Properties

Label 567.2.w.a.37.10
Level $567$
Weight $2$
Character 567.37
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(37,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.w (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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.10
Character \(\chi\) \(=\) 567.37
Dual form 567.2.w.a.46.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0910389 - 0.516307i) q^{2} +(1.62110 - 0.590032i) q^{4} +(-0.0290567 + 0.164789i) q^{5} +(-0.352779 + 2.62213i) q^{7} +(-0.976493 - 1.69134i) q^{8} +O(q^{10})\) \(q+(-0.0910389 - 0.516307i) q^{2} +(1.62110 - 0.590032i) q^{4} +(-0.0290567 + 0.164789i) q^{5} +(-0.352779 + 2.62213i) q^{7} +(-0.976493 - 1.69134i) q^{8} +0.0877269 q^{10} +(0.765229 + 4.33983i) q^{11} +(2.84925 + 2.39080i) q^{13} +(1.38594 - 0.0565734i) q^{14} +(1.85872 - 1.55965i) q^{16} +5.82553 q^{17} -2.90577 q^{19} +(0.0501268 + 0.284283i) q^{20} +(2.17102 - 0.790186i) q^{22} +(-3.96175 - 3.32431i) q^{23} +(4.67215 + 1.70052i) q^{25} +(0.974996 - 1.68874i) q^{26} +(0.975250 + 4.45888i) q^{28} +(4.36652 - 3.66395i) q^{29} +(-4.90997 + 1.78708i) q^{31} +(-3.96662 - 3.32839i) q^{32} +(-0.530350 - 3.00776i) q^{34} +(-0.421846 - 0.134324i) q^{35} +(-1.57282 - 2.72421i) q^{37} +(0.264538 + 1.50027i) q^{38} +(0.307087 - 0.111770i) q^{40} +(-0.151822 - 0.127394i) q^{41} +(-0.469933 - 0.171042i) q^{43} +(3.80115 + 6.58378i) q^{44} +(-1.35569 + 2.34812i) q^{46} +(2.74267 + 0.998251i) q^{47} +(-6.75109 - 1.85006i) q^{49} +(0.452646 - 2.56708i) q^{50} +(6.02956 + 2.19458i) q^{52} +(-2.31775 - 4.01446i) q^{53} -0.737389 q^{55} +(4.77938 - 1.96382i) q^{56} +(-2.28925 - 1.92091i) q^{58} +(2.66671 + 2.23764i) q^{59} +(8.98407 + 3.26993i) q^{61} +(1.36968 + 2.37236i) q^{62} +(1.06902 - 1.85160i) q^{64} +(-0.476766 + 0.400054i) q^{65} +(2.47407 - 14.0311i) q^{67} +(9.44377 - 3.43725i) q^{68} +(-0.0309482 + 0.230031i) q^{70} +(3.85452 - 6.67622i) q^{71} +(-6.89159 + 11.9366i) q^{73} +(-1.26334 + 1.06007i) q^{74} +(-4.71055 + 1.71450i) q^{76} +(-11.6495 + 0.475528i) q^{77} +(-0.654200 - 3.71015i) q^{79} +(0.203004 + 0.351613i) q^{80} +(-0.0519526 + 0.0899846i) q^{82} +(-13.0814 + 10.9766i) q^{83} +(-0.169271 + 0.959981i) q^{85} +(-0.0455279 + 0.258201i) q^{86} +(6.59287 - 5.53207i) q^{88} +7.43742 q^{89} +(-7.27413 + 6.62766i) q^{91} +(-8.38384 - 3.05147i) q^{92} +(0.265714 - 1.50694i) q^{94} +(0.0844320 - 0.478838i) q^{95} +(-4.44029 - 1.61613i) q^{97} +(-0.340587 + 3.65407i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0910389 0.516307i −0.0643742 0.365084i −0.999929 0.0119032i \(-0.996211\pi\)
0.935555 0.353181i \(-0.114900\pi\)
\(3\) 0 0
\(4\) 1.62110 0.590032i 0.810550 0.295016i
\(5\) −0.0290567 + 0.164789i −0.0129945 + 0.0736957i −0.990615 0.136679i \(-0.956357\pi\)
0.977621 + 0.210374i \(0.0674683\pi\)
\(6\) 0 0
\(7\) −0.352779 + 2.62213i −0.133338 + 0.991071i
\(8\) −0.976493 1.69134i −0.345243 0.597978i
\(9\) 0 0
\(10\) 0.0877269 0.0277417
\(11\) 0.765229 + 4.33983i 0.230725 + 1.30851i 0.851432 + 0.524465i \(0.175735\pi\)
−0.620707 + 0.784043i \(0.713154\pi\)
\(12\) 0 0
\(13\) 2.84925 + 2.39080i 0.790238 + 0.663089i 0.945804 0.324737i \(-0.105276\pi\)
−0.155566 + 0.987825i \(0.549720\pi\)
\(14\) 1.38594 0.0565734i 0.370408 0.0151199i
\(15\) 0 0
\(16\) 1.85872 1.55965i 0.464679 0.389912i
\(17\) 5.82553 1.41290 0.706449 0.707764i \(-0.250296\pi\)
0.706449 + 0.707764i \(0.250296\pi\)
\(18\) 0 0
\(19\) −2.90577 −0.666630 −0.333315 0.942816i \(-0.608167\pi\)
−0.333315 + 0.942816i \(0.608167\pi\)
\(20\) 0.0501268 + 0.284283i 0.0112087 + 0.0635676i
\(21\) 0 0
\(22\) 2.17102 0.790186i 0.462863 0.168468i
\(23\) −3.96175 3.32431i −0.826083 0.693166i 0.128305 0.991735i \(-0.459046\pi\)
−0.954388 + 0.298569i \(0.903491\pi\)
\(24\) 0 0
\(25\) 4.67215 + 1.70052i 0.934430 + 0.340105i
\(26\) 0.974996 1.68874i 0.191212 0.331190i
\(27\) 0 0
\(28\) 0.975250 + 4.45888i 0.184305 + 0.842649i
\(29\) 4.36652 3.66395i 0.810843 0.680378i −0.139966 0.990156i \(-0.544699\pi\)
0.950809 + 0.309778i \(0.100255\pi\)
\(30\) 0 0
\(31\) −4.90997 + 1.78708i −0.881856 + 0.320969i −0.742959 0.669337i \(-0.766578\pi\)
−0.138898 + 0.990307i \(0.544356\pi\)
\(32\) −3.96662 3.32839i −0.701206 0.588382i
\(33\) 0 0
\(34\) −0.530350 3.00776i −0.0909543 0.515827i
\(35\) −0.421846 0.134324i −0.0713050 0.0227049i
\(36\) 0 0
\(37\) −1.57282 2.72421i −0.258570 0.447857i 0.707289 0.706925i \(-0.249918\pi\)
−0.965859 + 0.259068i \(0.916585\pi\)
\(38\) 0.264538 + 1.50027i 0.0429138 + 0.243376i
\(39\) 0 0
\(40\) 0.307087 0.111770i 0.0485546 0.0176724i
\(41\) −0.151822 0.127394i −0.0237106 0.0198956i 0.630855 0.775900i \(-0.282704\pi\)
−0.654566 + 0.756005i \(0.727149\pi\)
\(42\) 0 0
\(43\) −0.469933 0.171042i −0.0716641 0.0260836i 0.305939 0.952051i \(-0.401030\pi\)
−0.377603 + 0.925967i \(0.623252\pi\)
\(44\) 3.80115 + 6.58378i 0.573045 + 0.992543i
\(45\) 0 0
\(46\) −1.35569 + 2.34812i −0.199886 + 0.346212i
\(47\) 2.74267 + 0.998251i 0.400060 + 0.145610i 0.534211 0.845351i \(-0.320609\pi\)
−0.134152 + 0.990961i \(0.542831\pi\)
\(48\) 0 0
\(49\) −6.75109 1.85006i −0.964442 0.264294i
\(50\) 0.452646 2.56708i 0.0640138 0.363040i
\(51\) 0 0
\(52\) 6.02956 + 2.19458i 0.836150 + 0.304334i
\(53\) −2.31775 4.01446i −0.318368 0.551429i 0.661780 0.749698i \(-0.269801\pi\)
−0.980148 + 0.198269i \(0.936468\pi\)
\(54\) 0 0
\(55\) −0.737389 −0.0994295
\(56\) 4.77938 1.96382i 0.638672 0.262427i
\(57\) 0 0
\(58\) −2.28925 1.92091i −0.300593 0.252227i
\(59\) 2.66671 + 2.23764i 0.347177 + 0.291316i 0.799655 0.600460i \(-0.205016\pi\)
−0.452479 + 0.891775i \(0.649460\pi\)
\(60\) 0 0
\(61\) 8.98407 + 3.26993i 1.15029 + 0.418672i 0.845620 0.533785i \(-0.179231\pi\)
0.304672 + 0.952457i \(0.401453\pi\)
\(62\) 1.36968 + 2.37236i 0.173950 + 0.301290i
\(63\) 0 0
\(64\) 1.06902 1.85160i 0.133628 0.231450i
\(65\) −0.476766 + 0.400054i −0.0591356 + 0.0496206i
\(66\) 0 0
\(67\) 2.47407 14.0311i 0.302255 1.71418i −0.333895 0.942610i \(-0.608363\pi\)
0.636150 0.771565i \(-0.280526\pi\)
\(68\) 9.44377 3.43725i 1.14523 0.416828i
\(69\) 0 0
\(70\) −0.0309482 + 0.230031i −0.00369901 + 0.0274940i
\(71\) 3.85452 6.67622i 0.457447 0.792321i −0.541378 0.840779i \(-0.682097\pi\)
0.998825 + 0.0484578i \(0.0154306\pi\)
\(72\) 0 0
\(73\) −6.89159 + 11.9366i −0.806599 + 1.39707i 0.108607 + 0.994085i \(0.465361\pi\)
−0.915206 + 0.402986i \(0.867972\pi\)
\(74\) −1.26334 + 1.06007i −0.146860 + 0.123230i
\(75\) 0 0
\(76\) −4.71055 + 1.71450i −0.540337 + 0.196666i
\(77\) −11.6495 + 0.475528i −1.32759 + 0.0541915i
\(78\) 0 0
\(79\) −0.654200 3.71015i −0.0736033 0.417425i −0.999239 0.0390088i \(-0.987580\pi\)
0.925636 0.378416i \(-0.123531\pi\)
\(80\) 0.203004 + 0.351613i 0.0226965 + 0.0393115i
\(81\) 0 0
\(82\) −0.0519526 + 0.0899846i −0.00573721 + 0.00993713i
\(83\) −13.0814 + 10.9766i −1.43587 + 1.20484i −0.493739 + 0.869610i \(0.664370\pi\)
−0.942135 + 0.335232i \(0.891185\pi\)
\(84\) 0 0
\(85\) −0.169271 + 0.959981i −0.0183600 + 0.104125i
\(86\) −0.0455279 + 0.258201i −0.00490940 + 0.0278426i
\(87\) 0 0
\(88\) 6.59287 5.53207i 0.702802 0.589721i
\(89\) 7.43742 0.788365 0.394182 0.919032i \(-0.371028\pi\)
0.394182 + 0.919032i \(0.371028\pi\)
\(90\) 0 0
\(91\) −7.27413 + 6.62766i −0.762536 + 0.694767i
\(92\) −8.38384 3.05147i −0.874076 0.318138i
\(93\) 0 0
\(94\) 0.265714 1.50694i 0.0274063 0.155429i
\(95\) 0.0844320 0.478838i 0.00866254 0.0491277i
\(96\) 0 0
\(97\) −4.44029 1.61613i −0.450843 0.164094i 0.106612 0.994301i \(-0.466000\pi\)
−0.557455 + 0.830207i \(0.688222\pi\)
\(98\) −0.340587 + 3.65407i −0.0344045 + 0.369117i
\(99\) 0 0
\(100\) 8.57739 0.857739
\(101\) −8.08668 + 6.78553i −0.804655 + 0.675185i −0.949326 0.314294i \(-0.898232\pi\)
0.144671 + 0.989480i \(0.453788\pi\)
\(102\) 0 0
\(103\) 1.97305 11.1897i 0.194410 1.10256i −0.718845 0.695170i \(-0.755329\pi\)
0.913256 0.407387i \(-0.133560\pi\)
\(104\) 1.26138 7.15363i 0.123688 0.701471i
\(105\) 0 0
\(106\) −1.86169 + 1.56214i −0.180823 + 0.151729i
\(107\) −3.33654 + 5.77905i −0.322555 + 0.558682i −0.981015 0.193934i \(-0.937875\pi\)
0.658459 + 0.752616i \(0.271208\pi\)
\(108\) 0 0
\(109\) 4.03004 + 6.98023i 0.386008 + 0.668585i 0.991908 0.126955i \(-0.0405205\pi\)
−0.605901 + 0.795540i \(0.707187\pi\)
\(110\) 0.0671311 + 0.380719i 0.00640070 + 0.0363002i
\(111\) 0 0
\(112\) 3.43388 + 5.42400i 0.324471 + 0.512519i
\(113\) −19.4781 + 7.08946i −1.83235 + 0.666921i −0.840136 + 0.542376i \(0.817525\pi\)
−0.992214 + 0.124544i \(0.960253\pi\)
\(114\) 0 0
\(115\) 0.662923 0.556258i 0.0618179 0.0518714i
\(116\) 4.91672 8.51602i 0.456506 0.790692i
\(117\) 0 0
\(118\) 0.912535 1.58056i 0.0840056 0.145502i
\(119\) −2.05512 + 15.2753i −0.188393 + 1.40028i
\(120\) 0 0
\(121\) −7.91191 + 2.87970i −0.719264 + 0.261791i
\(122\) 0.870391 4.93623i 0.0788015 0.446905i
\(123\) 0 0
\(124\) −6.90511 + 5.79408i −0.620097 + 0.520324i
\(125\) −0.834311 + 1.44507i −0.0746230 + 0.129251i
\(126\) 0 0
\(127\) −9.57031 16.5763i −0.849228 1.47091i −0.881898 0.471440i \(-0.843735\pi\)
0.0326704 0.999466i \(-0.489599\pi\)
\(128\) −10.7849 3.92538i −0.953258 0.346958i
\(129\) 0 0
\(130\) 0.249955 + 0.209737i 0.0219225 + 0.0183952i
\(131\) −6.04416 5.07165i −0.528081 0.443112i 0.339357 0.940658i \(-0.389790\pi\)
−0.867438 + 0.497545i \(0.834235\pi\)
\(132\) 0 0
\(133\) 1.02509 7.61930i 0.0888869 0.660677i
\(134\) −7.46961 −0.645276
\(135\) 0 0
\(136\) −5.68859 9.85293i −0.487793 0.844882i
\(137\) 2.08979 + 0.760623i 0.178543 + 0.0649844i 0.429745 0.902950i \(-0.358604\pi\)
−0.251202 + 0.967935i \(0.580826\pi\)
\(138\) 0 0
\(139\) 1.70860 9.68995i 0.144921 0.821891i −0.822509 0.568753i \(-0.807426\pi\)
0.967430 0.253138i \(-0.0814627\pi\)
\(140\) −0.763110 + 0.0311498i −0.0644946 + 0.00263264i
\(141\) 0 0
\(142\) −3.79789 1.38232i −0.318712 0.116002i
\(143\) −8.19534 + 14.1947i −0.685329 + 1.18702i
\(144\) 0 0
\(145\) 0.476900 + 0.826015i 0.0396044 + 0.0685968i
\(146\) 6.79035 + 2.47148i 0.561973 + 0.204541i
\(147\) 0 0
\(148\) −4.15707 3.48820i −0.341709 0.286728i
\(149\) 13.6915 4.98332i 1.12166 0.408249i 0.286399 0.958110i \(-0.407542\pi\)
0.835256 + 0.549861i \(0.185319\pi\)
\(150\) 0 0
\(151\) −0.638711 3.62231i −0.0519776 0.294779i 0.947727 0.319082i \(-0.103375\pi\)
−0.999705 + 0.0243026i \(0.992263\pi\)
\(152\) 2.83747 + 4.91464i 0.230149 + 0.398630i
\(153\) 0 0
\(154\) 1.30608 + 5.97145i 0.105247 + 0.481193i
\(155\) −0.151823 0.861033i −0.0121947 0.0691599i
\(156\) 0 0
\(157\) −9.90610 8.31221i −0.790593 0.663386i 0.155299 0.987867i \(-0.450366\pi\)
−0.945892 + 0.324481i \(0.894810\pi\)
\(158\) −1.85602 + 0.675537i −0.147657 + 0.0537428i
\(159\) 0 0
\(160\) 0.663738 0.556942i 0.0524731 0.0440301i
\(161\) 10.1144 9.21547i 0.797124 0.726281i
\(162\) 0 0
\(163\) −5.79198 + 10.0320i −0.453663 + 0.785767i −0.998610 0.0527032i \(-0.983216\pi\)
0.544947 + 0.838470i \(0.316550\pi\)
\(164\) −0.321285 0.116938i −0.0250881 0.00913133i
\(165\) 0 0
\(166\) 6.85824 + 5.75475i 0.532303 + 0.446655i
\(167\) −11.8334 + 4.30699i −0.915693 + 0.333285i −0.756524 0.653966i \(-0.773104\pi\)
−0.159170 + 0.987251i \(0.550882\pi\)
\(168\) 0 0
\(169\) 0.144844 + 0.821452i 0.0111419 + 0.0631887i
\(170\) 0.511056 0.0391962
\(171\) 0 0
\(172\) −0.862728 −0.0657824
\(173\) 12.4806 10.4724i 0.948880 0.796204i −0.0302289 0.999543i \(-0.509624\pi\)
0.979108 + 0.203339i \(0.0651792\pi\)
\(174\) 0 0
\(175\) −6.10722 + 11.6511i −0.461663 + 0.880738i
\(176\) 8.19094 + 6.87302i 0.617415 + 0.518073i
\(177\) 0 0
\(178\) −0.677095 3.83999i −0.0507504 0.287820i
\(179\) −3.97648 −0.297216 −0.148608 0.988896i \(-0.547479\pi\)
−0.148608 + 0.988896i \(0.547479\pi\)
\(180\) 0 0
\(181\) −0.0601490 0.104181i −0.00447084 0.00774372i 0.863781 0.503867i \(-0.168090\pi\)
−0.868252 + 0.496123i \(0.834756\pi\)
\(182\) 4.08414 + 3.15231i 0.302736 + 0.233665i
\(183\) 0 0
\(184\) −1.75389 + 9.94682i −0.129299 + 0.733289i
\(185\) 0.494619 0.180027i 0.0363651 0.0132358i
\(186\) 0 0
\(187\) 4.45786 + 25.2818i 0.325991 + 1.84879i
\(188\) 5.03514 0.367226
\(189\) 0 0
\(190\) −0.254914 −0.0184934
\(191\) 2.28213 + 12.9426i 0.165129 + 0.936493i 0.948931 + 0.315482i \(0.102166\pi\)
−0.783802 + 0.621010i \(0.786723\pi\)
\(192\) 0 0
\(193\) −5.65411 + 2.05793i −0.406992 + 0.148133i −0.537400 0.843327i \(-0.680593\pi\)
0.130408 + 0.991460i \(0.458371\pi\)
\(194\) −0.430183 + 2.43969i −0.0308853 + 0.175159i
\(195\) 0 0
\(196\) −12.0358 + 0.984231i −0.859700 + 0.0703022i
\(197\) −7.14867 12.3819i −0.509321 0.882171i −0.999942 0.0107972i \(-0.996563\pi\)
0.490620 0.871374i \(-0.336770\pi\)
\(198\) 0 0
\(199\) 1.31297 0.0930741 0.0465371 0.998917i \(-0.485181\pi\)
0.0465371 + 0.998917i \(0.485181\pi\)
\(200\) −1.68617 9.56273i −0.119230 0.676187i
\(201\) 0 0
\(202\) 4.23962 + 3.55747i 0.298299 + 0.250302i
\(203\) 8.06692 + 12.7421i 0.566187 + 0.894323i
\(204\) 0 0
\(205\) 0.0254045 0.0213169i 0.00177432 0.00148884i
\(206\) −5.95696 −0.415041
\(207\) 0 0
\(208\) 9.02474 0.625753
\(209\) −2.22358 12.6105i −0.153808 0.872290i
\(210\) 0 0
\(211\) 18.9172 6.88531i 1.30232 0.474005i 0.404566 0.914509i \(-0.367423\pi\)
0.897751 + 0.440504i \(0.145200\pi\)
\(212\) −6.12597 5.14030i −0.420733 0.353037i
\(213\) 0 0
\(214\) 3.28752 + 1.19656i 0.224730 + 0.0817952i
\(215\) 0.0418404 0.0724697i 0.00285349 0.00494239i
\(216\) 0 0
\(217\) −2.95382 13.5050i −0.200519 0.916779i
\(218\) 3.23705 2.71621i 0.219241 0.183965i
\(219\) 0 0
\(220\) −1.19538 + 0.435083i −0.0805926 + 0.0293333i
\(221\) 16.5984 + 13.9277i 1.11653 + 0.936877i
\(222\) 0 0
\(223\) 2.38617 + 13.5327i 0.159790 + 0.906214i 0.954275 + 0.298930i \(0.0966297\pi\)
−0.794485 + 0.607284i \(0.792259\pi\)
\(224\) 10.1268 9.22680i 0.676625 0.616492i
\(225\) 0 0
\(226\) 5.43361 + 9.41129i 0.361439 + 0.626030i
\(227\) −2.30630 13.0797i −0.153074 0.868128i −0.960525 0.278193i \(-0.910265\pi\)
0.807451 0.589935i \(-0.200847\pi\)
\(228\) 0 0
\(229\) 13.3651 4.86451i 0.883192 0.321456i 0.139695 0.990195i \(-0.455388\pi\)
0.743497 + 0.668739i \(0.233166\pi\)
\(230\) −0.347552 0.291631i −0.0229169 0.0192296i
\(231\) 0 0
\(232\) −10.4609 3.80744i −0.686788 0.249971i
\(233\) −10.2255 17.7111i −0.669897 1.16030i −0.977933 0.208921i \(-0.933005\pi\)
0.308036 0.951375i \(-0.400328\pi\)
\(234\) 0 0
\(235\) −0.244193 + 0.422955i −0.0159294 + 0.0275905i
\(236\) 5.64329 + 2.05399i 0.367347 + 0.133703i
\(237\) 0 0
\(238\) 8.07384 0.329570i 0.523349 0.0213629i
\(239\) −0.879905 + 4.99019i −0.0569163 + 0.322788i −0.999951 0.00990621i \(-0.996847\pi\)
0.943035 + 0.332695i \(0.107958\pi\)
\(240\) 0 0
\(241\) −5.26663 1.91690i −0.339254 0.123478i 0.166775 0.985995i \(-0.446665\pi\)
−0.506028 + 0.862517i \(0.668887\pi\)
\(242\) 2.20710 + 3.82281i 0.141878 + 0.245740i
\(243\) 0 0
\(244\) 16.4934 1.05588
\(245\) 0.501033 1.05875i 0.0320098 0.0676408i
\(246\) 0 0
\(247\) −8.27925 6.94712i −0.526796 0.442035i
\(248\) 7.81711 + 6.55933i 0.496387 + 0.416518i
\(249\) 0 0
\(250\) 0.822055 + 0.299203i 0.0519913 + 0.0189233i
\(251\) −3.77146 6.53236i −0.238053 0.412319i 0.722103 0.691786i \(-0.243176\pi\)
−0.960155 + 0.279467i \(0.909842\pi\)
\(252\) 0 0
\(253\) 11.3953 19.7372i 0.716414 1.24087i
\(254\) −7.68718 + 6.45031i −0.482337 + 0.404728i
\(255\) 0 0
\(256\) −0.302321 + 1.71455i −0.0188950 + 0.107159i
\(257\) 7.73949 2.81694i 0.482776 0.175716i −0.0891550 0.996018i \(-0.528417\pi\)
0.571931 + 0.820302i \(0.306194\pi\)
\(258\) 0 0
\(259\) 7.69808 3.16310i 0.478335 0.196545i
\(260\) −0.536841 + 0.929835i −0.0332934 + 0.0576659i
\(261\) 0 0
\(262\) −2.06828 + 3.58236i −0.127779 + 0.221319i
\(263\) 7.23383 6.06990i 0.446057 0.374286i −0.391913 0.920002i \(-0.628187\pi\)
0.837970 + 0.545716i \(0.183742\pi\)
\(264\) 0 0
\(265\) 0.728884 0.265292i 0.0447750 0.0162968i
\(266\) −4.02722 + 0.164389i −0.246925 + 0.0100794i
\(267\) 0 0
\(268\) −4.26811 24.2056i −0.260716 1.47860i
\(269\) 7.22050 + 12.5063i 0.440242 + 0.762521i 0.997707 0.0676791i \(-0.0215594\pi\)
−0.557465 + 0.830200i \(0.688226\pi\)
\(270\) 0 0
\(271\) −0.0795025 + 0.137702i −0.00482943 + 0.00836482i −0.868430 0.495812i \(-0.834871\pi\)
0.863601 + 0.504177i \(0.168204\pi\)
\(272\) 10.8280 9.08577i 0.656544 0.550906i
\(273\) 0 0
\(274\) 0.202463 1.14822i 0.0122312 0.0693666i
\(275\) −3.80472 + 21.5776i −0.229433 + 1.30118i
\(276\) 0 0
\(277\) −7.95742 + 6.67707i −0.478115 + 0.401186i −0.849744 0.527195i \(-0.823244\pi\)
0.371629 + 0.928381i \(0.378799\pi\)
\(278\) −5.15854 −0.309389
\(279\) 0 0
\(280\) 0.184742 + 0.844650i 0.0110405 + 0.0504775i
\(281\) 15.0687 + 5.48457i 0.898924 + 0.327182i 0.749822 0.661640i \(-0.230139\pi\)
0.149103 + 0.988822i \(0.452361\pi\)
\(282\) 0 0
\(283\) 0.0723941 0.410567i 0.00430338 0.0244057i −0.982580 0.185838i \(-0.940500\pi\)
0.986884 + 0.161432i \(0.0516112\pi\)
\(284\) 2.30937 13.0971i 0.137036 0.777170i
\(285\) 0 0
\(286\) 8.07495 + 2.93904i 0.477482 + 0.173789i
\(287\) 0.387602 0.353154i 0.0228794 0.0208460i
\(288\) 0 0
\(289\) 16.9368 0.996283
\(290\) 0.383061 0.321427i 0.0224941 0.0188748i
\(291\) 0 0
\(292\) −4.12899 + 23.4166i −0.241631 + 1.37036i
\(293\) 5.33332 30.2467i 0.311576 1.76703i −0.279234 0.960223i \(-0.590081\pi\)
0.590810 0.806811i \(-0.298808\pi\)
\(294\) 0 0
\(295\) −0.446223 + 0.374426i −0.0259801 + 0.0217999i
\(296\) −3.07170 + 5.32034i −0.178539 + 0.309239i
\(297\) 0 0
\(298\) −3.81939 6.61537i −0.221251 0.383218i
\(299\) −3.34025 18.9435i −0.193172 1.09553i
\(300\) 0 0
\(301\) 0.614275 1.17188i 0.0354062 0.0675463i
\(302\) −1.81208 + 0.659543i −0.104273 + 0.0379524i
\(303\) 0 0
\(304\) −5.40100 + 4.53198i −0.309769 + 0.259927i
\(305\) −0.799895 + 1.38546i −0.0458018 + 0.0793311i
\(306\) 0 0
\(307\) −3.38224 + 5.85821i −0.193035 + 0.334346i −0.946254 0.323423i \(-0.895166\pi\)
0.753220 + 0.657769i \(0.228500\pi\)
\(308\) −18.6045 + 7.64448i −1.06009 + 0.435585i
\(309\) 0 0
\(310\) −0.430736 + 0.156775i −0.0244642 + 0.00890423i
\(311\) −0.660957 + 3.74847i −0.0374794 + 0.212556i −0.997796 0.0663558i \(-0.978863\pi\)
0.960317 + 0.278912i \(0.0899739\pi\)
\(312\) 0 0
\(313\) 13.6497 11.4534i 0.771526 0.647387i −0.169573 0.985518i \(-0.554239\pi\)
0.941099 + 0.338131i \(0.109795\pi\)
\(314\) −3.38981 + 5.87133i −0.191298 + 0.331338i
\(315\) 0 0
\(316\) −3.24963 5.62853i −0.182806 0.316630i
\(317\) 9.06781 + 3.30041i 0.509299 + 0.185370i 0.583872 0.811846i \(-0.301537\pi\)
−0.0745729 + 0.997216i \(0.523759\pi\)
\(318\) 0 0
\(319\) 19.2423 + 16.1462i 1.07736 + 0.904014i
\(320\) 0.274061 + 0.229964i 0.0153205 + 0.0128554i
\(321\) 0 0
\(322\) −5.67882 4.38316i −0.316468 0.244264i
\(323\) −16.9277 −0.941880
\(324\) 0 0
\(325\) 9.24649 + 16.0154i 0.512903 + 0.888374i
\(326\) 5.70689 + 2.07714i 0.316076 + 0.115042i
\(327\) 0 0
\(328\) −0.0672125 + 0.381181i −0.00371119 + 0.0210472i
\(329\) −3.58510 + 6.83947i −0.197653 + 0.377072i
\(330\) 0 0
\(331\) −13.0406 4.74638i −0.716775 0.260885i −0.0422189 0.999108i \(-0.513443\pi\)
−0.674556 + 0.738224i \(0.735665\pi\)
\(332\) −14.7298 + 25.5127i −0.808401 + 1.40019i
\(333\) 0 0
\(334\) 3.30103 + 5.71755i 0.180624 + 0.312850i
\(335\) 2.24028 + 0.815396i 0.122400 + 0.0445498i
\(336\) 0 0
\(337\) 24.4425 + 20.5097i 1.33147 + 1.11723i 0.983733 + 0.179639i \(0.0574930\pi\)
0.347734 + 0.937593i \(0.386951\pi\)
\(338\) 0.410936 0.149568i 0.0223519 0.00813544i
\(339\) 0 0
\(340\) 0.292015 + 1.65610i 0.0158367 + 0.0898146i
\(341\) −11.5129 19.9409i −0.623457 1.07986i
\(342\) 0 0
\(343\) 7.23273 17.0496i 0.390531 0.920590i
\(344\) 0.169598 + 0.961836i 0.00914409 + 0.0518587i
\(345\) 0 0
\(346\) −6.54321 5.49041i −0.351765 0.295166i
\(347\) 22.1987 8.07967i 1.19169 0.433739i 0.331373 0.943500i \(-0.392488\pi\)
0.860316 + 0.509761i \(0.170266\pi\)
\(348\) 0 0
\(349\) 0.379417 0.318369i 0.0203097 0.0170419i −0.632576 0.774498i \(-0.718003\pi\)
0.652886 + 0.757456i \(0.273558\pi\)
\(350\) 6.57153 + 2.09251i 0.351263 + 0.111849i
\(351\) 0 0
\(352\) 11.4093 19.7614i 0.608116 1.05329i
\(353\) −20.6890 7.53018i −1.10116 0.400791i −0.273419 0.961895i \(-0.588155\pi\)
−0.827745 + 0.561104i \(0.810377\pi\)
\(354\) 0 0
\(355\) 0.988165 + 0.829169i 0.0524464 + 0.0440077i
\(356\) 12.0568 4.38832i 0.639009 0.232580i
\(357\) 0 0
\(358\) 0.362015 + 2.05309i 0.0191331 + 0.108509i
\(359\) 33.3784 1.76164 0.880822 0.473448i \(-0.156991\pi\)
0.880822 + 0.473448i \(0.156991\pi\)
\(360\) 0 0
\(361\) −10.5565 −0.555605
\(362\) −0.0483136 + 0.0405399i −0.00253931 + 0.00213073i
\(363\) 0 0
\(364\) −7.88157 + 15.0361i −0.413106 + 0.788104i
\(365\) −1.76677 1.48249i −0.0924767 0.0775972i
\(366\) 0 0
\(367\) 5.35778 + 30.3855i 0.279674 + 1.58611i 0.723713 + 0.690101i \(0.242434\pi\)
−0.444039 + 0.896007i \(0.646455\pi\)
\(368\) −12.5485 −0.654136
\(369\) 0 0
\(370\) −0.137979 0.238986i −0.00717317 0.0124243i
\(371\) 11.3441 4.66122i 0.588955 0.241999i
\(372\) 0 0
\(373\) −2.46530 + 13.9814i −0.127648 + 0.723929i 0.852051 + 0.523458i \(0.175358\pi\)
−0.979700 + 0.200471i \(0.935753\pi\)
\(374\) 12.6473 4.60326i 0.653978 0.238029i
\(375\) 0 0
\(376\) −0.989823 5.61357i −0.0510462 0.289498i
\(377\) 21.2011 1.09191
\(378\) 0 0
\(379\) −31.8848 −1.63781 −0.818907 0.573926i \(-0.805420\pi\)
−0.818907 + 0.573926i \(0.805420\pi\)
\(380\) −0.145657 0.826062i −0.00747205 0.0423761i
\(381\) 0 0
\(382\) 6.47459 2.35656i 0.331269 0.120572i
\(383\) −2.72859 + 15.4746i −0.139425 + 0.790716i 0.832251 + 0.554399i \(0.187052\pi\)
−0.971676 + 0.236318i \(0.924059\pi\)
\(384\) 0 0
\(385\) 0.260135 1.93353i 0.0132577 0.0985417i
\(386\) 1.57727 + 2.73191i 0.0802808 + 0.139050i
\(387\) 0 0
\(388\) −8.15173 −0.413841
\(389\) −4.01215 22.7541i −0.203424 1.15368i −0.899900 0.436096i \(-0.856361\pi\)
0.696476 0.717580i \(-0.254750\pi\)
\(390\) 0 0
\(391\) −23.0793 19.3658i −1.16717 0.979373i
\(392\) 3.46333 + 13.2249i 0.174924 + 0.667960i
\(393\) 0 0
\(394\) −5.74204 + 4.81814i −0.289280 + 0.242734i
\(395\) 0.630400 0.0317189
\(396\) 0 0
\(397\) 6.26112 0.314237 0.157118 0.987580i \(-0.449780\pi\)
0.157118 + 0.987580i \(0.449780\pi\)
\(398\) −0.119532 0.677897i −0.00599158 0.0339799i
\(399\) 0 0
\(400\) 11.3364 4.12612i 0.566821 0.206306i
\(401\) −22.5668 18.9358i −1.12693 0.945607i −0.127996 0.991775i \(-0.540855\pi\)
−0.998934 + 0.0461680i \(0.985299\pi\)
\(402\) 0 0
\(403\) −18.2623 6.64692i −0.909708 0.331107i
\(404\) −9.10564 + 15.7714i −0.453022 + 0.784658i
\(405\) 0 0
\(406\) 5.84446 5.32504i 0.290056 0.264277i
\(407\) 10.6190 8.91042i 0.526365 0.441673i
\(408\) 0 0
\(409\) 16.2666 5.92057i 0.804334 0.292754i 0.0930527 0.995661i \(-0.470337\pi\)
0.711281 + 0.702908i \(0.248115\pi\)
\(410\) −0.0133189 0.0111758i −0.000657771 0.000551936i
\(411\) 0 0
\(412\) −3.40379 19.3038i −0.167692 0.951031i
\(413\) −6.80813 + 6.20307i −0.335006 + 0.305233i
\(414\) 0 0
\(415\) −1.42872 2.47462i −0.0701331 0.121474i
\(416\) −3.34436 18.9668i −0.163971 0.929924i
\(417\) 0 0
\(418\) −6.30849 + 2.29610i −0.308558 + 0.112306i
\(419\) 8.30352 + 6.96748i 0.405653 + 0.340384i 0.822674 0.568513i \(-0.192481\pi\)
−0.417021 + 0.908897i \(0.636926\pi\)
\(420\) 0 0
\(421\) 3.82428 + 1.39192i 0.186384 + 0.0678382i 0.433526 0.901141i \(-0.357269\pi\)
−0.247142 + 0.968979i \(0.579491\pi\)
\(422\) −5.27714 9.14028i −0.256887 0.444942i
\(423\) 0 0
\(424\) −4.52654 + 7.84019i −0.219828 + 0.380754i
\(425\) 27.2178 + 9.90646i 1.32026 + 0.480534i
\(426\) 0 0
\(427\) −11.7436 + 22.4038i −0.568311 + 1.08420i
\(428\) −1.99903 + 11.3371i −0.0966270 + 0.547999i
\(429\) 0 0
\(430\) −0.0412257 0.0150049i −0.00198808 0.000723603i
\(431\) 0.857208 + 1.48473i 0.0412902 + 0.0715168i 0.885932 0.463815i \(-0.153520\pi\)
−0.844642 + 0.535332i \(0.820187\pi\)
\(432\) 0 0
\(433\) −7.74104 −0.372011 −0.186005 0.982549i \(-0.559554\pi\)
−0.186005 + 0.982549i \(0.559554\pi\)
\(434\) −6.70382 + 2.75456i −0.321794 + 0.132223i
\(435\) 0 0
\(436\) 10.6517 + 8.93780i 0.510122 + 0.428043i
\(437\) 11.5119 + 9.65967i 0.550691 + 0.462085i
\(438\) 0 0
\(439\) 7.29847 + 2.65643i 0.348337 + 0.126784i 0.510263 0.860019i \(-0.329548\pi\)
−0.161926 + 0.986803i \(0.551770\pi\)
\(440\) 0.720056 + 1.24717i 0.0343273 + 0.0594566i
\(441\) 0 0
\(442\) 5.67987 9.83782i 0.270164 0.467937i
\(443\) 11.5210 9.66731i 0.547381 0.459308i −0.326672 0.945138i \(-0.605927\pi\)
0.874053 + 0.485830i \(0.161483\pi\)
\(444\) 0 0
\(445\) −0.216107 + 1.22560i −0.0102444 + 0.0580991i
\(446\) 6.76978 2.46400i 0.320558 0.116674i
\(447\) 0 0
\(448\) 4.47801 + 3.45632i 0.211566 + 0.163296i
\(449\) 5.62232 9.73814i 0.265334 0.459571i −0.702317 0.711864i \(-0.747851\pi\)
0.967651 + 0.252293i \(0.0811846\pi\)
\(450\) 0 0
\(451\) 0.436688 0.756366i 0.0205628 0.0356159i
\(452\) −27.3930 + 22.9855i −1.28846 + 1.08115i
\(453\) 0 0
\(454\) −6.54316 + 2.38152i −0.307086 + 0.111770i
\(455\) −0.880800 1.39127i −0.0412925 0.0652238i
\(456\) 0 0
\(457\) 1.37539 + 7.80022i 0.0643380 + 0.364879i 0.999930 + 0.0117969i \(0.00375515\pi\)
−0.935592 + 0.353082i \(0.885134\pi\)
\(458\) −3.72833 6.45766i −0.174213 0.301746i
\(459\) 0 0
\(460\) 0.746454 1.29290i 0.0348036 0.0602816i
\(461\) −31.5097 + 26.4397i −1.46755 + 1.23142i −0.549179 + 0.835705i \(0.685059\pi\)
−0.918373 + 0.395717i \(0.870496\pi\)
\(462\) 0 0
\(463\) −1.09506 + 6.21042i −0.0508919 + 0.288623i −0.999623 0.0274624i \(-0.991257\pi\)
0.948731 + 0.316085i \(0.102368\pi\)
\(464\) 2.40166 13.6205i 0.111494 0.632314i
\(465\) 0 0
\(466\) −8.21347 + 6.89192i −0.380482 + 0.319262i
\(467\) −22.0979 −1.02257 −0.511285 0.859411i \(-0.670830\pi\)
−0.511285 + 0.859411i \(0.670830\pi\)
\(468\) 0 0
\(469\) 35.9186 + 11.4372i 1.65857 + 0.528121i
\(470\) 0.240606 + 0.0875734i 0.0110983 + 0.00403946i
\(471\) 0 0
\(472\) 1.18057 6.69535i 0.0543402 0.308178i
\(473\) 0.382685 2.17031i 0.0175959 0.0997911i
\(474\) 0 0
\(475\) −13.5762 4.94133i −0.622919 0.226724i
\(476\) 5.68135 + 25.9753i 0.260404 + 1.19058i
\(477\) 0 0
\(478\) 2.65658 0.121509
\(479\) 26.7411 22.4384i 1.22183 1.02524i 0.223104 0.974795i \(-0.428381\pi\)
0.998727 0.0504428i \(-0.0160633\pi\)
\(480\) 0 0
\(481\) 2.03168 11.5222i 0.0926367 0.525369i
\(482\) −0.510240 + 2.89371i −0.0232408 + 0.131805i
\(483\) 0 0
\(484\) −11.1269 + 9.33656i −0.505767 + 0.424389i
\(485\) 0.395340 0.684750i 0.0179515 0.0310929i
\(486\) 0 0
\(487\) 4.47185 + 7.74547i 0.202639 + 0.350981i 0.949378 0.314136i \(-0.101715\pi\)
−0.746739 + 0.665117i \(0.768382\pi\)
\(488\) −3.24233 18.3881i −0.146773 0.832392i
\(489\) 0 0
\(490\) −0.592252 0.162300i −0.0267552 0.00733196i
\(491\) −12.0705 + 4.39330i −0.544734 + 0.198267i −0.599705 0.800221i \(-0.704715\pi\)
0.0549715 + 0.998488i \(0.482493\pi\)
\(492\) 0 0
\(493\) 25.4373 21.3444i 1.14564 0.961305i
\(494\) −2.83312 + 4.90710i −0.127468 + 0.220781i
\(495\) 0 0
\(496\) −6.33901 + 10.9795i −0.284630 + 0.492994i
\(497\) 16.1461 + 12.4623i 0.724252 + 0.559009i
\(498\) 0 0
\(499\) −27.5613 + 10.0315i −1.23381 + 0.449071i −0.874902 0.484300i \(-0.839074\pi\)
−0.358911 + 0.933372i \(0.616852\pi\)
\(500\) −0.499864 + 2.83487i −0.0223546 + 0.126779i
\(501\) 0 0
\(502\) −3.02936 + 2.54193i −0.135207 + 0.113452i
\(503\) −19.2874 + 33.4067i −0.859982 + 1.48953i 0.0119637 + 0.999928i \(0.496192\pi\)
−0.871945 + 0.489603i \(0.837142\pi\)
\(504\) 0 0
\(505\) −0.883206 1.52976i −0.0393021 0.0680733i
\(506\) −11.2279 4.08661i −0.499139 0.181672i
\(507\) 0 0
\(508\) −25.2950 21.2250i −1.12228 0.941707i
\(509\) 7.19261 + 6.03532i 0.318807 + 0.267511i 0.788121 0.615521i \(-0.211054\pi\)
−0.469314 + 0.883031i \(0.655499\pi\)
\(510\) 0 0
\(511\) −28.8680 22.2816i −1.27705 0.985679i
\(512\) −22.0413 −0.974098
\(513\) 0 0
\(514\) −2.15900 3.73951i −0.0952296 0.164942i
\(515\) 1.78661 + 0.650272i 0.0787274 + 0.0286544i
\(516\) 0 0
\(517\) −2.23347 + 12.6666i −0.0982277 + 0.557077i
\(518\) −2.33396 3.68661i −0.102548 0.161980i
\(519\) 0 0
\(520\) 1.14219 + 0.415722i 0.0500881 + 0.0182306i
\(521\) −10.8653 + 18.8192i −0.476016 + 0.824483i −0.999622 0.0274767i \(-0.991253\pi\)
0.523607 + 0.851960i \(0.324586\pi\)
\(522\) 0 0
\(523\) −6.95293 12.0428i −0.304031 0.526596i 0.673014 0.739629i \(-0.264999\pi\)
−0.977045 + 0.213033i \(0.931666\pi\)
\(524\) −12.7906 4.65541i −0.558761 0.203372i
\(525\) 0 0
\(526\) −3.79250 3.18228i −0.165361 0.138754i
\(527\) −28.6032 + 10.4107i −1.24597 + 0.453497i
\(528\) 0 0
\(529\) 0.650571 + 3.68957i 0.0282857 + 0.160416i
\(530\) −0.203329 0.352176i −0.00883205 0.0152976i
\(531\) 0 0
\(532\) −2.83385 12.9565i −0.122863 0.561735i
\(533\) −0.128005 0.725952i −0.00554451 0.0314445i
\(534\) 0 0
\(535\) −0.855373 0.717743i −0.0369810 0.0310307i
\(536\) −26.1473 + 9.51683i −1.12939 + 0.411064i
\(537\) 0 0
\(538\) 5.79974 4.86656i 0.250044 0.209812i
\(539\) 2.86281 30.7143i 0.123310 1.32296i
\(540\) 0 0
\(541\) 6.05930 10.4950i 0.260510 0.451216i −0.705868 0.708344i \(-0.749443\pi\)
0.966377 + 0.257128i \(0.0827760\pi\)
\(542\) 0.0783346 + 0.0285115i 0.00336476 + 0.00122467i
\(543\) 0 0
\(544\) −23.1077 19.3896i −0.990734 0.831324i
\(545\) −1.26736 + 0.461282i −0.0542878 + 0.0197591i
\(546\) 0 0
\(547\) 3.20992 + 18.2043i 0.137246 + 0.778361i 0.973269 + 0.229667i \(0.0737637\pi\)
−0.836023 + 0.548694i \(0.815125\pi\)
\(548\) 3.83656 0.163890
\(549\) 0 0
\(550\) 11.4871 0.489810
\(551\) −12.6881 + 10.6466i −0.540532 + 0.453560i
\(552\) 0 0
\(553\) 9.95928 0.406533i 0.423512 0.0172875i
\(554\) 4.17186 + 3.50060i 0.177245 + 0.148726i
\(555\) 0 0
\(556\) −2.94757 16.7165i −0.125005 0.708938i
\(557\) −10.8392 −0.459270 −0.229635 0.973277i \(-0.573753\pi\)
−0.229635 + 0.973277i \(0.573753\pi\)
\(558\) 0 0
\(559\) −0.930028 1.61086i −0.0393360 0.0681319i
\(560\) −0.993590 + 0.408260i −0.0419868 + 0.0172522i
\(561\) 0 0
\(562\) 1.45988 8.27940i 0.0615814 0.349245i
\(563\) 13.5783 4.94209i 0.572257 0.208284i −0.0396511 0.999214i \(-0.512625\pi\)
0.611908 + 0.790929i \(0.290402\pi\)
\(564\) 0 0
\(565\) −0.602293 3.41577i −0.0253386 0.143703i
\(566\) −0.218570 −0.00918717
\(567\) 0 0
\(568\) −15.0556 −0.631721
\(569\) 3.93291 + 22.3046i 0.164876 + 0.935058i 0.949192 + 0.314697i \(0.101903\pi\)
−0.784316 + 0.620361i \(0.786986\pi\)
\(570\) 0 0
\(571\) 12.2245 4.44936i 0.511580 0.186200i −0.0733150 0.997309i \(-0.523358\pi\)
0.584895 + 0.811109i \(0.301136\pi\)
\(572\) −4.91011 + 27.8466i −0.205302 + 1.16433i
\(573\) 0 0
\(574\) −0.217623 0.167971i −0.00908341 0.00701097i
\(575\) −12.8568 22.2687i −0.536168 0.928670i
\(576\) 0 0
\(577\) −35.9124 −1.49505 −0.747527 0.664231i \(-0.768759\pi\)
−0.747527 + 0.664231i \(0.768759\pi\)
\(578\) −1.54191 8.74460i −0.0641350 0.363728i
\(579\) 0 0
\(580\) 1.26048 + 1.05767i 0.0523385 + 0.0439172i
\(581\) −24.1673 38.1735i −1.00263 1.58370i
\(582\) 0 0
\(583\) 15.6485 13.1306i 0.648093 0.543815i
\(584\) 26.9184 1.11389
\(585\) 0 0
\(586\) −16.1022 −0.665174
\(587\) −2.72345 15.4454i −0.112409 0.637501i −0.988001 0.154450i \(-0.950640\pi\)
0.875592 0.483051i \(-0.160472\pi\)
\(588\) 0 0
\(589\) 14.2672 5.19285i 0.587872 0.213968i
\(590\) 0.233942 + 0.196301i 0.00963126 + 0.00808158i
\(591\) 0 0
\(592\) −7.17223 2.61048i −0.294777 0.107290i
\(593\) −5.12430 + 8.87554i −0.210430 + 0.364475i −0.951849 0.306567i \(-0.900820\pi\)
0.741419 + 0.671042i \(0.234153\pi\)
\(594\) 0 0
\(595\) −2.45748 0.782509i −0.100747 0.0320798i
\(596\) 19.2550 16.1569i 0.788718 0.661813i
\(597\) 0 0
\(598\) −9.47659 + 3.44920i −0.387526 + 0.141048i
\(599\) −2.14768 1.80211i −0.0877517 0.0736324i 0.597857 0.801603i \(-0.296019\pi\)
−0.685608 + 0.727971i \(0.740464\pi\)
\(600\) 0 0
\(601\) −4.55665 25.8420i −0.185870 1.05412i −0.924833 0.380373i \(-0.875796\pi\)
0.738963 0.673746i \(-0.235316\pi\)
\(602\) −0.660975 0.210468i −0.0269393 0.00857802i
\(603\) 0 0
\(604\) −3.17269 5.49527i −0.129095 0.223599i
\(605\) −0.244648 1.38747i −0.00994635 0.0564085i
\(606\) 0 0
\(607\) 28.6778 10.4379i 1.16400 0.423660i 0.313472 0.949597i \(-0.398508\pi\)
0.850523 + 0.525938i \(0.176285\pi\)
\(608\) 11.5261 + 9.67154i 0.467445 + 0.392233i
\(609\) 0 0
\(610\) 0.788144 + 0.286861i 0.0319110 + 0.0116147i
\(611\) 5.42792 + 9.40144i 0.219590 + 0.380342i
\(612\) 0 0
\(613\) 12.8303 22.2228i 0.518212 0.897570i −0.481564 0.876411i \(-0.659931\pi\)
0.999776 0.0211587i \(-0.00673554\pi\)
\(614\) 3.33255 + 1.21295i 0.134491 + 0.0489507i
\(615\) 0 0
\(616\) 12.1800 + 19.2389i 0.490745 + 0.775158i
\(617\) −6.93374 + 39.3232i −0.279142 + 1.58309i 0.446348 + 0.894860i \(0.352724\pi\)
−0.725490 + 0.688233i \(0.758387\pi\)
\(618\) 0 0
\(619\) 45.7767 + 16.6614i 1.83992 + 0.669677i 0.989682 + 0.143283i \(0.0457661\pi\)
0.850241 + 0.526394i \(0.176456\pi\)
\(620\) −0.754158 1.30624i −0.0302877 0.0524599i
\(621\) 0 0
\(622\) 1.99554 0.0800138
\(623\) −2.62376 + 19.5018i −0.105119 + 0.781325i
\(624\) 0 0
\(625\) 18.8300 + 15.8002i 0.753199 + 0.632009i
\(626\) −7.15615 6.00472i −0.286017 0.239997i
\(627\) 0 0
\(628\) −20.9632 7.63000i −0.836525 0.304470i
\(629\) −9.16253 15.8700i −0.365334 0.632777i
\(630\) 0 0
\(631\) −4.78233 + 8.28324i −0.190382 + 0.329751i −0.945377 0.325980i \(-0.894306\pi\)
0.754995 + 0.655730i \(0.227639\pi\)
\(632\) −5.63630 + 4.72941i −0.224200 + 0.188126i
\(633\) 0 0
\(634\) 0.878504 4.98224i 0.0348898 0.197870i
\(635\) 3.00966 1.09543i 0.119435 0.0434707i
\(636\) 0 0
\(637\) −14.8124 21.4118i −0.586889 0.848366i
\(638\) 6.58461 11.4049i 0.260687 0.451523i
\(639\) 0 0
\(640\) 0.960230 1.66317i 0.0379564 0.0657425i
\(641\) −17.8850 + 15.0073i −0.706416 + 0.592753i −0.923591 0.383379i \(-0.874760\pi\)
0.217175 + 0.976133i \(0.430316\pi\)
\(642\) 0 0
\(643\) 8.05707 2.93253i 0.317740 0.115648i −0.178227 0.983989i \(-0.557036\pi\)
0.495967 + 0.868342i \(0.334814\pi\)
\(644\) 10.9590 20.9070i 0.431844 0.823851i
\(645\) 0 0
\(646\) 1.54108 + 8.73988i 0.0606328 + 0.343866i
\(647\) −23.6773 41.0103i −0.930852 1.61228i −0.781869 0.623443i \(-0.785734\pi\)
−0.148983 0.988840i \(-0.547600\pi\)
\(648\) 0 0
\(649\) −7.67032 + 13.2854i −0.301086 + 0.521497i
\(650\) 7.42708 6.23206i 0.291314 0.244441i
\(651\) 0 0
\(652\) −3.47017 + 19.6803i −0.135902 + 0.770741i
\(653\) 6.09997 34.5947i 0.238710 1.35379i −0.595947 0.803024i \(-0.703223\pi\)
0.834657 0.550770i \(-0.185666\pi\)
\(654\) 0 0
\(655\) 1.01137 0.848643i 0.0395176 0.0331592i
\(656\) −0.480883 −0.0187753
\(657\) 0 0
\(658\) 3.85765 + 1.22835i 0.150387 + 0.0478862i
\(659\) 32.0994 + 11.6832i 1.25042 + 0.455114i 0.880542 0.473968i \(-0.157179\pi\)
0.369874 + 0.929082i \(0.379401\pi\)
\(660\) 0 0
\(661\) 1.35395 7.67861i 0.0526624 0.298663i −0.947089 0.320972i \(-0.895990\pi\)
0.999751 + 0.0223085i \(0.00710159\pi\)
\(662\) −1.26339 + 7.16505i −0.0491031 + 0.278478i
\(663\) 0 0
\(664\) 31.3391 + 11.4065i 1.21619 + 0.442658i
\(665\) 1.22579 + 0.390315i 0.0475340 + 0.0151358i
\(666\) 0 0
\(667\) −29.4792 −1.14144
\(668\) −16.6418 + 13.9641i −0.643891 + 0.540289i
\(669\) 0 0
\(670\) 0.217042 1.23091i 0.00838507 0.0475541i
\(671\) −7.31608 + 41.4915i −0.282434 + 1.60176i
\(672\) 0 0
\(673\) −36.7385 + 30.8273i −1.41617 + 1.18830i −0.462809 + 0.886458i \(0.653158\pi\)
−0.953357 + 0.301846i \(0.902397\pi\)
\(674\) 8.36408 14.4870i 0.322172 0.558019i
\(675\) 0 0
\(676\) 0.719490 + 1.24619i 0.0276727 + 0.0479305i
\(677\) −0.667582 3.78605i −0.0256573 0.145510i 0.969288 0.245928i \(-0.0790928\pi\)
−0.994945 + 0.100419i \(0.967982\pi\)
\(678\) 0 0
\(679\) 5.80415 11.0729i 0.222743 0.424938i
\(680\) 1.78894 0.651122i 0.0686028 0.0249694i
\(681\) 0 0
\(682\) −9.24751 + 7.75958i −0.354105 + 0.297130i
\(683\) −12.9081 + 22.3575i −0.493916 + 0.855487i −0.999975 0.00701138i \(-0.997768\pi\)
0.506060 + 0.862498i \(0.331102\pi\)
\(684\) 0 0
\(685\) −0.186064 + 0.322273i −0.00710915 + 0.0123134i
\(686\) −9.46128 2.18214i −0.361233 0.0833145i
\(687\) 0 0
\(688\) −1.14024 + 0.415012i −0.0434711 + 0.0158222i
\(689\) 2.99394 16.9795i 0.114060 0.646866i
\(690\) 0 0
\(691\) −23.7181 + 19.9018i −0.902278 + 0.757101i −0.970634 0.240560i \(-0.922669\pi\)
0.0683562 + 0.997661i \(0.478225\pi\)
\(692\) 14.0532 24.3408i 0.534221 0.925298i
\(693\) 0 0
\(694\) −6.19254 10.7258i −0.235066 0.407146i
\(695\) 1.54715 + 0.563115i 0.0586866 + 0.0213602i
\(696\) 0 0
\(697\) −0.884443 0.742136i −0.0335007 0.0281104i
\(698\) −0.198918 0.166912i −0.00752915 0.00631771i
\(699\) 0 0
\(700\) −3.02592 + 22.4910i −0.114369 + 0.850080i
\(701\) 16.6949 0.630556 0.315278 0.948999i \(-0.397902\pi\)
0.315278 + 0.948999i \(0.397902\pi\)
\(702\) 0 0
\(703\) 4.57026 + 7.91593i 0.172371 + 0.298555i
\(704\) 8.85369 + 3.22248i 0.333686 + 0.121452i
\(705\) 0 0
\(706\) −2.00438 + 11.3674i −0.0754360 + 0.427819i
\(707\) −14.9397 23.5981i −0.561866 0.887497i
\(708\) 0 0
\(709\) 13.9167 + 5.06528i 0.522654 + 0.190230i 0.589855 0.807509i \(-0.299185\pi\)
−0.0672014 + 0.997739i \(0.521407\pi\)
\(710\) 0.338145 0.585684i 0.0126903 0.0219803i
\(711\) 0 0
\(712\) −7.26259 12.5792i −0.272177 0.471424i
\(713\) 25.3929 + 9.24225i 0.950971 + 0.346125i
\(714\) 0 0
\(715\) −2.10100 1.76295i −0.0785730 0.0659306i
\(716\) −6.44627 + 2.34625i −0.240909 + 0.0876835i
\(717\) 0 0
\(718\) −3.03873 17.2335i −0.113404 0.643149i
\(719\) 18.8263 + 32.6081i 0.702102 + 1.21608i 0.967727 + 0.252000i \(0.0810883\pi\)
−0.265625 + 0.964076i \(0.585578\pi\)
\(720\) 0 0
\(721\) 28.6448 + 9.12108i 1.06679 + 0.339687i
\(722\) 0.961052 + 5.45040i 0.0357666 + 0.202843i
\(723\) 0 0
\(724\) −0.158978 0.133398i −0.00590836 0.00495770i
\(725\) 26.6317 9.69314i 0.989076 0.359994i
\(726\) 0 0
\(727\) 2.73015 2.29087i 0.101256 0.0849635i −0.590755 0.806851i \(-0.701170\pi\)
0.692010 + 0.721888i \(0.256725\pi\)
\(728\) 18.3127 + 5.83114i 0.678715 + 0.216117i
\(729\) 0 0
\(730\) −0.604577 + 1.04716i −0.0223764 + 0.0387571i
\(731\) −2.73761 0.996408i −0.101254 0.0368535i
\(732\) 0 0
\(733\) −33.4801 28.0931i −1.23661 1.03764i −0.997781 0.0665826i \(-0.978790\pi\)
−0.238834 0.971060i \(-0.576765\pi\)
\(734\) 15.2005 5.53252i 0.561060 0.204209i
\(735\) 0 0
\(736\) 4.65019 + 26.3725i 0.171408 + 0.972104i
\(737\) 62.7859 2.31275
\(738\) 0 0
\(739\) 13.4386 0.494348 0.247174 0.968971i \(-0.420498\pi\)
0.247174 + 0.968971i \(0.420498\pi\)
\(740\) 0.695606 0.583683i 0.0255710 0.0214566i
\(741\) 0 0
\(742\) −3.43938 5.43268i −0.126263 0.199440i
\(743\) 28.4384 + 23.8627i 1.04331 + 0.875437i 0.992374 0.123265i \(-0.0393365\pi\)
0.0509315 + 0.998702i \(0.483781\pi\)
\(744\) 0 0
\(745\) 0.423363 + 2.40101i 0.0155108 + 0.0879662i
\(746\) 7.44314 0.272513
\(747\) 0 0
\(748\) 22.1437 + 38.3540i 0.809654 + 1.40236i
\(749\) −13.9763 10.7875i −0.510685 0.394168i
\(750\) 0 0
\(751\) 5.74504 32.5818i 0.209640 1.18893i −0.680330 0.732906i \(-0.738164\pi\)
0.889970 0.456020i \(-0.150725\pi\)
\(752\) 6.65476 2.42214i 0.242674 0.0883262i
\(753\) 0 0
\(754\) −1.93012 10.9463i −0.0702909 0.398640i
\(755\) 0.615474 0.0223994
\(756\) 0 0
\(757\) 50.3539 1.83014 0.915072 0.403291i \(-0.132134\pi\)
0.915072 + 0.403291i \(0.132134\pi\)
\(758\) 2.90276 + 16.4624i 0.105433 + 0.597940i
\(759\) 0 0
\(760\) −0.892323 + 0.324779i −0.0323680 + 0.0117810i
\(761\) 5.20712 29.5310i 0.188758 1.07050i −0.732274 0.681011i \(-0.761541\pi\)
0.921031 0.389488i \(-0.127348\pi\)
\(762\) 0 0
\(763\) −19.7248 + 8.10479i −0.714084 + 0.293413i
\(764\) 11.3361 + 19.6347i 0.410126 + 0.710358i
\(765\) 0 0
\(766\) 8.23807 0.297654
\(767\) 2.24837 + 12.7512i 0.0811841 + 0.460418i
\(768\) 0 0
\(769\) −17.8704 14.9950i −0.644423 0.540735i 0.260950 0.965352i \(-0.415964\pi\)
−0.905373 + 0.424617i \(0.860409\pi\)
\(770\) −1.02198 + 0.0417166i −0.0368295 + 0.00150336i
\(771\) 0 0
\(772\) −7.95164 + 6.67222i −0.286186 + 0.240138i
\(773\) 37.6553 1.35437 0.677184 0.735814i \(-0.263200\pi\)
0.677184 + 0.735814i \(0.263200\pi\)
\(774\) 0 0
\(775\) −25.9791 −0.933197
\(776\) 1.60249 + 9.08817i 0.0575260 + 0.326246i
\(777\) 0 0
\(778\) −11.3828 + 4.14301i −0.408094 + 0.148534i
\(779\) 0.441160 + 0.370177i 0.0158062 + 0.0132630i
\(780\) 0 0
\(781\) 31.9232 + 11.6191i 1.14230 + 0.415764i
\(782\) −7.89761 + 13.6791i −0.282418 + 0.489162i
\(783\) 0