Properties

Label 729.2.e.r.568.2
Level $729$
Weight $2$
Character 729.568
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 568.2
Root \(0.984808 - 0.173648i\) of defining polynomial
Character \(\chi\) \(=\) 729.568
Dual form 729.2.e.r.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.85083 + 0.673648i) q^{2} +(1.43969 + 1.20805i) q^{4} +(0.642788 - 3.64543i) q^{5} +(-1.79813 + 1.50881i) q^{7} +(-0.118782 - 0.205737i) q^{8} +O(q^{10})\) \(q+(1.85083 + 0.673648i) q^{2} +(1.43969 + 1.20805i) q^{4} +(0.642788 - 3.64543i) q^{5} +(-1.79813 + 1.50881i) q^{7} +(-0.118782 - 0.205737i) q^{8} +(3.64543 - 6.31407i) q^{10} +(-0.378297 - 2.14543i) q^{11} +(4.43242 - 1.61327i) q^{13} +(-4.34445 + 1.58125i) q^{14} +(-0.733956 - 4.16247i) q^{16} +(1.46756 - 2.54189i) q^{17} +(3.11334 + 5.39246i) q^{19} +(5.32926 - 4.47178i) q^{20} +(0.745100 - 4.22567i) q^{22} +(0.397600 + 0.333626i) q^{23} +(-8.17752 - 2.97637i) q^{25} +9.29044 q^{26} -4.41147 q^{28} +(3.28212 + 1.19459i) q^{29} +(-3.29813 - 2.76746i) q^{31} +(1.36310 - 7.73055i) q^{32} +(4.42855 - 3.71599i) q^{34} +(4.34445 + 7.52481i) q^{35} +(-1.20574 + 2.08840i) q^{37} +(2.12965 + 12.0778i) q^{38} +(-0.826352 + 0.300767i) q^{40} +(-2.34791 + 0.854570i) q^{41} +(0.184793 + 1.04801i) q^{43} +(2.04715 - 3.54576i) q^{44} +(0.511144 + 0.885328i) q^{46} +(-0.181985 + 0.152704i) q^{47} +(-0.258770 + 1.46756i) q^{49} +(-13.1302 - 11.0175i) q^{50} +(8.33022 + 3.03195i) q^{52} +4.66717 q^{53} -8.06418 q^{55} +(0.524005 + 0.190722i) q^{56} +(5.26991 + 4.42198i) q^{58} +(-2.31164 + 13.1099i) q^{59} +(-2.81521 + 2.36224i) q^{61} +(-4.24000 - 7.34389i) q^{62} +(3.50387 - 6.06888i) q^{64} +(-3.03195 - 17.1951i) q^{65} +(-13.4363 + 4.89041i) q^{67} +(5.18355 - 1.88666i) q^{68} +(2.97178 + 16.8538i) q^{70} +(-0.601535 + 1.04189i) q^{71} +(2.34002 + 4.05304i) q^{73} +(-3.63846 + 3.05303i) q^{74} +(-2.03209 + 11.5245i) q^{76} +(3.91728 + 3.28699i) q^{77} +(12.0287 + 4.37808i) q^{79} -15.6458 q^{80} -4.92127 q^{82} +(10.6222 + 3.86618i) q^{83} +(-8.32295 - 6.98378i) q^{85} +(-0.363970 + 2.06418i) q^{86} +(-0.396459 + 0.332669i) q^{88} +(-0.349643 - 0.605600i) q^{89} +(-5.53596 + 9.58856i) q^{91} +(0.169386 + 0.960637i) q^{92} +(-0.439693 + 0.160035i) q^{94} +(21.6591 - 7.88326i) q^{95} +(-1.23055 - 6.97881i) q^{97} +(-1.46756 + 2.54189i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.85083 + 0.673648i 1.30874 + 0.476341i 0.899832 0.436236i \(-0.143689\pi\)
0.408904 + 0.912577i \(0.365911\pi\)
\(3\) 0 0
\(4\) 1.43969 + 1.20805i 0.719846 + 0.604023i
\(5\) 0.642788 3.64543i 0.287463 1.63029i −0.408888 0.912585i \(-0.634083\pi\)
0.696351 0.717701i \(-0.254806\pi\)
\(6\) 0 0
\(7\) −1.79813 + 1.50881i −0.679631 + 0.570278i −0.915898 0.401410i \(-0.868520\pi\)
0.236268 + 0.971688i \(0.424076\pi\)
\(8\) −0.118782 0.205737i −0.0419959 0.0727390i
\(9\) 0 0
\(10\) 3.64543 6.31407i 1.15279 1.99668i
\(11\) −0.378297 2.14543i −0.114061 0.646871i −0.987211 0.159420i \(-0.949038\pi\)
0.873150 0.487452i \(-0.162073\pi\)
\(12\) 0 0
\(13\) 4.43242 1.61327i 1.22933 0.447440i 0.355963 0.934500i \(-0.384153\pi\)
0.873369 + 0.487060i \(0.161931\pi\)
\(14\) −4.34445 + 1.58125i −1.16110 + 0.422607i
\(15\) 0 0
\(16\) −0.733956 4.16247i −0.183489 1.04062i
\(17\) 1.46756 2.54189i 0.355936 0.616499i −0.631342 0.775505i \(-0.717496\pi\)
0.987278 + 0.159006i \(0.0508289\pi\)
\(18\) 0 0
\(19\) 3.11334 + 5.39246i 0.714249 + 1.23712i 0.963248 + 0.268612i \(0.0865651\pi\)
−0.248999 + 0.968504i \(0.580102\pi\)
\(20\) 5.32926 4.47178i 1.19166 0.999921i
\(21\) 0 0
\(22\) 0.745100 4.22567i 0.158856 0.900916i
\(23\) 0.397600 + 0.333626i 0.0829053 + 0.0695658i 0.683298 0.730139i \(-0.260545\pi\)
−0.600393 + 0.799705i \(0.704989\pi\)
\(24\) 0 0
\(25\) −8.17752 2.97637i −1.63550 0.595275i
\(26\) 9.29044 1.82201
\(27\) 0 0
\(28\) −4.41147 −0.833690
\(29\) 3.28212 + 1.19459i 0.609474 + 0.221830i 0.628273 0.777993i \(-0.283762\pi\)
−0.0187992 + 0.999823i \(0.505984\pi\)
\(30\) 0 0
\(31\) −3.29813 2.76746i −0.592362 0.497051i 0.296618 0.954996i \(-0.404141\pi\)
−0.888980 + 0.457945i \(0.848586\pi\)
\(32\) 1.36310 7.73055i 0.240965 1.36658i
\(33\) 0 0
\(34\) 4.42855 3.71599i 0.759490 0.637288i
\(35\) 4.34445 + 7.52481i 0.734347 + 1.27193i
\(36\) 0 0
\(37\) −1.20574 + 2.08840i −0.198222 + 0.343330i −0.947952 0.318413i \(-0.896850\pi\)
0.749730 + 0.661744i \(0.230183\pi\)
\(38\) 2.12965 + 12.0778i 0.345475 + 1.95929i
\(39\) 0 0
\(40\) −0.826352 + 0.300767i −0.130658 + 0.0475555i
\(41\) −2.34791 + 0.854570i −0.366682 + 0.133461i −0.518788 0.854903i \(-0.673617\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(42\) 0 0
\(43\) 0.184793 + 1.04801i 0.0281806 + 0.159820i 0.995651 0.0931655i \(-0.0296986\pi\)
−0.967470 + 0.252986i \(0.918587\pi\)
\(44\) 2.04715 3.54576i 0.308619 0.534543i
\(45\) 0 0
\(46\) 0.511144 + 0.885328i 0.0753641 + 0.130534i
\(47\) −0.181985 + 0.152704i −0.0265453 + 0.0222741i −0.655964 0.754792i \(-0.727738\pi\)
0.629418 + 0.777067i \(0.283293\pi\)
\(48\) 0 0
\(49\) −0.258770 + 1.46756i −0.0369672 + 0.209651i
\(50\) −13.1302 11.0175i −1.85689 1.55812i
\(51\) 0 0
\(52\) 8.33022 + 3.03195i 1.15519 + 0.420456i
\(53\) 4.66717 0.641085 0.320543 0.947234i \(-0.396135\pi\)
0.320543 + 0.947234i \(0.396135\pi\)
\(54\) 0 0
\(55\) −8.06418 −1.08737
\(56\) 0.524005 + 0.190722i 0.0700231 + 0.0254863i
\(57\) 0 0
\(58\) 5.26991 + 4.42198i 0.691974 + 0.580635i
\(59\) −2.31164 + 13.1099i −0.300949 + 1.70677i 0.341035 + 0.940051i \(0.389223\pi\)
−0.641984 + 0.766718i \(0.721889\pi\)
\(60\) 0 0
\(61\) −2.81521 + 2.36224i −0.360450 + 0.302454i −0.804970 0.593315i \(-0.797819\pi\)
0.444520 + 0.895769i \(0.353374\pi\)
\(62\) −4.24000 7.34389i −0.538480 0.932675i
\(63\) 0 0
\(64\) 3.50387 6.06888i 0.437984 0.758610i
\(65\) −3.03195 17.1951i −0.376067 2.13278i
\(66\) 0 0
\(67\) −13.4363 + 4.89041i −1.64150 + 0.597459i −0.987301 0.158860i \(-0.949218\pi\)
−0.654203 + 0.756319i \(0.726996\pi\)
\(68\) 5.18355 1.88666i 0.628598 0.228791i
\(69\) 0 0
\(70\) 2.97178 + 16.8538i 0.355196 + 2.01442i
\(71\) −0.601535 + 1.04189i −0.0713891 + 0.123649i −0.899510 0.436900i \(-0.856077\pi\)
0.828121 + 0.560549i \(0.189410\pi\)
\(72\) 0 0
\(73\) 2.34002 + 4.05304i 0.273879 + 0.474372i 0.969852 0.243696i \(-0.0783599\pi\)
−0.695973 + 0.718068i \(0.745027\pi\)
\(74\) −3.63846 + 3.05303i −0.422963 + 0.354908i
\(75\) 0 0
\(76\) −2.03209 + 11.5245i −0.233097 + 1.32196i
\(77\) 3.91728 + 3.28699i 0.446416 + 0.374587i
\(78\) 0 0
\(79\) 12.0287 + 4.37808i 1.35333 + 0.492573i 0.913986 0.405745i \(-0.132988\pi\)
0.439346 + 0.898318i \(0.355210\pi\)
\(80\) −15.6458 −1.74925
\(81\) 0 0
\(82\) −4.92127 −0.543464
\(83\) 10.6222 + 3.86618i 1.16594 + 0.424369i 0.851217 0.524814i \(-0.175865\pi\)
0.314726 + 0.949183i \(0.398087\pi\)
\(84\) 0 0
\(85\) −8.32295 6.98378i −0.902750 0.757498i
\(86\) −0.363970 + 2.06418i −0.0392479 + 0.222586i
\(87\) 0 0
\(88\) −0.396459 + 0.332669i −0.0422627 + 0.0354626i
\(89\) −0.349643 0.605600i −0.0370621 0.0641935i 0.846899 0.531753i \(-0.178467\pi\)
−0.883961 + 0.467560i \(0.845133\pi\)
\(90\) 0 0
\(91\) −5.53596 + 9.58856i −0.580326 + 1.00515i
\(92\) 0.169386 + 0.960637i 0.0176597 + 0.100153i
\(93\) 0 0
\(94\) −0.439693 + 0.160035i −0.0453508 + 0.0165064i
\(95\) 21.6591 7.88326i 2.22217 0.808805i
\(96\) 0 0
\(97\) −1.23055 6.97881i −0.124944 0.708591i −0.981341 0.192274i \(-0.938414\pi\)
0.856398 0.516317i \(-0.172697\pi\)
\(98\) −1.46756 + 2.54189i −0.148246 + 0.256770i
\(99\) 0 0
\(100\) −8.17752 14.1639i −0.817752 1.41639i
\(101\) 3.58288 3.00640i 0.356510 0.299148i −0.446888 0.894590i \(-0.647468\pi\)
0.803398 + 0.595442i \(0.203023\pi\)
\(102\) 0 0
\(103\) −2.36571 + 13.4166i −0.233101 + 1.32198i 0.613476 + 0.789713i \(0.289771\pi\)
−0.846577 + 0.532267i \(0.821340\pi\)
\(104\) −0.858402 0.720285i −0.0841733 0.0706298i
\(105\) 0 0
\(106\) 8.63816 + 3.14403i 0.839012 + 0.305375i
\(107\) 11.6340 1.12470 0.562350 0.826900i \(-0.309898\pi\)
0.562350 + 0.826900i \(0.309898\pi\)
\(108\) 0 0
\(109\) 14.6040 1.39881 0.699405 0.714725i \(-0.253448\pi\)
0.699405 + 0.714725i \(0.253448\pi\)
\(110\) −14.9254 5.43242i −1.42309 0.517961i
\(111\) 0 0
\(112\) 7.60014 + 6.37727i 0.718145 + 0.602596i
\(113\) 0.815422 4.62449i 0.0767084 0.435035i −0.922131 0.386877i \(-0.873554\pi\)
0.998840 0.0481580i \(-0.0153351\pi\)
\(114\) 0 0
\(115\) 1.47178 1.23497i 0.137244 0.115162i
\(116\) 3.28212 + 5.68479i 0.304737 + 0.527820i
\(117\) 0 0
\(118\) −13.1099 + 22.7071i −1.20687 + 2.09036i
\(119\) 1.19637 + 6.78493i 0.109671 + 0.621973i
\(120\) 0 0
\(121\) 5.87686 2.13900i 0.534260 0.194455i
\(122\) −6.80180 + 2.47565i −0.615806 + 0.224135i
\(123\) 0 0
\(124\) −1.40508 7.96859i −0.126180 0.715601i
\(125\) −6.85240 + 11.8687i −0.612897 + 1.06157i
\(126\) 0 0
\(127\) −3.04576 5.27541i −0.270267 0.468117i 0.698663 0.715451i \(-0.253779\pi\)
−0.968930 + 0.247334i \(0.920445\pi\)
\(128\) −1.45323 + 1.21941i −0.128449 + 0.107781i
\(129\) 0 0
\(130\) 5.97178 33.8677i 0.523760 2.97039i
\(131\) 7.92734 + 6.65183i 0.692615 + 0.581173i 0.919662 0.392711i \(-0.128463\pi\)
−0.227047 + 0.973884i \(0.572907\pi\)
\(132\) 0 0
\(133\) −13.7344 4.99892i −1.19093 0.433461i
\(134\) −28.1627 −2.43289
\(135\) 0 0
\(136\) −0.697281 −0.0597914
\(137\) −17.9337 6.52734i −1.53218 0.557668i −0.568027 0.823010i \(-0.692293\pi\)
−0.964154 + 0.265342i \(0.914515\pi\)
\(138\) 0 0
\(139\) −17.8516 14.9793i −1.51416 1.27053i −0.855138 0.518400i \(-0.826528\pi\)
−0.659018 0.752128i \(-0.729028\pi\)
\(140\) −2.83564 + 16.0817i −0.239655 + 1.35915i
\(141\) 0 0
\(142\) −1.81521 + 1.52314i −0.152329 + 0.127819i
\(143\) −5.13793 8.89915i −0.429655 0.744184i
\(144\) 0 0
\(145\) 6.46451 11.1969i 0.536848 0.929848i
\(146\) 1.60067 + 9.07785i 0.132472 + 0.751288i
\(147\) 0 0
\(148\) −4.25877 + 1.55007i −0.350069 + 0.127415i
\(149\) −14.5708 + 5.30335i −1.19369 + 0.434467i −0.861017 0.508576i \(-0.830172\pi\)
−0.332671 + 0.943043i \(0.607950\pi\)
\(150\) 0 0
\(151\) −1.02481 5.81201i −0.0833983 0.472975i −0.997691 0.0679204i \(-0.978364\pi\)
0.914292 0.405055i \(-0.132748\pi\)
\(152\) 0.739620 1.28106i 0.0599911 0.103908i
\(153\) 0 0
\(154\) 5.03596 + 8.72254i 0.405809 + 0.702882i
\(155\) −12.2086 + 10.2442i −0.980617 + 0.822836i
\(156\) 0 0
\(157\) −0.210485 + 1.19372i −0.0167985 + 0.0952691i −0.992054 0.125810i \(-0.959847\pi\)
0.975256 + 0.221079i \(0.0709580\pi\)
\(158\) 19.3138 + 16.2062i 1.53652 + 1.28930i
\(159\) 0 0
\(160\) −27.3050 9.93821i −2.15865 0.785684i
\(161\) −1.21832 −0.0960168
\(162\) 0 0
\(163\) 2.77332 0.217223 0.108612 0.994084i \(-0.465360\pi\)
0.108612 + 0.994084i \(0.465360\pi\)
\(164\) −4.41263 1.60607i −0.344569 0.125413i
\(165\) 0 0
\(166\) 17.0556 + 14.3113i 1.32377 + 1.11077i
\(167\) −0.664738 + 3.76991i −0.0514389 + 0.291725i −0.999665 0.0258705i \(-0.991764\pi\)
0.948226 + 0.317595i \(0.102875\pi\)
\(168\) 0 0
\(169\) 7.08512 5.94512i 0.545009 0.457317i
\(170\) −10.6998 18.5326i −0.820635 1.42138i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −1.22064 6.92262i −0.0928039 0.526317i −0.995398 0.0958248i \(-0.969451\pi\)
0.902594 0.430492i \(-0.141660\pi\)
\(174\) 0 0
\(175\) 19.1951 6.98643i 1.45101 0.528124i
\(176\) −8.65263 + 3.14930i −0.652217 + 0.237387i
\(177\) 0 0
\(178\) −0.239170 1.35640i −0.0179266 0.101667i
\(179\) 7.19269 12.4581i 0.537607 0.931163i −0.461425 0.887179i \(-0.652662\pi\)
0.999032 0.0439838i \(-0.0140050\pi\)
\(180\) 0 0
\(181\) −6.60014 11.4318i −0.490584 0.849717i 0.509357 0.860555i \(-0.329883\pi\)
−0.999941 + 0.0108384i \(0.996550\pi\)
\(182\) −16.7055 + 14.0175i −1.23829 + 1.03905i
\(183\) 0 0
\(184\) 0.0214114 0.121430i 0.00157847 0.00895193i
\(185\) 6.83807 + 5.73783i 0.502745 + 0.421853i
\(186\) 0 0
\(187\) −6.00862 2.18696i −0.439394 0.159926i
\(188\) −0.446476 −0.0325626
\(189\) 0 0
\(190\) 45.3979 3.29351
\(191\) −12.6138 4.59105i −0.912703 0.332197i −0.157372 0.987539i \(-0.550302\pi\)
−0.755332 + 0.655343i \(0.772524\pi\)
\(192\) 0 0
\(193\) 11.4945 + 9.64506i 0.827395 + 0.694267i 0.954691 0.297598i \(-0.0961855\pi\)
−0.127296 + 0.991865i \(0.540630\pi\)
\(194\) 2.42371 13.7456i 0.174013 0.986874i
\(195\) 0 0
\(196\) −2.14543 + 1.80023i −0.153245 + 0.128588i
\(197\) 11.1606 + 19.3307i 0.795158 + 1.37725i 0.922739 + 0.385426i \(0.125946\pi\)
−0.127580 + 0.991828i \(0.540721\pi\)
\(198\) 0 0
\(199\) 4.55051 7.88171i 0.322577 0.558720i −0.658442 0.752631i \(-0.728784\pi\)
0.981019 + 0.193912i \(0.0621176\pi\)
\(200\) 0.358995 + 2.03596i 0.0253847 + 0.143964i
\(201\) 0 0
\(202\) 8.65657 3.15074i 0.609074 0.221685i
\(203\) −7.70410 + 2.80406i −0.540722 + 0.196807i
\(204\) 0 0
\(205\) 1.60607 + 9.10846i 0.112173 + 0.636162i
\(206\) −13.4166 + 23.2383i −0.934781 + 1.61909i
\(207\) 0 0
\(208\) −9.96838 17.2657i −0.691183 1.19716i
\(209\) 10.3914 8.71941i 0.718787 0.603134i
\(210\) 0 0
\(211\) −1.03802 + 5.88690i −0.0714602 + 0.405271i 0.928005 + 0.372568i \(0.121523\pi\)
−0.999465 + 0.0327028i \(0.989589\pi\)
\(212\) 6.71929 + 5.63816i 0.461483 + 0.387230i
\(213\) 0 0
\(214\) 21.5326 + 7.83721i 1.47194 + 0.535741i
\(215\) 3.93923 0.268653
\(216\) 0 0
\(217\) 10.1061 0.686045
\(218\) 27.0296 + 9.83796i 1.83067 + 0.666311i
\(219\) 0 0
\(220\) −11.6099 9.74189i −0.782742 0.656798i
\(221\) 2.40409 13.6343i 0.161717 0.917141i
\(222\) 0 0
\(223\) −6.81908 + 5.72189i −0.456639 + 0.383166i −0.841893 0.539645i \(-0.818558\pi\)
0.385253 + 0.922811i \(0.374114\pi\)
\(224\) 9.21291 + 15.9572i 0.615564 + 1.06619i
\(225\) 0 0
\(226\) 4.62449 8.00984i 0.307616 0.532807i
\(227\) −1.85256 10.5064i −0.122959 0.697334i −0.982499 0.186266i \(-0.940361\pi\)
0.859540 0.511068i \(-0.170750\pi\)
\(228\) 0 0
\(229\) 7.77244 2.82894i 0.513617 0.186941i −0.0721913 0.997391i \(-0.522999\pi\)
0.585809 + 0.810449i \(0.300777\pi\)
\(230\) 3.55596 1.29426i 0.234473 0.0853412i
\(231\) 0 0
\(232\) −0.144086 0.817150i −0.00945968 0.0536485i
\(233\) −6.36965 + 11.0326i −0.417290 + 0.722767i −0.995666 0.0930034i \(-0.970353\pi\)
0.578376 + 0.815770i \(0.303687\pi\)
\(234\) 0 0
\(235\) 0.439693 + 0.761570i 0.0286824 + 0.0496793i
\(236\) −19.1654 + 16.0817i −1.24756 + 1.04683i
\(237\) 0 0
\(238\) −2.35638 + 13.3637i −0.152742 + 0.866240i
\(239\) 11.5026 + 9.65183i 0.744041 + 0.624325i 0.933920 0.357483i \(-0.116365\pi\)
−0.189878 + 0.981808i \(0.560809\pi\)
\(240\) 0 0
\(241\) −0.747626 0.272114i −0.0481588 0.0175284i 0.317828 0.948148i \(-0.397046\pi\)
−0.365987 + 0.930620i \(0.619269\pi\)
\(242\) 12.3180 0.791832
\(243\) 0 0
\(244\) −6.90673 −0.442158
\(245\) 5.18355 + 1.88666i 0.331165 + 0.120534i
\(246\) 0 0
\(247\) 22.4991 + 18.8790i 1.43158 + 1.20124i
\(248\) −0.177610 + 1.00727i −0.0112782 + 0.0639620i
\(249\) 0 0
\(250\) −20.6780 + 17.3509i −1.30779 + 1.09737i
\(251\) −4.15749 7.20099i −0.262419 0.454522i 0.704465 0.709738i \(-0.251187\pi\)
−0.966884 + 0.255216i \(0.917853\pi\)
\(252\) 0 0
\(253\) 0.565360 0.979232i 0.0355439 0.0615638i
\(254\) −2.08342 11.8157i −0.130726 0.741381i
\(255\) 0 0
\(256\) −16.6814 + 6.07153i −1.04259 + 0.379471i
\(257\) 24.0752 8.76264i 1.50177 0.546599i 0.545250 0.838274i \(-0.316435\pi\)
0.956517 + 0.291675i \(0.0942126\pi\)
\(258\) 0 0
\(259\) −0.982926 5.57445i −0.0610760 0.346379i
\(260\) 16.4073 28.4183i 1.01754 1.76243i
\(261\) 0 0
\(262\) 10.1912 + 17.6517i 0.629614 + 1.09052i
\(263\) 21.4990 18.0398i 1.32569 1.11238i 0.340622 0.940200i \(-0.389362\pi\)
0.985065 0.172183i \(-0.0550821\pi\)
\(264\) 0 0
\(265\) 3.00000 17.0138i 0.184289 1.04515i
\(266\) −22.0526 18.5043i −1.35213 1.13457i
\(267\) 0 0
\(268\) −25.2520 9.19096i −1.54251 0.561427i
\(269\) −30.1710 −1.83956 −0.919778 0.392439i \(-0.871631\pi\)
−0.919778 + 0.392439i \(0.871631\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) −11.6577 4.24304i −0.706849 0.257272i
\(273\) 0 0
\(274\) −28.7952 24.1620i −1.73958 1.45968i
\(275\) −3.29207 + 18.6702i −0.198519 + 1.12586i
\(276\) 0 0
\(277\) 16.1800 13.5767i 0.972165 0.815743i −0.0107242 0.999942i \(-0.503414\pi\)
0.982889 + 0.184199i \(0.0589692\pi\)
\(278\) −22.9496 39.7499i −1.37643 2.38404i
\(279\) 0 0
\(280\) 1.03209 1.78763i 0.0616791 0.106831i
\(281\) −0.303415 1.72075i −0.0181002 0.102651i 0.974419 0.224738i \(-0.0721526\pi\)
−0.992519 + 0.122086i \(0.961041\pi\)
\(282\) 0 0
\(283\) 6.84864 2.49270i 0.407109 0.148176i −0.130345 0.991469i \(-0.541608\pi\)
0.537454 + 0.843293i \(0.319386\pi\)
\(284\) −2.12467 + 0.773318i −0.126076 + 0.0458880i
\(285\) 0 0
\(286\) −3.51455 19.9320i −0.207820 1.17860i
\(287\) 2.93247 5.07919i 0.173098 0.299815i
\(288\) 0 0
\(289\) 4.19253 + 7.26168i 0.246620 + 0.427158i
\(290\) 19.5075 16.3687i 1.14552 0.961204i
\(291\) 0 0
\(292\) −1.52734 + 8.66198i −0.0893809 + 0.506904i
\(293\) −11.7595 9.86736i −0.686995 0.576458i 0.231046 0.972943i \(-0.425785\pi\)
−0.918041 + 0.396485i \(0.870230\pi\)
\(294\) 0 0
\(295\) 46.3055 + 16.8538i 2.69601 + 0.981267i
\(296\) 0.572881 0.0332980
\(297\) 0 0
\(298\) −30.5408 −1.76918
\(299\) 2.30056 + 0.837334i 0.133045 + 0.0484243i
\(300\) 0 0
\(301\) −1.91353 1.60565i −0.110294 0.0925479i
\(302\) 2.01849 11.4474i 0.116151 0.658726i
\(303\) 0 0
\(304\) 20.1609 16.9170i 1.15631 0.970257i
\(305\) 6.80180 + 11.7811i 0.389470 + 0.674581i
\(306\) 0 0
\(307\) −8.38191 + 14.5179i −0.478381 + 0.828580i −0.999693 0.0247861i \(-0.992110\pi\)
0.521312 + 0.853366i \(0.325443\pi\)
\(308\) 1.66885 + 9.46451i 0.0950914 + 0.539290i
\(309\) 0 0
\(310\) −29.4971 + 10.7361i −1.67532 + 0.609767i
\(311\) −15.0568 + 5.48024i −0.853794 + 0.310756i −0.731586 0.681749i \(-0.761220\pi\)
−0.122208 + 0.992505i \(0.538998\pi\)
\(312\) 0 0
\(313\) 5.97447 + 33.8829i 0.337697 + 1.91517i 0.398789 + 0.917043i \(0.369431\pi\)
−0.0610920 + 0.998132i \(0.519458\pi\)
\(314\) −1.19372 + 2.06758i −0.0673654 + 0.116680i
\(315\) 0 0
\(316\) 12.0287 + 20.8343i 0.676666 + 1.17202i
\(317\) 12.4950 10.4846i 0.701791 0.588872i −0.220492 0.975389i \(-0.570766\pi\)
0.922283 + 0.386516i \(0.126322\pi\)
\(318\) 0 0
\(319\) 1.32130 7.49346i 0.0739786 0.419553i
\(320\) −19.8714 16.6741i −1.11085 0.932111i
\(321\) 0 0
\(322\) −2.25490 0.820717i −0.125661 0.0457367i
\(323\) 18.2761 1.01691
\(324\) 0 0
\(325\) −41.0479 −2.27693
\(326\) 5.13295 + 1.86824i 0.284288 + 0.103472i
\(327\) 0 0
\(328\) 0.454707 + 0.381545i 0.0251070 + 0.0210673i
\(329\) 0.0968323 0.549163i 0.00533854 0.0302763i
\(330\) 0 0
\(331\) −24.1917 + 20.2992i −1.32969 + 1.11575i −0.345545 + 0.938402i \(0.612306\pi\)
−0.984149 + 0.177343i \(0.943250\pi\)
\(332\) 10.6222 + 18.3983i 0.582972 + 1.00974i
\(333\) 0 0
\(334\) −3.76991 + 6.52968i −0.206281 + 0.357288i
\(335\) 9.19096 + 52.1245i 0.502156 + 2.84787i
\(336\) 0 0
\(337\) −5.64290 + 2.05385i −0.307389 + 0.111880i −0.491109 0.871098i \(-0.663408\pi\)
0.183720 + 0.982979i \(0.441186\pi\)
\(338\) 17.1183 6.23055i 0.931113 0.338897i
\(339\) 0 0
\(340\) −3.54576 20.1090i −0.192296 1.09056i
\(341\) −4.68972 + 8.12284i −0.253963 + 0.439876i
\(342\) 0 0
\(343\) −9.96451 17.2590i −0.538033 0.931900i
\(344\) 0.193665 0.162504i 0.0104417 0.00876162i
\(345\) 0 0
\(346\) 2.40420 13.6349i 0.129251 0.733017i
\(347\) −17.6423 14.8037i −0.947089 0.794702i 0.0317162 0.999497i \(-0.489903\pi\)
−0.978805 + 0.204795i \(0.934347\pi\)
\(348\) 0 0
\(349\) 10.8687 + 3.95589i 0.581789 + 0.211754i 0.616114 0.787657i \(-0.288706\pi\)
−0.0343254 + 0.999411i \(0.510928\pi\)
\(350\) 40.2332 2.15056
\(351\) 0 0
\(352\) −17.1010 −0.911487
\(353\) −2.00589 0.730085i −0.106763 0.0388585i 0.288086 0.957604i \(-0.406981\pi\)
−0.394849 + 0.918746i \(0.629203\pi\)
\(354\) 0 0
\(355\) 3.41147 + 2.86257i 0.181062 + 0.151929i
\(356\) 0.228213 1.29426i 0.0120953 0.0685958i
\(357\) 0 0
\(358\) 21.7049 18.2125i 1.14714 0.962563i
\(359\) 12.1118 + 20.9782i 0.639234 + 1.10719i 0.985601 + 0.169087i \(0.0540818\pi\)
−0.346367 + 0.938099i \(0.612585\pi\)
\(360\) 0 0
\(361\) −9.88578 + 17.1227i −0.520304 + 0.901193i
\(362\) −4.51476 25.6045i −0.237290 1.34574i
\(363\) 0 0
\(364\) −19.5535 + 7.11689i −1.02488 + 0.373027i
\(365\) 16.2792 5.92514i 0.852092 0.310136i
\(366\) 0 0
\(367\) −0.492259 2.79174i −0.0256957 0.145728i 0.969261 0.246036i \(-0.0791282\pi\)
−0.994956 + 0.100308i \(0.968017\pi\)
\(368\) 1.09689 1.89986i 0.0571792 0.0990372i
\(369\) 0 0
\(370\) 8.79086 + 15.2262i 0.457015 + 0.791573i
\(371\) −8.39220 + 7.04189i −0.435701 + 0.365597i
\(372\) 0 0
\(373\) −5.00686 + 28.3953i −0.259246 + 1.47025i 0.525689 + 0.850677i \(0.323807\pi\)
−0.784935 + 0.619578i \(0.787304\pi\)
\(374\) −9.64771 8.09539i −0.498871 0.418603i
\(375\) 0 0
\(376\) 0.0530334 + 0.0193026i 0.00273499 + 0.000995455i
\(377\) 16.4749 0.848501
\(378\) 0 0
\(379\) 32.1985 1.65393 0.826963 0.562256i \(-0.190066\pi\)
0.826963 + 0.562256i \(0.190066\pi\)
\(380\) 40.7057 + 14.8157i 2.08816 + 0.760028i
\(381\) 0 0
\(382\) −20.2533 16.9945i −1.03625 0.869516i
\(383\) −0.116735 + 0.662037i −0.00596488 + 0.0338285i −0.987645 0.156708i \(-0.949912\pi\)
0.981680 + 0.190537i \(0.0610229\pi\)
\(384\) 0 0
\(385\) 14.5005 12.1673i 0.739012 0.620105i
\(386\) 14.7771 + 25.5947i 0.752134 + 1.30273i
\(387\) 0 0
\(388\) 6.65910 11.5339i 0.338065 0.585545i
\(389\) 0.739620 + 4.19459i 0.0375002 + 0.212674i 0.997800 0.0662958i \(-0.0211181\pi\)
−0.960300 + 0.278970i \(0.910007\pi\)
\(390\) 0 0
\(391\) 1.43154 0.521038i 0.0723962 0.0263500i
\(392\) 0.332669 0.121082i 0.0168023 0.00611554i
\(393\) 0 0
\(394\) 7.63429 + 43.2962i 0.384610 + 2.18123i
\(395\) 23.6919 41.0355i 1.19207 2.06472i
\(396\) 0 0
\(397\) 4.43242 + 7.67717i 0.222457 + 0.385306i 0.955553 0.294818i \(-0.0952591\pi\)
−0.733097 + 0.680124i \(0.761926\pi\)
\(398\) 13.7317 11.5223i 0.688309 0.577560i
\(399\) 0 0
\(400\) −6.38713 + 36.2232i −0.319356 + 1.81116i
\(401\) −28.4079 23.8371i −1.41862 1.19037i −0.952072 0.305874i \(-0.901051\pi\)
−0.466552 0.884494i \(-0.654504\pi\)
\(402\) 0 0
\(403\) −19.0834 6.94578i −0.950610 0.345994i
\(404\) 8.79012 0.437325
\(405\) 0 0
\(406\) −16.1480 −0.801410
\(407\) 4.93664 + 1.79679i 0.244700 + 0.0890635i
\(408\) 0 0
\(409\) −2.59627 2.17853i −0.128377 0.107721i 0.576339 0.817211i \(-0.304481\pi\)
−0.704716 + 0.709490i \(0.748925\pi\)
\(410\) −3.16333 + 17.9402i −0.156226 + 0.886001i
\(411\) 0 0
\(412\) −19.6138 + 16.4579i −0.966303 + 0.810824i
\(413\) −15.6238 27.0612i −0.768798 1.33160i
\(414\) 0 0
\(415\) 20.9217 36.2375i 1.02701 1.77883i
\(416\) −6.42960 36.4641i −0.315237 1.78780i
\(417\) 0 0
\(418\) 25.1065 9.13803i 1.22800 0.446956i
\(419\) −19.4106 + 7.06489i −0.948272 + 0.345143i −0.769427 0.638735i \(-0.779458\pi\)
−0.178845 + 0.983877i \(0.557236\pi\)
\(420\) 0 0
\(421\) 4.78106 + 27.1147i 0.233015 + 1.32149i 0.846755 + 0.531983i \(0.178553\pi\)
−0.613740 + 0.789508i \(0.710336\pi\)
\(422\) −5.88690 + 10.1964i −0.286570 + 0.496353i
\(423\) 0 0
\(424\) −0.554378 0.960210i −0.0269230 0.0466319i
\(425\) −19.5666 + 16.4183i −0.949120 + 0.796406i
\(426\) 0 0
\(427\) 1.49794 8.49524i 0.0724904 0.411114i
\(428\) 16.7494 + 14.0544i 0.809611 + 0.679344i
\(429\) 0 0
\(430\) 7.29086 + 2.65366i 0.351596 + 0.127971i
\(431\) 2.58110 0.124327 0.0621636 0.998066i \(-0.480200\pi\)
0.0621636 + 0.998066i \(0.480200\pi\)
\(432\) 0 0
\(433\) −27.0137 −1.29820 −0.649098 0.760704i \(-0.724854\pi\)
−0.649098 + 0.760704i \(0.724854\pi\)
\(434\) 18.7046 + 6.80793i 0.897852 + 0.326791i
\(435\) 0 0
\(436\) 21.0253 + 17.6423i 1.00693 + 0.844913i
\(437\) −0.561202 + 3.18273i −0.0268459 + 0.152251i
\(438\) 0 0
\(439\) 8.97044 7.52709i 0.428136 0.359248i −0.403112 0.915151i \(-0.632072\pi\)
0.831248 + 0.555902i \(0.187627\pi\)
\(440\) 0.957882 + 1.65910i 0.0456652 + 0.0790945i
\(441\) 0 0
\(442\) 13.6343 23.6153i 0.648517 1.12326i
\(443\) −0.361323 2.04916i −0.0171670 0.0973587i 0.975020 0.222115i \(-0.0712961\pi\)
−0.992187 + 0.124757i \(0.960185\pi\)
\(444\) 0 0
\(445\) −2.43242 + 0.885328i −0.115308 + 0.0419686i
\(446\) −16.4755 + 5.99660i −0.780138 + 0.283947i
\(447\) 0 0
\(448\) 2.85638 + 16.1993i 0.134951 + 0.765347i
\(449\) 5.27541 9.13728i 0.248962 0.431215i −0.714276 0.699864i \(-0.753244\pi\)
0.963238 + 0.268649i \(0.0865772\pi\)
\(450\) 0 0
\(451\) 2.72163 + 4.71400i 0.128157 + 0.221974i
\(452\) 6.76055 5.67277i 0.317989 0.266825i
\(453\) 0 0
\(454\) 3.64883 20.6936i 0.171248 0.971197i
\(455\) 31.3960 + 26.3444i 1.47187 + 1.23504i
\(456\) 0 0
\(457\) 7.43242 + 2.70518i 0.347674 + 0.126543i 0.509954 0.860202i \(-0.329663\pi\)
−0.162280 + 0.986745i \(0.551885\pi\)
\(458\) 16.2912 0.761238
\(459\) 0 0
\(460\) 3.61081 0.168355
\(461\) −36.7352 13.3705i −1.71093 0.622727i −0.713935 0.700212i \(-0.753089\pi\)
−0.996994 + 0.0774846i \(0.975311\pi\)
\(462\) 0 0
\(463\) 18.1498 + 15.2295i 0.843491 + 0.707773i 0.958346 0.285609i \(-0.0921959\pi\)
−0.114855 + 0.993382i \(0.536640\pi\)
\(464\) 2.56353 14.5385i 0.119009 0.674932i
\(465\) 0 0
\(466\) −19.2212 + 16.1285i −0.890406 + 0.747139i
\(467\) −17.3576 30.0642i −0.803214 1.39121i −0.917490 0.397758i \(-0.869788\pi\)
0.114277 0.993449i \(-0.463545\pi\)
\(468\) 0 0
\(469\) 16.7815 29.0665i 0.774899 1.34216i
\(470\) 0.300767 + 1.70574i 0.0138734 + 0.0786798i
\(471\) 0 0
\(472\) 2.97178 1.08164i 0.136787 0.0497865i
\(473\) 2.17853 0.792919i 0.100169 0.0364584i
\(474\) 0 0
\(475\) −9.40941 53.3634i −0.431734 2.44848i
\(476\) −6.47410 + 11.2135i −0.296740 + 0.513969i
\(477\) 0 0
\(478\) 14.7875 + 25.6126i 0.676362 + 1.17149i
\(479\) 4.96529 4.16637i 0.226870 0.190366i −0.522266 0.852782i \(-0.674913\pi\)
0.749136 + 0.662416i \(0.230469\pi\)
\(480\) 0 0
\(481\) −1.97519 + 11.2018i −0.0900607 + 0.510760i
\(482\) −1.20042 1.00727i −0.0546777 0.0458801i
\(483\) 0 0
\(484\) 11.0449 + 4.02001i 0.502040 + 0.182728i
\(485\) −26.2317 −1.19112
\(486\) 0 0
\(487\) 19.9828 0.905505 0.452753 0.891636i \(-0.350442\pi\)
0.452753 + 0.891636i \(0.350442\pi\)
\(488\) 0.820397 + 0.298600i 0.0371376 + 0.0135170i
\(489\) 0 0
\(490\) 8.32295 + 6.98378i 0.375992 + 0.315495i
\(491\) 4.55428 25.8286i 0.205532 1.16563i −0.691068 0.722789i \(-0.742860\pi\)
0.896600 0.442840i \(-0.146029\pi\)
\(492\) 0 0
\(493\) 7.85323 6.58964i 0.353692 0.296782i
\(494\) 28.9243 + 50.0984i 1.30137 + 2.25403i
\(495\) 0 0
\(496\) −9.09879 + 15.7596i −0.408548 + 0.707626i
\(497\) −0.490376 2.78106i −0.0219964 0.124748i
\(498\) 0 0
\(499\) −5.93629 + 2.16063i −0.265745 + 0.0967232i −0.471456 0.881890i \(-0.656271\pi\)
0.205711 + 0.978613i \(0.434049\pi\)
\(500\) −24.2033 + 8.80928i −1.08240 + 0.393963i
\(501\) 0 0
\(502\) −2.84389 16.1285i −0.126929 0.719851i
\(503\) −10.9131 + 18.9020i −0.486589 + 0.842798i −0.999881 0.0154166i \(-0.995093\pi\)
0.513292 + 0.858214i \(0.328426\pi\)
\(504\) 0 0
\(505\) −8.65657 14.9936i −0.385212 0.667208i
\(506\) 1.70604 1.43154i 0.0758429 0.0636398i
\(507\) 0 0
\(508\) 1.98798 11.2744i 0.0882023 0.500220i
\(509\) −22.2866 18.7007i −0.987837 0.828893i −0.00258346 0.999997i \(-0.500822\pi\)
−0.985253 + 0.171103i \(0.945267\pi\)
\(510\) 0 0
\(511\) −10.3229 3.75725i −0.456660 0.166211i
\(512\) −31.1704 −1.37755
\(513\) 0 0
\(514\) 50.4620 2.22579
\(515\) 47.3887 + 17.2481i 2.08820 + 0.760042i
\(516\) 0 0
\(517\) 0.396459 + 0.332669i 0.0174363 + 0.0146308i
\(518\) 1.93599 10.9795i 0.0850623 0.482413i
\(519\) 0 0
\(520\) −3.17752 + 2.66625i −0.139343 + 0.116923i
\(521\) −6.84743 11.8601i −0.299991 0.519600i 0.676142 0.736771i \(-0.263650\pi\)
−0.976134 + 0.217171i \(0.930317\pi\)
\(522\) 0 0
\(523\) −6.57532 + 11.3888i −0.287519 + 0.497997i −0.973217 0.229889i \(-0.926164\pi\)
0.685698 + 0.727886i \(0.259497\pi\)
\(524\) 3.37722 + 19.1532i 0.147535 + 0.836710i
\(525\) 0 0
\(526\) 51.9436 18.9059i 2.26485 0.824338i
\(527\) −11.8748 + 4.32207i −0.517274 + 0.188272i
\(528\) 0 0
\(529\) −3.94713 22.3853i −0.171614 0.973273i
\(530\) 17.0138 29.4688i 0.739034 1.28004i
\(531\) 0 0
\(532\) −13.7344 23.7887i −0.595463 1.03137i
\(533\) −9.02828 + 7.57563i −0.391058 + 0.328137i
\(534\) 0 0
\(535\) 7.47818 42.4109i 0.323310 1.83358i
\(536\) 2.60213 + 2.18345i 0.112395 + 0.0943106i
\(537\) 0 0
\(538\) −55.8414 20.3246i −2.40749 0.876256i
\(539\) 3.24644 0.139834
\(540\) 0 0
\(541\) 6.26083 0.269174 0.134587 0.990902i \(-0.457029\pi\)
0.134587 + 0.990902i \(0.457029\pi\)
\(542\) −35.1658 12.7993i −1.51050 0.549778i
\(543\) 0 0
\(544\) −17.6498 14.8099i −0.756728 0.634970i
\(545\) 9.38728 53.2379i 0.402107 2.28046i
\(546\) 0 0
\(547\) −24.0371 + 20.1696i −1.02775 + 0.862388i −0.990582 0.136921i \(-0.956279\pi\)
−0.0371720 + 0.999309i \(0.511835\pi\)
\(548\) −17.9337 31.0621i −0.766091 1.32691i
\(549\) 0 0
\(550\) −18.6702 + 32.3378i −0.796102 + 1.37889i
\(551\) 3.77655 + 21.4179i 0.160886 + 0.912432i
\(552\) 0 0
\(553\) −28.2349 + 10.2767i −1.20067 + 0.437008i
\(554\) 39.0925 14.2285i 1.66088 0.604511i
\(555\) 0 0
\(556\) −7.60519 43.1312i −0.322532 1.82917i
\(557\) −21.7196 + 37.6195i −0.920290 + 1.59399i −0.121324 + 0.992613i \(0.538714\pi\)
−0.798966 + 0.601376i \(0.794619\pi\)
\(558\) 0 0
\(559\) 2.50980 + 4.34710i 0.106153 + 0.183863i
\(560\) 28.1332 23.6065i 1.18884 0.997558i
\(561\) 0 0
\(562\) 0.597611 3.38922i 0.0252087 0.142966i
\(563\) 24.5269 + 20.5805i 1.03369 + 0.867366i 0.991285 0.131734i \(-0.0420546\pi\)
0.0424018 + 0.999101i \(0.486499\pi\)
\(564\) 0 0
\(565\) −16.3341 5.94512i −0.687180 0.250113i
\(566\) 14.3549 0.603381
\(567\) 0 0
\(568\) 0.285807 0.0119922
\(569\) −6.36355 2.31614i −0.266774 0.0970977i 0.205170 0.978726i \(-0.434225\pi\)
−0.471944 + 0.881629i \(0.656447\pi\)
\(570\) 0 0
\(571\) −16.2041 13.5969i −0.678122 0.569012i 0.237335 0.971428i \(-0.423726\pi\)
−0.915457 + 0.402416i \(0.868171\pi\)
\(572\) 3.35354 19.0189i 0.140219 0.795220i
\(573\) 0 0
\(574\) 8.84911 7.42528i 0.369355 0.309925i
\(575\) −2.25838 3.91164i −0.0941811 0.163127i
\(576\) 0 0
\(577\) −5.95811 + 10.3198i −0.248039 + 0.429617i −0.962982 0.269567i \(-0.913120\pi\)
0.714942 + 0.699183i \(0.246453\pi\)
\(578\) 2.86786 + 16.2645i 0.119287 + 0.676512i
\(579\) 0 0
\(580\) 22.8332 8.31061i 0.948098 0.345079i
\(581\) −24.9336 + 9.07507i −1.03442 + 0.376497i
\(582\) 0 0
\(583\) −1.76558 10.0131i −0.0731228 0.414700i
\(584\) 0.555907 0.962859i 0.0230036 0.0398434i
\(585\) 0 0
\(586\) −15.1177 26.1846i −0.624506 1.08168i
\(587\) 0.0994798 0.0834734i 0.00410597 0.00344532i −0.640732 0.767764i \(-0.721369\pi\)
0.644838 + 0.764319i \(0.276925\pi\)
\(588\) 0 0
\(589\) 4.65523 26.4011i 0.191815 1.08784i
\(590\) 74.3501 + 62.3872i 3.06095 + 2.56844i
\(591\) 0 0
\(592\) 9.57785 + 3.48605i 0.393647 + 0.143276i
\(593\) −26.2622 −1.07846 −0.539230 0.842158i \(-0.681285\pi\)
−0.539230 + 0.842158i \(0.681285\pi\)
\(594\) 0 0
\(595\) 25.5030 1.04552
\(596\) −27.3842 9.96703i −1.12170 0.408266i
\(597\) 0 0
\(598\) 3.69388 + 3.09953i 0.151054 + 0.126749i
\(599\) −4.79185 + 27.1759i −0.195790 + 1.11038i 0.715500 + 0.698613i \(0.246199\pi\)
−0.911290 + 0.411766i \(0.864912\pi\)
\(600\) 0 0
\(601\) 1.02094 0.856674i 0.0416452 0.0349445i −0.621728 0.783234i \(-0.713569\pi\)
0.663373 + 0.748289i \(0.269124\pi\)
\(602\) −2.45999 4.26083i −0.100262 0.173658i
\(603\) 0 0
\(604\) 5.54576 9.60554i 0.225654 0.390844i
\(605\) −4.02001 22.7986i −0.163437 0.926895i
\(606\) 0 0
\(607\) 11.8068 4.29731i 0.479221 0.174422i −0.0911037 0.995841i \(-0.529039\pi\)
0.570325 + 0.821419i \(0.306817\pi\)
\(608\) 45.9305 16.7173i 1.86273 0.677978i
\(609\) 0 0
\(610\) 4.65270 + 26.3868i 0.188382 + 1.06837i
\(611\) −0.560282 + 0.970437i −0.0226666 + 0.0392597i
\(612\) 0 0
\(613\) 6.99912 + 12.1228i 0.282692 + 0.489637i 0.972047 0.234787i \(-0.0754393\pi\)
−0.689355 + 0.724424i \(0.742106\pi\)
\(614\) −25.2935 + 21.2237i −1.02076 + 0.856521i
\(615\) 0 0
\(616\) 0.210952 1.19637i 0.00849948 0.0482030i
\(617\) −18.4209 15.4569i −0.741596 0.622273i 0.191670 0.981459i \(-0.438610\pi\)
−0.933266 + 0.359187i \(0.883054\pi\)
\(618\) 0 0
\(619\) −6.45723 2.35024i −0.259538 0.0944642i 0.208974 0.977921i \(-0.432988\pi\)
−0.468512 + 0.883457i \(0.655210\pi\)
\(620\) −29.9521 −1.20291
\(621\) 0 0
\(622\) −31.5594 −1.26542
\(623\) 1.54244 + 0.561403i 0.0617967 + 0.0224921i
\(624\) 0 0
\(625\) 5.53003 + 4.64025i 0.221201 + 0.185610i
\(626\) −11.7674 + 66.7363i −0.470320 + 2.66732i
\(627\) 0 0
\(628\) −1.74510 + 1.46431i −0.0696371 + 0.0584324i
\(629\) 3.53898 + 6.12970i 0.141109 + 0.244407i
\(630\) 0 0
\(631\) 17.6887 30.6377i 0.704175 1.21967i −0.262814 0.964847i \(-0.584651\pi\)
0.966989 0.254820i \(-0.0820161\pi\)
\(632\) −0.528061 2.99479i −0.0210052 0.119126i
\(633\) 0 0
\(634\) 30.1891 10.9879i 1.19896 0.436387i
\(635\) −21.1889 + 7.71213i −0.840856 + 0.306047i
\(636\) 0 0
\(637\) 1.22059 + 6.92231i 0.0483615 + 0.274272i
\(638\) 7.49346 12.9791i 0.296669 0.513846i
\(639\) 0 0
\(640\) 3.51114 + 6.08148i 0.138790 + 0.240392i
\(641\) 14.6879 12.3246i 0.580136 0.486792i −0.304855 0.952399i \(-0.598608\pi\)
0.884992 + 0.465606i \(0.154164\pi\)
\(642\) 0 0
\(643\) 3.36468 19.0820i 0.132690 0.752521i −0.843751 0.536735i \(-0.819657\pi\)
0.976441 0.215786i \(-0.0692315\pi\)
\(644\) −1.75400 1.47178i −0.0691173 0.0579963i
\(645\) 0 0
\(646\) 33.8259 + 12.3116i 1.33086 + 0.484395i
\(647\) −8.77141 −0.344840 −0.172420 0.985024i \(-0.555159\pi\)
−0.172420 + 0.985024i \(0.555159\pi\)
\(648\) 0 0
\(649\) 29.0009 1.13839
\(650\) −75.9728 27.6518i −2.97990 1.08459i
\(651\) 0 0
\(652\) 3.99273 + 3.35029i 0.156367 + 0.131208i
\(653\) −5.69729 + 32.3109i −0.222952 + 1.26442i 0.643609 + 0.765354i \(0.277436\pi\)
−0.866562 + 0.499070i \(0.833675\pi\)
\(654\) 0 0
\(655\) 29.3444 24.6228i 1.14658 0.962094i
\(656\) 5.28039 + 9.14590i 0.206164 + 0.357087i
\(657\) 0 0
\(658\) 0.549163 0.951178i 0.0214086 0.0370808i
\(659\) −3.23882 18.3682i −0.126166 0.715525i −0.980608 0.195978i \(-0.937212\pi\)
0.854442 0.519547i \(-0.173899\pi\)
\(660\) 0 0
\(661\) −34.2117 + 12.4520i −1.33068 + 0.484329i −0.906866 0.421420i \(-0.861532\pi\)
−0.423816 + 0.905748i \(0.639310\pi\)
\(662\) −58.4492 + 21.2738i −2.27169 + 0.826829i
\(663\) 0 0
\(664\) −0.466319 2.64462i −0.0180967 0.102631i
\(665\) −27.0515 + 46.8546i −1.04901 + 1.81694i
\(666\) 0 0
\(667\) 0.906422 + 1.56997i 0.0350968 + 0.0607894i
\(668\) −5.51125 + 4.62449i −0.213237 + 0.178927i
\(669\) 0 0
\(670\) −18.1027 + 102.665i −0.699367 + 3.96631i
\(671\) 6.13300 + 5.14620i 0.236762 + 0.198667i
\(672\) 0 0
\(673\) −37.0146 13.4722i −1.42681 0.519316i −0.490793 0.871276i \(-0.663293\pi\)
−0.936015 + 0.351960i \(0.885515\pi\)
\(674\) −11.8276 −0.455584
\(675\) 0 0
\(676\) 17.3824 0.668553
\(677\) 29.7651 + 10.8336i 1.14397 + 0.416370i 0.843345 0.537373i \(-0.180583\pi\)
0.300623 + 0.953743i \(0.402806\pi\)
\(678\) 0 0
\(679\) 12.7424 + 10.6922i 0.489009 + 0.410327i
\(680\) −0.448204 + 2.54189i −0.0171878 + 0.0974770i
\(681\) 0 0
\(682\) −14.1518 + 11.8748i −0.541901 + 0.454709i
\(683\) −14.5328 25.1716i −0.556083 0.963164i −0.997818 0.0660187i \(-0.978970\pi\)
0.441735 0.897145i \(-0.354363\pi\)
\(684\) 0 0
\(685\) −35.3225 + 61.1804i −1.34960 + 2.33758i
\(686\) −6.81612 38.6562i −0.260241 1.47590i
\(687\) 0 0
\(688\) 4.22668 1.53839i 0.161141 0.0586504i
\(689\) 20.6869 7.52940i 0.788107 0.286847i
\(690\) 0 0
\(691\) 0.930303 + 5.27601i 0.0353904 + 0.200709i 0.997376 0.0723898i \(-0.0230626\pi\)
−0.961986 + 0.273099i \(0.911951\pi\)
\(692\) 6.60549 11.4410i 0.251103 0.434923i
\(693\) 0 0
\(694\) −22.6805 39.2838i −0.860940 1.49119i
\(695\) −66.0808 + 55.4484i −2.50659 + 2.10328i
\(696\) 0 0
\(697\) −1.27348 + 7.22227i −0.0482365 + 0.273563i
\(698\) 17.4513 + 14.6434i 0.660541 + 0.554260i
\(699\) 0 0
\(700\) 36.0749 + 13.1302i 1.36350 + 0.496275i
\(701\) 25.6536 0.968922 0.484461 0.874813i \(-0.339016\pi\)
0.484461 + 0.874813i \(0.339016\pi\)
\(702\) 0 0
\(703\) −15.0155 −0.566320
\(704\) −14.3459 5.22147i −0.540680 0.196791i
\(705\) 0 0
\(706\) −3.22075 2.70253i −0.121215 0.101711i
\(707\) −1.90641 + 10.8118i −0.0716980 + 0.406620i
\(708\) 0 0
\(709\) −3.59311 + 3.01498i −0.134942 + 0.113230i −0.707761 0.706452i \(-0.750294\pi\)
0.572818 + 0.819682i \(0.305850\pi\)
\(710\) 4.38571 + 7.59627i 0.164593 + 0.285083i
\(711\) 0 0
\(712\) −0.0830629 + 0.143869i −0.00311291 + 0.00539173i
\(713\) −0.388040 2.20068i −0.0145322 0.0824163i
\(714\) 0 0
\(715\) −35.7438 + 13.0097i −1.33674 + 0.486535i
\(716\) 25.4052 9.24675i 0.949438 0.345567i
\(717\) 0 0
\(718\) 8.28493 + 46.9862i 0.309191 + 1.75351i
\(719\) 19.5335 33.8330i 0.728476 1.26176i −0.229052 0.973414i \(-0.573562\pi\)
0.957527 0.288343i \(-0.0931042\pi\)
\(720\) 0 0
\(721\) −15.9893 27.6943i −0.595473 1.03139i
\(722\) −29.8316 + 25.0317i −1.11022 + 0.931583i
\(723\) 0 0
\(724\) 4.30793 24.4315i 0.160103 0.907990i
\(725\) −23.2840 19.5376i −0.864747 0.725609i
\(726\) 0 0
\(727\) 10.1725 + 3.70247i 0.377276 + 0.137317i 0.523696 0.851905i \(-0.324553\pi\)
−0.146420 + 0.989223i \(0.546775\pi\)
\(728\) 2.63030 0.0974853
\(729\) 0 0
\(730\) 34.1215 1.26290
\(731\) 2.93512 + 1.06830i 0.108559 + 0.0395124i
\(732\) 0 0
\(733\) −2.61406 2.19345i −0.0965524 0.0810171i 0.593234 0.805030i \(-0.297851\pi\)
−0.689786 + 0.724013i \(0.742295\pi\)
\(734\) 0.969561 5.49866i 0.0357872 0.202959i
\(735\) 0 0
\(736\) 3.12108 2.61890i 0.115045 0.0965339i
\(737\) 15.5749 + 26.9766i 0.573710 + 0.993695i
\(738\) 0 0
\(739\) −13.1505 + 22.7773i −0.483748 + 0.837877i −0.999826 0.0186653i \(-0.994058\pi\)
0.516077 + 0.856542i \(0.327392\pi\)
\(740\) 2.91317 + 16.5214i 0.107090 + 0.607339i
\(741\) 0 0
\(742\) −20.2763 + 7.37997i −0.744367 + 0.270927i
\(743\) 27.1984 9.89940i 0.997811 0.363174i 0.209071 0.977900i \(-0.432956\pi\)
0.788740 + 0.614727i \(0.210734\pi\)
\(744\) 0 0
\(745\) 9.96703 + 56.5259i 0.365164 + 2.07095i
\(746\) −28.3953 + 49.1822i −1.03963 + 1.80069i
\(747\) 0 0
\(748\) −6.00862 10.4072i −0.219697 0.380526i
\(749\) −20.9194 + 17.5535i −0.764380 + 0.641391i
\(750\) 0 0
\(751\) −3.37716 + 19.1528i −0.123234 + 0.698897i 0.859106 + 0.511797i \(0.171020\pi\)
−0.982341 + 0.187100i \(0.940091\pi\)
\(752\) 0.769193 + 0.645430i 0.0280496 + 0.0235364i
\(753\) 0 0
\(754\) 30.4923 + 11.0983i 1.11046 + 0.404176i
\(755\) −21.8460 −0.795058
\(756\) 0 0
\(757\) 6.59627 0.239745 0.119873 0.992789i \(-0.461751\pi\)
0.119873 + 0.992789i \(0.461751\pi\)
\(758\) 59.5941 + 21.6905i 2.16455 + 0.787833i
\(759\) 0 0
\(760\) −4.19459 3.51968i −0.152154 0.127672i
\(761\) −1.79373 + 10.1728i −0.0650228 + 0.368763i 0.934882 + 0.354959i \(0.115505\pi\)
−0.999905 + 0.0138038i \(0.995606\pi\)
\(762\) 0 0
\(763\) −26.2600 + 22.0347i −0.950674 + 0.797710i
\(764\) −12.6138 21.8478i −0.456352 0.790424i
\(765\) 0 0
\(766\) −0.662037 + 1.14668i −0.0239204 + 0.0414313i
\(767\) 10.9037 + 61.8380i 0.393710 + 2.23284i
\(768\) 0 0
\(769\) −42.1536 + 15.3427i −1.52010 + 0.553271i −0.961173 0.275947i \(-0.911009\pi\)
−0.558926 + 0.829217i \(0.688786\pi\)
\(770\) 35.0344 12.7515i 1.26255 0.459532i
\(771\) 0 0
\(772\) 4.89693 + 27.7718i 0.176244 + 0.999531i
\(773\) 21.4677 37.1832i 0.772141 1.33739i −0.164247 0.986419i \(-0.552519\pi\)
0.936388 0.350968i \(-0.114147\pi\)
\(774\) 0 0
\(775\) 18.7335 + 32.4475i 0.672929 + 1.16555i
\(776\) −1.28963 + 1.08213i −0.0462951 + 0.0388462i
\(777\) 0 0
\(778\) −1.45677 + 8.26173i −0.0522276 + 0.296198i
\(779\) −11.9181 10.0005i −0.427010 0.358304i
\(780\) 0 0