Properties

Label 162.2.e.b.73.2
Level $162$
Weight $2$
Character 162.73
Analytic conductor $1.294$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,2,Mod(19,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\), degree \(6\), not 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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} - 1584 x^{3} + 936 x^{2} - 342 x + 57 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 73.2
Root \(0.500000 + 2.42499i\) of defining polynomial
Character \(\chi\) \(=\) 162.73
Dual form 162.2.e.b.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(3.10057 - 2.60168i) q^{5} +(0.144365 - 0.0525446i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\) \(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(3.10057 - 2.60168i) q^{5} +(0.144365 - 0.0525446i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.02375 + 3.50524i) q^{10} +(-0.169211 - 0.141985i) q^{11} +(0.103202 + 0.585289i) q^{13} +(0.0266776 + 0.151296i) q^{14} +(0.766044 + 0.642788i) q^{16} +(2.78255 + 4.81952i) q^{17} +(-1.91041 + 3.30893i) q^{19} +(-3.80341 + 1.38433i) q^{20} +(0.169211 - 0.141985i) q^{22} +(-5.50570 - 2.00391i) q^{23} +(1.97651 - 11.2093i) q^{25} -0.594318 q^{26} -0.153630 q^{28} +(-0.129880 + 0.736585i) q^{29} +(-4.77702 - 1.73869i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-5.22949 + 1.90338i) q^{34} +(0.310909 - 0.538510i) q^{35} +(-1.87388 - 3.24566i) q^{37} +(-2.92692 - 2.45598i) q^{38} +(-0.702841 - 3.98601i) q^{40} +(-0.690156 - 3.91407i) q^{41} +(7.81896 + 6.56088i) q^{43} +(0.110445 + 0.191296i) q^{44} +(2.92952 - 5.07408i) q^{46} +(-0.447025 + 0.162704i) q^{47} +(-5.34423 + 4.48434i) q^{49} +(10.6958 + 3.89296i) q^{50} +(0.103202 - 0.585289i) q^{52} -3.29955 q^{53} -0.894051 q^{55} +(0.0266776 - 0.151296i) q^{56} +(-0.702841 - 0.255813i) q^{58} +(-5.57221 + 4.67564i) q^{59} +(-3.16654 + 1.15253i) q^{61} +(2.54180 - 4.40252i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(1.84272 + 1.54623i) q^{65} +(1.29509 + 7.34481i) q^{67} +(-0.966370 - 5.48056i) q^{68} +(0.476340 + 0.399697i) q^{70} +(1.42889 + 2.47490i) q^{71} +(0.638922 - 1.10665i) q^{73} +(3.52175 - 1.28181i) q^{74} +(2.92692 - 2.45598i) q^{76} +(-0.0318887 - 0.0116066i) q^{77} +(-0.574268 + 3.25684i) q^{79} +4.04750 q^{80} +3.97445 q^{82} +(1.43627 - 8.14551i) q^{83} +(21.1664 + 7.70392i) q^{85} +(-7.81896 + 6.56088i) q^{86} +(-0.207568 + 0.0755487i) q^{88} +(-2.47882 + 4.29345i) q^{89} +(0.0456525 + 0.0790725i) q^{91} +(4.48829 + 3.76612i) q^{92} +(-0.0826070 - 0.468487i) q^{94} +(2.68543 + 15.2298i) q^{95} +(4.33127 + 3.63437i) q^{97} +(-3.48820 - 6.04174i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.173648 + 0.984808i −0.122788 + 0.696364i
\(3\) 0 0
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) 3.10057 2.60168i 1.38661 1.16351i 0.419925 0.907559i \(-0.362056\pi\)
0.966690 0.255949i \(-0.0823880\pi\)
\(6\) 0 0
\(7\) 0.144365 0.0525446i 0.0545648 0.0198600i −0.314594 0.949226i \(-0.601868\pi\)
0.369158 + 0.929366i \(0.379646\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) 0 0
\(10\) 2.02375 + 3.50524i 0.639966 + 1.10845i
\(11\) −0.169211 0.141985i −0.0510191 0.0428101i 0.616922 0.787025i \(-0.288380\pi\)
−0.667941 + 0.744215i \(0.732824\pi\)
\(12\) 0 0
\(13\) 0.103202 + 0.585289i 0.0286231 + 0.162330i 0.995769 0.0918925i \(-0.0292916\pi\)
−0.967146 + 0.254222i \(0.918180\pi\)
\(14\) 0.0266776 + 0.151296i 0.00712988 + 0.0404356i
\(15\) 0 0
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 2.78255 + 4.81952i 0.674868 + 1.16891i 0.976507 + 0.215484i \(0.0691328\pi\)
−0.301639 + 0.953422i \(0.597534\pi\)
\(18\) 0 0
\(19\) −1.91041 + 3.30893i −0.438278 + 0.759120i −0.997557 0.0698599i \(-0.977745\pi\)
0.559279 + 0.828980i \(0.311078\pi\)
\(20\) −3.80341 + 1.38433i −0.850468 + 0.309545i
\(21\) 0 0
\(22\) 0.169211 0.141985i 0.0360760 0.0302713i
\(23\) −5.50570 2.00391i −1.14802 0.417844i −0.303215 0.952922i \(-0.598060\pi\)
−0.844803 + 0.535078i \(0.820282\pi\)
\(24\) 0 0
\(25\) 1.97651 11.2093i 0.395302 2.24187i
\(26\) −0.594318 −0.116555
\(27\) 0 0
\(28\) −0.153630 −0.0290333
\(29\) −0.129880 + 0.736585i −0.0241181 + 0.136780i −0.994489 0.104839i \(-0.966567\pi\)
0.970371 + 0.241619i \(0.0776785\pi\)
\(30\) 0 0
\(31\) −4.77702 1.73869i −0.857978 0.312278i −0.124689 0.992196i \(-0.539793\pi\)
−0.733289 + 0.679917i \(0.762016\pi\)
\(32\) −0.766044 + 0.642788i −0.135419 + 0.113630i
\(33\) 0 0
\(34\) −5.22949 + 1.90338i −0.896850 + 0.326427i
\(35\) 0.310909 0.538510i 0.0525532 0.0910248i
\(36\) 0 0
\(37\) −1.87388 3.24566i −0.308065 0.533584i 0.669874 0.742474i \(-0.266348\pi\)
−0.977939 + 0.208891i \(0.933015\pi\)
\(38\) −2.92692 2.45598i −0.474809 0.398412i
\(39\) 0 0
\(40\) −0.702841 3.98601i −0.111129 0.630244i
\(41\) −0.690156 3.91407i −0.107784 0.611275i −0.990072 0.140564i \(-0.955109\pi\)
0.882287 0.470711i \(-0.156003\pi\)
\(42\) 0 0
\(43\) 7.81896 + 6.56088i 1.19238 + 1.00053i 0.999815 + 0.0192411i \(0.00612500\pi\)
0.192565 + 0.981284i \(0.438319\pi\)
\(44\) 0.110445 + 0.191296i 0.0166502 + 0.0288390i
\(45\) 0 0
\(46\) 2.92952 5.07408i 0.431935 0.748133i
\(47\) −0.447025 + 0.162704i −0.0652054 + 0.0237328i −0.374417 0.927260i \(-0.622157\pi\)
0.309212 + 0.950993i \(0.399935\pi\)
\(48\) 0 0
\(49\) −5.34423 + 4.48434i −0.763462 + 0.640620i
\(50\) 10.6958 + 3.89296i 1.51262 + 0.550548i
\(51\) 0 0
\(52\) 0.103202 0.585289i 0.0143116 0.0811650i
\(53\) −3.29955 −0.453228 −0.226614 0.973985i \(-0.572766\pi\)
−0.226614 + 0.973985i \(0.572766\pi\)
\(54\) 0 0
\(55\) −0.894051 −0.120554
\(56\) 0.0266776 0.151296i 0.00356494 0.0202178i
\(57\) 0 0
\(58\) −0.702841 0.255813i −0.0922876 0.0335899i
\(59\) −5.57221 + 4.67564i −0.725440 + 0.608716i −0.928884 0.370370i \(-0.879231\pi\)
0.203444 + 0.979086i \(0.434786\pi\)
\(60\) 0 0
\(61\) −3.16654 + 1.15253i −0.405434 + 0.147566i −0.536684 0.843783i \(-0.680323\pi\)
0.131250 + 0.991349i \(0.458101\pi\)
\(62\) 2.54180 4.40252i 0.322809 0.559121i
\(63\) 0 0
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 1.84272 + 1.54623i 0.228561 + 0.191786i
\(66\) 0 0
\(67\) 1.29509 + 7.34481i 0.158220 + 0.897312i 0.955782 + 0.294075i \(0.0950115\pi\)
−0.797562 + 0.603237i \(0.793877\pi\)
\(68\) −0.966370 5.48056i −0.117190 0.664615i
\(69\) 0 0
\(70\) 0.476340 + 0.399697i 0.0569335 + 0.0477729i
\(71\) 1.42889 + 2.47490i 0.169578 + 0.293717i 0.938271 0.345900i \(-0.112426\pi\)
−0.768694 + 0.639617i \(0.779093\pi\)
\(72\) 0 0
\(73\) 0.638922 1.10665i 0.0747802 0.129523i −0.826210 0.563362i \(-0.809508\pi\)
0.900991 + 0.433838i \(0.142841\pi\)
\(74\) 3.52175 1.28181i 0.409395 0.149008i
\(75\) 0 0
\(76\) 2.92692 2.45598i 0.335740 0.281720i
\(77\) −0.0318887 0.0116066i −0.00363406 0.00132269i
\(78\) 0 0
\(79\) −0.574268 + 3.25684i −0.0646102 + 0.366423i 0.935310 + 0.353828i \(0.115120\pi\)
−0.999921 + 0.0125947i \(0.995991\pi\)
\(80\) 4.04750 0.452524
\(81\) 0 0
\(82\) 3.97445 0.438904
\(83\) 1.43627 8.14551i 0.157651 0.894085i −0.798670 0.601769i \(-0.794463\pi\)
0.956322 0.292316i \(-0.0944261\pi\)
\(84\) 0 0
\(85\) 21.1664 + 7.70392i 2.29581 + 0.835608i
\(86\) −7.81896 + 6.56088i −0.843140 + 0.707478i
\(87\) 0 0
\(88\) −0.207568 + 0.0755487i −0.0221269 + 0.00805352i
\(89\) −2.47882 + 4.29345i −0.262755 + 0.455105i −0.966973 0.254879i \(-0.917964\pi\)
0.704218 + 0.709984i \(0.251298\pi\)
\(90\) 0 0
\(91\) 0.0456525 + 0.0790725i 0.00478569 + 0.00828905i
\(92\) 4.48829 + 3.76612i 0.467936 + 0.392645i
\(93\) 0 0
\(94\) −0.0826070 0.468487i −0.00852026 0.0483208i
\(95\) 2.68543 + 15.2298i 0.275519 + 1.56255i
\(96\) 0 0
\(97\) 4.33127 + 3.63437i 0.439774 + 0.369014i 0.835625 0.549301i \(-0.185106\pi\)
−0.395851 + 0.918315i \(0.629550\pi\)
\(98\) −3.48820 6.04174i −0.352361 0.610308i
\(99\) 0 0
\(100\) −5.69113 + 9.85733i −0.569113 + 0.985733i
\(101\) 14.8467 5.40376i 1.47730 0.537694i 0.527229 0.849723i \(-0.323231\pi\)
0.950072 + 0.312029i \(0.101009\pi\)
\(102\) 0 0
\(103\) 8.19426 6.87580i 0.807404 0.677493i −0.142582 0.989783i \(-0.545541\pi\)
0.949987 + 0.312290i \(0.101096\pi\)
\(104\) 0.558476 + 0.203269i 0.0547631 + 0.0199321i
\(105\) 0 0
\(106\) 0.572961 3.24943i 0.0556509 0.315612i
\(107\) −1.85236 −0.179075 −0.0895374 0.995983i \(-0.528539\pi\)
−0.0895374 + 0.995983i \(0.528539\pi\)
\(108\) 0 0
\(109\) −14.5495 −1.39359 −0.696793 0.717273i \(-0.745390\pi\)
−0.696793 + 0.717273i \(0.745390\pi\)
\(110\) 0.155250 0.880468i 0.0148025 0.0839494i
\(111\) 0 0
\(112\) 0.144365 + 0.0525446i 0.0136412 + 0.00496500i
\(113\) 10.2514 8.60195i 0.964371 0.809204i −0.0172875 0.999851i \(-0.505503\pi\)
0.981659 + 0.190647i \(0.0610586\pi\)
\(114\) 0 0
\(115\) −22.2843 + 8.11083i −2.07802 + 0.756339i
\(116\) 0.373974 0.647742i 0.0347226 0.0601413i
\(117\) 0 0
\(118\) −3.63700 6.29947i −0.334813 0.579913i
\(119\) 0.654943 + 0.549562i 0.0600385 + 0.0503783i
\(120\) 0 0
\(121\) −1.90166 10.7848i −0.172878 0.980439i
\(122\) −0.585154 3.31857i −0.0529773 0.300449i
\(123\) 0 0
\(124\) 3.89426 + 3.26767i 0.349715 + 0.293446i
\(125\) −12.9161 22.3713i −1.15525 2.00095i
\(126\) 0 0
\(127\) 9.31545 16.1348i 0.826612 1.43173i −0.0740688 0.997253i \(-0.523598\pi\)
0.900681 0.434481i \(-0.143068\pi\)
\(128\) 0.939693 0.342020i 0.0830579 0.0302306i
\(129\) 0 0
\(130\) −1.84272 + 1.54623i −0.161617 + 0.135613i
\(131\) −6.45330 2.34881i −0.563828 0.205217i 0.0443519 0.999016i \(-0.485878\pi\)
−0.608180 + 0.793799i \(0.708100\pi\)
\(132\) 0 0
\(133\) −0.101930 + 0.578075i −0.00883847 + 0.0501254i
\(134\) −7.45812 −0.644283
\(135\) 0 0
\(136\) 5.56510 0.477204
\(137\) −2.60219 + 14.7577i −0.222320 + 1.26084i 0.645423 + 0.763826i \(0.276681\pi\)
−0.867743 + 0.497014i \(0.834430\pi\)
\(138\) 0 0
\(139\) −17.0110 6.19150i −1.44286 0.525156i −0.502269 0.864711i \(-0.667501\pi\)
−0.940586 + 0.339555i \(0.889724\pi\)
\(140\) −0.476340 + 0.399697i −0.0402581 + 0.0337805i
\(141\) 0 0
\(142\) −2.68543 + 0.977416i −0.225356 + 0.0820229i
\(143\) 0.0656393 0.113691i 0.00548904 0.00950729i
\(144\) 0 0
\(145\) 1.51366 + 2.62174i 0.125703 + 0.217723i
\(146\) 0.978886 + 0.821383i 0.0810132 + 0.0679781i
\(147\) 0 0
\(148\) 0.650793 + 3.69083i 0.0534949 + 0.303384i
\(149\) 2.60884 + 14.7955i 0.213725 + 1.21209i 0.883106 + 0.469174i \(0.155448\pi\)
−0.669381 + 0.742919i \(0.733441\pi\)
\(150\) 0 0
\(151\) −4.32258 3.62708i −0.351767 0.295167i 0.449732 0.893163i \(-0.351519\pi\)
−0.801499 + 0.597996i \(0.795964\pi\)
\(152\) 1.91041 + 3.30893i 0.154955 + 0.268389i
\(153\) 0 0
\(154\) 0.0169676 0.0293888i 0.00136729 0.00236822i
\(155\) −19.3350 + 7.03736i −1.55302 + 0.565254i
\(156\) 0 0
\(157\) 5.54978 4.65682i 0.442921 0.371655i −0.393880 0.919162i \(-0.628868\pi\)
0.836801 + 0.547507i \(0.184423\pi\)
\(158\) −3.10764 1.13109i −0.247230 0.0899845i
\(159\) 0 0
\(160\) −0.702841 + 3.98601i −0.0555645 + 0.315122i
\(161\) −0.900125 −0.0709398
\(162\) 0 0
\(163\) 14.1079 1.10501 0.552506 0.833509i \(-0.313672\pi\)
0.552506 + 0.833509i \(0.313672\pi\)
\(164\) −0.690156 + 3.91407i −0.0538921 + 0.305637i
\(165\) 0 0
\(166\) 7.77235 + 2.82890i 0.603251 + 0.219566i
\(167\) 10.5889 8.88510i 0.819390 0.687550i −0.133439 0.991057i \(-0.542602\pi\)
0.952829 + 0.303507i \(0.0981576\pi\)
\(168\) 0 0
\(169\) 11.8841 4.32546i 0.914161 0.332727i
\(170\) −11.2624 + 19.5070i −0.863785 + 1.49612i
\(171\) 0 0
\(172\) −5.10346 8.83945i −0.389135 0.674002i
\(173\) 3.00999 + 2.52568i 0.228845 + 0.192024i 0.749999 0.661439i \(-0.230054\pi\)
−0.521154 + 0.853463i \(0.674498\pi\)
\(174\) 0 0
\(175\) −0.303651 1.72209i −0.0229539 0.130178i
\(176\) −0.0383571 0.217534i −0.00289127 0.0163972i
\(177\) 0 0
\(178\) −3.79778 3.18671i −0.284656 0.238854i
\(179\) 1.42211 + 2.46317i 0.106294 + 0.184106i 0.914266 0.405115i \(-0.132768\pi\)
−0.807972 + 0.589220i \(0.799435\pi\)
\(180\) 0 0
\(181\) −6.46274 + 11.1938i −0.480372 + 0.832028i −0.999746 0.0225186i \(-0.992832\pi\)
0.519375 + 0.854547i \(0.326165\pi\)
\(182\) −0.0857987 + 0.0312282i −0.00635982 + 0.00231479i
\(183\) 0 0
\(184\) −4.48829 + 3.76612i −0.330881 + 0.277642i
\(185\) −14.2543 5.18813i −1.04800 0.381439i
\(186\) 0 0
\(187\) 0.213461 1.21060i 0.0156098 0.0885277i
\(188\) 0.475715 0.0346951
\(189\) 0 0
\(190\) −15.4648 −1.12193
\(191\) 3.49774 19.8367i 0.253088 1.43533i −0.547846 0.836579i \(-0.684552\pi\)
0.800934 0.598753i \(-0.204337\pi\)
\(192\) 0 0
\(193\) −9.03669 3.28909i −0.650476 0.236754i −0.00435663 0.999991i \(-0.501387\pi\)
−0.646119 + 0.763237i \(0.723609\pi\)
\(194\) −4.33127 + 3.63437i −0.310967 + 0.260932i
\(195\) 0 0
\(196\) 6.55567 2.38607i 0.468262 0.170433i
\(197\) 3.77527 6.53895i 0.268977 0.465881i −0.699621 0.714514i \(-0.746648\pi\)
0.968598 + 0.248633i \(0.0799812\pi\)
\(198\) 0 0
\(199\) 6.07071 + 10.5148i 0.430341 + 0.745372i 0.996903 0.0786471i \(-0.0250600\pi\)
−0.566562 + 0.824019i \(0.691727\pi\)
\(200\) −8.71932 7.31638i −0.616549 0.517346i
\(201\) 0 0
\(202\) 2.74356 + 15.5595i 0.193036 + 1.09476i
\(203\) 0.0199534 + 0.113162i 0.00140046 + 0.00794238i
\(204\) 0 0
\(205\) −12.3230 10.3403i −0.860678 0.722195i
\(206\) 5.34842 + 9.26374i 0.372642 + 0.645435i
\(207\) 0 0
\(208\) −0.297159 + 0.514694i −0.0206043 + 0.0356876i
\(209\) 0.793081 0.288658i 0.0548586 0.0199669i
\(210\) 0 0
\(211\) −5.53378 + 4.64340i −0.380961 + 0.319665i −0.813080 0.582152i \(-0.802211\pi\)
0.432118 + 0.901817i \(0.357766\pi\)
\(212\) 3.10057 + 1.12851i 0.212948 + 0.0775066i
\(213\) 0 0
\(214\) 0.321660 1.82422i 0.0219882 0.124701i
\(215\) 41.3125 2.81749
\(216\) 0 0
\(217\) −0.780993 −0.0530173
\(218\) 2.52649 14.3284i 0.171115 0.970443i
\(219\) 0 0
\(220\) 0.840133 + 0.305783i 0.0566418 + 0.0206159i
\(221\) −2.53365 + 2.12598i −0.170432 + 0.143009i
\(222\) 0 0
\(223\) 23.9856 8.73004i 1.60619 0.584607i 0.625512 0.780214i \(-0.284890\pi\)
0.980682 + 0.195607i \(0.0626678\pi\)
\(224\) −0.0768150 + 0.133048i −0.00513242 + 0.00888961i
\(225\) 0 0
\(226\) 6.69113 + 11.5894i 0.445087 + 0.770914i
\(227\) −10.9999 9.22998i −0.730086 0.612615i 0.200069 0.979782i \(-0.435883\pi\)
−0.930155 + 0.367167i \(0.880328\pi\)
\(228\) 0 0
\(229\) 0.704853 + 3.99742i 0.0465780 + 0.264157i 0.999200 0.0400010i \(-0.0127361\pi\)
−0.952622 + 0.304158i \(0.901625\pi\)
\(230\) −4.11798 23.3542i −0.271531 1.53993i
\(231\) 0 0
\(232\) 0.572961 + 0.480772i 0.0376168 + 0.0315642i
\(233\) 8.48936 + 14.7040i 0.556157 + 0.963292i 0.997813 + 0.0661072i \(0.0210579\pi\)
−0.441656 + 0.897185i \(0.645609\pi\)
\(234\) 0 0
\(235\) −0.962728 + 1.66749i −0.0628014 + 0.108775i
\(236\) 6.83533 2.48786i 0.444942 0.161946i
\(237\) 0 0
\(238\) −0.654943 + 0.549562i −0.0424536 + 0.0356228i
\(239\) 20.0419 + 7.29464i 1.29640 + 0.471851i 0.895823 0.444412i \(-0.146587\pi\)
0.400577 + 0.916263i \(0.368810\pi\)
\(240\) 0 0
\(241\) −1.86745 + 10.5909i −0.120293 + 0.682217i 0.863699 + 0.504007i \(0.168142\pi\)
−0.983993 + 0.178210i \(0.942970\pi\)
\(242\) 10.9512 0.703970
\(243\) 0 0
\(244\) 3.36977 0.215727
\(245\) −4.90330 + 27.8080i −0.313260 + 1.77659i
\(246\) 0 0
\(247\) −2.13384 0.776653i −0.135773 0.0494172i
\(248\) −3.89426 + 3.26767i −0.247286 + 0.207497i
\(249\) 0 0
\(250\) 24.2743 8.83513i 1.53524 0.558783i
\(251\) 2.08811 3.61672i 0.131801 0.228285i −0.792570 0.609781i \(-0.791257\pi\)
0.924371 + 0.381495i \(0.124591\pi\)
\(252\) 0 0
\(253\) 0.647101 + 1.12081i 0.0406829 + 0.0704649i
\(254\) 14.2721 + 11.9757i 0.895511 + 0.751423i
\(255\) 0 0
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) −2.83797 16.0949i −0.177028 1.00397i −0.935777 0.352592i \(-0.885301\pi\)
0.758750 0.651382i \(-0.225811\pi\)
\(258\) 0 0
\(259\) −0.441065 0.370098i −0.0274065 0.0229967i
\(260\) −1.20275 2.08323i −0.0745914 0.129196i
\(261\) 0 0
\(262\) 3.43373 5.94740i 0.212137 0.367431i
\(263\) −2.51963 + 0.917071i −0.155367 + 0.0565490i −0.418533 0.908202i \(-0.637456\pi\)
0.263166 + 0.964751i \(0.415233\pi\)
\(264\) 0 0
\(265\) −10.2305 + 8.58439i −0.628453 + 0.527335i
\(266\) −0.551593 0.200763i −0.0338203 0.0123096i
\(267\) 0 0
\(268\) 1.29509 7.34481i 0.0791101 0.448656i
\(269\) −22.3509 −1.36276 −0.681380 0.731930i \(-0.738620\pi\)
−0.681380 + 0.731930i \(0.738620\pi\)
\(270\) 0 0
\(271\) 25.4813 1.54788 0.773941 0.633258i \(-0.218283\pi\)
0.773941 + 0.633258i \(0.218283\pi\)
\(272\) −0.966370 + 5.48056i −0.0585948 + 0.332308i
\(273\) 0 0
\(274\) −14.0817 5.12531i −0.850705 0.309631i
\(275\) −1.92601 + 1.61611i −0.116143 + 0.0974552i
\(276\) 0 0
\(277\) 2.41221 0.877972i 0.144936 0.0527523i −0.268534 0.963270i \(-0.586539\pi\)
0.413469 + 0.910518i \(0.364317\pi\)
\(278\) 9.05137 15.6774i 0.542865 0.940270i
\(279\) 0 0
\(280\) −0.310909 0.538510i −0.0185804 0.0321821i
\(281\) −16.2374 13.6248i −0.968642 0.812787i 0.0136956 0.999906i \(-0.495640\pi\)
−0.982337 + 0.187119i \(0.940085\pi\)
\(282\) 0 0
\(283\) −3.40928 19.3350i −0.202660 1.14934i −0.901079 0.433655i \(-0.857224\pi\)
0.698419 0.715689i \(-0.253887\pi\)
\(284\) −0.496247 2.81436i −0.0294468 0.167001i
\(285\) 0 0
\(286\) 0.100565 + 0.0843843i 0.00594655 + 0.00498975i
\(287\) −0.305297 0.528791i −0.0180211 0.0312135i
\(288\) 0 0
\(289\) −6.98519 + 12.0987i −0.410894 + 0.711689i
\(290\) −2.84475 + 1.03540i −0.167049 + 0.0608010i
\(291\) 0 0
\(292\) −0.978886 + 0.821383i −0.0572850 + 0.0480678i
\(293\) 20.1808 + 7.34522i 1.17898 + 0.429112i 0.855840 0.517240i \(-0.173041\pi\)
0.323136 + 0.946352i \(0.395263\pi\)
\(294\) 0 0
\(295\) −5.11247 + 28.9942i −0.297659 + 1.68811i
\(296\) −3.74777 −0.217835
\(297\) 0 0
\(298\) −15.0237 −0.870301
\(299\) 0.604666 3.42923i 0.0349688 0.198318i
\(300\) 0 0
\(301\) 1.47352 + 0.536318i 0.0849324 + 0.0309129i
\(302\) 4.32258 3.62708i 0.248737 0.208715i
\(303\) 0 0
\(304\) −3.59040 + 1.30680i −0.205923 + 0.0749500i
\(305\) −6.81956 + 11.8118i −0.390487 + 0.676343i
\(306\) 0 0
\(307\) −2.82636 4.89540i −0.161309 0.279395i 0.774029 0.633150i \(-0.218238\pi\)
−0.935338 + 0.353754i \(0.884905\pi\)
\(308\) 0.0259959 + 0.0218132i 0.00148126 + 0.00124292i
\(309\) 0 0
\(310\) −3.57296 20.2633i −0.202931 1.15088i
\(311\) −1.61574 9.16334i −0.0916205 0.519605i −0.995731 0.0923061i \(-0.970576\pi\)
0.904110 0.427299i \(-0.140535\pi\)
\(312\) 0 0
\(313\) −2.05976 1.72835i −0.116425 0.0976920i 0.582717 0.812675i \(-0.301990\pi\)
−0.699141 + 0.714983i \(0.746434\pi\)
\(314\) 3.62236 + 6.27412i 0.204422 + 0.354069i
\(315\) 0 0
\(316\) 1.65354 2.86401i 0.0930189 0.161113i
\(317\) −26.2511 + 9.55461i −1.47441 + 0.536641i −0.949294 0.314391i \(-0.898200\pi\)
−0.525114 + 0.851032i \(0.675977\pi\)
\(318\) 0 0
\(319\) 0.126561 0.106197i 0.00708607 0.00594592i
\(320\) −3.80341 1.38433i −0.212617 0.0773862i
\(321\) 0 0
\(322\) 0.156305 0.886450i 0.00871054 0.0494000i
\(323\) −21.2633 −1.18312
\(324\) 0 0
\(325\) 6.76468 0.375237
\(326\) −2.44980 + 13.8935i −0.135682 + 0.769491i
\(327\) 0 0
\(328\) −3.73476 1.35934i −0.206218 0.0750571i
\(329\) −0.0559856 + 0.0469775i −0.00308659 + 0.00258995i
\(330\) 0 0
\(331\) −0.794144 + 0.289045i −0.0436501 + 0.0158873i −0.363753 0.931495i \(-0.618505\pi\)
0.320103 + 0.947383i \(0.396283\pi\)
\(332\) −4.13558 + 7.16304i −0.226970 + 0.393123i
\(333\) 0 0
\(334\) 6.91138 + 11.9709i 0.378174 + 0.655017i
\(335\) 23.1244 + 19.4037i 1.26342 + 1.06014i
\(336\) 0 0
\(337\) 5.09088 + 28.8718i 0.277318 + 1.57275i 0.731501 + 0.681840i \(0.238820\pi\)
−0.454183 + 0.890908i \(0.650069\pi\)
\(338\) 2.19609 + 12.4547i 0.119452 + 0.677444i
\(339\) 0 0
\(340\) −17.2550 14.4786i −0.935782 0.785214i
\(341\) 0.561457 + 0.972472i 0.0304046 + 0.0526623i
\(342\) 0 0
\(343\) −1.07360 + 1.85953i −0.0579688 + 0.100405i
\(344\) 9.59137 3.49097i 0.517132 0.188221i
\(345\) 0 0
\(346\) −3.00999 + 2.52568i −0.161818 + 0.135781i
\(347\) −18.9820 6.90888i −1.01901 0.370888i −0.222121 0.975019i \(-0.571298\pi\)
−0.796885 + 0.604131i \(0.793520\pi\)
\(348\) 0 0
\(349\) 1.66866 9.46343i 0.0893212 0.506566i −0.907019 0.421090i \(-0.861648\pi\)
0.996340 0.0854761i \(-0.0272411\pi\)
\(350\) 1.74866 0.0934697
\(351\) 0 0
\(352\) 0.220890 0.0117735
\(353\) 1.70637 9.67729i 0.0908208 0.515070i −0.905127 0.425141i \(-0.860225\pi\)
0.995948 0.0899297i \(-0.0286642\pi\)
\(354\) 0 0
\(355\) 10.8693 + 3.95609i 0.576881 + 0.209968i
\(356\) 3.79778 3.18671i 0.201282 0.168896i
\(357\) 0 0
\(358\) −2.67269 + 0.972781i −0.141256 + 0.0514131i
\(359\) 5.94469 10.2965i 0.313749 0.543429i −0.665422 0.746467i \(-0.731748\pi\)
0.979171 + 0.203039i \(0.0650817\pi\)
\(360\) 0 0
\(361\) 2.20067 + 3.81167i 0.115825 + 0.200614i
\(362\) −9.90149 8.30834i −0.520411 0.436676i
\(363\) 0 0
\(364\) −0.0158550 0.0899179i −0.000831026 0.00471298i
\(365\) −0.898122 5.09350i −0.0470098 0.266606i
\(366\) 0 0
\(367\) −27.7867 23.3158i −1.45045 1.21708i −0.932248 0.361821i \(-0.882155\pi\)
−0.518207 0.855255i \(-0.673400\pi\)
\(368\) −2.92952 5.07408i −0.152712 0.264505i
\(369\) 0 0
\(370\) 7.58455 13.1368i 0.394302 0.682951i
\(371\) −0.476340 + 0.173374i −0.0247303 + 0.00900111i
\(372\) 0 0
\(373\) 10.8389 9.09489i 0.561215 0.470916i −0.317502 0.948258i \(-0.602844\pi\)
0.878718 + 0.477342i \(0.158400\pi\)
\(374\) 1.15514 + 0.420436i 0.0597308 + 0.0217403i
\(375\) 0 0
\(376\) −0.0826070 + 0.468487i −0.00426013 + 0.0241604i
\(377\) −0.444519 −0.0228939
\(378\) 0 0
\(379\) −29.5237 −1.51653 −0.758265 0.651946i \(-0.773953\pi\)
−0.758265 + 0.651946i \(0.773953\pi\)
\(380\) 2.68543 15.2298i 0.137760 0.781273i
\(381\) 0 0
\(382\) 18.9279 + 6.88921i 0.968438 + 0.352483i
\(383\) −18.9404 + 15.8929i −0.967811 + 0.812090i −0.982206 0.187807i \(-0.939862\pi\)
0.0143953 + 0.999896i \(0.495418\pi\)
\(384\) 0 0
\(385\) −0.129070 + 0.0469775i −0.00657800 + 0.00239420i
\(386\) 4.80832 8.32826i 0.244737 0.423897i
\(387\) 0 0
\(388\) −2.82704 4.89657i −0.143521 0.248586i
\(389\) −11.1425 9.34969i −0.564948 0.474048i 0.315017 0.949086i \(-0.397990\pi\)
−0.879965 + 0.475038i \(0.842434\pi\)
\(390\) 0 0
\(391\) −5.66201 32.1108i −0.286340 1.62391i
\(392\) 1.21144 + 6.87041i 0.0611869 + 0.347008i
\(393\) 0 0
\(394\) 5.78404 + 4.85339i 0.291396 + 0.244510i
\(395\) 6.69270 + 11.5921i 0.336746 + 0.583262i
\(396\) 0 0
\(397\) −2.10870 + 3.65238i −0.105833 + 0.183308i −0.914078 0.405538i \(-0.867084\pi\)
0.808245 + 0.588846i \(0.200418\pi\)
\(398\) −11.4092 + 4.15261i −0.571891 + 0.208151i
\(399\) 0 0
\(400\) 8.71932 7.31638i 0.435966 0.365819i
\(401\) −15.2143 5.53755i −0.759765 0.276532i −0.0670561 0.997749i \(-0.521361\pi\)
−0.692709 + 0.721217i \(0.743583\pi\)
\(402\) 0 0
\(403\) 0.524638 2.97537i 0.0261341 0.148214i
\(404\) −15.7995 −0.786056
\(405\) 0 0
\(406\) −0.114907 −0.00570275
\(407\) −0.143753 + 0.815266i −0.00712559 + 0.0404112i
\(408\) 0 0
\(409\) −3.70550 1.34869i −0.183225 0.0666885i 0.248778 0.968560i \(-0.419971\pi\)
−0.432003 + 0.901872i \(0.642193\pi\)
\(410\) 12.3230 10.3403i 0.608591 0.510669i
\(411\) 0 0
\(412\) −10.0517 + 3.65854i −0.495214 + 0.180243i
\(413\) −0.558753 + 0.967788i −0.0274944 + 0.0476217i
\(414\) 0 0
\(415\) −16.7388 28.9924i −0.821674 1.42318i
\(416\) −0.455274 0.382020i −0.0223216 0.0187301i
\(417\) 0 0
\(418\) 0.146555 + 0.831157i 0.00716826 + 0.0406532i
\(419\) 5.98994 + 33.9707i 0.292628 + 1.65957i 0.676690 + 0.736268i \(0.263414\pi\)
−0.384062 + 0.923307i \(0.625475\pi\)
\(420\) 0 0
\(421\) −8.80184 7.38562i −0.428976 0.359953i 0.402589 0.915381i \(-0.368110\pi\)
−0.831565 + 0.555427i \(0.812555\pi\)
\(422\) −3.61192 6.25603i −0.175826 0.304539i
\(423\) 0 0
\(424\) −1.64978 + 2.85750i −0.0801202 + 0.138772i
\(425\) 59.5234 21.6647i 2.88731 1.05089i
\(426\) 0 0
\(427\) −0.396579 + 0.332769i −0.0191918 + 0.0161038i
\(428\) 1.74065 + 0.633546i 0.0841376 + 0.0306236i
\(429\) 0 0
\(430\) −7.17384 + 40.6849i −0.345954 + 1.96200i
\(431\) −24.6371 −1.18673 −0.593364 0.804934i \(-0.702201\pi\)
−0.593364 + 0.804934i \(0.702201\pi\)
\(432\) 0 0
\(433\) 12.8011 0.615181 0.307590 0.951519i \(-0.400477\pi\)
0.307590 + 0.951519i \(0.400477\pi\)
\(434\) 0.135618 0.769128i 0.00650988 0.0369193i
\(435\) 0 0
\(436\) 13.6720 + 4.97621i 0.654771 + 0.238317i
\(437\) 17.1489 14.3897i 0.820345 0.688351i
\(438\) 0 0
\(439\) 34.1541 12.4311i 1.63009 0.593303i 0.644822 0.764333i \(-0.276932\pi\)
0.985266 + 0.171029i \(0.0547093\pi\)
\(440\) −0.447025 + 0.774271i −0.0213111 + 0.0369119i
\(441\) 0 0
\(442\) −1.65372 2.86433i −0.0786595 0.136242i
\(443\) 29.5753 + 24.8166i 1.40516 + 1.17907i 0.958752 + 0.284245i \(0.0917428\pi\)
0.446412 + 0.894828i \(0.352702\pi\)
\(444\) 0 0
\(445\) 3.48444 + 19.7612i 0.165178 + 0.936772i
\(446\) 4.43236 + 25.1372i 0.209878 + 1.19028i
\(447\) 0 0
\(448\) −0.117687 0.0987515i −0.00556021 0.00466557i
\(449\) −7.76357 13.4469i −0.366385 0.634598i 0.622612 0.782531i \(-0.286072\pi\)
−0.988997 + 0.147932i \(0.952738\pi\)
\(450\) 0 0
\(451\) −0.438957 + 0.760296i −0.0206697 + 0.0358010i
\(452\) −12.5752 + 4.57700i −0.591488 + 0.215284i
\(453\) 0 0
\(454\) 10.9999 9.22998i 0.516249 0.433184i
\(455\) 0.347270 + 0.126396i 0.0162803 + 0.00592554i
\(456\) 0 0
\(457\) −6.26933 + 35.5551i −0.293267 + 1.66320i 0.380897 + 0.924618i \(0.375615\pi\)
−0.674164 + 0.738582i \(0.735496\pi\)
\(458\) −4.05908 −0.189669
\(459\) 0 0
\(460\) 23.7145 1.10569
\(461\) −1.72646 + 9.79122i −0.0804091 + 0.456023i 0.917844 + 0.396941i \(0.129928\pi\)
−0.998253 + 0.0590816i \(0.981183\pi\)
\(462\) 0 0
\(463\) 18.0852 + 6.58248i 0.840492 + 0.305914i 0.726158 0.687528i \(-0.241304\pi\)
0.114334 + 0.993442i \(0.463527\pi\)
\(464\) −0.572961 + 0.480772i −0.0265991 + 0.0223193i
\(465\) 0 0
\(466\) −15.9548 + 5.80707i −0.739091 + 0.269007i
\(467\) 15.7918 27.3521i 0.730756 1.26571i −0.225805 0.974173i \(-0.572501\pi\)
0.956561 0.291534i \(-0.0941655\pi\)
\(468\) 0 0
\(469\) 0.572895 + 0.992284i 0.0264539 + 0.0458194i
\(470\) −1.47498 1.23766i −0.0680359 0.0570889i
\(471\) 0 0
\(472\) 1.26312 + 7.16349i 0.0581397 + 0.329727i
\(473\) −0.391508 2.22035i −0.0180015 0.102092i
\(474\) 0 0
\(475\) 33.3149 + 27.9545i 1.52859 + 1.28264i
\(476\) −0.427484 0.740423i −0.0195937 0.0339372i
\(477\) 0 0
\(478\) −10.6640 + 18.4707i −0.487762 + 0.844829i
\(479\) 10.6027 3.85905i 0.484448 0.176325i −0.0882381 0.996099i \(-0.528124\pi\)
0.572686 + 0.819775i \(0.305901\pi\)
\(480\) 0 0
\(481\) 1.70626 1.43172i 0.0777988 0.0652809i
\(482\) −10.1057 3.67817i −0.460301 0.167536i
\(483\) 0 0
\(484\) −1.90166 + 10.7848i −0.0864390 + 0.490220i
\(485\) 22.8849 1.03915
\(486\) 0 0
\(487\) −29.3219 −1.32870 −0.664352 0.747420i \(-0.731292\pi\)
−0.664352 + 0.747420i \(0.731292\pi\)
\(488\) −0.585154 + 3.31857i −0.0264887 + 0.150225i
\(489\) 0 0
\(490\) −26.5341 9.65761i −1.19869 0.436287i
\(491\) 7.76464 6.51531i 0.350413 0.294032i −0.450543 0.892755i \(-0.648769\pi\)
0.800956 + 0.598723i \(0.204325\pi\)
\(492\) 0 0
\(493\) −3.91138 + 1.42363i −0.176160 + 0.0641169i
\(494\) 1.13539 1.96655i 0.0510836 0.0884794i
\(495\) 0 0
\(496\) −2.54180 4.40252i −0.114130 0.197679i
\(497\) 0.336324 + 0.282209i 0.0150862 + 0.0126588i
\(498\) 0 0
\(499\) 3.87086 + 21.9527i 0.173284 + 0.982740i 0.940106 + 0.340881i \(0.110725\pi\)
−0.766823 + 0.641859i \(0.778164\pi\)
\(500\) 4.48571 + 25.4398i 0.200607 + 1.13770i
\(501\) 0 0
\(502\) 3.19918 + 2.68443i 0.142786 + 0.119812i
\(503\) −7.31535 12.6706i −0.326175 0.564952i 0.655574 0.755131i \(-0.272427\pi\)
−0.981750 + 0.190179i \(0.939093\pi\)
\(504\) 0 0
\(505\) 31.9743 55.3811i 1.42284 2.46443i
\(506\) −1.21615 + 0.442643i −0.0540646 + 0.0196779i
\(507\) 0 0
\(508\) −14.2721 + 11.9757i −0.633222 + 0.531336i
\(509\) 6.70321 + 2.43977i 0.297115 + 0.108141i 0.486276 0.873805i \(-0.338355\pi\)
−0.189162 + 0.981946i \(0.560577\pi\)
\(510\) 0 0
\(511\) 0.0340898 0.193333i 0.00150804 0.00855254i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 16.3432 0.720868
\(515\) 7.51818 42.6377i 0.331291 1.87884i
\(516\) 0 0
\(517\) 0.0987433 + 0.0359396i 0.00434273 + 0.00158062i
\(518\) 0.441065 0.370098i 0.0193793 0.0162612i
\(519\) 0 0
\(520\) 2.26043 0.822730i 0.0991265 0.0360791i
\(521\) −4.12053 + 7.13696i −0.180524 + 0.312676i −0.942059 0.335447i \(-0.891113\pi\)
0.761535 + 0.648123i \(0.224446\pi\)
\(522\) 0 0
\(523\) 11.2705 + 19.5211i 0.492826 + 0.853599i 0.999966 0.00826425i \(-0.00263062\pi\)
−0.507140 + 0.861864i \(0.669297\pi\)
\(524\) 5.26078 + 4.41432i 0.229818 + 0.192840i
\(525\) 0 0
\(526\) −0.465609 2.64060i −0.0203015 0.115136i
\(527\) −4.91264 27.8610i −0.213998 1.21364i
\(528\) 0 0
\(529\) 8.67807 + 7.28176i 0.377307 + 0.316598i
\(530\) −6.67747 11.5657i −0.290051 0.502383i
\(531\) 0 0
\(532\) 0.293496 0.508350i 0.0127247 0.0220398i
\(533\) 2.21963 0.807881i 0.0961430 0.0349932i
\(534\) 0 0
\(535\) −5.74337 + 4.81926i −0.248308 + 0.208355i
\(536\) 7.00834 + 2.55083i 0.302714 + 0.110179i
\(537\) 0 0
\(538\) 3.88120 22.0114i 0.167330 0.948977i
\(539\) 1.54101 0.0663762
\(540\) 0 0
\(541\) −31.4683 −1.35293 −0.676464 0.736476i \(-0.736488\pi\)
−0.676464 + 0.736476i \(0.736488\pi\)
\(542\) −4.42479 + 25.0942i −0.190061 + 1.07789i
\(543\) 0 0
\(544\) −5.22949 1.90338i −0.224212 0.0816066i
\(545\) −45.1115 + 37.8531i −1.93237 + 1.62145i
\(546\) 0 0
\(547\) −28.3635 + 10.3235i −1.21274 + 0.441400i −0.867652 0.497171i \(-0.834372\pi\)
−0.345085 + 0.938571i \(0.612150\pi\)
\(548\) 7.49271 12.9777i 0.320073 0.554382i
\(549\) 0 0
\(550\) −1.25711 2.17738i −0.0536034 0.0928439i
\(551\) −2.18918 1.83694i −0.0932623 0.0782563i
\(552\) 0 0
\(553\) 0.0882249 + 0.500348i 0.00375170 + 0.0212770i
\(554\) 0.445758 + 2.52802i 0.0189385 + 0.107405i
\(555\) 0 0
\(556\) 13.8675 + 11.6362i 0.588113 + 0.493486i
\(557\) 16.4210 + 28.4420i 0.695779 + 1.20512i 0.969917 + 0.243434i \(0.0782741\pi\)
−0.274138 + 0.961690i \(0.588393\pi\)
\(558\) 0 0
\(559\) −3.03308 + 5.25345i −0.128286 + 0.222197i
\(560\) 0.584317 0.212674i 0.0246919 0.00898712i
\(561\) 0 0
\(562\) 16.2374 13.6248i 0.684933 0.574727i
\(563\) 17.5885 + 6.40168i 0.741266 + 0.269799i 0.684926 0.728613i \(-0.259835\pi\)
0.0563401 + 0.998412i \(0.482057\pi\)
\(564\) 0 0
\(565\) 9.40560 53.3418i 0.395697 2.24411i
\(566\) 19.6332 0.825246
\(567\) 0 0
\(568\) 2.85777 0.119910
\(569\) 1.38771 7.87008i 0.0581757 0.329931i −0.941805 0.336160i \(-0.890872\pi\)
0.999981 + 0.00622922i \(0.00198284\pi\)
\(570\) 0 0
\(571\) 26.7013 + 9.71847i 1.11741 + 0.406705i 0.833708 0.552206i \(-0.186214\pi\)
0.283706 + 0.958911i \(0.408436\pi\)
\(572\) −0.100565 + 0.0843843i −0.00420485 + 0.00352828i
\(573\) 0 0
\(574\) 0.573771 0.208836i 0.0239488 0.00871663i
\(575\) −33.3446 + 57.7545i −1.39057 + 2.40853i
\(576\) 0 0
\(577\) −23.5780 40.8383i −0.981564 1.70012i −0.656307 0.754494i \(-0.727883\pi\)
−0.325257 0.945626i \(-0.605451\pi\)
\(578\) −10.7019 8.97999i −0.445142 0.373518i
\(579\) 0 0
\(580\) −0.525688 2.98133i −0.0218280 0.123793i
\(581\) −0.220655 1.25139i −0.00915429 0.0519166i
\(582\) 0 0
\(583\) 0.558322 + 0.468487i 0.0231233 + 0.0194028i
\(584\) −0.638922 1.10665i −0.0264388 0.0457933i
\(585\) 0 0
\(586\) −10.7380 + 18.5988i −0.443582 + 0.768307i
\(587\) −16.5971 + 6.04086i −0.685036 + 0.249333i −0.661008 0.750378i \(-0.729871\pi\)
−0.0240279 + 0.999711i \(0.507649\pi\)
\(588\) 0 0
\(589\) 14.8793 12.4852i 0.613090 0.514443i
\(590\) −27.6660 10.0696i −1.13899 0.414559i
\(591\) 0 0
\(592\) 0.650793 3.69083i 0.0267474 0.151692i
\(593\) −4.89941 −0.201195 −0.100597 0.994927i \(-0.532075\pi\)
−0.100597 + 0.994927i \(0.532075\pi\)
\(594\) 0 0
\(595\) 3.46048 0.141866
\(596\) 2.60884 14.7955i 0.106862 0.606046i
\(597\) 0 0
\(598\) 3.27214 + 1.19096i 0.133808 + 0.0487020i
\(599\) −13.8351 + 11.6090i −0.565288 + 0.474333i −0.880078 0.474828i \(-0.842510\pi\)
0.314791 + 0.949161i \(0.398066\pi\)
\(600\) 0 0
\(601\) −3.04117 + 1.10690i −0.124052 + 0.0451513i −0.403300 0.915068i \(-0.632137\pi\)
0.279248 + 0.960219i \(0.409915\pi\)
\(602\) −0.784045 + 1.35801i −0.0319553 + 0.0553482i
\(603\) 0 0
\(604\) 2.82136 + 4.88675i 0.114800 + 0.198839i
\(605\) −33.9549 28.4916i −1.38046 1.15835i
\(606\) 0 0
\(607\) 4.71790 + 26.7566i 0.191494 + 1.08602i 0.917324 + 0.398141i \(0.130345\pi\)
−0.725830 + 0.687874i \(0.758544\pi\)
\(608\) −0.663478 3.76277i −0.0269076 0.152601i
\(609\) 0 0
\(610\) −10.4482 8.76706i −0.423034 0.354968i
\(611\) −0.141363 0.244848i −0.00571893 0.00990547i
\(612\) 0 0
\(613\) −13.6622 + 23.6636i −0.551810 + 0.955763i 0.446334 + 0.894866i \(0.352729\pi\)
−0.998144 + 0.0608964i \(0.980604\pi\)
\(614\) 5.31182 1.93335i 0.214368 0.0780235i
\(615\) 0 0
\(616\) −0.0259959 + 0.0218132i −0.00104741 + 0.000878878i
\(617\) 25.0923 + 9.13284i 1.01018 + 0.367674i 0.793501 0.608569i \(-0.208256\pi\)
0.216676 + 0.976244i \(0.430478\pi\)
\(618\) 0 0
\(619\) 6.92886 39.2955i 0.278494 1.57942i −0.449145 0.893459i \(-0.648271\pi\)
0.727639 0.685960i \(-0.240618\pi\)
\(620\) 20.5759 0.826347
\(621\) 0 0
\(622\) 9.30470 0.373085
\(623\) −0.132258 + 0.750073i −0.00529881 + 0.0300510i
\(624\) 0 0
\(625\) −44.7712 16.2954i −1.79085 0.651816i
\(626\) 2.05976 1.72835i 0.0823247 0.0690786i
\(627\) 0 0
\(628\) −6.80782 + 2.47784i −0.271661 + 0.0988767i
\(629\) 10.4284 18.0624i 0.415806 0.720197i
\(630\) 0 0
\(631\) 4.36875 + 7.56690i 0.173917 + 0.301234i 0.939786 0.341763i \(-0.111024\pi\)
−0.765869 + 0.642997i \(0.777691\pi\)
\(632\) 2.53337 + 2.12575i 0.100772 + 0.0845578i
\(633\) 0 0
\(634\) −4.85100 27.5114i −0.192658 1.09262i
\(635\) −13.0946 74.2629i −0.519642 2.94703i
\(636\) 0 0
\(637\) −3.17617 2.66512i −0.125845 0.105596i
\(638\) 0.0826070 + 0.143079i 0.00327044 + 0.00566457i
\(639\) 0 0
\(640\) 2.02375 3.50524i 0.0799958 0.138557i
\(641\) 17.0222 6.19556i 0.672335 0.244710i 0.0167821 0.999859i \(-0.494658\pi\)
0.655553 + 0.755149i \(0.272436\pi\)
\(642\) 0 0
\(643\) −24.5762 + 20.6219i −0.969191 + 0.813247i −0.982424 0.186665i \(-0.940232\pi\)
0.0132331 + 0.999912i \(0.495788\pi\)
\(644\) 0.845841 + 0.307861i 0.0333308 + 0.0121314i
\(645\) 0 0
\(646\) 3.69233 20.9402i 0.145273 0.823882i
\(647\) 11.1390 0.437918 0.218959 0.975734i \(-0.429734\pi\)
0.218959 + 0.975734i \(0.429734\pi\)
\(648\) 0 0
\(649\) 1.60675 0.0630705
\(650\) −1.17467 + 6.66191i −0.0460745 + 0.261302i
\(651\) 0 0
\(652\) −13.2570 4.82517i −0.519186 0.188968i
\(653\) −1.15447 + 0.968718i −0.0451780 + 0.0379089i −0.665097 0.746757i \(-0.731610\pi\)
0.619919 + 0.784666i \(0.287165\pi\)
\(654\) 0 0
\(655\) −26.1197 + 9.50681i −1.02058 + 0.371462i
\(656\) 1.98722 3.44197i 0.0775881 0.134386i
\(657\) 0 0
\(658\) −0.0365420 0.0632926i −0.00142456 0.00246740i
\(659\) 6.06158 + 5.08627i 0.236126 + 0.198133i 0.753171 0.657825i \(-0.228523\pi\)
−0.517045 + 0.855958i \(0.672968\pi\)
\(660\) 0 0
\(661\) −5.26138 29.8388i −0.204644 1.16059i −0.897999 0.439998i \(-0.854979\pi\)
0.693355 0.720597i \(-0.256132\pi\)
\(662\) −0.146752 0.832272i −0.00570368 0.0323472i
\(663\) 0 0
\(664\) −6.33608 5.31660i −0.245888 0.206324i
\(665\) 1.18793 + 2.05755i 0.0460658 + 0.0797883i
\(666\) 0 0
\(667\) 2.19113 3.79515i 0.0848409 0.146949i
\(668\) −12.9892 + 4.72767i −0.502565 + 0.182919i
\(669\) 0 0
\(670\) −23.1244 + 19.4037i −0.893373 + 0.749629i
\(671\) 0.699457 + 0.254581i 0.0270022 + 0.00982801i
\(672\) 0 0
\(673\) −3.85949 + 21.8883i −0.148772 + 0.843731i 0.815488 + 0.578774i \(0.196469\pi\)
−0.964260 + 0.264956i \(0.914642\pi\)
\(674\) −29.3172 −1.12926
\(675\) 0 0
\(676\) −12.6468 −0.486415
\(677\) −7.00672 + 39.7371i −0.269290 + 1.52722i 0.487245 + 0.873266i \(0.338002\pi\)
−0.756535 + 0.653954i \(0.773109\pi\)
\(678\) 0 0
\(679\) 0.816250 + 0.297091i 0.0313248 + 0.0114013i
\(680\) 17.2550 14.4786i 0.661698 0.555230i
\(681\) 0 0
\(682\) −1.05519 + 0.384059i −0.0404055 + 0.0147064i
\(683\) −12.5504 + 21.7380i −0.480229 + 0.831780i −0.999743 0.0226815i \(-0.992780\pi\)
0.519514 + 0.854462i \(0.326113\pi\)
\(684\) 0 0
\(685\) 30.3267 + 52.5274i 1.15872 + 2.00697i
\(686\) −1.64485 1.38019i −0.0628005 0.0526959i
\(687\) 0 0
\(688\) 1.77241 + 10.0519i 0.0675726 + 0.383223i
\(689\) −0.340521 1.93119i −0.0129728 0.0735725i
\(690\) 0 0
\(691\) −2.21137 1.85556i −0.0841245 0.0705889i 0.599756 0.800183i \(-0.295264\pi\)
−0.683880 + 0.729594i \(0.739709\pi\)
\(692\) −1.96463 3.40284i −0.0746840 0.129356i
\(693\) 0 0
\(694\) 10.1001 17.4939i 0.383395 0.664059i
\(695\) −68.8521 + 25.0601i −2.61171 + 0.950584i
\(696\) 0 0
\(697\) 16.9435 14.2173i 0.641782 0.538519i
\(698\) 9.02990 + 3.28661i 0.341787 + 0.124400i
\(699\) 0 0
\(700\) −0.303651 + 1.72209i −0.0114769 + 0.0650889i
\(701\) 24.5608 0.927648 0.463824 0.885927i \(-0.346477\pi\)
0.463824 + 0.885927i \(0.346477\pi\)
\(702\) 0 0
\(703\) 14.3195 0.540072
\(704\) −0.0383571 + 0.217534i −0.00144564 + 0.00819862i
\(705\) 0 0
\(706\) 9.23396 + 3.36089i 0.347525 + 0.126489i
\(707\) 1.85941 1.56023i 0.0699302 0.0586784i
\(708\) 0 0
\(709\) 20.9978 7.64257i 0.788588 0.287023i 0.0838392 0.996479i \(-0.473282\pi\)
0.704749 + 0.709457i \(0.251060\pi\)
\(710\) −5.78342 + 10.0172i −0.217048 + 0.375938i
\(711\) 0 0
\(712\) 2.47882 + 4.29345i 0.0928979 + 0.160904i
\(713\) 22.8167 + 19.1454i 0.854490 + 0.717003i
\(714\) 0 0
\(715\) −0.0922680 0.523278i −0.00345063 0.0195695i
\(716\) −0.493894 2.80101i −0.0184577 0.104679i
\(717\) 0 0
\(718\) 9.10779 + 7.64235i 0.339900 + 0.285210i
\(719\) −18.3086 31.7114i −0.682796 1.18264i −0.974124 0.226014i \(-0.927430\pi\)
0.291328 0.956623i \(-0.405903\pi\)
\(720\) 0 0
\(721\) 0.821678 1.42319i 0.0306009 0.0530023i
\(722\) −4.13591 + 1.50535i −0.153923 + 0.0560232i
\(723\) 0 0
\(724\) 9.90149 8.30834i 0.367986 0.308777i
\(725\) 7.99992 + 2.91173i 0.297110 + 0.108139i
\(726\) 0 0
\(727\) 2.38849 13.5458i 0.0885842 0.502386i −0.907941 0.419097i \(-0.862347\pi\)
0.996525 0.0832885i \(-0.0265423\pi\)
\(728\) 0.0913051 0.00338399
\(729\) 0 0
\(730\) 5.17208 0.191427
\(731\) −9.86367 + 55.9396i −0.364821 + 2.06900i
\(732\) 0 0
\(733\) −30.6892 11.1699i −1.13353 0.412571i −0.293957 0.955819i \(-0.594972\pi\)
−0.839573 + 0.543247i \(0.817195\pi\)
\(734\) 27.7867 23.3158i 1.02563 0.860603i
\(735\) 0 0
\(736\) 5.50570 2.00391i 0.202943 0.0738652i
\(737\) 0.823710 1.42671i 0.0303418 0.0525535i
\(738\) 0 0
\(739\) 14.0540 + 24.3423i 0.516986 + 0.895445i 0.999805 + 0.0197257i \(0.00627929\pi\)
−0.482820 + 0.875720i \(0.660387\pi\)
\(740\) 11.6202 + 9.75050i 0.427167 + 0.358436i
\(741\) 0 0
\(742\) −0.0880241 0.499209i −0.00323147 0.0183266i
\(743\) 2.01338 + 11.4184i 0.0738636 + 0.418901i 0.999209 + 0.0397752i \(0.0126642\pi\)
−0.925345 + 0.379126i \(0.876225\pi\)
\(744\) 0 0
\(745\) 46.5820 + 39.0870i 1.70663 + 1.43204i
\(746\) 7.07457 + 12.2535i 0.259018 + 0.448633i
\(747\) 0 0
\(748\) −0.614637 + 1.06458i −0.0224734 + 0.0389250i
\(749\) −0.267417 + 0.0973316i −0.00977119 + 0.00355642i
\(750\) 0 0
\(751\) −31.0515 + 26.0553i −1.13309 + 0.950772i −0.999191 0.0402230i \(-0.987193\pi\)
−0.133896 + 0.990995i \(0.542749\pi\)
\(752\) −0.447025 0.162704i −0.0163013 0.00593320i
\(753\) 0 0
\(754\) 0.0771899 0.437766i 0.00281109 0.0159425i
\(755\) −22.8390 −0.831194
\(756\) 0 0
\(757\) 51.1841 1.86032 0.930158 0.367159i \(-0.119669\pi\)
0.930158 + 0.367159i \(0.119669\pi\)
\(758\) 5.12674 29.0752i 0.186211 1.05606i
\(759\) 0 0
\(760\) 14.5321 + 5.28926i 0.527136 + 0.191862i
\(761\) −3.01606 + 2.53078i −0.109332 + 0.0917406i −0.695815 0.718221i \(-0.744957\pi\)
0.586483 + 0.809962i \(0.300512\pi\)
\(762\) 0 0
\(763\) −2.10043 + 0.764495i −0.0760408 + 0.0276766i
\(764\) −10.0714 + 17.4441i −0.364369 + 0.631105i
\(765\) 0 0
\(766\) −12.3625 21.4125i −0.446675 0.773664i
\(767\) −3.31166 2.77882i −0.119577 0.100337i
\(768\) 0 0
\(769\) −7.45807 42.2968i −0.268945 1.52526i −0.757562 0.652763i \(-0.773610\pi\)
0.488617 0.872498i \(-0.337501\pi\)
\(770\) −0.0238511 0.135266i −0.000859534 0.00487466i
\(771\) 0 0
\(772\) 7.36678 + 6.18146i 0.265136 + 0.222476i
\(773\) −10.6680 18.4775i −0.383702 0.664591i 0.607886 0.794024i \(-0.292018\pi\)
−0.991588 + 0.129433i \(0.958684\pi\)
\(774\) 0 0
\(775\) −28.9314 + 50.1107i −1.03925 + 1.80003i
\(776\) 5.31309 1.93381i 0.190729 0.0694196i
\(777\) 0 0
\(778\) 11.1425 9.34969i 0.399479 0.335203i
\(779\) 14.2