Properties

Label 189.2.f.a.127.2
Level $189$
Weight $2$
Character 189.127
Analytic conductor $1.509$
Analytic rank $0$
Dimension $6$
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] = [189,2,Mod(64,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.f (of order \(3\), degree \(2\), 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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 127.2
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 189.127
Dual form 189.2.f.a.64.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.119562 + 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(0.590972 + 1.02359i) q^{5} +(0.500000 - 0.866025i) q^{7} -0.942820 q^{8} +O(q^{10})\) \(q+(-0.119562 + 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(0.590972 + 1.02359i) q^{5} +(0.500000 - 0.866025i) q^{7} -0.942820 q^{8} -0.282630 q^{10} +(-1.85185 + 3.20750i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.119562 + 0.207087i) q^{14} +(-1.83009 + 3.16982i) q^{16} +6.94282 q^{17} +1.94282 q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(-2.80150 - 4.85235i) q^{23} +(1.80150 - 3.12030i) q^{25} +0.239123 q^{26} +1.94282 q^{28} +(0.119562 - 0.207087i) q^{29} +(-0.830095 - 1.43777i) q^{31} +(-1.38044 - 2.39099i) q^{32} +(-0.830095 + 1.43777i) q^{34} +1.18194 q^{35} -9.54583 q^{37} +(-0.232287 + 0.402332i) q^{38} +(-0.557180 - 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} -7.19562 q^{44} +1.33981 q^{46} +(2.91423 - 5.04759i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.430782 + 0.746136i) q^{50} +(0.971410 - 1.68253i) q^{52} +11.6030 q^{53} -4.37756 q^{55} +(-0.471410 + 0.816506i) q^{56} +(0.0285900 + 0.0495193i) q^{58} +(1.30150 + 2.25427i) q^{59} +(3.80150 - 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(0.590972 - 1.02359i) q^{65} +(-1.75404 - 3.03809i) q^{67} +(6.74433 + 11.6815i) q^{68} +(-0.141315 + 0.244765i) q^{70} -8.60301 q^{71} +15.1488 q^{73} +(1.14132 - 1.97682i) q^{74} +(1.88727 + 3.26886i) q^{76} +(1.85185 + 3.20750i) q^{77} +(-3.68878 + 6.38915i) q^{79} -4.32614 q^{80} +2.43474 q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(-0.266078 - 0.460861i) q^{86} +(1.74596 - 3.02409i) q^{88} -2.74720 q^{89} -1.00000 q^{91} +(5.44282 - 9.42724i) q^{92} +(0.696860 + 1.20700i) q^{94} +(1.14815 + 1.98866i) q^{95} +(-3.58414 + 6.20790i) q^{97} +0.239123 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} - 10 q^{35} - 6 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} - 9 q^{47} - 3 q^{49} + 10 q^{50} - 3 q^{52} + 36 q^{53} - 12 q^{55} + 6 q^{56} + 9 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} + 6 q^{68} - 18 q^{71} + 6 q^{73} + 6 q^{74} + 21 q^{76} + 2 q^{77} - 15 q^{79} - 22 q^{80} + 18 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 4 q^{89} - 6 q^{91} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.119562 + 0.207087i −0.0845428 + 0.146433i −0.905196 0.424994i \(-0.860276\pi\)
0.820653 + 0.571426i \(0.193610\pi\)
\(3\) 0 0
\(4\) 0.971410 + 1.68253i 0.485705 + 0.841266i
\(5\) 0.590972 + 1.02359i 0.264291 + 0.457765i 0.967378 0.253339i \(-0.0815289\pi\)
−0.703087 + 0.711104i \(0.748196\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −0.942820 −0.333337
\(9\) 0 0
\(10\) −0.282630 −0.0893755
\(11\) −1.85185 + 3.20750i −0.558353 + 0.967096i 0.439281 + 0.898350i \(0.355233\pi\)
−0.997634 + 0.0687465i \(0.978100\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0.119562 + 0.207087i 0.0319542 + 0.0553463i
\(15\) 0 0
\(16\) −1.83009 + 3.16982i −0.457524 + 0.792454i
\(17\) 6.94282 1.68388 0.841941 0.539570i \(-0.181413\pi\)
0.841941 + 0.539570i \(0.181413\pi\)
\(18\) 0 0
\(19\) 1.94282 0.445713 0.222857 0.974851i \(-0.428462\pi\)
0.222857 + 0.974851i \(0.428462\pi\)
\(20\) −1.14815 + 1.98866i −0.256735 + 0.444677i
\(21\) 0 0
\(22\) −0.442820 0.766987i −0.0944096 0.163522i
\(23\) −2.80150 4.85235i −0.584154 1.01178i −0.994980 0.100071i \(-0.968093\pi\)
0.410826 0.911714i \(-0.365240\pi\)
\(24\) 0 0
\(25\) 1.80150 3.12030i 0.360301 0.624060i
\(26\) 0.239123 0.0468959
\(27\) 0 0
\(28\) 1.94282 0.367158
\(29\) 0.119562 0.207087i 0.0222020 0.0384551i −0.854711 0.519104i \(-0.826266\pi\)
0.876913 + 0.480649i \(0.159599\pi\)
\(30\) 0 0
\(31\) −0.830095 1.43777i −0.149089 0.258231i 0.781802 0.623527i \(-0.214301\pi\)
−0.930891 + 0.365297i \(0.880968\pi\)
\(32\) −1.38044 2.39099i −0.244029 0.422671i
\(33\) 0 0
\(34\) −0.830095 + 1.43777i −0.142360 + 0.246575i
\(35\) 1.18194 0.199785
\(36\) 0 0
\(37\) −9.54583 −1.56932 −0.784662 0.619923i \(-0.787164\pi\)
−0.784662 + 0.619923i \(0.787164\pi\)
\(38\) −0.232287 + 0.402332i −0.0376819 + 0.0652669i
\(39\) 0 0
\(40\) −0.557180 0.965064i −0.0880979 0.152590i
\(41\) −5.09097 8.81782i −0.795076 1.37711i −0.922791 0.385301i \(-0.874097\pi\)
0.127715 0.991811i \(-0.459236\pi\)
\(42\) 0 0
\(43\) −1.11273 + 1.92730i −0.169689 + 0.293910i −0.938311 0.345794i \(-0.887610\pi\)
0.768622 + 0.639704i \(0.220943\pi\)
\(44\) −7.19562 −1.08478
\(45\) 0 0
\(46\) 1.33981 0.197544
\(47\) 2.91423 5.04759i 0.425084 0.736267i −0.571344 0.820711i \(-0.693578\pi\)
0.996428 + 0.0844432i \(0.0269112\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0.430782 + 0.746136i 0.0609217 + 0.105520i
\(51\) 0 0
\(52\) 0.971410 1.68253i 0.134710 0.233325i
\(53\) 11.6030 1.59380 0.796898 0.604114i \(-0.206473\pi\)
0.796898 + 0.604114i \(0.206473\pi\)
\(54\) 0 0
\(55\) −4.37756 −0.590270
\(56\) −0.471410 + 0.816506i −0.0629948 + 0.109110i
\(57\) 0 0
\(58\) 0.0285900 + 0.0495193i 0.00375405 + 0.00650220i
\(59\) 1.30150 + 2.25427i 0.169442 + 0.293481i 0.938224 0.346029i \(-0.112470\pi\)
−0.768782 + 0.639511i \(0.779137\pi\)
\(60\) 0 0
\(61\) 3.80150 6.58440i 0.486733 0.843046i −0.513151 0.858298i \(-0.671522\pi\)
0.999884 + 0.0152524i \(0.00485519\pi\)
\(62\) 0.396990 0.0504178
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) 0.590972 1.02359i 0.0733010 0.126961i
\(66\) 0 0
\(67\) −1.75404 3.03809i −0.214290 0.371161i 0.738763 0.673966i \(-0.235410\pi\)
−0.953053 + 0.302804i \(0.902077\pi\)
\(68\) 6.74433 + 11.6815i 0.817870 + 1.41659i
\(69\) 0 0
\(70\) −0.141315 + 0.244765i −0.0168904 + 0.0292550i
\(71\) −8.60301 −1.02099 −0.510495 0.859881i \(-0.670538\pi\)
−0.510495 + 0.859881i \(0.670538\pi\)
\(72\) 0 0
\(73\) 15.1488 1.77304 0.886519 0.462693i \(-0.153117\pi\)
0.886519 + 0.462693i \(0.153117\pi\)
\(74\) 1.14132 1.97682i 0.132675 0.229800i
\(75\) 0 0
\(76\) 1.88727 + 3.26886i 0.216485 + 0.374963i
\(77\) 1.85185 + 3.20750i 0.211038 + 0.365528i
\(78\) 0 0
\(79\) −3.68878 + 6.38915i −0.415020 + 0.718836i −0.995431 0.0954881i \(-0.969559\pi\)
0.580410 + 0.814324i \(0.302892\pi\)
\(80\) −4.32614 −0.483677
\(81\) 0 0
\(82\) 2.43474 0.268872
\(83\) −3.47141 + 6.01266i −0.381037 + 0.659975i −0.991211 0.132292i \(-0.957766\pi\)
0.610174 + 0.792267i \(0.291100\pi\)
\(84\) 0 0
\(85\) 4.10301 + 7.10662i 0.445034 + 0.770821i
\(86\) −0.266078 0.460861i −0.0286920 0.0496960i
\(87\) 0 0
\(88\) 1.74596 3.02409i 0.186120 0.322369i
\(89\) −2.74720 −0.291203 −0.145602 0.989343i \(-0.546512\pi\)
−0.145602 + 0.989343i \(0.546512\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 5.44282 9.42724i 0.567453 0.982858i
\(93\) 0 0
\(94\) 0.696860 + 1.20700i 0.0718756 + 0.124492i
\(95\) 1.14815 + 1.98866i 0.117798 + 0.204032i
\(96\) 0 0
\(97\) −3.58414 + 6.20790i −0.363914 + 0.630317i −0.988601 0.150558i \(-0.951893\pi\)
0.624687 + 0.780875i \(0.285226\pi\)
\(98\) 0.239123 0.0241551
\(99\) 0 0
\(100\) 7.00000 0.700000
\(101\) −6.39248 + 11.0721i −0.636075 + 1.10171i 0.350211 + 0.936671i \(0.386110\pi\)
−0.986286 + 0.165044i \(0.947223\pi\)
\(102\) 0 0
\(103\) 2.19850 + 3.80791i 0.216624 + 0.375204i 0.953774 0.300526i \(-0.0971621\pi\)
−0.737150 + 0.675730i \(0.763829\pi\)
\(104\) 0.471410 + 0.816506i 0.0462256 + 0.0800650i
\(105\) 0 0
\(106\) −1.38727 + 2.40283i −0.134744 + 0.233384i
\(107\) −13.7278 −1.32711 −0.663557 0.748126i \(-0.730954\pi\)
−0.663557 + 0.748126i \(0.730954\pi\)
\(108\) 0 0
\(109\) 1.26320 0.120993 0.0604963 0.998168i \(-0.480732\pi\)
0.0604963 + 0.998168i \(0.480732\pi\)
\(110\) 0.523388 0.906535i 0.0499031 0.0864347i
\(111\) 0 0
\(112\) 1.83009 + 3.16982i 0.172928 + 0.299520i
\(113\) 6.08126 + 10.5330i 0.572076 + 0.990866i 0.996353 + 0.0853326i \(0.0271953\pi\)
−0.424276 + 0.905533i \(0.639471\pi\)
\(114\) 0 0
\(115\) 3.31122 5.73520i 0.308773 0.534810i
\(116\) 0.464574 0.0431346
\(117\) 0 0
\(118\) −0.622440 −0.0573003
\(119\) 3.47141 6.01266i 0.318224 0.551180i
\(120\) 0 0
\(121\) −1.35868 2.35331i −0.123517 0.213937i
\(122\) 0.909028 + 1.57448i 0.0822996 + 0.142547i
\(123\) 0 0
\(124\) 1.61273 2.79332i 0.144827 0.250848i
\(125\) 10.1683 0.909478
\(126\) 0 0
\(127\) 1.33981 0.118889 0.0594445 0.998232i \(-0.481067\pi\)
0.0594445 + 0.998232i \(0.481067\pi\)
\(128\) 3.55718 6.16122i 0.314413 0.544580i
\(129\) 0 0
\(130\) 0.141315 + 0.244765i 0.0123942 + 0.0214673i
\(131\) −2.48345 4.30146i −0.216980 0.375820i 0.736903 0.675998i \(-0.236287\pi\)
−0.953883 + 0.300178i \(0.902954\pi\)
\(132\) 0 0
\(133\) 0.971410 1.68253i 0.0842319 0.145894i
\(134\) 0.838864 0.0724668
\(135\) 0 0
\(136\) −6.54583 −0.561300
\(137\) −2.16991 + 3.75839i −0.185387 + 0.321101i −0.943707 0.330782i \(-0.892687\pi\)
0.758320 + 0.651883i \(0.226021\pi\)
\(138\) 0 0
\(139\) −1.97141 3.41458i −0.167213 0.289621i 0.770226 0.637771i \(-0.220143\pi\)
−0.937439 + 0.348150i \(0.886810\pi\)
\(140\) 1.14815 + 1.98866i 0.0970365 + 0.168072i
\(141\) 0 0
\(142\) 1.02859 1.78157i 0.0863174 0.149506i
\(143\) 3.70370 0.309719
\(144\) 0 0
\(145\) 0.282630 0.0234712
\(146\) −1.81122 + 3.13713i −0.149898 + 0.259630i
\(147\) 0 0
\(148\) −9.27292 16.0612i −0.762229 1.32022i
\(149\) 5.55555 + 9.62249i 0.455128 + 0.788305i 0.998696 0.0510606i \(-0.0162602\pi\)
−0.543568 + 0.839365i \(0.682927\pi\)
\(150\) 0 0
\(151\) −6.96169 + 12.0580i −0.566535 + 0.981267i 0.430370 + 0.902652i \(0.358383\pi\)
−0.996905 + 0.0786145i \(0.974950\pi\)
\(152\) −1.83173 −0.148573
\(153\) 0 0
\(154\) −0.885640 −0.0713669
\(155\) 0.981125 1.69936i 0.0788059 0.136496i
\(156\) 0 0
\(157\) −0.0285900 0.0495193i −0.00228173 0.00395207i 0.864882 0.501975i \(-0.167393\pi\)
−0.867164 + 0.498023i \(0.834060\pi\)
\(158\) −0.882073 1.52780i −0.0701740 0.121545i
\(159\) 0 0
\(160\) 1.63160 2.82601i 0.128989 0.223416i
\(161\) −5.60301 −0.441579
\(162\) 0 0
\(163\) −1.50808 −0.118122 −0.0590610 0.998254i \(-0.518811\pi\)
−0.0590610 + 0.998254i \(0.518811\pi\)
\(164\) 9.89084 17.1314i 0.772345 1.33774i
\(165\) 0 0
\(166\) −0.830095 1.43777i −0.0644279 0.111592i
\(167\) −7.34213 12.7169i −0.568151 0.984067i −0.996749 0.0805714i \(-0.974325\pi\)
0.428598 0.903496i \(-0.359008\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) −1.96225 −0.150498
\(171\) 0 0
\(172\) −4.32365 −0.329675
\(173\) 0.126398 0.218928i 0.00960987 0.0166448i −0.861180 0.508299i \(-0.830274\pi\)
0.870790 + 0.491655i \(0.163608\pi\)
\(174\) 0 0
\(175\) −1.80150 3.12030i −0.136181 0.235872i
\(176\) −6.77812 11.7400i −0.510920 0.884939i
\(177\) 0 0
\(178\) 0.328460 0.568910i 0.0246191 0.0426416i
\(179\) −14.1923 −1.06079 −0.530393 0.847752i \(-0.677956\pi\)
−0.530393 + 0.847752i \(0.677956\pi\)
\(180\) 0 0
\(181\) −1.43147 −0.106400 −0.0532002 0.998584i \(-0.516942\pi\)
−0.0532002 + 0.998584i \(0.516942\pi\)
\(182\) 0.119562 0.207087i 0.00886250 0.0153503i
\(183\) 0 0
\(184\) 2.64132 + 4.57489i 0.194720 + 0.337266i
\(185\) −5.64132 9.77104i −0.414758 0.718381i
\(186\) 0 0
\(187\) −12.8571 + 22.2691i −0.940201 + 1.62848i
\(188\) 11.3236 0.825862
\(189\) 0 0
\(190\) −0.549100 −0.0398359
\(191\) 7.53379 13.0489i 0.545126 0.944186i −0.453473 0.891270i \(-0.649815\pi\)
0.998599 0.0529159i \(-0.0168515\pi\)
\(192\) 0 0
\(193\) 3.92395 + 6.79647i 0.282452 + 0.489221i 0.971988 0.235030i \(-0.0755190\pi\)
−0.689536 + 0.724251i \(0.742186\pi\)
\(194\) −0.857050 1.48445i −0.0615326 0.106578i
\(195\) 0 0
\(196\) 0.971410 1.68253i 0.0693864 0.120181i
\(197\) −6.69002 −0.476644 −0.238322 0.971186i \(-0.576597\pi\)
−0.238322 + 0.971186i \(0.576597\pi\)
\(198\) 0 0
\(199\) −19.9396 −1.41348 −0.706739 0.707475i \(-0.749834\pi\)
−0.706739 + 0.707475i \(0.749834\pi\)
\(200\) −1.69850 + 2.94188i −0.120102 + 0.208022i
\(201\) 0 0
\(202\) −1.52859 2.64760i −0.107551 0.186284i
\(203\) −0.119562 0.207087i −0.00839158 0.0145346i
\(204\) 0 0
\(205\) 6.01724 10.4222i 0.420262 0.727916i
\(206\) −1.05142 −0.0732561
\(207\) 0 0
\(208\) 3.66019 0.253789
\(209\) −3.59781 + 6.23159i −0.248866 + 0.431048i
\(210\) 0 0
\(211\) 9.04583 + 15.6678i 0.622741 + 1.07862i 0.988973 + 0.148095i \(0.0473141\pi\)
−0.366233 + 0.930523i \(0.619353\pi\)
\(212\) 11.2713 + 19.5224i 0.774115 + 1.34081i
\(213\) 0 0
\(214\) 1.64132 2.84284i 0.112198 0.194333i
\(215\) −2.63036 −0.179389
\(216\) 0 0
\(217\) −1.66019 −0.112701
\(218\) −0.151030 + 0.261592i −0.0102291 + 0.0177172i
\(219\) 0 0
\(220\) −4.25241 7.36538i −0.286697 0.496574i
\(221\) −3.47141 6.01266i −0.233512 0.404455i
\(222\) 0 0
\(223\) 11.3285 19.6215i 0.758610 1.31395i −0.184950 0.982748i \(-0.559212\pi\)
0.943560 0.331203i \(-0.107454\pi\)
\(224\) −2.76088 −0.184469
\(225\) 0 0
\(226\) −2.90834 −0.193460
\(227\) −2.64132 + 4.57489i −0.175310 + 0.303646i −0.940269 0.340433i \(-0.889426\pi\)
0.764958 + 0.644080i \(0.222760\pi\)
\(228\) 0 0
\(229\) −9.66827 16.7459i −0.638897 1.10660i −0.985675 0.168655i \(-0.946058\pi\)
0.346778 0.937947i \(-0.387276\pi\)
\(230\) 0.791790 + 1.37142i 0.0522091 + 0.0904288i
\(231\) 0 0
\(232\) −0.112725 + 0.195246i −0.00740077 + 0.0128185i
\(233\) 16.9806 1.11243 0.556217 0.831037i \(-0.312252\pi\)
0.556217 + 0.831037i \(0.312252\pi\)
\(234\) 0 0
\(235\) 6.88891 0.449383
\(236\) −2.52859 + 4.37965i −0.164597 + 0.285091i
\(237\) 0 0
\(238\) 0.830095 + 1.43777i 0.0538071 + 0.0931966i
\(239\) 8.44282 + 14.6234i 0.546121 + 0.945909i 0.998535 + 0.0541011i \(0.0172293\pi\)
−0.452415 + 0.891808i \(0.649437\pi\)
\(240\) 0 0
\(241\) −13.5728 + 23.5088i −0.874300 + 1.51433i −0.0167933 + 0.999859i \(0.505346\pi\)
−0.857507 + 0.514473i \(0.827988\pi\)
\(242\) 0.649786 0.0417699
\(243\) 0 0
\(244\) 14.7713 0.945634
\(245\) 0.590972 1.02359i 0.0377558 0.0653950i
\(246\) 0 0
\(247\) −0.971410 1.68253i −0.0618093 0.107057i
\(248\) 0.782630 + 1.35556i 0.0496971 + 0.0860778i
\(249\) 0 0
\(250\) −1.21574 + 2.10571i −0.0768898 + 0.133177i
\(251\) 19.0780 1.20419 0.602096 0.798424i \(-0.294332\pi\)
0.602096 + 0.798424i \(0.294332\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) −0.160190 + 0.277457i −0.0100512 + 0.0174092i
\(255\) 0 0
\(256\) −5.80959 10.0625i −0.363099 0.628906i
\(257\) −7.42107 12.8537i −0.462913 0.801790i 0.536191 0.844097i \(-0.319863\pi\)
−0.999105 + 0.0423070i \(0.986529\pi\)
\(258\) 0 0
\(259\) −4.77292 + 8.26693i −0.296575 + 0.513682i
\(260\) 2.29630 0.142411
\(261\) 0 0
\(262\) 1.18770 0.0733764
\(263\) −3.87072 + 6.70429i −0.238679 + 0.413404i −0.960335 0.278847i \(-0.910048\pi\)
0.721656 + 0.692251i \(0.243381\pi\)
\(264\) 0 0
\(265\) 6.85705 + 11.8768i 0.421225 + 0.729584i
\(266\) 0.232287 + 0.402332i 0.0142424 + 0.0246686i
\(267\) 0 0
\(268\) 3.40778 5.90246i 0.208164 0.360550i
\(269\) 1.51135 0.0921486 0.0460743 0.998938i \(-0.485329\pi\)
0.0460743 + 0.998938i \(0.485329\pi\)
\(270\) 0 0
\(271\) −21.9806 −1.33522 −0.667612 0.744509i \(-0.732684\pi\)
−0.667612 + 0.744509i \(0.732684\pi\)
\(272\) −12.7060 + 22.0075i −0.770416 + 1.33440i
\(273\) 0 0
\(274\) −0.518875 0.898718i −0.0313464 0.0542935i
\(275\) 6.67223 + 11.5566i 0.402350 + 0.696892i
\(276\) 0 0
\(277\) 5.41423 9.37772i 0.325310 0.563453i −0.656265 0.754530i \(-0.727865\pi\)
0.981575 + 0.191077i \(0.0611982\pi\)
\(278\) 0.942820 0.0565466
\(279\) 0 0
\(280\) −1.11436 −0.0665957
\(281\) −8.43831 + 14.6156i −0.503387 + 0.871892i 0.496605 + 0.867977i \(0.334580\pi\)
−0.999992 + 0.00391559i \(0.998754\pi\)
\(282\) 0 0
\(283\) 7.65856 + 13.2650i 0.455254 + 0.788523i 0.998703 0.0509194i \(-0.0162152\pi\)
−0.543449 + 0.839442i \(0.682882\pi\)
\(284\) −8.35705 14.4748i −0.495900 0.858923i
\(285\) 0 0
\(286\) −0.442820 + 0.766987i −0.0261845 + 0.0453529i
\(287\) −10.1819 −0.601021
\(288\) 0 0
\(289\) 31.2028 1.83546
\(290\) −0.0337917 + 0.0585290i −0.00198432 + 0.00343694i
\(291\) 0 0
\(292\) 14.7157 + 25.4884i 0.861173 + 1.49160i
\(293\) −4.68482 8.11435i −0.273690 0.474045i 0.696114 0.717932i \(-0.254911\pi\)
−0.969804 + 0.243886i \(0.921578\pi\)
\(294\) 0 0
\(295\) −1.53831 + 2.66442i −0.0895636 + 0.155129i
\(296\) 9.00000 0.523114
\(297\) 0 0
\(298\) −2.65692 −0.153911
\(299\) −2.80150 + 4.85235i −0.162015 + 0.280619i
\(300\) 0 0
\(301\) 1.11273 + 1.92730i 0.0641364 + 0.111088i
\(302\) −1.66470 2.88335i −0.0957929 0.165918i
\(303\) 0 0
\(304\) −3.55555 + 6.15838i −0.203925 + 0.353208i
\(305\) 8.98633 0.514556
\(306\) 0 0
\(307\) 2.71410 0.154902 0.0774509 0.996996i \(-0.475322\pi\)
0.0774509 + 0.996996i \(0.475322\pi\)
\(308\) −3.59781 + 6.23159i −0.205004 + 0.355078i
\(309\) 0 0
\(310\) 0.234610 + 0.406356i 0.0133249 + 0.0230795i
\(311\) −6.99028 12.1075i −0.396383 0.686555i 0.596894 0.802320i \(-0.296401\pi\)
−0.993277 + 0.115765i \(0.963068\pi\)
\(312\) 0 0
\(313\) 9.52696 16.5012i 0.538495 0.932701i −0.460490 0.887665i \(-0.652326\pi\)
0.998985 0.0450364i \(-0.0143404\pi\)
\(314\) 0.0136731 0.000771615
\(315\) 0 0
\(316\) −14.3333 −0.806309
\(317\) −2.00972 + 3.48093i −0.112877 + 0.195508i −0.916929 0.399050i \(-0.869340\pi\)
0.804052 + 0.594559i \(0.202673\pi\)
\(318\) 0 0
\(319\) 0.442820 + 0.766987i 0.0247932 + 0.0429430i
\(320\) −3.93598 6.81732i −0.220028 0.381100i
\(321\) 0 0
\(322\) 0.669905 1.16031i 0.0373323 0.0646615i
\(323\) 13.4887 0.750529
\(324\) 0 0
\(325\) −3.60301 −0.199859
\(326\) 0.180309 0.312304i 0.00998637 0.0172969i
\(327\) 0 0
\(328\) 4.79987 + 8.31362i 0.265028 + 0.459043i
\(329\) −2.91423 5.04759i −0.160667 0.278283i
\(330\) 0 0
\(331\) 6.18878 10.7193i 0.340166 0.589185i −0.644297 0.764775i \(-0.722850\pi\)
0.984463 + 0.175590i \(0.0561834\pi\)
\(332\) −13.4887 −0.740286
\(333\) 0 0
\(334\) 3.51135 0.192133
\(335\) 2.07318 3.59085i 0.113270 0.196189i
\(336\) 0 0
\(337\) −6.12997 10.6174i −0.333920 0.578367i 0.649356 0.760484i \(-0.275038\pi\)
−0.983277 + 0.182117i \(0.941705\pi\)
\(338\) 1.43474 + 2.48504i 0.0780395 + 0.135168i
\(339\) 0 0
\(340\) −7.97141 + 13.8069i −0.432310 + 0.748784i
\(341\) 6.14884 0.332978
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 1.04910 1.81709i 0.0565637 0.0979711i
\(345\) 0 0
\(346\) 0.0302247 + 0.0523508i 0.00162489 + 0.00281440i
\(347\) 3.32489 + 5.75888i 0.178490 + 0.309153i 0.941363 0.337394i \(-0.109546\pi\)
−0.762874 + 0.646547i \(0.776212\pi\)
\(348\) 0 0
\(349\) −5.71737 + 9.90278i −0.306044 + 0.530083i −0.977493 0.210967i \(-0.932339\pi\)
0.671449 + 0.741050i \(0.265672\pi\)
\(350\) 0.861564 0.0460525
\(351\) 0 0
\(352\) 10.2255 0.545018
\(353\) −11.0978 + 19.2220i −0.590677 + 1.02308i 0.403465 + 0.914995i \(0.367806\pi\)
−0.994141 + 0.108087i \(0.965528\pi\)
\(354\) 0 0
\(355\) −5.08414 8.80598i −0.269838 0.467373i
\(356\) −2.66866 4.62226i −0.141439 0.244979i
\(357\) 0 0
\(358\) 1.69686 2.93905i 0.0896819 0.155334i
\(359\) 7.55623 0.398803 0.199401 0.979918i \(-0.436100\pi\)
0.199401 + 0.979918i \(0.436100\pi\)
\(360\) 0 0
\(361\) −15.2255 −0.801339
\(362\) 0.171149 0.296439i 0.00899539 0.0155805i
\(363\) 0 0
\(364\) −0.971410 1.68253i −0.0509157 0.0881886i
\(365\) 8.95254 + 15.5062i 0.468597 + 0.811634i
\(366\) 0 0
\(367\) 9.26157 16.0415i 0.483450 0.837360i −0.516370 0.856366i \(-0.672717\pi\)
0.999819 + 0.0190063i \(0.00605025\pi\)
\(368\) 20.5081 1.06906
\(369\) 0 0
\(370\) 2.69794 0.140259
\(371\) 5.80150 10.0485i 0.301199 0.521692i
\(372\) 0 0
\(373\) −7.83009 13.5621i −0.405427 0.702220i 0.588944 0.808174i \(-0.299544\pi\)
−0.994371 + 0.105954i \(0.966210\pi\)
\(374\) −3.07442 5.32505i −0.158974 0.275352i
\(375\) 0 0
\(376\) −2.74759 + 4.75897i −0.141696 + 0.245425i
\(377\) −0.239123 −0.0123155
\(378\) 0 0
\(379\) 4.03775 0.207405 0.103703 0.994608i \(-0.466931\pi\)
0.103703 + 0.994608i \(0.466931\pi\)
\(380\) −2.23065 + 3.86360i −0.114430 + 0.198199i
\(381\) 0 0
\(382\) 1.80150 + 3.12030i 0.0921730 + 0.159648i
\(383\) 0.112725 + 0.195246i 0.00575998 + 0.00997659i 0.868891 0.495003i \(-0.164833\pi\)
−0.863131 + 0.504980i \(0.831500\pi\)
\(384\) 0 0
\(385\) −2.18878 + 3.79108i −0.111551 + 0.193211i
\(386\) −1.87661 −0.0955171
\(387\) 0 0
\(388\) −13.9267 −0.707019
\(389\) 12.6316 21.8786i 0.640448 1.10929i −0.344885 0.938645i \(-0.612082\pi\)
0.985333 0.170643i \(-0.0545844\pi\)
\(390\) 0 0
\(391\) −19.4503 33.6890i −0.983646 1.70373i
\(392\) 0.471410 + 0.816506i 0.0238098 + 0.0412398i
\(393\) 0 0
\(394\) 0.799870 1.38542i 0.0402969 0.0697962i
\(395\) −8.71986 −0.438744
\(396\) 0 0
\(397\) −20.3009 −1.01888 −0.509438 0.860508i \(-0.670147\pi\)
−0.509438 + 0.860508i \(0.670147\pi\)
\(398\) 2.38401 4.12922i 0.119499 0.206979i
\(399\) 0 0
\(400\) 6.59385 + 11.4209i 0.329693 + 0.571044i
\(401\) −7.61273 13.1856i −0.380161 0.658459i 0.610924 0.791689i \(-0.290798\pi\)
−0.991085 + 0.133231i \(0.957465\pi\)
\(402\) 0 0
\(403\) −0.830095 + 1.43777i −0.0413500 + 0.0716203i
\(404\) −24.8389 −1.23578
\(405\) 0 0
\(406\) 0.0571799 0.00283779
\(407\) 17.6774 30.6182i 0.876238 1.51769i
\(408\) 0 0
\(409\) −0.828460 1.43494i −0.0409647 0.0709530i 0.844816 0.535057i \(-0.179710\pi\)
−0.885781 + 0.464104i \(0.846376\pi\)
\(410\) 1.43886 + 2.49218i 0.0710603 + 0.123080i
\(411\) 0 0
\(412\) −4.27128 + 7.39807i −0.210431 + 0.364477i
\(413\) 2.60301 0.128086
\(414\) 0 0
\(415\) −8.20602 −0.402818
\(416\) −1.38044 + 2.39099i −0.0676816 + 0.117228i
\(417\) 0 0
\(418\) −0.860320 1.49012i −0.0420796 0.0728840i
\(419\) 16.6871 + 28.9030i 0.815220 + 1.41200i 0.909170 + 0.416426i \(0.136718\pi\)
−0.0939492 + 0.995577i \(0.529949\pi\)
\(420\) 0 0
\(421\) −9.12025 + 15.7967i −0.444494 + 0.769886i −0.998017 0.0629481i \(-0.979950\pi\)
0.553523 + 0.832834i \(0.313283\pi\)
\(422\) −4.32614 −0.210593
\(423\) 0 0
\(424\) −10.9396 −0.531272
\(425\) 12.5075 21.6637i 0.606704 1.05084i
\(426\) 0 0
\(427\) −3.80150 6.58440i −0.183968 0.318641i
\(428\) −13.3353 23.0974i −0.644586 1.11646i
\(429\) 0 0
\(430\) 0.314490 0.544712i 0.0151660 0.0262684i
\(431\) −29.2826 −1.41049 −0.705247 0.708961i \(-0.749164\pi\)
−0.705247 + 0.708961i \(0.749164\pi\)
\(432\) 0 0
\(433\) −12.2449 −0.588451 −0.294226 0.955736i \(-0.595062\pi\)
−0.294226 + 0.955736i \(0.595062\pi\)
\(434\) 0.198495 0.343803i 0.00952807 0.0165031i
\(435\) 0 0
\(436\) 1.22708 + 2.12537i 0.0587667 + 0.101787i
\(437\) −5.44282 9.42724i −0.260365 0.450966i
\(438\) 0 0
\(439\) 2.41586 4.18440i 0.115303 0.199711i −0.802598 0.596520i \(-0.796549\pi\)
0.917901 + 0.396810i \(0.129883\pi\)
\(440\) 4.12725 0.196759
\(441\) 0 0
\(442\) 1.66019 0.0789672
\(443\) 0.622440 1.07810i 0.0295730 0.0512220i −0.850860 0.525392i \(-0.823919\pi\)
0.880433 + 0.474170i \(0.157252\pi\)
\(444\) 0 0
\(445\) −1.62352 2.81202i −0.0769622 0.133302i
\(446\) 2.70890 + 4.69195i 0.128270 + 0.222170i
\(447\) 0 0
\(448\) −3.33009 + 5.76789i −0.157332 + 0.272507i
\(449\) −8.82846 −0.416641 −0.208320 0.978061i \(-0.566800\pi\)
−0.208320 + 0.978061i \(0.566800\pi\)
\(450\) 0 0
\(451\) 37.7108 1.77573
\(452\) −11.8148 + 20.4638i −0.555721 + 0.962537i
\(453\) 0 0
\(454\) −0.631600 1.09396i −0.0296425 0.0513422i
\(455\) −0.590972 1.02359i −0.0277052 0.0479868i
\(456\) 0 0
\(457\) 5.25404 9.10026i 0.245774 0.425692i −0.716575 0.697510i \(-0.754291\pi\)
0.962349 + 0.271817i \(0.0876247\pi\)
\(458\) 4.62382 0.216057
\(459\) 0 0
\(460\) 12.8662 0.599890
\(461\) 11.2758 19.5302i 0.525166 0.909614i −0.474404 0.880307i \(-0.657337\pi\)
0.999570 0.0293073i \(-0.00933013\pi\)
\(462\) 0 0
\(463\) −5.19850 9.00406i −0.241595 0.418454i 0.719574 0.694416i \(-0.244337\pi\)
−0.961169 + 0.275962i \(0.911004\pi\)
\(464\) 0.437618 + 0.757977i 0.0203159 + 0.0351882i
\(465\) 0 0
\(466\) −2.03022 + 3.51645i −0.0940483 + 0.162897i
\(467\) −13.3171 −0.616242 −0.308121 0.951347i \(-0.599700\pi\)
−0.308121 + 0.951347i \(0.599700\pi\)
\(468\) 0 0
\(469\) −3.50808 −0.161988
\(470\) −0.823649 + 1.42660i −0.0379921 + 0.0658043i
\(471\) 0 0
\(472\) −1.22708 2.12537i −0.0564812 0.0978282i
\(473\) −4.12120 7.13812i −0.189493 0.328211i
\(474\) 0 0
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) 13.4887 0.618251
\(477\) 0 0
\(478\) −4.03775 −0.184682
\(479\) 7.26771 12.5880i 0.332070 0.575163i −0.650847 0.759209i \(-0.725586\pi\)
0.982918 + 0.184046i \(0.0589195\pi\)
\(480\) 0 0
\(481\) 4.77292 + 8.26693i 0.217626 + 0.376940i
\(482\) −3.24557 5.62149i −0.147832 0.256052i
\(483\) 0 0
\(484\) 2.63968 4.57206i 0.119985 0.207821i
\(485\) −8.47249 −0.384716
\(486\) 0 0
\(487\) 13.0539 0.591529 0.295765 0.955261i \(-0.404426\pi\)
0.295765 + 0.955261i \(0.404426\pi\)
\(488\) −3.58414 + 6.20790i −0.162246 + 0.281019i
\(489\) 0 0
\(490\) 0.141315 + 0.244765i 0.00638396 + 0.0110574i
\(491\) 9.67223 + 16.7528i 0.436502 + 0.756043i 0.997417 0.0718303i \(-0.0228840\pi\)
−0.560915 + 0.827873i \(0.689551\pi\)
\(492\) 0 0
\(493\) 0.830095 1.43777i 0.0373856 0.0647538i
\(494\) 0.464574 0.0209022
\(495\) 0 0
\(496\) 6.07661 0.272848
\(497\) −4.30150 + 7.45043i −0.192949 + 0.334197i
\(498\) 0 0
\(499\) 18.1111 + 31.3693i 0.810764 + 1.40428i 0.912330 + 0.409455i \(0.134281\pi\)
−0.101566 + 0.994829i \(0.532385\pi\)
\(500\) 9.87756 + 17.1084i 0.441738 + 0.765112i
\(501\) 0 0
\(502\) −2.28100 + 3.95080i −0.101806 + 0.176333i
\(503\) −15.6764 −0.698974 −0.349487 0.936941i \(-0.613644\pi\)
−0.349487 + 0.936941i \(0.613644\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) −2.48113 + 4.29743i −0.110299 + 0.191044i
\(507\) 0 0
\(508\) 1.30150 + 2.25427i 0.0577449 + 0.100017i
\(509\) 17.1517 + 29.7076i 0.760237 + 1.31677i 0.942729 + 0.333561i \(0.108250\pi\)
−0.182492 + 0.983207i \(0.558416\pi\)
\(510\) 0 0
\(511\) 7.57442 13.1193i 0.335073 0.580363i
\(512\) 17.0071 0.751616
\(513\) 0 0
\(514\) 3.54910 0.156544
\(515\) −2.59850 + 4.50073i −0.114503 + 0.198326i
\(516\) 0 0
\(517\) 10.7934 + 18.6948i 0.474694 + 0.822195i
\(518\) −1.14132 1.97682i −0.0501465 0.0868563i
\(519\) 0 0
\(520\) −0.557180 + 0.965064i −0.0244340 + 0.0423209i
\(521\) 10.2449 0.448836 0.224418 0.974493i \(-0.427952\pi\)
0.224418 + 0.974493i \(0.427952\pi\)
\(522\) 0 0
\(523\) 30.6030 1.33818 0.669088 0.743183i \(-0.266685\pi\)
0.669088 + 0.743183i \(0.266685\pi\)
\(524\) 4.82489 8.35696i 0.210776 0.365075i
\(525\) 0 0
\(526\) −0.925580 1.60315i −0.0403572 0.0699007i
\(527\) −5.76320 9.98215i −0.251049 0.434829i
\(528\) 0 0
\(529\) −4.19686 + 7.26918i −0.182472 + 0.316051i
\(530\) −3.27936 −0.142446
\(531\) 0 0
\(532\) 3.77455 0.163647
\(533\) −5.09097 + 8.81782i −0.220514 + 0.381942i
\(534\) 0 0
\(535\) −8.11273 14.0517i −0.350744 0.607506i
\(536\) 1.65374 + 2.86437i 0.0714309 + 0.123722i
\(537\) 0 0
\(538\) −0.180699 + 0.312981i −0.00779051 + 0.0134936i
\(539\) 3.70370 0.159530
\(540\) 0 0
\(541\) −26.0917 −1.12177 −0.560884 0.827894i \(-0.689539\pi\)
−0.560884 + 0.827894i \(0.689539\pi\)
\(542\) 2.62803 4.55189i 0.112884 0.195520i
\(543\) 0 0
\(544\) −9.58414 16.6002i −0.410916 0.711728i
\(545\) 0.746515 + 1.29300i 0.0319772 + 0.0553861i
\(546\) 0 0
\(547\) 5.46169 9.45993i 0.233525 0.404478i −0.725318 0.688414i \(-0.758307\pi\)
0.958843 + 0.283937i \(0.0916405\pi\)
\(548\) −8.43147 −0.360175
\(549\) 0 0
\(550\) −3.19097 −0.136063
\(551\) 0.232287 0.402332i 0.00989575 0.0171399i
\(552\) 0 0
\(553\) 3.68878 + 6.38915i 0.156863 + 0.271694i
\(554\) 1.29467 + 2.24243i 0.0550052 + 0.0952718i
\(555\) 0 0
\(556\) 3.83009 6.63392i 0.162432 0.281341i
\(557\) 13.9442 0.590835 0.295417 0.955368i \(-0.404541\pi\)
0.295417 + 0.955368i \(0.404541\pi\)
\(558\) 0 0
\(559\) 2.22545 0.0941265
\(560\) −2.16307 + 3.74654i −0.0914063 + 0.158320i
\(561\) 0 0
\(562\) −2.01780 3.49492i −0.0851156 0.147424i
\(563\) 15.1287 + 26.2037i 0.637600 + 1.10435i 0.985958 + 0.166993i \(0.0534059\pi\)
−0.348358 + 0.937361i \(0.613261\pi\)
\(564\) 0 0
\(565\) −7.18770 + 12.4495i −0.302389 + 0.523753i
\(566\) −3.66268 −0.153954
\(567\) 0 0
\(568\) 8.11109 0.340334
\(569\) −10.5676 + 18.3036i −0.443016 + 0.767326i −0.997912 0.0645936i \(-0.979425\pi\)
0.554896 + 0.831920i \(0.312758\pi\)
\(570\) 0 0
\(571\) 16.3932 + 28.3938i 0.686033 + 1.18824i 0.973111 + 0.230336i \(0.0739826\pi\)
−0.287078 + 0.957907i \(0.592684\pi\)
\(572\) 3.59781 + 6.23159i 0.150432 + 0.260556i
\(573\) 0 0
\(574\) 1.21737 2.10855i 0.0508120 0.0880090i
\(575\) −20.1877 −0.841885
\(576\) 0 0
\(577\) −17.3743 −0.723301 −0.361651 0.932314i \(-0.617787\pi\)
−0.361651 + 0.932314i \(0.617787\pi\)
\(578\) −3.73065 + 6.46168i −0.155175 + 0.268770i
\(579\) 0 0
\(580\) 0.274550 + 0.475534i 0.0114001 + 0.0197455i
\(581\) 3.47141 + 6.01266i 0.144018 + 0.249447i
\(582\) 0 0
\(583\) −21.4870 + 37.2166i −0.889901 + 1.54135i
\(584\) −14.2826 −0.591019
\(585\) 0 0
\(586\) 2.24050 0.0925542
\(587\) 8.48796 14.7016i 0.350336 0.606799i −0.635973 0.771712i \(-0.719401\pi\)
0.986308 + 0.164913i \(0.0527342\pi\)
\(588\) 0 0
\(589\) −1.61273 2.79332i −0.0664512 0.115097i
\(590\) −0.367845 0.637125i −0.0151439 0.0262300i
\(591\) 0 0
\(592\) 17.4698 30.2585i 0.718003 1.24362i
\(593\) 13.0733 0.536858 0.268429 0.963300i \(-0.413496\pi\)
0.268429 + 0.963300i \(0.413496\pi\)
\(594\) 0 0
\(595\) 8.20602 0.336414
\(596\) −10.7934 + 18.6948i −0.442116 + 0.765767i
\(597\) 0 0
\(598\) −0.669905 1.16031i −0.0273945 0.0474486i
\(599\) 14.6030 + 25.2932i 0.596663 + 1.03345i 0.993310 + 0.115479i \(0.0368403\pi\)
−0.396647 + 0.917971i \(0.629826\pi\)
\(600\) 0 0
\(601\) −3.89536 + 6.74695i −0.158895 + 0.275214i −0.934470 0.356041i \(-0.884126\pi\)
0.775576 + 0.631255i \(0.217460\pi\)
\(602\) −0.532157 −0.0216891
\(603\) 0 0
\(604\) −27.0506 −1.10067
\(605\) 1.60589 2.78148i 0.0652887 0.113083i
\(606\) 0 0
\(607\) 9.82038 + 17.0094i 0.398597 + 0.690390i 0.993553 0.113368i \(-0.0361639\pi\)
−0.594956 + 0.803758i \(0.702831\pi\)
\(608\) −2.68194 4.64526i −0.108767 0.188390i
\(609\) 0 0
\(610\) −1.07442 + 1.86095i −0.0435020 + 0.0753477i
\(611\) −5.82846 −0.235794
\(612\) 0 0
\(613\) 23.5653 0.951792 0.475896 0.879502i \(-0.342124\pi\)
0.475896 + 0.879502i \(0.342124\pi\)
\(614\) −0.324502 + 0.562054i −0.0130958 + 0.0226827i
\(615\) 0 0
\(616\) −1.74596 3.02409i −0.0703467 0.121844i
\(617\) −5.33009 9.23200i −0.214582 0.371666i 0.738562 0.674186i \(-0.235505\pi\)
−0.953143 + 0.302520i \(0.902172\pi\)
\(618\) 0 0
\(619\) 9.00752 15.6015i 0.362043 0.627077i −0.626254 0.779619i \(-0.715413\pi\)
0.988297 + 0.152542i \(0.0487460\pi\)
\(620\) 3.81230 0.153106
\(621\) 0 0
\(622\) 3.34308 0.134045
\(623\) −1.37360 + 2.37915i −0.0550322 + 0.0953186i
\(624\) 0 0
\(625\) −2.99837 5.19332i −0.119935 0.207733i
\(626\) 2.27812 + 3.94581i 0.0910519 + 0.157706i
\(627\) 0 0
\(628\) 0.0555452 0.0962071i 0.00221649 0.00383908i
\(629\) −66.2750 −2.64256
\(630\) 0 0
\(631\) 12.4703 0.496436 0.248218 0.968704i \(-0.420155\pi\)
0.248218 + 0.968704i \(0.420155\pi\)
\(632\) 3.47786 6.02382i 0.138342 0.239615i
\(633\) 0 0
\(634\) −0.480570 0.832371i −0.0190859 0.0330577i
\(635\) 0.791790 + 1.37142i 0.0314212 + 0.0544232i
\(636\) 0 0
\(637\) −0.500000 + 0.866025i −0.0198107 + 0.0343132i
\(638\) −0.211777 −0.00838434
\(639\) 0 0
\(640\) 8.40877 0.332386
\(641\) 9.57279 16.5806i 0.378102 0.654892i −0.612684 0.790328i \(-0.709910\pi\)
0.990786 + 0.135436i \(0.0432434\pi\)
\(642\) 0 0
\(643\) −3.24433 5.61934i −0.127944 0.221605i 0.794936 0.606693i \(-0.207504\pi\)
−0.922880 + 0.385088i \(0.874171\pi\)
\(644\) −5.44282 9.42724i −0.214477 0.371485i
\(645\) 0 0
\(646\) −1.61273 + 2.79332i −0.0634518 + 0.109902i
\(647\) 48.0988 1.89096 0.945479 0.325682i \(-0.105594\pi\)
0.945479 + 0.325682i \(0.105594\pi\)
\(648\) 0 0
\(649\) −9.64076 −0.378433
\(650\) 0.430782 0.746136i 0.0168967 0.0292659i
\(651\) 0 0
\(652\) −1.46496 2.53739i −0.0573724 0.0993720i
\(653\) −21.6202 37.4474i −0.846066 1.46543i −0.884692 0.466175i \(-0.845632\pi\)
0.0386267 0.999254i \(-0.487702\pi\)
\(654\) 0 0
\(655\) 2.93530 5.08408i 0.114691 0.198651i
\(656\) 37.2678 1.45506
\(657\) 0 0
\(658\) 1.39372 0.0543329
\(659\) −1.25404 + 2.17206i −0.0488505 + 0.0846115i −0.889417 0.457097i \(-0.848889\pi\)
0.840566 + 0.541709i \(0.182222\pi\)
\(660\) 0 0
\(661\) 21.1677 + 36.6636i 0.823329 + 1.42605i 0.903190 + 0.429241i \(0.141219\pi\)
−0.0798613 + 0.996806i \(0.525448\pi\)
\(662\) 1.47988 + 2.56323i 0.0575172 + 0.0996227i
\(663\) 0 0
\(664\) 3.27292 5.66886i 0.127014 0.219994i
\(665\) 2.29630 0.0890468
\(666\) 0 0
\(667\) −1.33981 −0.0518777
\(668\) 14.2644 24.7067i 0.551908 0.955933i
\(669\) 0 0
\(670\) 0.495745 + 0.858655i 0.0191523 + 0.0331727i
\(671\) 14.0796 + 24.3866i 0.543538 + 0.941435i
\(672\) 0 0
\(673\) −6.70765 + 11.6180i −0.258561 + 0.447841i −0.965857 0.259077i \(-0.916582\pi\)
0.707296 + 0.706918i \(0.249915\pi\)
\(674\) 2.93163 0.112922
\(675\) 0 0
\(676\) 23.3138 0.896686
\(677\) 0.981125 1.69936i 0.0377077 0.0653117i −0.846556 0.532300i \(-0.821328\pi\)
0.884263 + 0.466989i \(0.154661\pi\)
\(678\) 0 0
\(679\) 3.58414 + 6.20790i 0.137546 + 0.238237i
\(680\) −3.86840 6.70027i −0.148346 0.256943i
\(681\) 0 0
\(682\) −0.735165 + 1.27334i −0.0281509 + 0.0487589i
\(683\) −27.1672 −1.03952 −0.519761 0.854312i \(-0.673979\pi\)
−0.519761 + 0.854312i \(0.673979\pi\)
\(684\) 0 0
\(685\) −5.12941 −0.195985
\(686\) 0.119562 0.207087i 0.00456488 0.00790661i
\(687\) 0 0
\(688\) −4.07279 7.05427i −0.155273 0.268942i
\(689\) −5.80150 10.0485i −0.221020 0.382817i
\(690\) 0 0
\(691\) 25.1586 43.5759i 0.957077 1.65771i 0.227534 0.973770i \(-0.426934\pi\)
0.729543 0.683935i \(-0.239733\pi\)
\(692\) 0.491138 0.0186703
\(693\) 0 0
\(694\) −1.59012 −0.0603601
\(695\) 2.33009 4.03584i 0.0883855 0.153088i
\(696\) 0 0
\(697\) −35.3457 61.2205i −1.33881 2.31889i
\(698\) −1.36716 2.36798i −0.0517476 0.0896295i
\(699\) 0 0
\(700\) 3.50000 6.06218i 0.132288 0.229129i
\(701\) −45.1672 −1.70594 −0.852970 0.521960i \(-0.825201\pi\)
−0.852970 + 0.521960i \(0.825201\pi\)
\(702\) 0 0
\(703\) −18.5458 −0.699469
\(704\) 12.3337 21.3625i 0.464842 0.805131i
\(705\) 0 0
\(706\) −2.65374 4.59642i −0.0998750 0.172989i
\(707\) 6.39248 + 11.0721i 0.240414 + 0.416409i
\(708\) 0 0
\(709\) −19.8090 + 34.3102i −0.743944 + 1.28855i 0.206743 + 0.978395i \(0.433714\pi\)
−0.950687 + 0.310153i \(0.899620\pi\)
\(710\) 2.43147 0.0912514
\(711\) 0 0
\(712\) 2.59012 0.0970688
\(713\) −4.65103 + 8.05582i −0.174182 + 0.301693i
\(714\) 0 0
\(715\) 2.18878 + 3.79108i 0.0818557 + 0.141778i
\(716\) −13.7866 23.8791i −0.515229 0.892403i
\(717\) 0 0
\(718\) −0.903436 + 1.56480i −0.0337159 + 0.0583977i
\(719\) 22.0377 0.821869 0.410935 0.911665i \(-0.365202\pi\)
0.410935 + 0.911665i \(0.365202\pi\)
\(720\) 0 0
\(721\) 4.39699 0.163752
\(722\) 1.82038 3.15299i 0.0677475 0.117342i
\(723\) 0 0
\(724\) −1.39054 2.40849i −0.0516792 0.0895110i
\(725\) −0.430782 0.746136i −0.0159988 0.0277108i
\(726\) 0 0
\(727\) −14.0555 + 24.3449i −0.521291 + 0.902903i 0.478402 + 0.878141i \(0.341216\pi\)
−0.999693 + 0.0247621i \(0.992117\pi\)
\(728\) 0.942820 0.0349432
\(729\) 0 0
\(730\) −4.28152 −0.158466
\(731\) −7.72545 + 13.3809i −0.285736 + 0.494909i
\(732\) 0 0
\(733\) −5.93474 10.2793i −0.219205 0.379674i 0.735360 0.677676i \(-0.237013\pi\)
−0.954565 + 0.298003i \(0.903680\pi\)
\(734\) 2.21466 + 3.83590i 0.0817444 + 0.141586i
\(735\) 0 0
\(736\) −7.73461 + 13.3967i −0.285102 + 0.493810i
\(737\) 12.9929 0.478598
\(738\) 0 0
\(739\) −12.1844 −0.448212 −0.224106 0.974565i \(-0.571946\pi\)
−0.224106 + 0.974565i \(0.571946\pi\)
\(740\) 10.9601 18.9834i 0.402900 0.697843i
\(741\) 0 0
\(742\) 1.38727 + 2.40283i 0.0509285 + 0.0882107i
\(743\) −22.2427 38.5255i −0.816005 1.41336i −0.908604 0.417659i \(-0.862851\pi\)
0.0925987 0.995704i \(-0.470483\pi\)
\(744\) 0 0
\(745\) −6.56634 + 11.3732i −0.240572 + 0.416683i
\(746\) 3.74472 0.137104
\(747\) 0 0
\(748\) −49.9579 −1.82664
\(749\) −6.86389 + 11.8886i −0.250801 + 0.434400i
\(750\) 0 0
\(751\) −21.4029 37.0709i −0.781002 1.35274i −0.931358 0.364104i \(-0.881375\pi\)
0.150356 0.988632i \(-0.451958\pi\)
\(752\) 10.6666 + 18.4752i 0.388972 + 0.673720i
\(753\) 0 0
\(754\) 0.0285900 0.0495193i 0.00104119 0.00180339i
\(755\) −16.4567 −0.598919
\(756\) 0 0
\(757\) −22.4919 −0.817483 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(758\) −0.482760 + 0.836165i −0.0175346 + 0.0303709i
\(759\) 0 0
\(760\) −1.08250 1.87495i −0.0392664 0.0680114i
\(761\) −7.16827 12.4158i −0.259850 0.450073i 0.706352 0.707861i \(-0.250340\pi\)
−0.966201 + 0.257788i \(0.917006\pi\)
\(762\) 0 0
\(763\) 0.631600 1.09396i 0.0228655 0.0396041i
\(764\) 29.2736 1.05908
\(765\) 0 0
\(766\) −0.0539104 −0.00194786
\(767\) 1.30150 2.25427i 0.0469946 0.0813971i
\(768\) 0 0
\(769\) 15.6105 + 27.0382i 0.562930 + 0.975024i 0.997239 + 0.0742597i \(0.0236594\pi\)
−0.434309 + 0.900764i \(0.643007\pi\)
\(770\) −0.523388 0.906535i −0.0188616 0.0326693i
\(771\) 0 0
\(772\) −7.62352 + 13.2043i −0.274376 + 0.475234i
\(773\) −4.38005 −0.157539 −0.0787697 0.996893i \(-0.525099\pi\)
−0.0787697 + 0.996893i \(0.525099\pi\)
\(774\) 0 0
\(775\) −5.98168 −0.214868
\(776\) 3.37919 5.85294i 0.121306 0.210108i
\(777\) 0 0
\(778\) 3.02051 + 5.23168i 0.108291 + 0.187565i
\(779\) −9.89084 17.1314i −0.354376 0.613798i
\(780\) 0 0
\(781\) 15.9315 27.5941i 0.570073 0.987395i
\(782\) 9.30206 0.332641
\(783\) 0 0