i −0.636192 + 0.636192i
\(189\) 2.81977 8.67836i 0.205108 0.631258i
\(190\) 6.70248 2.56836i 0.486249 0.186328i
\(191\) −8.26779 6.00690i −0.598236 0.434644i 0.247016 0.969011i \(-0.420550\pi\)
−0.845252 + 0.534367i \(0.820550\pi\)
\(192\) −1.01188 + 1.98593i −0.0730264 + 0.143322i
\(193\) −10.0127 + 19.6510i −0.720728 + 1.41451i 0.181563 + 0.983379i \(0.441885\pi\)
−0.902290 + 0.431129i \(0.858115\pi\)
\(194\) −8.88068 6.45219i −0.637596 0.463240i
\(195\) −13.5652 6.04910i −0.971423 0.433185i
\(196\) −2.69855 + 8.30529i −0.192754 + 0.593235i
\(197\) 10.9542 10.9542i 0.780453 0.780453i −0.199454 0.979907i \(-0.563917\pi\)
0.979907 + 0.199454i \(0.0639168\pi\)
\(198\) −2.45793 + 6.04608i −0.174678 + 0.429676i
\(199\) 7.77743i 0.551327i −0.961254 0.275664i \(-0.911102\pi\)
0.961254 0.275664i \(-0.0888976\pi\)
\(200\) 0.267505 4.99284i 0.0189155 0.353047i
\(201\) −5.98629 + 4.34929i −0.422240 + 0.306776i
\(202\) 1.20345 + 7.59830i 0.0846746 + 0.534614i
\(203\) −0.288405 0.146949i −0.0202420 0.0103138i
\(204\) −3.21388 9.89130i −0.225016 0.692529i
\(205\) −6.21120 0.656487i −0.433809 0.0458511i
\(206\) −3.35070 4.61184i −0.233454 0.321322i
\(207\) 12.7502 6.49657i 0.886202 0.451543i
\(208\) −2.10729 2.10729i −0.146114 0.146114i
\(209\) 10.6078 0.905046i 0.733753 0.0626033i
\(210\) 5.12756 19.0918i 0.353836 1.31746i
\(211\) 9.07668 + 2.94919i 0.624864 + 0.203031i 0.604299 0.796758i \(-0.293453\pi\)
0.0205655 + 0.999789i \(0.493453\pi\)
\(212\) −3.64528 0.577356i −0.250359 0.0396530i
\(213\) 14.1471 2.24067i 0.969340 0.153528i
\(214\) −11.9778 + 3.89182i −0.818785 + 0.266039i
\(215\) 6.54387 0.339122i 0.446288 0.0231279i
\(216\) −1.35222 + 1.86118i −0.0920071 + 0.126637i
\(217\) 1.20621 7.61569i 0.0818826 0.516986i
\(218\) −5.93682 11.6517i −0.402092 0.789150i
\(219\) 17.4222 1.17729
\(220\) 2.43366 7.00552i 0.164077 0.472312i
\(221\) 13.9060 0.935420
\(222\) −5.92903 11.6364i −0.397930 0.780982i
\(223\) 2.90351 18.3320i 0.194433 1.22760i −0.676589 0.736361i \(-0.736543\pi\)
0.871023 0.491243i \(-0.163457\pi\)
\(224\) 2.33142 3.20892i 0.155774 0.214405i
\(225\) −2.05691 + 9.62181i −0.137128 + 0.641454i
\(226\) 0.398272 0.129407i 0.0264927 0.00860799i
\(227\) −11.1178 + 1.76089i −0.737915 + 0.116874i −0.514067 0.857750i \(-0.671862\pi\)
−0.223848 + 0.974624i \(0.571862\pi\)
\(228\) −7.06652 1.11923i −0.467992 0.0741226i
\(229\) −4.10397 1.33346i −0.271198 0.0881177i 0.170261 0.985399i \(-0.445539\pi\)
−0.441459 + 0.897281i \(0.645539\pi\)
\(230\) −14.0867 + 8.12199i −0.928848 + 0.535548i
\(231\) 15.1556 25.1006i 0.997167 1.65150i
\(232\) 0.0577038 + 0.0577038i 0.00378844 + 0.00378844i
\(233\) −13.0340 + 6.64117i −0.853887 + 0.435077i −0.825421 0.564518i \(-0.809062\pi\)
−0.0284660 + 0.999595i \(0.509062\pi\)
\(234\) 3.44706 + 4.74447i 0.225341 + 0.310156i
\(235\) −21.4474 + 17.3471i −1.39907 + 1.13160i
\(236\) −0.780579 2.40237i −0.0508113 0.156381i
\(237\) −24.4624 12.4642i −1.58900 0.809638i
\(238\) 2.89532 + 18.2804i 0.187676 + 1.18494i
\(239\) 6.12048 4.44679i 0.395901 0.287639i −0.371968 0.928245i \(-0.621317\pi\)
0.767869 + 0.640606i \(0.221317\pi\)
\(240\) −2.71686 + 4.17826i −0.175373 + 0.269706i
\(241\) 6.31704i 0.406917i −0.979084 0.203458i \(-0.934782\pi\)
0.979084 0.203458i \(-0.0652181\pi\)
\(242\) 6.34809 8.98342i 0.408070 0.577476i
\(243\) 12.5054 12.5054i 0.802220 0.802220i
\(244\) −0.554319 + 1.70602i −0.0354867 + 0.109217i
\(245\) −7.95271 + 17.8341i −0.508080 + 1.13938i
\(246\) 5.03668 + 3.65936i 0.321127 + 0.233313i
\(247\) 4.34299 8.52359i 0.276338 0.542343i
\(248\) −0.882540 + 1.73208i −0.0560413 + 0.109987i
\(249\) 27.2620 + 19.8070i 1.72766 + 1.25522i
\(250\) 1.76831 11.0396i 0.111838 0.698206i
\(251\) 6.45616 19.8700i 0.407509 1.25418i −0.511273 0.859418i \(-0.670826\pi\)
0.918782 0.394765i \(-0.129174\pi\)
\(252\) −5.51921 + 5.51921i −0.347678 + 0.347678i
\(253\) −23.4142 + 5.78429i −1.47204 + 0.363655i
\(254\) 8.68006i 0.544636i
\(255\) −4.82189 22.7505i −0.301958 1.42469i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 0.961438 + 6.07028i 0.0599729 + 0.378654i 0.999359 + 0.0357933i \(0.0113958\pi\)
−0.939386 + 0.342860i \(0.888604\pi\)
\(258\) −5.81965 2.96526i −0.362315 0.184609i
\(259\) 7.18185 + 22.1035i 0.446259 + 1.37344i
\(260\) −4.19067 5.18122i −0.259894 0.321326i
\(261\) −0.0943906 0.129918i −0.00584263 0.00804169i
\(262\) 1.17609 0.599250i 0.0726594 0.0370218i
\(263\) 17.2139 + 17.2139i 1.06145 + 1.06145i 0.997984 + 0.0634691i \(0.0202164\pi\)
0.0634691 + 0.997984i \(0.479784\pi\)
\(264\) −5.58948 + 4.83777i −0.344009 + 0.297744i
\(265\) −7.97025 2.14061i −0.489609 0.131496i
\(266\) 12.1090 + 3.93447i 0.742453 + 0.241238i
\(267\) −13.1886 2.08887i −0.807129 0.127837i
\(268\) −3.27896 + 0.519336i −0.200294 + 0.0317235i
\(269\) −25.5811 + 8.31179i −1.55971 + 0.506779i −0.956729 0.290980i \(-0.906019\pi\)
−0.602976 + 0.797759i \(0.706019\pi\)
\(270\) −3.44435 + 3.82085i −0.209616 + 0.232529i
\(271\) 13.3592 18.3874i 0.811515 1.11695i −0.179573 0.983745i \(-0.557472\pi\)
0.991088 0.133210i \(-0.0425284\pi\)
\(272\) 0.729954 4.60875i 0.0442600 0.279446i
\(273\) −11.9611 23.4750i −0.723920 1.42077i
\(274\) 17.9247 1.08287
\(275\) 7.05819 15.0061i 0.425625 0.904900i
\(276\) 16.2080 0.975610
\(277\) −9.44205 18.5311i −0.567318 1.11342i −0.979334 0.202247i \(-0.935175\pi\)
0.412017 0.911176i \(-0.364825\pi\)
\(278\) −0.387709 + 2.44790i −0.0232532 + 0.146815i
\(279\) 2.24852 3.09482i 0.134615 0.185282i
\(280\) 5.93853 6.58767i 0.354895 0.393689i
\(281\) −6.11005 + 1.98528i −0.364495 + 0.118432i −0.485538 0.874216i \(-0.661376\pi\)
0.121043 + 0.992647i \(0.461376\pi\)
\(282\) 27.1572 4.30129i 1.61719 0.256138i
\(283\) 0.957628 + 0.151673i 0.0569251 + 0.00901605i 0.184832 0.982770i \(-0.440826\pi\)
−0.127907 + 0.991786i \(0.540826\pi\)
\(284\) 6.11179 + 1.98584i 0.362668 + 0.117838i
\(285\) −15.4506 4.14965i −0.915217 0.245804i
\(286\) −3.84242 9.10663i −0.227207 0.538487i
\(287\) −7.83411 7.83411i −0.462433 0.462433i
\(288\) 1.75336 0.893382i 0.103318 0.0526430i
\(289\) 2.80573 + 3.86175i 0.165043 + 0.227162i
\(290\) 0.114753 + 0.141877i 0.00673852 + 0.00833131i
\(291\) 7.56058 + 23.2691i 0.443209 + 1.36406i
\(292\) 6.96467 + 3.54868i 0.407577 + 0.207671i
\(293\) −0.677974 4.28056i −0.0396077 0.250073i 0.959938 0.280212i \(-0.0904049\pi\)
−0.999546 + 0.0301394i \(0.990405\pi\)
\(294\) 15.7467 11.4407i 0.918367 0.667233i
\(295\) −1.17113 5.52558i −0.0681858 0.321711i
\(296\) 5.85939i 0.340570i
\(297\) −6.47932 + 4.02936i −0.375968 + 0.233807i
\(298\) −7.76258 + 7.76258i −0.449674 + 0.449674i
\(299\) −6.69682 + 20.6107i −0.387287 + 1.19195i
\(300\) −7.02345 + 8.65258i −0.405499 + 0.499557i
\(301\) 9.40354 + 6.83207i 0.542011 + 0.393794i
\(302\) −5.64104 + 11.0712i −0.324605 + 0.637074i
\(303\) 7.78443 15.2778i 0.447204 0.877687i
\(304\) −2.59693 1.88678i −0.148944 0.108214i
\(305\) −1.63360 + 3.66336i −0.0935394 + 0.209764i
\(306\) −2.83750 + 8.73293i −0.162209 + 0.499228i
\(307\) −13.5031 + 13.5031i −0.770662 + 0.770662i −0.978222 0.207560i \(-0.933448\pi\)
0.207560 + 0.978222i \(0.433448\pi\)
\(308\) 11.1712 6.94716i 0.636540 0.395851i
\(309\) 12.7058i 0.722805i
\(310\) −2.36958 + 3.64418i −0.134583 + 0.206975i
\(311\) −18.7825 + 13.6463i −1.06506 + 0.773812i −0.975018 0.222126i \(-0.928700\pi\)
−0.0900427 + 0.995938i \(0.528700\pi\)
\(312\) 1.03910 + 6.56060i 0.0588273 + 0.371421i
\(313\) 30.1218 + 15.3478i 1.70258 + 0.867510i 0.985322 + 0.170707i \(0.0546052\pi\)
0.717263 + 0.696803i \(0.245395\pi\)
\(314\) −1.75719 5.40807i −0.0991638 0.305195i
\(315\) −13.5702 + 10.9758i −0.764591 + 0.618416i
\(316\) −7.24024 9.96533i −0.407295 0.560594i
\(317\) 10.5767 5.38910i 0.594047 0.302682i −0.130999 0.991382i \(-0.541818\pi\)
0.725046 + 0.688700i \(0.241818\pi\)
\(318\) 5.81674 + 5.81674i 0.326187 + 0.326187i
\(319\) 0.105217 + 0.249366i 0.00589100 + 0.0139618i
\(320\) −1.93714 + 1.11690i −0.108290 + 0.0624368i
\(321\) 26.6969 + 8.67435i 1.49008 + 0.484155i
\(322\) −28.4884 4.51212i −1.58760 0.251451i
\(323\) 14.7940 2.34314i 0.823159 0.130376i
\(324\) 10.4912 3.40880i 0.582846 0.189378i
\(325\) −8.10097 12.5063i −0.449361 0.693726i
\(326\) −7.12396 + 9.80529i −0.394560 + 0.543065i
\(327\) −4.55956 + 28.7879i −0.252144 + 1.59198i
\(328\) 1.26809 + 2.48877i 0.0700185 + 0.137419i
\(329\) −48.9309 −2.69765
\(330\) −13.5662 + 9.44396i −0.746797 + 0.519873i
\(331\) 11.2700 0.619456 0.309728 0.950825i \(-0.399762\pi\)
0.309728 + 0.950825i \(0.399762\pi\)
\(332\) 6.86376 + 13.4709i 0.376698 + 0.739311i
\(333\) −1.80375 + 11.3884i −0.0988447 + 0.624081i
\(334\) −2.41316 + 3.32144i −0.132042 + 0.181741i
\(335\) −7.41342 + 0.384185i −0.405039 + 0.0209903i
\(336\) −8.40798 + 2.73192i −0.458693 + 0.149038i
\(337\) −16.5766 + 2.62548i −0.902987 + 0.143019i −0.590627 0.806945i \(-0.701119\pi\)
−0.312360 + 0.949964i \(0.601119\pi\)
\(338\) 4.06794 + 0.644298i 0.221267 + 0.0350452i
\(339\) −0.887696 0.288430i −0.0482130 0.0156654i
\(340\) 2.70638 10.0768i 0.146774 0.546493i
\(341\) −4.87500 + 4.21938i −0.263996 + 0.228492i
\(342\) 4.46660 + 4.46660i 0.241526 + 0.241526i
\(343\) −6.12358 + 3.12012i −0.330642 + 0.168471i
\(344\) −1.72247 2.37077i −0.0928691 0.127823i
\(345\) 36.0415 + 3.80938i 1.94041 + 0.205090i
\(346\) −4.01194 12.3475i −0.215683 0.663804i
\(347\) −6.10579 3.11106i −0.327776 0.167010i 0.282357 0.959309i \(-0.408884\pi\)
−0.610133 + 0.792299i \(0.708884\pi\)
\(348\) −0.0284535 0.179649i −0.00152527 0.00963017i
\(349\) 9.07565 6.59384i 0.485808 0.352960i −0.317762 0.948171i \(-0.602931\pi\)
0.803570 + 0.595210i \(0.202931\pi\)
\(350\) 14.7537 13.2532i 0.788618 0.708411i
\(351\) 6.85598i 0.365945i
\(352\) −3.21983 + 0.795433i −0.171617 + 0.0423967i
\(353\) −15.7594 + 15.7594i −0.838790 + 0.838790i −0.988700 0.149910i \(-0.952102\pi\)
0.149910 + 0.988700i \(0.452102\pi\)
\(354\) −1.73981 + 5.35457i −0.0924696 + 0.284592i
\(355\) 13.1240 + 5.85233i 0.696547 + 0.310610i
\(356\) −4.84677 3.52138i −0.256878 0.186633i
\(357\) 18.7282 36.7561i 0.991200 1.94534i
\(358\) 3.69445 7.25077i 0.195258 0.383215i
\(359\) 12.7399 + 9.25607i 0.672386 + 0.488517i 0.870823 0.491597i \(-0.163587\pi\)
−0.198437 + 0.980114i \(0.563587\pi\)
\(360\) 4.10889 1.57451i 0.216557 0.0829837i
\(361\) −2.68723 + 8.27043i −0.141433 + 0.435286i
\(362\) 11.9704 11.9704i 0.629152 0.629152i
\(363\) −23.2159 + 7.88222i −1.21852 + 0.413709i
\(364\) 11.8206i 0.619570i
\(365\) 14.6532 + 9.52804i 0.766982 + 0.498720i
\(366\) 3.23459 2.35007i 0.169075 0.122840i
\(367\) 4.35420 + 27.4914i 0.227288 + 1.43504i 0.792389 + 0.610016i \(0.208837\pi\)
−0.565102 + 0.825021i \(0.691163\pi\)
\(368\) 6.47929 + 3.30136i 0.337756 + 0.172096i
\(369\) −1.69854 5.22757i −0.0884225 0.272136i
\(370\) 1.37713 13.0294i 0.0715937 0.677368i
\(371\) −8.60461 11.8432i −0.446729 0.614870i
\(372\) 3.86058 1.96706i 0.200162 0.101987i
\(373\) −19.2605 19.2605i −0.997270 0.997270i 0.00272613 0.999996i \(-0.499132\pi\)
−0.999996 + 0.00272613i \(0.999132\pi\)
\(374\) 7.99929 13.2483i 0.413633 0.685056i
\(375\) −17.6515 + 17.5899i −0.911522 + 0.908337i
\(376\) 11.7324 + 3.81210i 0.605054 + 0.196594i
\(377\) 0.240203 + 0.0380445i 0.0123711 + 0.00195939i
\(378\) −9.01262 + 1.42746i −0.463559 + 0.0734206i
\(379\) 20.6465 6.70844i 1.06054 0.344590i 0.273742 0.961803i \(-0.411739\pi\)
0.786796 + 0.617214i \(0.211739\pi\)
\(380\) −5.33129 4.80595i −0.273489 0.246540i
\(381\) 11.3717 15.6518i 0.582590 0.801866i
\(382\) −1.59869 + 10.0937i −0.0817960 + 0.516440i
\(383\) 14.7184 + 28.8865i 0.752075 + 1.47603i 0.875263 + 0.483647i \(0.160688\pi\)
−0.123188 + 0.992383i \(0.539312\pi\)
\(384\) 2.22887 0.113741
\(385\) 26.4741 12.8227i 1.34924 0.653506i
\(386\) 22.0548 1.12256
\(387\) 2.61800 + 5.13811i 0.133080 + 0.261185i
\(388\) −1.71720 + 10.8420i −0.0871776 + 0.550418i
\(389\) 6.37358 8.77248i 0.323153 0.444782i −0.616273 0.787532i \(-0.711358\pi\)
0.939427 + 0.342750i \(0.111358\pi\)
\(390\) 0.768684 + 14.8329i 0.0389238 + 0.751093i
\(391\) −32.2713 + 10.4856i −1.63203 + 0.530278i
\(392\) 8.62518 1.36610i 0.435638 0.0689982i
\(393\) −2.90580 0.460233i −0.146578 0.0232157i
\(394\) −14.7333 4.78715i −0.742255 0.241173i
\(395\) −13.7578 23.8614i −0.692232 1.20060i
\(396\) 6.50297 0.554829i 0.326787 0.0278812i
\(397\) −1.10287 1.10287i −0.0553516 0.0553516i 0.678889 0.734241i \(-0.262462\pi\)
−0.734241 + 0.678889i \(0.762462\pi\)
\(398\) −6.92974 + 3.53088i −0.347356 + 0.176987i
\(399\) −16.6804 22.9586i −0.835064 1.14937i
\(400\) −4.57010 + 2.02835i −0.228505 + 0.101418i
\(401\) −6.24701 19.2263i −0.311961 0.960116i −0.976987 0.213297i \(-0.931580\pi\)
0.665027 0.746820i \(-0.268420\pi\)
\(402\) 6.59297 + 3.35928i 0.328827 + 0.167546i
\(403\) 0.906274 + 5.72199i 0.0451447 + 0.285033i
\(404\) 6.22378 4.52184i 0.309644 0.224970i
\(405\) 24.1303 5.11435i 1.19904 0.254134i
\(406\) 0.323684i 0.0160642i
\(407\) 7.31866 18.0026i 0.362773 0.892357i
\(408\) −7.35414 + 7.35414i −0.364084 + 0.364084i
\(409\) 6.20451 19.0955i 0.306793 0.944212i −0.672209 0.740362i \(-0.734654\pi\)
0.979002 0.203851i \(-0.0653457\pi\)
\(410\) 2.23489 + 5.83226i 0.110373 + 0.288035i
\(411\) −32.3217 23.4831i −1.59431 1.15834i
\(412\) −2.58799 + 5.07922i −0.127501 + 0.250235i
\(413\) 4.54865 8.92723i 0.223825 0.439280i
\(414\) −11.5770 8.41116i −0.568977 0.413386i
\(415\) 12.0968 + 31.5682i 0.593807 + 1.54962i
\(416\) −0.920920 + 2.83430i −0.0451518 + 0.138963i
\(417\) 3.90609 3.90609i 0.191282 0.191282i
\(418\) −5.62222 9.04069i −0.274992 0.442195i
\(419\) 0.0907865i 0.00443521i −0.999998 0.00221761i \(-0.999294\pi\)
0.999998 0.00221761i \(-0.000705886\pi\)
\(420\) −19.3388 + 4.09879i −0.943635 + 0.200001i
\(421\) 25.5580 18.5690i 1.24562 0.904997i 0.247662 0.968846i \(-0.420338\pi\)
0.997960 + 0.0638492i \(0.0203377\pi\)
\(422\) −1.49298 9.42628i −0.0726770 0.458864i
\(423\) −21.6298 11.0210i −1.05168 0.535857i
\(424\) 1.14050 + 3.51008i 0.0553873 + 0.170465i
\(425\) 8.38648 21.7716i 0.406804 1.05608i
\(426\) −8.41909 11.5879i −0.407906 0.561434i
\(427\) −6.33958 + 3.23018i −0.306794 + 0.156319i
\(428\) 8.90544 + 8.90544i 0.430461 + 0.430461i
\(429\) −5.00194 + 21.4549i −0.241496 + 1.03585i
\(430\) −3.27301 5.67667i −0.157839 0.273753i
\(431\) −6.52048 2.11863i −0.314081 0.102051i 0.147735 0.989027i \(-0.452802\pi\)
−0.461815 + 0.886976i \(0.652802\pi\)
\(432\) 2.27222 + 0.359884i 0.109322 + 0.0173149i
\(433\) −16.4334 + 2.60280i −0.789740 + 0.125083i −0.538259 0.842780i \(-0.680918\pi\)
−0.251481 + 0.967862i \(0.580918\pi\)
\(434\) −7.33323 + 2.38271i −0.352006 + 0.114374i
\(435\) −0.0210488 0.406169i −0.00100921 0.0194743i
\(436\) −7.68644 + 10.5795i −0.368114 + 0.506665i
\(437\) −3.65158 + 23.0552i −0.174679 + 1.10288i
\(438\) −7.90953 15.5233i −0.377932 0.741733i
\(439\) −0.201886 −0.00963548 −0.00481774 0.999988i \(-0.501534\pi\)
−0.00481774 + 0.999988i \(0.501534\pi\)
\(440\) −7.34682 + 1.01203i −0.350246 + 0.0482468i
\(441\) −17.1846 −0.818313
\(442\) −6.31320 12.3904i −0.300288 0.589349i
\(443\) −1.46049 + 9.22116i −0.0693899 + 0.438111i 0.928395 + 0.371594i \(0.121189\pi\)
−0.997785 + 0.0665168i \(0.978811\pi\)
\(444\) −7.67636 + 10.5656i −0.364304 + 0.501421i
\(445\) −9.95004 8.96957i −0.471677 0.425198i
\(446\) −17.6521 + 5.73552i −0.835852 + 0.271585i
\(447\) 24.1671 3.82769i 1.14307 0.181044i
\(448\) −3.91761 0.620489i −0.185090 0.0293153i
\(449\) −28.7015 9.32569i −1.35451 0.440107i −0.460303 0.887762i \(-0.652259\pi\)
−0.894206 + 0.447655i \(0.852259\pi\)
\(450\) 9.50692 2.53549i 0.448160 0.119524i
\(451\) 0.787538 + 9.23048i 0.0370837 + 0.434647i
\(452\) −0.296114 0.296114i −0.0139280 0.0139280i
\(453\) 24.6761 12.5731i 1.15939 0.590737i
\(454\) 6.61634 + 9.10662i 0.310520 + 0.427395i
\(455\) 2.77821 26.2854i 0.130244 1.23228i
\(456\) 2.21090 + 6.80444i 0.103535 + 0.318647i
\(457\) 24.4688 + 12.4675i 1.14460 + 0.583203i 0.920260 0.391308i \(-0.127977\pi\)
0.224340 + 0.974511i \(0.427977\pi\)
\(458\) 0.675042 + 4.26205i 0.0315426 + 0.199152i
\(459\) −8.68461 + 6.30974i −0.405363 + 0.294513i
\(460\) 13.6320 + 8.86401i 0.635594 + 0.413287i
\(461\) 14.8765i 0.692866i 0.938075 + 0.346433i \(0.112607\pi\)
−0.938075 + 0.346433i \(0.887393\pi\)
\(462\) −29.2453 2.10832i −1.36062 0.0980880i
\(463\) 19.4801 19.4801i 0.905318 0.905318i −0.0905720 0.995890i \(-0.528870\pi\)
0.995890 + 0.0905720i \(0.0288695\pi\)
\(464\) 0.0252175 0.0776115i 0.00117069 0.00360302i
\(465\) 9.04701 3.46677i 0.419545 0.160768i
\(466\) 11.8346 + 8.59837i 0.548229 + 0.398312i
\(467\) 13.8779 27.2368i 0.642191 1.26037i −0.308793 0.951129i \(-0.599925\pi\)
0.950984 0.309241i \(-0.100075\pi\)
\(468\) 2.66242 5.22530i 0.123071 0.241539i
\(469\) −10.6531 7.73992i −0.491914 0.357396i
\(470\) 25.1933 + 11.2344i 1.16208 + 0.518203i
\(471\) −3.91653 + 12.0539i −0.180464 + 0.555412i
\(472\) −1.78616 + 1.78616i −0.0822145 + 0.0822145i
\(473\) −2.33096 9.43549i −0.107178 0.433844i
\(474\) 27.4548i 1.26104i
\(475\) −10.7255 11.9399i −0.492122 0.547841i
\(476\) 14.9735 10.8789i 0.686308 0.498632i
\(477\) −1.13615 7.17334i −0.0520205 0.328445i
\(478\) −6.74076 3.43459i −0.308315 0.157094i
\(479\) −3.79842 11.6903i −0.173554 0.534145i 0.826010 0.563655i \(-0.190605\pi\)
−0.999564 + 0.0295100i \(0.990605\pi\)
\(480\) 4.95629 + 0.523850i 0.226223 + 0.0239104i
\(481\) −10.2639 14.1270i −0.467992 0.644136i
\(482\) −5.62853 + 2.86788i −0.256372 + 0.130628i
\(483\) 45.4587 + 45.4587i 2.06844 + 2.06844i
\(484\) −10.8863 1.57780i −0.494830 0.0717182i
\(485\) −6.36670 + 23.7055i −0.289097 + 1.07641i
\(486\) −16.8197 5.46505i −0.762957 0.247900i
\(487\) −6.26281 0.991932i −0.283795 0.0449487i 0.0129141 0.999917i \(-0.495889\pi\)
−0.296709 + 0.954968i \(0.595889\pi\)
\(488\) 1.77173 0.280615i 0.0802025 0.0127028i
\(489\) 25.6917 8.34774i 1.16182 0.377498i
\(490\) 19.5007 1.01058i 0.880954 0.0456535i
\(491\) −13.6000 + 18.7188i −0.613761 + 0.844770i −0.996880 0.0789292i \(-0.974850\pi\)
0.383119 + 0.923699i \(0.374850\pi\)
\(492\) 0.973911 6.14903i 0.0439073 0.277220i
\(493\) 0.172874 + 0.339284i 0.00778585 + 0.0152806i
\(494\) −9.56625 −0.430406
\(495\) 14.5909 + 0.294630i 0.655814 + 0.0132426i
\(496\) 1.94396 0.0872864
\(497\) 11.5721 + 22.7114i 0.519078 + 1.01875i
\(498\) 5.27147 33.2828i 0.236220 1.49144i
\(499\) 24.4517 33.6549i 1.09461 1.50660i 0.252263 0.967659i \(-0.418825\pi\)
0.842345 0.538939i \(-0.181175\pi\)
\(500\) −10.6392 + 3.43630i −0.475798 + 0.153676i
\(501\) 8.70279 2.82771i 0.388812 0.126333i
\(502\) −20.6353 + 3.26832i −0.921000 + 0.145872i
\(503\) −14.7659 2.33868i −0.658377 0.104277i −0.181698 0.983354i \(-0.558159\pi\)
−0.476678 + 0.879078i \(0.658159\pi\)
\(504\) 7.42332 + 2.41198i 0.330661 + 0.107438i
\(505\) 14.9025 8.59236i 0.663151 0.382355i
\(506\) 15.7837 + 18.2362i 0.701669 + 0.810697i
\(507\) −6.49117 6.49117i −0.288283 0.288283i
\(508\) 7.73399 3.94067i 0.343140 0.174839i
\(509\) 14.5639 + 20.0455i 0.645534 + 0.888501i 0.998896 0.0469857i \(-0.0149615\pi\)
−0.353362 + 0.935487i \(0.614962\pi\)
\(510\) −18.0817 + 14.6248i −0.800672 + 0.647598i
\(511\) 9.58085 + 29.4868i 0.423832 + 1.30442i
\(512\) 0.891007 + 0.453990i 0.0393773 + 0.0200637i
\(513\) 1.15522 + 7.29376i 0.0510041 + 0.322027i
\(514\) 4.97218 3.61250i 0.219313 0.159340i
\(515\) −6.94864 + 10.6863i −0.306194 + 0.470896i
\(516\) 6.53154i 0.287535i
\(517\) 31.2857 + 26.3668i 1.37594 + 1.15961i
\(518\) 16.4338 16.4338i 0.722062 0.722062i
\(519\) −8.94207 + 27.5209i −0.392513 + 1.20803i
\(520\) −2.71398 + 6.08614i −0.119016 + 0.266895i
\(521\) −2.66594 1.93692i −0.116797 0.0848580i 0.527853 0.849336i \(-0.322997\pi\)
−0.644650 + 0.764477i \(0.722997\pi\)
\(522\) −0.0729049 + 0.143084i −0.00319096 + 0.00626262i
\(523\) 15.1878 29.8077i 0.664116 1.30340i −0.275543 0.961289i \(-0.588858\pi\)
0.939659 0.342112i \(-0.111142\pi\)
\(524\) −1.06787 0.775854i −0.0466502 0.0338933i
\(525\) −43.9666 + 4.56922i −1.91886 + 0.199417i
\(526\) 7.52274 23.1526i 0.328007 1.00950i
\(527\) −6.41410 + 6.41410i −0.279402 + 0.279402i
\(528\) 6.84805 + 2.78396i 0.298023 + 0.121156i
\(529\) 29.8802i 1.29914i
\(530\) 1.71112 + 8.07336i 0.0743265 + 0.350684i
\(531\) 4.02145 2.92175i 0.174516 0.126793i
\(532\) −1.99176 12.5754i −0.0863535 0.545215i
\(533\) 7.41692 + 3.77911i 0.321262 + 0.163691i
\(534\) 4.12630 + 12.6994i 0.178563 + 0.549559i
\(535\) 17.7098 + 21.8959i 0.765663 + 0.946643i
\(536\) 1.95135 + 2.68580i 0.0842854 + 0.116009i
\(537\) −16.1610 + 8.23444i −0.697399 + 0.355342i
\(538\) 19.0194 + 19.0194i 0.819986 + 0.819986i
\(539\) 28.2067 + 6.57603i 1.21495 + 0.283250i
\(540\) 4.96810 + 1.33431i 0.213793 + 0.0574194i
\(541\) −1.96815 0.639490i −0.0846173 0.0274938i 0.266402 0.963862i \(-0.414165\pi\)
−0.351020 + 0.936368i \(0.614165\pi\)
\(542\) −22.4482 3.55545i −0.964235 0.152720i
\(543\) −37.2674 + 5.90257i −1.59930 + 0.253303i
\(544\) −4.43782 + 1.44193i −0.190270 + 0.0618224i
\(545\) −19.5787 + 21.7189i −0.838659 + 0.930334i
\(546\) −15.4862 + 21.3149i −0.662747 + 0.912193i
\(547\) 2.25132 14.2143i 0.0962595 0.607758i −0.891650 0.452726i \(-0.850452\pi\)
0.987909 0.155033i \(-0.0495483\pi\)
\(548\) −8.13766 15.9711i −0.347624 0.682250i
\(549\) −3.52995 −0.150654
\(550\) −16.5749 + 0.523718i −0.706754 + 0.0223314i
\(551\) 0.261952 0.0111595
\(552\) −7.35830 14.4415i −0.313190 0.614670i
\(553\) 7.64308 48.2565i 0.325017 2.05207i
\(554\) −12.2247 + 16.8259i −0.519378 + 0.714862i
\(555\) −19.5530 + 21.6904i −0.829979 + 0.920705i
\(556\) 2.35711 0.765872i 0.0999637 0.0324802i
\(557\) −17.8430 + 2.82606i −0.756033 + 0.119744i −0.522540 0.852615i \(-0.675016\pi\)
−0.233493 + 0.972359i \(0.575016\pi\)
\(558\) −3.77831 0.598426i −0.159949 0.0253334i
\(559\) −8.30573 2.69870i −0.351295 0.114143i
\(560\) −8.56569 2.30053i −0.361967 0.0972150i
\(561\) −31.7808 + 13.4095i −1.34179 + 0.566148i
\(562\) 4.54280 + 4.54280i 0.191626 + 0.191626i
\(563\) −36.8694 + 18.7859i −1.55386 + 0.791731i −0.999186 0.0403368i \(-0.987157\pi\)
−0.554674 + 0.832068i \(0.687157\pi\)
\(564\) −16.1616 22.2445i −0.680526 0.936664i
\(565\) −0.588868 0.728059i −0.0247738 0.0306297i
\(566\) −0.299612 0.922111i −0.0125936 0.0387592i
\(567\) 38.9854 + 19.8641i 1.63723 + 0.834212i
\(568\) −1.00530 6.34720i −0.0421814 0.266323i
\(569\) 16.9040 12.2815i 0.708653 0.514867i −0.174086 0.984731i \(-0.555697\pi\)
0.882739 + 0.469864i \(0.155697\pi\)
\(570\) 3.31708 + 15.6505i 0.138937 + 0.655529i
\(571\) 0.865366i 0.0362145i −0.999836 0.0181072i \(-0.994236\pi\)
0.999836 0.0181072i \(-0.00576403\pi\)
\(572\) −6.36965 + 7.55794i −0.266328 + 0.316013i
\(573\) 16.1065 16.1065i 0.672858 0.672858i
\(574\) −3.42363 + 10.5369i −0.142900 + 0.439800i
\(575\) 28.2298 + 22.9147i 1.17727 + 0.955607i
\(576\) −1.59202 1.15667i −0.0663341 0.0481945i
\(577\) −5.60142 + 10.9934i −0.233190 + 0.457661i −0.977716 0.209932i \(-0.932676\pi\)
0.744526 + 0.667594i \(0.232676\pi\)
\(578\) 2.16707 4.25312i 0.0901384 0.176907i
\(579\) −39.7690 28.8939i −1.65274 1.20079i
\(580\) 0.0743167 0.166656i 0.00308583 0.00692003i
\(581\) −18.5310 + 57.0326i −0.768797 + 2.36611i
\(582\) 17.3005 17.3005i 0.717127 0.717127i
\(583\) −0.880162 + 12.2090i −0.0364526 + 0.505647i
\(584\) 7.81664i 0.323455i
\(585\) 7.14848 10.9937i 0.295553 0.454531i
\(586\) −3.50621 + 2.54741i −0.144840 + 0.105233i
\(587\) −1.30289 8.22614i −0.0537761 0.339529i −0.999877 0.0156582i \(-0.995016\pi\)
0.946101 0.323871i \(-0.104984\pi\)
\(588\) −17.3426 8.83648i −0.715195 0.364410i
\(589\) 1.92829 + 5.93466i 0.0794537 + 0.244533i
\(590\) −4.39164 + 3.55204i −0.180801 + 0.146235i
\(591\) 20.2954 + 27.9342i 0.834841 + 1.14906i
\(592\) −5.22076 + 2.66011i −0.214572 + 0.109330i
\(593\) −21.2622 21.2622i −0.873133 0.873133i 0.119680 0.992813i \(-0.461813\pi\)
−0.992813 + 0.119680i \(0.961813\pi\)
\(594\) 6.53173 + 3.94383i 0.268000 + 0.161817i
\(595\) 35.8531 20.6719i 1.46983 0.847466i
\(596\) 10.4406 + 3.39237i 0.427665 + 0.138957i
\(597\) 17.1214 + 2.71177i 0.700733 + 0.110985i
\(598\) 21.4046 3.39015i 0.875297 0.138634i
\(599\) −31.8537 + 10.3499i −1.30151 + 0.422885i −0.876105 0.482120i \(-0.839867\pi\)
−0.425401 + 0.905005i \(0.639867\pi\)
\(600\) 10.8981 + 2.32975i 0.444913 + 0.0951117i
\(601\) −12.4882 + 17.1885i −0.509403 + 0.701133i −0.983819 0.179168i \(-0.942659\pi\)
0.474415 + 0.880301i \(0.342659\pi\)
\(602\) 1.81830 11.4803i 0.0741084 0.467902i
\(603\) −2.96588 5.82086i −0.120780 0.237044i
\(604\) 12.4255 0.505585
\(605\) −23.8367 6.06712i −0.969101 0.246664i
\(606\) −17.1467 −0.696537
\(607\) −15.2661 29.9613i −0.619630 1.21609i −0.961100 0.276200i \(-0.910925\pi\)
0.341470 0.939893i \(-0.389075\pi\)
\(608\) −0.502151 + 3.17046i −0.0203649 + 0.128579i
\(609\) 0.424057 0.583664i 0.0171836 0.0236513i
\(610\) 4.00572 0.207588i 0.162187 0.00840498i
\(611\) 34.9645 11.3607i 1.41451 0.459604i
\(612\) 9.06929 1.43643i 0.366604 0.0580644i
\(613\) 17.0295 + 2.69721i 0.687816 + 0.108939i 0.490553 0.871411i \(-0.336795\pi\)
0.197263 + 0.980351i \(0.436795\pi\)
\(614\) 18.1616 + 5.90107i 0.732943 + 0.238148i
\(615\) 3.61088 13.4446i 0.145605 0.542139i
\(616\) −11.2616 6.79970i −0.453743 0.273968i
\(617\) −15.8379 15.8379i −0.637611 0.637611i 0.312355 0.949965i \(-0.398882\pi\)
−0.949965 + 0.312355i \(0.898882\pi\)
\(618\) 11.3209 5.76829i 0.455394 0.232035i
\(619\) 7.27397 + 10.0118i 0.292366 + 0.402407i 0.929781 0.368114i \(-0.119996\pi\)
−0.637415 + 0.770521i \(0.719996\pi\)
\(620\) 4.32275 + 0.456889i 0.173606 + 0.0183491i
\(621\) −5.16962 15.9105i −0.207450 0.638465i
\(622\) 20.6861 + 10.5401i 0.829435 + 0.422618i
\(623\) −3.71731 23.4702i −0.148931 0.940312i
\(624\) 5.37380 3.90429i 0.215124 0.156297i
\(625\) −24.4658 + 5.14072i −0.978630 + 0.205629i
\(626\) 33.8065i 1.35118i
\(627\) −1.70623 + 23.6677i −0.0681402 + 0.945198i
\(628\) −4.02088 + 4.02088i −0.160450 + 0.160450i
\(629\) 8.44886 26.0029i 0.336878 1.03680i
\(630\) 15.9402 + 7.10819i 0.635074 + 0.283197i
\(631\) −32.0471 23.2836i −1.27577 0.926905i −0.276358 0.961055i \(-0.589128\pi\)
−0.999417 + 0.0341502i \(0.989128\pi\)
\(632\) −5.59218 + 10.9753i −0.222445 + 0.436573i
\(633\) −9.65720 + 18.9533i −0.383839 + 0.753327i
\(634\) −9.60345 6.97731i −0.381402 0.277104i
\(635\) 18.1241 6.94507i 0.719233 0.275607i
\(636\) 2.54201 7.82350i 0.100797 0.310222i
\(637\) 18.4023 18.4023i 0.729127 0.729127i
\(638\) 0.174420 0.206959i 0.00690534 0.00819357i
\(639\) 12.6460i 0.500268i
\(640\) 1.87461 + 1.21894i 0.0741006 + 0.0481830i
\(641\) 26.3762 19.1634i 1.04180 0.756910i 0.0711615 0.997465i \(-0.477329\pi\)
0.970636 + 0.240555i \(0.0773294\pi\)
\(642\) −4.39124 27.7252i −0.173308 1.09423i
\(643\) −11.4937 5.85631i −0.453266 0.230950i 0.212426 0.977177i \(-0.431863\pi\)
−0.665692 + 0.746227i \(0.731863\pi\)
\(644\) 8.91314 + 27.4318i 0.351227 + 1.08097i
\(645\) −1.53511 + 14.5241i −0.0604448 + 0.571885i
\(646\) −8.80407 12.1178i −0.346392 0.476767i
\(647\) 0.708311 0.360903i 0.0278466 0.0141885i −0.440012 0.897992i \(-0.645026\pi\)
0.467858 + 0.883803i \(0.345026\pi\)
\(648\) −7.80018 7.80018i −0.306420 0.306420i
\(649\) −7.71885 + 3.25686i −0.302991 + 0.127843i
\(650\) −7.46545 + 12.8958i −0.292819 + 0.505814i
\(651\) 16.3448 + 5.31074i 0.640603 + 0.208144i
\(652\) 11.9708 + 1.89599i 0.468812 + 0.0742525i
\(653\) 3.86249 0.611758i 0.151151 0.0239400i −0.0804004 0.996763i \(-0.525620\pi\)
0.231551 + 0.972823i \(0.425620\pi\)
\(654\) 27.7202 9.00685i 1.08395 0.352196i
\(655\) −2.19226 1.97623i −0.0856586 0.0772179i
\(656\) 1.64181 2.25975i 0.0641017 0.0882285i
\(657\) −2.40626 + 15.1925i −0.0938772 + 0.592717i
\(658\) 22.2142 + 43.5978i 0.865999 + 1.69962i
\(659\) 2.33997 0.0911522 0.0455761 0.998961i \(-0.485488\pi\)
0.0455761 + 0.998961i \(0.485488\pi\)
\(660\) 14.5736 + 7.80014i 0.567276 + 0.303620i
\(661\) −28.1337 −1.09428 −0.547138 0.837043i \(-0.684283\pi\)
−0.547138 + 0.837043i \(0.684283\pi\)
\(662\) −5.11648 10.0417i −0.198858 0.390280i
\(663\) −4.84863 + 30.6130i −0.188305 + 1.18891i
\(664\) 8.88657 12.2313i 0.344866 0.474667i
\(665\) −1.47342 28.4319i −0.0571369 1.10254i
\(666\) 10.9660 3.56308i 0.424925 0.138067i
\(667\) −0.586120 + 0.0928322i −0.0226946 + 0.00359448i
\(668\) 4.05497 + 0.642245i 0.156892 + 0.0248492i
\(669\) 39.3442 + 12.7837i 1.52114 + 0.494247i
\(670\) 3.70793 + 6.43099i 0.143250 + 0.248451i
\(671\) 5.79403 + 1.35081i 0.223676 + 0.0521473i
\(672\) 6.25130 + 6.25130i 0.241149 + 0.241149i
\(673\) −18.4073 + 9.37899i −0.709550 + 0.361534i −0.771225 0.636563i \(-0.780356\pi\)
0.0616753 + 0.998096i \(0.480356\pi\)
\(674\) 9.86495 + 13.5779i 0.379984 + 0.523003i
\(675\) 10.7339 + 4.13472i 0.413147 + 0.159146i
\(676\) −1.27273 3.91706i −0.0489512 0.150656i
\(677\) 2.56283 + 1.30583i 0.0984976 + 0.0501870i 0.502545 0.864551i \(-0.332397\pi\)
−0.404048 + 0.914738i \(0.632397\pi\)
\(678\) 0.146013 + 0.921887i 0.00560758 + 0.0354049i
\(679\) −35.2247 + 25.5923i −1.35180 + 0.982141i
\(680\) −10.2072 + 2.16338i −0.391428 + 0.0829619i
\(681\) 25.0890i 0.961413i
\(682\) 5.97270 + 2.42810i 0.228706 + 0.0929768i
\(683\) 4.54465 4.54465i 0.173896 0.173896i −0.614793 0.788689i \(-0.710760\pi\)
0.788689 + 0.614793i \(0.210760\pi\)
\(684\) 1.95198 6.00757i 0.0746357 0.229705i
\(685\) −14.3419 37.4272i −0.547976 1.43002i
\(686\) 5.56010 + 4.03965i 0.212285 + 0.154234i
\(687\) 4.36646 8.56965i 0.166591 0.326953i
\(688\) −1.33039 + 2.61104i −0.0507206 + 0.0995448i
\(689\) 8.89833 + 6.46501i 0.338999 + 0.246297i
\(690\) −12.9683 33.8427i −0.493696 1.28837i
\(691\) 6.11570 18.8222i 0.232652 0.716030i −0.764772 0.644301i \(-0.777148\pi\)
0.997424 0.0717289i \(-0.0228516\pi\)
\(692\) −9.18030 + 9.18030i −0.348983 + 0.348983i
\(693\) 19.7950 + 16.6828i 0.751951 + 0.633726i
\(694\) 6.85269i 0.260124i
\(695\) 5.42147 1.14906i 0.205648 0.0435865i
\(696\) −0.147150 + 0.106911i −0.00557772 + 0.00405245i
\(697\) 2.03891 + 12.8732i 0.0772293 + 0.487607i
\(698\) −9.99542 5.09292i −0.378332 0.192770i
\(699\) −10.0754 31.0090i −0.381088 1.17287i
\(700\) −18.5067 7.12883i −0.699487 0.269445i
\(701\) −3.26547 4.49454i −0.123335 0.169756i 0.742885 0.669420i \(-0.233457\pi\)
−0.866220 + 0.499663i \(0.833457\pi\)
\(702\) 6.10872 3.11255i 0.230559 0.117476i
\(703\) −13.2996 13.2996i −0.501605 0.501605i
\(704\) 2.17051 + 2.50777i 0.0818041 + 0.0945151i
\(705\) −30.7101 53.2632i −1.15661 2.00601i
\(706\) 21.1964 + 6.88712i 0.797737 + 0.259200i
\(707\) 30.1382 + 4.77343i 1.13347 + 0.179523i
\(708\) 5.56081 0.880746i 0.208988 0.0331005i
\(709\) −31.7561 + 10.3182i −1.19262 + 0.387507i −0.837042 0.547138i \(-0.815717\pi\)
−0.355582 + 0.934645i \(0.615717\pi\)
\(710\) −0.743680 14.3504i −0.0279098 0.538562i
\(711\) 14.2477 19.6102i 0.534329 0.735440i
\(712\) −0.937189 + 5.91718i −0.0351226 + 0.221756i
\(713\) −6.41772 12.5955i −0.240346 0.471705i
\(714\) −41.2523 −1.54383
\(715\) −15.9404 + 15.3094i −0.596138 + 0.572539i
\(716\) −8.13773 −0.304121
\(717\) 7.65524 + 15.0242i 0.285890 + 0.561091i
\(718\) 2.46343 15.5535i 0.0919344 0.580451i
\(719\) 11.8552 16.3173i 0.442125 0.608532i −0.528558 0.848897i \(-0.677267\pi\)
0.970683 + 0.240365i \(0.0772671\pi\)
\(720\) −3.26829 2.94624i −0.121802 0.109800i
\(721\) −21.5043 + 6.98716i −0.800860 + 0.260215i
\(722\) 8.58898 1.36036i 0.319649 0.0506274i
\(723\) 13.9065 + 2.20257i 0.517188 + 0.0819146i
\(724\) −16.1002 5.23127i −0.598359 0.194419i
\(725\) 0.204426 0.353124i 0.00759219 0.0131147i
\(726\) 17.5629 + 17.1071i 0.651821 + 0.634904i
\(727\) 3.28024 + 3.28024i 0.121657 + 0.121657i 0.765314 0.643657i \(-0.222584\pi\)
−0.643657 + 0.765314i \(0.722584\pi\)
\(728\) −10.5323 + 5.36646i −0.390352 + 0.198894i
\(729\) 3.71759 + 5.11682i 0.137688 + 0.189512i
\(730\) 1.83714 17.3817i 0.0679957 0.643326i
\(731\) −4.22549 13.0047i −0.156285 0.480997i
\(732\) −3.56240 1.81513i −0.131670 0.0670892i
\(733\) 5.38308 + 33.9874i 0.198828 + 1.25535i 0.862009 + 0.506894i \(0.169206\pi\)
−0.663180 + 0.748460i \(0.730794\pi\)
\(734\) 22.5182 16.3604i 0.831162 0.603875i
\(735\) −36.4875 23.7255i −1.34586 0.875130i
\(736\) 7.27188i 0.268045i
\(737\) 2.64070 + 10.6893i 0.0972716 + 0.393745i
\(738\) −3.88668 + 3.88668i −0.143071 + 0.143071i
\(739\) 0.0954132 0.293652i 0.00350983 0.0108022i −0.949286 0.314413i \(-0.898192\pi\)
0.952796 + 0.303611i \(0.0981923\pi\)
\(740\) −12.2345 + 4.68820i −0.449749 + 0.172342i
\(741\) 17.2498 + 12.5327i 0.633686 + 0.460400i
\(742\) −6.64599 + 13.0435i −0.243982 + 0.478841i
\(743\) −0.565075 + 1.10902i −0.0207306 + 0.0406860i −0.901140 0.433529i \(-0.857268\pi\)
0.880409 + 0.474215i \(0.157268\pi\)
\(744\) −3.50533 2.54677i −0.128512 0.0933692i
\(745\) 22.4194 + 9.99742i 0.821382 + 0.366277i
\(746\) −8.41714 + 25.9053i −0.308173 + 0.948460i
\(747\) −21.0374 + 21.0374i −0.769716 + 0.769716i
\(748\) −15.4360 1.11279i −0.564395 0.0406878i
\(749\) 49.9542i 1.82529i
\(750\) 23.6863 + 7.74200i 0.864902 + 0.282698i
\(751\) −19.6696 + 14.2908i −0.717754 + 0.521479i −0.885666 0.464323i \(-0.846298\pi\)
0.167912 + 0.985802i \(0.446298\pi\)
\(752\) −1.92981 12.1843i −0.0703729 0.444317i
\(753\) 41.4912 + 21.1408i 1.51202 + 0.770415i
\(754\) −0.0751522 0.231295i −0.00273688 0.00842326i
\(755\) 27.6303 + 2.92035i 1.00557 + 0.106283i
\(756\) 5.36352 + 7.38225i 0.195069 + 0.268490i
\(757\) 25.1939 12.8369i 0.915688 0.466566i 0.0683747 0.997660i \(-0.478219\pi\)
0.847313 + 0.531093i \(0.178219\pi\)
\(758\) −15.3506 15.3506i −0.557558 0.557558i
\(759\) −4.56982 53.5614i −0.165874 1.94416i
\(760\) −1.86178 + 6.93207i −0.0675337 + 0.251453i
\(761\) −32.7506 10.6413i −1.18721 0.385747i −0.352168 0.935937i \(-0.614555\pi\)
−0.835040 + 0.550190i \(0.814555\pi\)
\(762\) −19.1085 3.02649i −0.692228 0.109638i
\(763\) −51.2305 + 8.11411i −1.85467 + 0.293750i
\(764\) 9.71936 3.15801i 0.351634 0.114253i
\(765\) 20.5048 1.06262i 0.741354 0.0384191i
\(766\) 19.0560 26.2284i 0.688522 0.947670i
\(767\) −1.17762 + 7.43522i −0.0425215 + 0.268470i
\(768\) −1.01188 1.98593i −0.0365132 0.0716612i
\(769\) 22.6026 0.815072 0.407536 0.913189i \(-0.366388\pi\)
0.407536 + 0.913189i \(0.366388\pi\)
\(770\) −23.4441 17.7672i −0.844866 0.640285i
\(771\) −13.6985 −0.493339
\(772\) −10.0127 19.6510i −0.360364 0.707254i
\(773\) −6.87959 + 43.4361i −0.247442 + 1.56229i 0.480716 + 0.876876i \(0.340377\pi\)
−0.728158 + 0.685410i \(0.759623\pi\)
\(774\) 3.38954 4.66530i 0.121835 0.167691i
\(775\) 9.50504 + 2.03195i 0.341431 + 0.0729898i
\(776\) 10.4399 3.39212i 0.374769 0.121770i
\(777\) −51.1632 + 8.10346i −1.83547 + 0.290710i
\(778\) −10.7099 1.69628i −0.383968 0.0608145i
\(779\) 8.52730 + 2.77069i 0.305522 + 0.0992701i
\(780\) 12.8672 7.41890i 0.460721 0.265639i
\(781\) 4.83924 20.7570i 0.173162 0.742746i
\(782\) 23.9936 + 23.9936i 0.858008 + 0.858008i
\(783\) −0.167275 + 0.0852307i −0.00597791 + 0.00304590i
\(784\) −5.13295 7.06490i −0.183320 0.252318i
\(785\) −9.88617 + 7.99612i −0.352853 + 0.285394i
\(786\) 0.909134 + 2.79803i 0.0324277 + 0.0998023i
\(787\) −17.0929 8.70928i −0.609297 0.310452i 0.121980 0.992533i \(-0.461075\pi\)
−0.731277 + 0.682080i \(0.761075\pi\)
\(788\) 2.42341 + 15.3008i 0.0863305 + 0.545069i
\(789\) −43.8970 + 31.8931i −1.56278 + 1.13542i
\(790\) −15.0147 + 23.0912i −0.534200 + 0.821547i
\(791\) 1.66102i 0.0590592i
\(792\) −3.44664 5.54230i −0.122471 0.196937i
\(793\) 3.78009 3.78009i 0.134235 0.134235i
\(794\) −0.481974 + 1.48336i −0.0171046 + 0.0526425i
\(795\) 7.49138 16.7995i 0.265692 0.595818i
\(796\) 6.29207 + 4.57146i 0.223017 + 0.162031i
\(797\) −1.75108 + 3.43669i −0.0620265 + 0.121734i −0.919938 0.392063i \(-0.871762\pi\)
0.857912 + 0.513797i \(0.171762\pi\)
\(798\) −12.8835 + 25.2853i −0.456071 + 0.895090i
\(799\) 46.5696 + 33.8348i 1.64751 + 1.19699i
\(800\) 3.88206 + 3.15113i 0.137251 + 0.111409i
\(801\) 3.64307 11.2122i 0.128722 0.396164i
\(802\) −14.2947 + 14.2947i −0.504763 + 0.504763i
\(803\) 9.76335 24.0161i 0.344541 0.847511i
\(804\) 7.39946i 0.260959i
\(805\) 13.3727 + 63.0945i 0.471325 + 2.22379i
\(806\) 4.68689 3.40522i 0.165089 0.119944i
\(807\) −9.37840 59.2129i −0.330135 2.08439i
\(808\) −6.85452 3.49255i −0.241141 0.122868i
\(809\) −9.68199 29.7981i −0.340400 1.04764i −0.964000 0.265901i \(-0.914330\pi\)
0.623600 0.781744i \(-0.285670\pi\)
\(810\) −15.5118 19.1784i −0.545031 0.673860i
\(811\) 29.8031 + 41.0204i 1.04653 + 1.44042i 0.891781 + 0.452467i \(0.149456\pi\)
0.154746 + 0.987954i \(0.450544\pi\)
\(812\) 0.288405 0.146949i 0.0101210 0.00515692i
\(813\) 35.8205 + 35.8205i 1.25628 + 1.25628i
\(814\) −19.3631 + 1.65204i −0.678675 + 0.0579041i
\(815\) 26.1736 + 7.02956i 0.916821 + 0.246235i
\(816\) 9.89130 + 3.21388i 0.346265 + 0.112508i
\(817\) −9.29081 1.47152i −0.325044 0.0514820i
\(818\) −19.8310 + 3.14092i −0.693375 + 0.109820i
\(819\) 22.1227 7.18810i 0.773030 0.251173i
\(820\) 4.18196 4.63910i 0.146040 0.162004i
\(821\) −3.78341 + 5.20742i −0.132042 + 0.181740i −0.869918 0.493196i \(-0.835829\pi\)
0.737877 + 0.674936i \(0.235829\pi\)
\(822\) −6.24985 + 39.4600i −0.217988 + 1.37632i
\(823\) −5.20789 10.2211i −0.181536 0.356284i 0.782249 0.622966i \(-0.214073\pi\)
−0.963784 + 0.266682i \(0.914073\pi\)
\(824\) 5.70055 0.198588
\(825\) 30.5737 + 20.7703i 1.06444 + 0.723128i
\(826\) −10.0193 −0.348615
\(827\) 8.69429 + 17.0635i 0.302330 + 0.593356i 0.991329 0.131407i \(-0.0419494\pi\)
−0.688999 + 0.724763i \(0.741949\pi\)
\(828\) −2.23856 + 14.1337i −0.0777955 + 0.491181i
\(829\) −1.12936 + 1.55443i −0.0392242 + 0.0539875i −0.828179 0.560464i \(-0.810623\pi\)
0.788954 + 0.614452i \(0.210623\pi\)
\(830\) 22.6356 25.1099i 0.785694 0.871579i
\(831\) 44.0869 14.3247i 1.52936 0.496919i
\(832\) 2.94347 0.466200i 0.102046 0.0161626i
\(833\) 40.2468 + 6.37447i 1.39447 + 0.220862i
\(834\) −5.25368 1.70703i −0.181920 0.0591094i
\(835\) 8.86603 + 2.38119i 0.306821 + 0.0824044i
\(836\) −5.50288 + 9.11382i −0.190321 + 0.315208i
\(837\) −3.16229 3.16229i −0.109305 0.109305i
\(838\) −0.0808914 + 0.0412162i −0.00279435 + 0.00142379i
\(839\) 1.68441 + 2.31839i 0.0581522 + 0.0800396i 0.837103 0.547046i \(-0.184248\pi\)
−0.778950 + 0.627085i \(0.784248\pi\)
\(840\) 12.4317 + 15.3702i 0.428933 + 0.530321i
\(841\) −8.95943 27.5743i −0.308946 0.950838i
\(842\) −28.1482 14.3422i −0.970051 0.494266i
\(843\) −2.24004 14.1430i −0.0771509 0.487112i
\(844\) −7.72108 + 5.60970i −0.265771 + 0.193094i
\(845\) −1.90952 9.00943i −0.0656895 0.309934i
\(846\) 24.2757i 0.834617i
\(847\) −26.1074 34.9580i −0.897062 1.20117i
\(848\) 2.60973 2.60973i 0.0896186 0.0896186i
\(849\) −0.667795 + 2.05526i −0.0229187 + 0.0705364i
\(850\) −23.2060 + 2.41168i −0.795959 + 0.0827199i
\(851\) 34.4712 + 25.0448i 1.18166 + 0.858526i
\(852\) −6.50269 + 12.7622i −0.222778 + 0.437227i
\(853\) −8.62287 + 16.9233i −0.295241 + 0.579444i −0.990208 0.139598i \(-0.955419\pi\)
0.694967 + 0.719042i \(0.255419\pi\)
\(854\) 5.75621 + 4.18213i 0.196974 + 0.143110i
\(855\) 5.75253 12.9001i 0.196733 0.441176i
\(856\) 3.89182 11.9778i 0.133020 0.409393i
\(857\) −9.24508 + 9.24508i −0.315806 + 0.315806i −0.847154 0.531348i \(-0.821686\pi\)
0.531348 + 0.847154i \(0.321686\pi\)
\(858\) 21.3873 5.28357i 0.730151 0.180378i
\(859\) 0.806684i 0.0275237i 0.999905 + 0.0137619i \(0.00438067\pi\)
−0.999905 + 0.0137619i \(0.995619\pi\)
\(860\) −3.57203 + 5.49343i −0.121805 + 0.187324i
\(861\) 19.9777 14.5147i 0.680839 0.494659i
\(862\) 1.07252 + 6.77163i 0.0365302 + 0.230643i
\(863\) −9.72398 4.95462i −0.331008 0.168657i 0.280586 0.959829i \(-0.409471\pi\)
−0.611594 + 0.791172i \(0.709471\pi\)
\(864\) −0.710906 2.18794i −0.0241855 0.0744353i
\(865\) −22.5717 + 18.2564i −0.767461 + 0.620737i
\(866\) 9.77973 + 13.4607i 0.332329 + 0.457412i
\(867\) −9.47964 + 4.83012i −0.321945 + 0.164039i
\(868\) 5.45223 + 5.45223i 0.185061 + 0.185061i
\(869\) −30.8903 + 26.7359i −1.04788 + 0.906954i
\(870\) −0.352343 + 0.203151i −0.0119455 + 0.00688747i
\(871\) 9.40940 + 3.05730i 0.318825 + 0.103593i
\(872\) 12.9160 + 2.04569i 0.437390 + 0.0692757i
\(873\) −21.3353 + 3.37918i −0.722091 + 0.114368i
\(874\) 22.2001 7.21325i 0.750930 0.243992i
\(875\) −39.4775 20.2019i −1.33458 0.682948i
\(876\) −10.2405 + 14.0949i −0.345995 + 0.476222i
\(877\) 5.12456 32.3552i 0.173044 1.09256i −0.736344 0.676608i \(-0.763449\pi\)
0.909388 0.415949i \(-0.136551\pi\)
\(878\) 0.0916542 + 0.179882i 0.00309318 + 0.00607071i
\(879\) 9.65972 0.325814
\(880\) 4.23712 + 6.08661i 0.142833 + 0.205180i
\(881\) 54.9218 1.85036 0.925181 0.379526i \(-0.123913\pi\)
0.925181 + 0.379526i \(0.123913\pi\)
\(882\) 7.80164 + 15.3116i 0.262695 + 0.515567i
\(883\) −2.20791 + 13.9402i −0.0743021 + 0.469125i 0.922280 + 0.386522i \(0.126324\pi\)
−0.996582 + 0.0826036i \(0.973676\pi\)
\(884\) −8.17375 + 11.2502i −0.274913 + 0.378385i
\(885\) 12.5725 0.651542i 0.422619 0.0219013i
\(886\) 8.87916 2.88501i 0.298301 0.0969240i
\(887\) −32.2431 + 5.10680i −1.08262 + 0.171470i −0.672157 0.740409i \(-0.734632\pi\)
−0.410460 + 0.911878i \(0.634632\pi\)
\(888\) 12.8990 + 2.04300i 0.432863 + 0.0685587i
\(889\) 32.7439 + 10.6391i 1.09820 + 0.356826i
\(890\) −3.47472 + 12.9377i −0.116473 + 0.433671i
\(891\) −14.2228 33.7084i −0.476481 1.12927i
\(892\) 13.1243 + 13.1243i 0.439434 + 0.439434i
\(893\) 35.2829 17.9776i 1.18070 0.601596i
\(894\) −14.3821 19.7953i −0.481011 0.662054i
\(895\) −18.0957 1.91261i −0.604874 0.0639315i
\(896\) 1.22570 + 3.77231i 0.0409477 + 0.126024i
\(897\) −43.0379 21.9289i −1.43699 0.732185i
\(898\) 4.72097 + 29.8070i 0.157541 + 0.994673i
\(899\) −0.128341 + 0.0932451i −0.00428041 + 0.00310990i
\(900\) −6.57519 7.31964i −0.219173 0.243988i
\(901\) 17.2216i 0.573735i
\(902\) 7.86689 4.89225i 0.261939 0.162894i
\(903\) −18.3190 + 18.3190i −0.609619 + 0.609619i
\(904\) −0.129407 + 0.398272i −0.00430400 + 0.0132463i
\(905\) −34.5722 15.4167i −1.14922 0.512469i
\(906\) −22.4055 16.2785i −0.744372 0.540818i
\(907\) 4.83372 9.48671i 0.160501 0.315001i −0.796725 0.604342i \(-0.793436\pi\)
0.957226 + 0.289341i \(0.0934361\pi\)
\(908\) 5.11030 10.0295i 0.169591 0.332841i
\(909\) 12.2474 + 8.89827i 0.406221 + 0.295137i
\(910\) −24.6817 + 9.45790i −0.818191 + 0.313526i
\(911\) 0.763148 2.34873i 0.0252842 0.0778168i −0.937618 0.347667i \(-0.886974\pi\)
0.962902 + 0.269850i \(0.0869741\pi\)
\(912\) 5.05907 5.05907i 0.167523 0.167523i
\(913\) 42.5810 26.4802i 1.40922 0.876367i
\(914\) 27.4619i 0.908360i
\(915\) −7.49503 4.87355i −0.247778 0.161115i
\(916\) 3.49105 2.53640i 0.115348 0.0838049i
\(917\) −0.819022 5.17110i −0.0270465 0.170765i
\(918\) 9.56475 + 4.87348i 0.315684 + 0.160849i
\(919\) 12.9101 + 39.7333i 0.425866 + 1.31068i 0.902163 + 0.431396i \(0.141979\pi\)
−0.476297 + 0.879285i \(0.658021\pi\)
\(920\) 1.70911 16.1703i 0.0563477 0.533121i
\(921\) −25.0179 34.4342i −0.824368 1.13465i
\(922\) 13.2550 6.75377i 0.436531 0.222424i
\(923\) −13.5421 13.5421i −0.445745 0.445745i
\(924\) 11.3986 + 27.0149i 0.374985 + 0.888726i
\(925\) −28.3075 + 7.54959i −0.930746 + 0.248229i
\(926\) −26.2007 8.51312i −0.861008 0.279759i
\(927\) −11.0797 1.75485i −0.363904 0.0576367i
\(928\) −0.0806009 + 0.0127659i −0.00264585 + 0.000419062i
\(929\) 28.4482 9.24339i 0.933356 0.303266i 0.197422 0.980319i \(-0.436743\pi\)
0.735934 + 0.677053i \(0.236743\pi\)
\(930\) −7.19617 6.48707i −0.235972 0.212719i
\(931\) 16.4767 22.6782i 0.540001 0.743247i
\(932\) 2.28839 14.4483i 0.0749587 0.473271i
\(933\) −23.4924 46.1065i −0.769107 1.50946i
\(934\) −30.5686 −1.00024
\(935\) −34.0631 6.10241i −1.11398 0.199570i
\(936\) −5.86449 −0.191687
\(937\) 13.7881 + 27.0607i 0.450439 + 0.884036i 0.998855 + 0.0478305i \(0.0152307\pi\)
−0.548417 + 0.836205i \(0.684769\pi\)
\(938\) −2.05992 + 13.0058i −0.0672587 + 0.424655i
\(939\) −44.2897 + 60.9595i −1.44534 + 1.98934i
\(940\) −1.42760 27.5476i −0.0465631 0.898505i
\(941\) 37.8725 12.3055i 1.23461 0.401149i 0.382227 0.924068i \(-0.375157\pi\)
0.852382 + 0.522920i \(0.175157\pi\)
\(942\) 12.5181 1.98268i 0.407863 0.0645991i
\(943\) −20.0618 3.17748i −0.653302 0.103473i
\(944\) 2.40237 + 0.780579i 0.0781906 + 0.0254057i
\(945\) 10.1917 + 17.6764i 0.331536 + 0.575012i
\(946\) −7.34885 + 6.36053i −0.238932 + 0.206799i
\(947\) −4.82949 4.82949i −0.156937 0.156937i 0.624271 0.781208i \(-0.285396\pi\)
−0.781208 + 0.624271i \(0.785396\pi\)
\(948\) 24.4624 12.4642i 0.794502 0.404819i
\(949\) −13.6924 18.8459i −0.444473 0.611764i
\(950\) −5.76924 + 14.9771i −0.187179 + 0.485923i
\(951\) 8.17590 + 25.1628i 0.265122 + 0.815961i
\(952\) −16.4909 8.40256i −0.534475 0.272328i
\(953\) −3.09310 19.5290i −0.100195 0.632608i −0.985769 0.168108i \(-0.946234\pi\)
0.885573 0.464499i \(-0.153766\pi\)
\(954\) −5.87569 + 4.26894i −0.190233 + 0.138212i
\(955\) 22.3550 4.73807i 0.723391 0.153320i
\(956\) 7.56533i 0.244680i
\(957\) −0.585647 + 0.144680i −0.0189313 + 0.00467683i
\(958\) −8.69172 + 8.69172i −0.280817 + 0.280817i
\(959\) 21.9704 67.6178i 0.709460 2.18349i
\(960\) −1.78335 4.65391i −0.0575575 0.150204i
\(961\) 22.0223 + 16.0001i 0.710396 + 0.516133i
\(962\) −7.92755 + 15.5587i −0.255595 + 0.501632i
\(963\) −11.2514 + 22.0822i −0.362572 + 0.711588i
\(964\) 5.11060 + 3.71307i 0.164601 + 0.119590i
\(965\) −17.6464 46.0508i −0.568059 1.48243i
\(966\) 19.8662 61.1418i 0.639184 1.96721i
\(967\) 1.05132 1.05132i 0.0338081 0.0338081i −0.690001 0.723809i \(-0.742390\pi\)
0.723809 + 0.690001i \(0.242390\pi\)
\(968\) 3.53643 + 10.4160i 0.113665 + 0.334784i
\(969\) 33.3848i 1.07247i
\(970\) 24.0122 5.08931i 0.770985 0.163408i
\(971\) −36.1581 + 26.2704i −1.16037 + 0.843057i −0.989825 0.142293i \(-0.954553\pi\)
−0.170544 + 0.985350i \(0.554553\pi\)
\(972\) 2.76659 + 17.4675i 0.0887383 + 0.560272i
\(973\) 8.75903 + 4.46295i 0.280802 + 0.143076i
\(974\) 1.95944 + 6.03053i 0.0627845 + 0.193231i
\(975\) 30.3563 13.4731i 0.972180 0.431484i
\(976\) −1.05438 1.45123i −0.0337498 0.0464526i
\(977\) −12.0814 + 6.15577i −0.386517 + 0.196940i −0.636441 0.771325i \(-0.719594\pi\)
0.249924 + 0.968265i \(0.419594\pi\)
\(978\) −19.1017 19.1017i −0.610804 0.610804i
\(979\) −10.2703 + 17.0096i −0.328240 + 0.543628i
\(980\) −9.75359 16.9165i −0.311567 0.540377i
\(981\) −24.4739 7.95206i −0.781392 0.253890i
\(982\) 22.8529 + 3.61954i 0.729265 + 0.115504i
\(983\) 25.7257 4.07455i 0.820523 0.129958i 0.267961 0.963430i \(-0.413650\pi\)
0.552562 + 0.833472i \(0.313650\pi\)
\(984\) −5.92098 + 1.92384i −0.188754 + 0.0613298i
\(985\) 1.79275 + 34.5938i 0.0571217 + 1.10225i
\(986\) 0.223821 0.308064i 0.00712792 0.00981074i
\(987\) 17.0608 107.718i 0.543052 3.42869i
\(988\) 4.34299 + 8.52359i 0.138169 + 0.271171i
\(989\) 21.3098 0.677611
\(990\) −6.36163 13.1344i −0.202186 0.417438i
\(991\) 34.9392 1.10988 0.554940 0.831890i \(-0.312741\pi\)
0.554940 + 0.831890i \(0.312741\pi\)
\(992\) −0.882540 1.73208i −0.0280207 0.0549936i
\(993\) −3.92953 + 24.8101i −0.124700 + 0.787324i
\(994\) 14.9824 20.6216i 0.475214 0.654076i
\(995\) 12.9171 + 11.6443i 0.409501 + 0.369149i
\(996\) −32.0484 + 10.4131i −1.01549 + 0.329953i
\(997\) 54.0159 8.55527i 1.71070 0.270948i 0.777129 0.629341i \(-0.216675\pi\)
0.933571 + 0.358393i \(0.116675\pi\)
\(998\) −41.0875 6.50762i −1.30060 0.205995i
\(999\) 12.8200 + 4.16548i 0.405607 + 0.131790i
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 110.2.k.a.57.1 yes 48
3.2 odd 2 990.2.bh.c.937.5 48
4.3 odd 2 880.2.cm.c.497.5 48
5.2 odd 4 550.2.bh.b.343.6 48
5.3 odd 4 inner 110.2.k.a.13.1 48
5.4 even 2 550.2.bh.b.57.6 48
11.6 odd 10 inner 110.2.k.a.17.1 yes 48
15.8 even 4 990.2.bh.c.343.4 48
20.3 even 4 880.2.cm.c.673.5 48
33.17 even 10 990.2.bh.c.127.4 48
44.39 even 10 880.2.cm.c.17.5 48
55.17 even 20 550.2.bh.b.193.6 48
55.28 even 20 inner 110.2.k.a.83.1 yes 48
55.39 odd 10 550.2.bh.b.457.6 48
165.83 odd 20 990.2.bh.c.523.5 48
220.83 odd 20 880.2.cm.c.193.5 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
110.2.k.a.13.1 48 5.3 odd 4 inner
110.2.k.a.17.1 yes 48 11.6 odd 10 inner
110.2.k.a.57.1 yes 48 1.1 even 1 trivial
110.2.k.a.83.1 yes 48 55.28 even 20 inner
550.2.bh.b.57.6 48 5.4 even 2
550.2.bh.b.193.6 48 55.17 even 20
550.2.bh.b.343.6 48 5.2 odd 4
550.2.bh.b.457.6 48 55.39 odd 10
880.2.cm.c.17.5 48 44.39 even 10
880.2.cm.c.193.5 48 220.83 odd 20
880.2.cm.c.497.5 48 4.3 odd 2
880.2.cm.c.673.5 48 20.3 even 4
990.2.bh.c.127.4 48 33.17 even 10
990.2.bh.c.343.4 48 15.8 even 4
990.2.bh.c.523.5 48 165.83 odd 20
990.2.bh.c.937.5 48 3.2 odd 2