Properties

Label 855.2.k.h.406.3
Level $855$
Weight $2$
Character 855.406
Analytic conductor $6.827$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 406.3
Root \(0.689667 + 1.19454i\) of defining polynomial
Character \(\chi\) \(=\) 855.406
Dual form 855.2.k.h.676.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.548719 + 0.950409i) q^{2} +(0.397815 - 0.689035i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.89307 q^{7} +3.06803 q^{8} +O(q^{10})\) \(q+(0.548719 + 0.950409i) q^{2} +(0.397815 - 0.689035i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.89307 q^{7} +3.06803 q^{8} +(-0.548719 + 0.950409i) q^{10} -0.134400 q^{11} +(-1.75687 + 3.04298i) q^{13} +(1.03876 + 1.79919i) q^{14} +(0.887858 + 1.53781i) q^{16} +(-0.830615 - 1.43867i) q^{17} +(2.10596 + 3.81640i) q^{19} +0.795629 q^{20} +(-0.0737478 - 0.127735i) q^{22} +(2.68492 - 4.65042i) q^{23} +(-0.500000 + 0.866025i) q^{25} -3.85611 q^{26} +(0.753090 - 1.30439i) q^{28} +(2.48530 - 4.30466i) q^{29} +6.56472 q^{31} +(2.09366 - 3.62633i) q^{32} +(0.911548 - 1.57885i) q^{34} +(0.946534 + 1.63944i) q^{35} -1.69819 q^{37} +(-2.47156 + 4.09566i) q^{38} +(1.53402 + 2.65699i) q^{40} +(5.31637 + 9.20823i) q^{41} +(-4.25392 - 7.36801i) q^{43} +(-0.0534662 + 0.0926063i) q^{44} +5.89307 q^{46} +(-5.55771 + 9.62623i) q^{47} -3.41630 q^{49} -1.09744 q^{50} +(1.39781 + 2.42109i) q^{52} +(-0.132424 + 0.229365i) q^{53} +(-0.0672000 - 0.116394i) q^{55} +5.80799 q^{56} +5.45492 q^{58} +(-3.44833 - 5.97269i) q^{59} +(-4.58794 + 7.94655i) q^{61} +(3.60219 + 6.23917i) q^{62} +8.14676 q^{64} -3.51373 q^{65} +(1.47677 - 2.55784i) q^{67} -1.32172 q^{68} +(-1.03876 + 1.79919i) q^{70} +(0.664176 + 1.15039i) q^{71} +(3.17119 + 5.49266i) q^{73} +(-0.931830 - 1.61398i) q^{74} +(3.46742 + 0.0671384i) q^{76} -0.254428 q^{77} +(0.733639 + 1.27070i) q^{79} +(-0.887858 + 1.53781i) q^{80} +(-5.83439 + 10.1055i) q^{82} -7.44736 q^{83} +(0.830615 - 1.43867i) q^{85} +(4.66842 - 8.08593i) q^{86} -0.412343 q^{88} +(4.86804 - 8.43169i) q^{89} +(-3.32587 + 5.76057i) q^{91} +(-2.13620 - 3.70001i) q^{92} -12.1985 q^{94} +(-2.25212 + 3.73202i) q^{95} +(-8.73447 - 15.1285i) q^{97} +(-1.87459 - 3.24688i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.548719 + 0.950409i 0.388003 + 0.672041i 0.992181 0.124809i \(-0.0398317\pi\)
−0.604178 + 0.796850i \(0.706498\pi\)
\(3\) 0 0
\(4\) 0.397815 0.689035i 0.198907 0.344518i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 1.89307 0.715512 0.357756 0.933815i \(-0.383542\pi\)
0.357756 + 0.933815i \(0.383542\pi\)
\(8\) 3.06803 1.08471
\(9\) 0 0
\(10\) −0.548719 + 0.950409i −0.173520 + 0.300546i
\(11\) −0.134400 −0.0405231 −0.0202615 0.999795i \(-0.506450\pi\)
−0.0202615 + 0.999795i \(0.506450\pi\)
\(12\) 0 0
\(13\) −1.75687 + 3.04298i −0.487267 + 0.843972i −0.999893 0.0146407i \(-0.995340\pi\)
0.512626 + 0.858612i \(0.328673\pi\)
\(14\) 1.03876 + 1.79919i 0.277621 + 0.480854i
\(15\) 0 0
\(16\) 0.887858 + 1.53781i 0.221964 + 0.384454i
\(17\) −0.830615 1.43867i −0.201454 0.348928i 0.747543 0.664213i \(-0.231233\pi\)
−0.948997 + 0.315285i \(0.897900\pi\)
\(18\) 0 0
\(19\) 2.10596 + 3.81640i 0.483141 + 0.875543i
\(20\) 0.795629 0.177908
\(21\) 0 0
\(22\) −0.0737478 0.127735i −0.0157231 0.0272332i
\(23\) 2.68492 4.65042i 0.559844 0.969679i −0.437664 0.899138i \(-0.644194\pi\)
0.997509 0.0705407i \(-0.0224725\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.85611 −0.756245
\(27\) 0 0
\(28\) 0.753090 1.30439i 0.142321 0.246507i
\(29\) 2.48530 4.30466i 0.461508 0.799355i −0.537528 0.843246i \(-0.680642\pi\)
0.999036 + 0.0438905i \(0.0139753\pi\)
\(30\) 0 0
\(31\) 6.56472 1.17906 0.589529 0.807747i \(-0.299313\pi\)
0.589529 + 0.807747i \(0.299313\pi\)
\(32\) 2.09366 3.62633i 0.370111 0.641050i
\(33\) 0 0
\(34\) 0.911548 1.57885i 0.156329 0.270770i
\(35\) 0.946534 + 1.63944i 0.159993 + 0.277117i
\(36\) 0 0
\(37\) −1.69819 −0.279181 −0.139590 0.990209i \(-0.544579\pi\)
−0.139590 + 0.990209i \(0.544579\pi\)
\(38\) −2.47156 + 4.09566i −0.400940 + 0.664404i
\(39\) 0 0
\(40\) 1.53402 + 2.65699i 0.242549 + 0.420107i
\(41\) 5.31637 + 9.20823i 0.830278 + 1.43808i 0.897818 + 0.440367i \(0.145152\pi\)
−0.0675398 + 0.997717i \(0.521515\pi\)
\(42\) 0 0
\(43\) −4.25392 7.36801i −0.648717 1.12361i −0.983430 0.181290i \(-0.941973\pi\)
0.334713 0.942320i \(-0.391361\pi\)
\(44\) −0.0534662 + 0.0926063i −0.00806034 + 0.0139609i
\(45\) 0 0
\(46\) 5.89307 0.868885
\(47\) −5.55771 + 9.62623i −0.810675 + 1.40413i 0.101718 + 0.994813i \(0.467566\pi\)
−0.912392 + 0.409316i \(0.865767\pi\)
\(48\) 0 0
\(49\) −3.41630 −0.488042
\(50\) −1.09744 −0.155201
\(51\) 0 0
\(52\) 1.39781 + 2.42109i 0.193842 + 0.335744i
\(53\) −0.132424 + 0.229365i −0.0181898 + 0.0315057i −0.874977 0.484164i \(-0.839124\pi\)
0.856787 + 0.515670i \(0.172457\pi\)
\(54\) 0 0
\(55\) −0.0672000 0.116394i −0.00906124 0.0156945i
\(56\) 5.80799 0.776125
\(57\) 0 0
\(58\) 5.45492 0.716266
\(59\) −3.44833 5.97269i −0.448935 0.777578i 0.549382 0.835571i \(-0.314863\pi\)
−0.998317 + 0.0579932i \(0.981530\pi\)
\(60\) 0 0
\(61\) −4.58794 + 7.94655i −0.587426 + 1.01745i 0.407142 + 0.913365i \(0.366525\pi\)
−0.994568 + 0.104087i \(0.966808\pi\)
\(62\) 3.60219 + 6.23917i 0.457478 + 0.792375i
\(63\) 0 0
\(64\) 8.14676 1.01834
\(65\) −3.51373 −0.435825
\(66\) 0 0
\(67\) 1.47677 2.55784i 0.180416 0.312490i −0.761606 0.648040i \(-0.775589\pi\)
0.942022 + 0.335550i \(0.108922\pi\)
\(68\) −1.32172 −0.160282
\(69\) 0 0
\(70\) −1.03876 + 1.79919i −0.124156 + 0.215044i
\(71\) 0.664176 + 1.15039i 0.0788232 + 0.136526i 0.902742 0.430181i \(-0.141550\pi\)
−0.823919 + 0.566707i \(0.808217\pi\)
\(72\) 0 0
\(73\) 3.17119 + 5.49266i 0.371159 + 0.642867i 0.989744 0.142851i \(-0.0456271\pi\)
−0.618585 + 0.785718i \(0.712294\pi\)
\(74\) −0.931830 1.61398i −0.108323 0.187621i
\(75\) 0 0
\(76\) 3.46742 + 0.0671384i 0.397740 + 0.00770130i
\(77\) −0.254428 −0.0289948
\(78\) 0 0
\(79\) 0.733639 + 1.27070i 0.0825408 + 0.142965i 0.904341 0.426811i \(-0.140363\pi\)
−0.821800 + 0.569776i \(0.807030\pi\)
\(80\) −0.887858 + 1.53781i −0.0992655 + 0.171933i
\(81\) 0 0
\(82\) −5.83439 + 10.1055i −0.644301 + 1.11596i
\(83\) −7.44736 −0.817454 −0.408727 0.912657i \(-0.634027\pi\)
−0.408727 + 0.912657i \(0.634027\pi\)
\(84\) 0 0
\(85\) 0.830615 1.43867i 0.0900928 0.156045i
\(86\) 4.66842 8.08593i 0.503408 0.871929i
\(87\) 0 0
\(88\) −0.412343 −0.0439559
\(89\) 4.86804 8.43169i 0.516011 0.893757i −0.483816 0.875170i \(-0.660750\pi\)
0.999827 0.0185878i \(-0.00591701\pi\)
\(90\) 0 0
\(91\) −3.32587 + 5.76057i −0.348646 + 0.603872i
\(92\) −2.13620 3.70001i −0.222714 0.385753i
\(93\) 0 0
\(94\) −12.1985 −1.25818
\(95\) −2.25212 + 3.73202i −0.231063 + 0.382897i
\(96\) 0 0
\(97\) −8.73447 15.1285i −0.886851 1.53607i −0.843577 0.537008i \(-0.819555\pi\)
−0.0432737 0.999063i \(-0.513779\pi\)
\(98\) −1.87459 3.24688i −0.189362 0.327984i
\(99\) 0 0
\(100\) 0.397815 + 0.689035i 0.0397815 + 0.0689035i
\(101\) 2.69865 4.67420i 0.268526 0.465101i −0.699955 0.714187i \(-0.746797\pi\)
0.968481 + 0.249086i \(0.0801301\pi\)
\(102\) 0 0
\(103\) 2.14750 0.211599 0.105800 0.994387i \(-0.466260\pi\)
0.105800 + 0.994387i \(0.466260\pi\)
\(104\) −5.39012 + 9.33596i −0.528545 + 0.915467i
\(105\) 0 0
\(106\) −0.290654 −0.0282308
\(107\) 1.00093 0.0967631 0.0483815 0.998829i \(-0.484594\pi\)
0.0483815 + 0.998829i \(0.484594\pi\)
\(108\) 0 0
\(109\) −8.13145 14.0841i −0.778852 1.34901i −0.932604 0.360902i \(-0.882469\pi\)
0.153752 0.988109i \(-0.450864\pi\)
\(110\) 0.0737478 0.127735i 0.00703158 0.0121790i
\(111\) 0 0
\(112\) 1.68077 + 2.91119i 0.158818 + 0.275081i
\(113\) −0.843010 −0.0793037 −0.0396519 0.999214i \(-0.512625\pi\)
−0.0396519 + 0.999214i \(0.512625\pi\)
\(114\) 0 0
\(115\) 5.36984 0.500740
\(116\) −1.97737 3.42491i −0.183595 0.317995i
\(117\) 0 0
\(118\) 3.78433 6.55466i 0.348376 0.603405i
\(119\) −1.57241 2.72349i −0.144143 0.249662i
\(120\) 0 0
\(121\) −10.9819 −0.998358
\(122\) −10.0700 −0.911692
\(123\) 0 0
\(124\) 2.61154 4.52332i 0.234523 0.406206i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.36984 + 16.2290i −0.831439 + 1.44009i 0.0654584 + 0.997855i \(0.479149\pi\)
−0.896897 + 0.442239i \(0.854184\pi\)
\(128\) 0.282960 + 0.490101i 0.0250104 + 0.0433193i
\(129\) 0 0
\(130\) −1.92805 3.33949i −0.169101 0.292892i
\(131\) 1.44322 + 2.49973i 0.126095 + 0.218402i 0.922160 0.386808i \(-0.126422\pi\)
−0.796066 + 0.605210i \(0.793089\pi\)
\(132\) 0 0
\(133\) 3.98673 + 7.22471i 0.345693 + 0.626461i
\(134\) 3.24133 0.280008
\(135\) 0 0
\(136\) −2.54835 4.41387i −0.218519 0.378487i
\(137\) −9.41579 + 16.3086i −0.804445 + 1.39334i 0.112220 + 0.993683i \(0.464204\pi\)
−0.916665 + 0.399656i \(0.869129\pi\)
\(138\) 0 0
\(139\) 9.08974 15.7439i 0.770982 1.33538i −0.166043 0.986118i \(-0.553099\pi\)
0.937025 0.349262i \(-0.113568\pi\)
\(140\) 1.50618 0.127295
\(141\) 0 0
\(142\) −0.728892 + 1.26248i −0.0611672 + 0.105945i
\(143\) 0.236123 0.408977i 0.0197456 0.0342003i
\(144\) 0 0
\(145\) 4.97059 0.412785
\(146\) −3.48018 + 6.02785i −0.288022 + 0.498868i
\(147\) 0 0
\(148\) −0.675565 + 1.17011i −0.0555311 + 0.0961827i
\(149\) −11.1272 19.2728i −0.911573 1.57889i −0.811842 0.583877i \(-0.801535\pi\)
−0.0997308 0.995014i \(-0.531798\pi\)
\(150\) 0 0
\(151\) 3.33482 0.271384 0.135692 0.990751i \(-0.456674\pi\)
0.135692 + 0.990751i \(0.456674\pi\)
\(152\) 6.46116 + 11.7088i 0.524069 + 0.949712i
\(153\) 0 0
\(154\) −0.139610 0.241811i −0.0112501 0.0194857i
\(155\) 3.28236 + 5.68521i 0.263645 + 0.456647i
\(156\) 0 0
\(157\) −3.63145 6.28986i −0.289822 0.501986i 0.683945 0.729533i \(-0.260263\pi\)
−0.973767 + 0.227548i \(0.926929\pi\)
\(158\) −0.805123 + 1.39451i −0.0640522 + 0.110942i
\(159\) 0 0
\(160\) 4.18732 0.331037
\(161\) 5.08273 8.80355i 0.400576 0.693817i
\(162\) 0 0
\(163\) −19.7783 −1.54916 −0.774578 0.632478i \(-0.782038\pi\)
−0.774578 + 0.632478i \(0.782038\pi\)
\(164\) 8.45972 0.660593
\(165\) 0 0
\(166\) −4.08651 7.07805i −0.317175 0.549363i
\(167\) −1.70160 + 2.94726i −0.131674 + 0.228066i −0.924322 0.381614i \(-0.875368\pi\)
0.792648 + 0.609679i \(0.208702\pi\)
\(168\) 0 0
\(169\) 0.326838 + 0.566100i 0.0251414 + 0.0435461i
\(170\) 1.82310 0.139825
\(171\) 0 0
\(172\) −6.76909 −0.516138
\(173\) −5.29286 9.16750i −0.402409 0.696992i 0.591607 0.806226i \(-0.298494\pi\)
−0.994016 + 0.109234i \(0.965160\pi\)
\(174\) 0 0
\(175\) −0.946534 + 1.63944i −0.0715512 + 0.123930i
\(176\) −0.119328 0.206682i −0.00899469 0.0155793i
\(177\) 0 0
\(178\) 10.6847 0.800855
\(179\) 14.6024 1.09144 0.545718 0.837969i \(-0.316257\pi\)
0.545718 + 0.837969i \(0.316257\pi\)
\(180\) 0 0
\(181\) 2.71630 4.70478i 0.201901 0.349703i −0.747240 0.664555i \(-0.768621\pi\)
0.949141 + 0.314851i \(0.101955\pi\)
\(182\) −7.29987 −0.541102
\(183\) 0 0
\(184\) 8.23742 14.2676i 0.607270 1.05182i
\(185\) −0.849095 1.47068i −0.0624267 0.108126i
\(186\) 0 0
\(187\) 0.111635 + 0.193357i 0.00816353 + 0.0141396i
\(188\) 4.42187 + 7.65891i 0.322498 + 0.558583i
\(189\) 0 0
\(190\) −4.78273 0.0926063i −0.346975 0.00671836i
\(191\) −20.4758 −1.48157 −0.740787 0.671740i \(-0.765547\pi\)
−0.740787 + 0.671740i \(0.765547\pi\)
\(192\) 0 0
\(193\) −5.51176 9.54664i −0.396745 0.687182i 0.596577 0.802556i \(-0.296527\pi\)
−0.993322 + 0.115373i \(0.963194\pi\)
\(194\) 9.58554 16.6026i 0.688202 1.19200i
\(195\) 0 0
\(196\) −1.35905 + 2.35395i −0.0970752 + 0.168139i
\(197\) 19.8532 1.41448 0.707242 0.706971i \(-0.249939\pi\)
0.707242 + 0.706971i \(0.249939\pi\)
\(198\) 0 0
\(199\) −10.5013 + 18.1888i −0.744417 + 1.28937i 0.206050 + 0.978542i \(0.433939\pi\)
−0.950467 + 0.310826i \(0.899394\pi\)
\(200\) −1.53402 + 2.65699i −0.108471 + 0.187878i
\(201\) 0 0
\(202\) 5.92321 0.416756
\(203\) 4.70483 8.14901i 0.330215 0.571948i
\(204\) 0 0
\(205\) −5.31637 + 9.20823i −0.371312 + 0.643131i
\(206\) 1.17837 + 2.04100i 0.0821011 + 0.142203i
\(207\) 0 0
\(208\) −6.23939 −0.432624
\(209\) −0.283041 0.512924i −0.0195784 0.0354797i
\(210\) 0 0
\(211\) 6.41284 + 11.1074i 0.441478 + 0.764663i 0.997799 0.0663046i \(-0.0211209\pi\)
−0.556321 + 0.830967i \(0.687788\pi\)
\(212\) 0.105360 + 0.182489i 0.00723617 + 0.0125334i
\(213\) 0 0
\(214\) 0.549227 + 0.951289i 0.0375444 + 0.0650288i
\(215\) 4.25392 7.36801i 0.290115 0.502494i
\(216\) 0 0
\(217\) 12.4275 0.843630
\(218\) 8.92377 15.4564i 0.604394 1.04684i
\(219\) 0 0
\(220\) −0.106932 −0.00720939
\(221\) 5.83712 0.392647
\(222\) 0 0
\(223\) −10.1972 17.6621i −0.682856 1.18274i −0.974105 0.226095i \(-0.927404\pi\)
0.291249 0.956647i \(-0.405929\pi\)
\(224\) 3.96344 6.86488i 0.264819 0.458679i
\(225\) 0 0
\(226\) −0.462576 0.801205i −0.0307701 0.0532954i
\(227\) −25.4172 −1.68700 −0.843500 0.537129i \(-0.819509\pi\)
−0.843500 + 0.537129i \(0.819509\pi\)
\(228\) 0 0
\(229\) 2.21553 0.146406 0.0732030 0.997317i \(-0.476678\pi\)
0.0732030 + 0.997317i \(0.476678\pi\)
\(230\) 2.94653 + 5.10355i 0.194289 + 0.336518i
\(231\) 0 0
\(232\) 7.62496 13.2068i 0.500603 0.867071i
\(233\) −7.07882 12.2609i −0.463749 0.803236i 0.535395 0.844602i \(-0.320163\pi\)
−0.999144 + 0.0413652i \(0.986829\pi\)
\(234\) 0 0
\(235\) −11.1154 −0.725089
\(236\) −5.48719 −0.357186
\(237\) 0 0
\(238\) 1.72562 2.98887i 0.111855 0.193739i
\(239\) −3.01476 −0.195008 −0.0975042 0.995235i \(-0.531086\pi\)
−0.0975042 + 0.995235i \(0.531086\pi\)
\(240\) 0 0
\(241\) 11.8896 20.5934i 0.765877 1.32654i −0.173904 0.984763i \(-0.555638\pi\)
0.939781 0.341776i \(-0.111028\pi\)
\(242\) −6.02600 10.4373i −0.387366 0.670937i
\(243\) 0 0
\(244\) 3.65030 + 6.32251i 0.233687 + 0.404757i
\(245\) −1.70815 2.95860i −0.109130 0.189018i
\(246\) 0 0
\(247\) −15.3131 0.296503i −0.974352 0.0188660i
\(248\) 20.1407 1.27894
\(249\) 0 0
\(250\) −0.548719 0.950409i −0.0347040 0.0601092i
\(251\) 8.59495 14.8869i 0.542509 0.939653i −0.456250 0.889851i \(-0.650808\pi\)
0.998759 0.0498012i \(-0.0158588\pi\)
\(252\) 0 0
\(253\) −0.360853 + 0.625016i −0.0226866 + 0.0392944i
\(254\) −20.5656 −1.29040
\(255\) 0 0
\(256\) 7.83623 13.5727i 0.489764 0.848297i
\(257\) −9.77143 + 16.9246i −0.609525 + 1.05573i 0.381794 + 0.924248i \(0.375307\pi\)
−0.991319 + 0.131481i \(0.958027\pi\)
\(258\) 0 0
\(259\) −3.21479 −0.199757
\(260\) −1.39781 + 2.42109i −0.0866888 + 0.150149i
\(261\) 0 0
\(262\) −1.58384 + 2.74330i −0.0978502 + 0.169482i
\(263\) 4.40680 + 7.63280i 0.271735 + 0.470659i 0.969306 0.245857i \(-0.0790692\pi\)
−0.697571 + 0.716515i \(0.745736\pi\)
\(264\) 0 0
\(265\) −0.264847 −0.0162694
\(266\) −4.67883 + 7.75336i −0.286878 + 0.475389i
\(267\) 0 0
\(268\) −1.17496 2.03510i −0.0717723 0.124313i
\(269\) 0.144181 + 0.249729i 0.00879088 + 0.0152263i 0.870387 0.492368i \(-0.163868\pi\)
−0.861596 + 0.507594i \(0.830535\pi\)
\(270\) 0 0
\(271\) 12.4356 + 21.5391i 0.755409 + 1.30841i 0.945171 + 0.326577i \(0.105895\pi\)
−0.189761 + 0.981830i \(0.560771\pi\)
\(272\) 1.47494 2.55466i 0.0894311 0.154899i
\(273\) 0 0
\(274\) −20.6665 −1.24851
\(275\) 0.0672000 0.116394i 0.00405231 0.00701881i
\(276\) 0 0
\(277\) −4.40486 −0.264662 −0.132331 0.991206i \(-0.542246\pi\)
−0.132331 + 0.991206i \(0.542246\pi\)
\(278\) 19.9509 1.19657
\(279\) 0 0
\(280\) 2.90399 + 5.02987i 0.173547 + 0.300592i
\(281\) −16.3607 + 28.3376i −0.975998 + 1.69048i −0.299398 + 0.954128i \(0.596786\pi\)
−0.676600 + 0.736350i \(0.736548\pi\)
\(282\) 0 0
\(283\) 0.664463 + 1.15088i 0.0394982 + 0.0684129i 0.885099 0.465403i \(-0.154091\pi\)
−0.845600 + 0.533816i \(0.820757\pi\)
\(284\) 1.05688 0.0627140
\(285\) 0 0
\(286\) 0.518260 0.0306454
\(287\) 10.0643 + 17.4318i 0.594074 + 1.02897i
\(288\) 0 0
\(289\) 7.12016 12.3325i 0.418833 0.725440i
\(290\) 2.72746 + 4.72410i 0.160162 + 0.277409i
\(291\) 0 0
\(292\) 5.04618 0.295305
\(293\) 7.72365 0.451220 0.225610 0.974218i \(-0.427562\pi\)
0.225610 + 0.974218i \(0.427562\pi\)
\(294\) 0 0
\(295\) 3.44833 5.97269i 0.200770 0.347743i
\(296\) −5.21010 −0.302831
\(297\) 0 0
\(298\) 12.2114 21.1507i 0.707386 1.22523i
\(299\) 9.43409 + 16.3403i 0.545588 + 0.944986i
\(300\) 0 0
\(301\) −8.05296 13.9481i −0.464165 0.803957i
\(302\) 1.82988 + 3.16944i 0.105298 + 0.182381i
\(303\) 0 0
\(304\) −3.99912 + 6.62700i −0.229366 + 0.380085i
\(305\) −9.17589 −0.525410
\(306\) 0 0
\(307\) 4.55001 + 7.88085i 0.259683 + 0.449784i 0.966157 0.257955i \(-0.0830486\pi\)
−0.706474 + 0.707739i \(0.749715\pi\)
\(308\) −0.101215 + 0.175310i −0.00576727 + 0.00998921i
\(309\) 0 0
\(310\) −3.60219 + 6.23917i −0.204590 + 0.354361i
\(311\) 12.4569 0.706364 0.353182 0.935555i \(-0.385100\pi\)
0.353182 + 0.935555i \(0.385100\pi\)
\(312\) 0 0
\(313\) −1.02277 + 1.77148i −0.0578101 + 0.100130i −0.893482 0.449099i \(-0.851745\pi\)
0.835672 + 0.549229i \(0.185078\pi\)
\(314\) 3.98530 6.90274i 0.224903 0.389544i
\(315\) 0 0
\(316\) 1.16741 0.0656719
\(317\) 11.7856 20.4133i 0.661947 1.14653i −0.318157 0.948038i \(-0.603064\pi\)
0.980103 0.198487i \(-0.0636029\pi\)
\(318\) 0 0
\(319\) −0.334024 + 0.578546i −0.0187017 + 0.0323923i
\(320\) 4.07338 + 7.05530i 0.227709 + 0.394403i
\(321\) 0 0
\(322\) 11.1560 0.621698
\(323\) 3.74129 6.19974i 0.208171 0.344963i
\(324\) 0 0
\(325\) −1.75687 3.04298i −0.0974534 0.168794i
\(326\) −10.8527 18.7975i −0.601077 1.04110i
\(327\) 0 0
\(328\) 16.3108 + 28.2511i 0.900613 + 1.55991i
\(329\) −10.5211 + 18.2231i −0.580048 + 1.00467i
\(330\) 0 0
\(331\) −18.7175 −1.02881 −0.514403 0.857549i \(-0.671986\pi\)
−0.514403 + 0.857549i \(0.671986\pi\)
\(332\) −2.96267 + 5.13150i −0.162598 + 0.281627i
\(333\) 0 0
\(334\) −3.73480 −0.204359
\(335\) 2.95354 0.161369
\(336\) 0 0
\(337\) 16.3440 + 28.3087i 0.890316 + 1.54207i 0.839497 + 0.543365i \(0.182850\pi\)
0.0508197 + 0.998708i \(0.483817\pi\)
\(338\) −0.358684 + 0.621259i −0.0195098 + 0.0337921i
\(339\) 0 0
\(340\) −0.660861 1.14465i −0.0358402 0.0620771i
\(341\) −0.882297 −0.0477791
\(342\) 0 0
\(343\) −19.7188 −1.06471
\(344\) −13.0512 22.6053i −0.703671 1.21879i
\(345\) 0 0
\(346\) 5.80859 10.0608i 0.312271 0.540870i
\(347\) −1.28333 2.22279i −0.0688927 0.119326i 0.829521 0.558475i \(-0.188613\pi\)
−0.898414 + 0.439149i \(0.855280\pi\)
\(348\) 0 0
\(349\) 16.6195 0.889619 0.444810 0.895625i \(-0.353271\pi\)
0.444810 + 0.895625i \(0.353271\pi\)
\(350\) −2.07752 −0.111048
\(351\) 0 0
\(352\) −0.281388 + 0.487378i −0.0149980 + 0.0259773i
\(353\) −28.3629 −1.50961 −0.754803 0.655951i \(-0.772268\pi\)
−0.754803 + 0.655951i \(0.772268\pi\)
\(354\) 0 0
\(355\) −0.664176 + 1.15039i −0.0352508 + 0.0610562i
\(356\) −3.87315 6.70850i −0.205277 0.355550i
\(357\) 0 0
\(358\) 8.01262 + 13.8783i 0.423480 + 0.733489i
\(359\) 8.69427 + 15.0589i 0.458866 + 0.794780i 0.998901 0.0468628i \(-0.0149224\pi\)
−0.540035 + 0.841643i \(0.681589\pi\)
\(360\) 0 0
\(361\) −10.1298 + 16.0744i −0.533150 + 0.846021i
\(362\) 5.96195 0.313353
\(363\) 0 0
\(364\) 2.64616 + 4.58328i 0.138696 + 0.240229i
\(365\) −3.17119 + 5.49266i −0.165987 + 0.287499i
\(366\) 0 0
\(367\) −12.9024 + 22.3477i −0.673501 + 1.16654i 0.303404 + 0.952862i \(0.401877\pi\)
−0.976905 + 0.213676i \(0.931456\pi\)
\(368\) 9.53531 0.497062
\(369\) 0 0
\(370\) 0.931830 1.61398i 0.0484435 0.0839067i
\(371\) −0.250687 + 0.434203i −0.0130150 + 0.0225427i
\(372\) 0 0
\(373\) 27.0663 1.40144 0.700719 0.713437i \(-0.252862\pi\)
0.700719 + 0.713437i \(0.252862\pi\)
\(374\) −0.122512 + 0.212197i −0.00633495 + 0.0109724i
\(375\) 0 0
\(376\) −17.0512 + 29.5336i −0.879349 + 1.52308i
\(377\) 8.73267 + 15.1254i 0.449755 + 0.778999i
\(378\) 0 0
\(379\) 12.4028 0.637092 0.318546 0.947907i \(-0.396806\pi\)
0.318546 + 0.947907i \(0.396806\pi\)
\(380\) 1.67557 + 3.03644i 0.0859547 + 0.155766i
\(381\) 0 0
\(382\) −11.2354 19.4604i −0.574855 0.995678i
\(383\) −2.67971 4.64139i −0.136927 0.237164i 0.789405 0.613873i \(-0.210389\pi\)
−0.926332 + 0.376709i \(0.877056\pi\)
\(384\) 0 0
\(385\) −0.127214 0.220341i −0.00648343 0.0112296i
\(386\) 6.04881 10.4769i 0.307877 0.533258i
\(387\) 0 0
\(388\) −13.8988 −0.705605
\(389\) 4.28467 7.42126i 0.217241 0.376273i −0.736722 0.676195i \(-0.763628\pi\)
0.953964 + 0.299923i \(0.0969608\pi\)
\(390\) 0 0
\(391\) −8.92053 −0.451131
\(392\) −10.4813 −0.529386
\(393\) 0 0
\(394\) 10.8939 + 18.8687i 0.548824 + 0.950592i
\(395\) −0.733639 + 1.27070i −0.0369134 + 0.0639359i
\(396\) 0 0
\(397\) 5.32227 + 9.21844i 0.267117 + 0.462660i 0.968116 0.250502i \(-0.0805957\pi\)
−0.700999 + 0.713162i \(0.747262\pi\)
\(398\) −23.0490 −1.15534
\(399\) 0 0
\(400\) −1.77572 −0.0887858
\(401\) 3.82604 + 6.62690i 0.191063 + 0.330932i 0.945603 0.325323i \(-0.105473\pi\)
−0.754539 + 0.656255i \(0.772140\pi\)
\(402\) 0 0
\(403\) −11.5333 + 19.9763i −0.574516 + 0.995091i
\(404\) −2.14713 3.71893i −0.106824 0.185024i
\(405\) 0 0
\(406\) 10.3265 0.512497
\(407\) 0.228237 0.0113133
\(408\) 0 0
\(409\) 8.84435 15.3189i 0.437325 0.757469i −0.560157 0.828386i \(-0.689259\pi\)
0.997482 + 0.0709173i \(0.0225927\pi\)
\(410\) −11.6688 −0.576280
\(411\) 0 0
\(412\) 0.854305 1.47970i 0.0420886 0.0728996i
\(413\) −6.52793 11.3067i −0.321218 0.556367i
\(414\) 0 0
\(415\) −3.72368 6.44961i −0.182788 0.316599i
\(416\) 7.35657 + 12.7420i 0.360685 + 0.624726i
\(417\) 0 0
\(418\) 0.332178 0.550456i 0.0162473 0.0269237i
\(419\) −1.18732 −0.0580045 −0.0290023 0.999579i \(-0.509233\pi\)
−0.0290023 + 0.999579i \(0.509233\pi\)
\(420\) 0 0
\(421\) −16.6836 28.8969i −0.813111 1.40835i −0.910677 0.413120i \(-0.864439\pi\)
0.0975661 0.995229i \(-0.468894\pi\)
\(422\) −7.03770 + 12.1896i −0.342590 + 0.593383i
\(423\) 0 0
\(424\) −0.406280 + 0.703698i −0.0197307 + 0.0341746i
\(425\) 1.66123 0.0805815
\(426\) 0 0
\(427\) −8.68529 + 15.0434i −0.420311 + 0.727999i
\(428\) 0.398183 0.689673i 0.0192469 0.0333366i
\(429\) 0 0
\(430\) 9.33683 0.450262
\(431\) −3.08799 + 5.34855i −0.148743 + 0.257631i −0.930763 0.365623i \(-0.880856\pi\)
0.782020 + 0.623253i \(0.214189\pi\)
\(432\) 0 0
\(433\) 9.27761 16.0693i 0.445854 0.772241i −0.552258 0.833673i \(-0.686234\pi\)
0.998111 + 0.0614325i \(0.0195669\pi\)
\(434\) 6.81918 + 11.8112i 0.327331 + 0.566954i
\(435\) 0 0
\(436\) −12.9392 −0.619677
\(437\) 23.4022 + 0.453129i 1.11948 + 0.0216761i
\(438\) 0 0
\(439\) 0.113656 + 0.196858i 0.00542450 + 0.00939550i 0.868725 0.495295i \(-0.164940\pi\)
−0.863300 + 0.504690i \(0.831607\pi\)
\(440\) −0.206172 0.357100i −0.00982884 0.0170241i
\(441\) 0 0
\(442\) 3.20294 + 5.54765i 0.152348 + 0.263875i
\(443\) −17.4913 + 30.2959i −0.831038 + 1.43940i 0.0661770 + 0.997808i \(0.478920\pi\)
−0.897216 + 0.441593i \(0.854414\pi\)
\(444\) 0 0
\(445\) 9.73608 0.461534
\(446\) 11.1908 19.3831i 0.529901 0.917815i
\(447\) 0 0
\(448\) 15.4224 0.728638
\(449\) 16.9509 0.799961 0.399980 0.916524i \(-0.369017\pi\)
0.399980 + 0.916524i \(0.369017\pi\)
\(450\) 0 0
\(451\) −0.714520 1.23759i −0.0336454 0.0582756i
\(452\) −0.335362 + 0.580864i −0.0157741 + 0.0273215i
\(453\) 0 0
\(454\) −13.9469 24.1568i −0.654561 1.13373i
\(455\) −6.65174 −0.311838
\(456\) 0 0
\(457\) 1.60241 0.0749578 0.0374789 0.999297i \(-0.488067\pi\)
0.0374789 + 0.999297i \(0.488067\pi\)
\(458\) 1.21570 + 2.10566i 0.0568060 + 0.0983909i
\(459\) 0 0
\(460\) 2.13620 3.70001i 0.0996009 0.172514i
\(461\) −4.37081 7.57046i −0.203569 0.352592i 0.746107 0.665826i \(-0.231921\pi\)
−0.949676 + 0.313234i \(0.898587\pi\)
\(462\) 0 0
\(463\) 21.1886 0.984718 0.492359 0.870392i \(-0.336135\pi\)
0.492359 + 0.870392i \(0.336135\pi\)
\(464\) 8.82636 0.409753
\(465\) 0 0
\(466\) 7.76857 13.4556i 0.359872 0.623316i
\(467\) −20.4516 −0.946388 −0.473194 0.880958i \(-0.656899\pi\)
−0.473194 + 0.880958i \(0.656899\pi\)
\(468\) 0 0
\(469\) 2.79563 4.84217i 0.129090 0.223591i
\(470\) −6.09924 10.5642i −0.281337 0.487290i
\(471\) 0 0
\(472\) −10.5796 18.3244i −0.486965 0.843449i
\(473\) 0.571727 + 0.990259i 0.0262880 + 0.0455322i
\(474\) 0 0
\(475\) −4.35808 0.0843840i −0.199963 0.00387180i
\(476\) −2.50211 −0.114684
\(477\) 0 0
\(478\) −1.65425 2.86525i −0.0756639 0.131054i
\(479\) 11.7746 20.3942i 0.537994 0.931833i −0.461018 0.887391i \(-0.652516\pi\)
0.999012 0.0444419i \(-0.0141510\pi\)
\(480\) 0 0
\(481\) 2.98350 5.16757i 0.136036 0.235621i
\(482\) 26.0962 1.18865
\(483\) 0 0
\(484\) −4.36877 + 7.56694i −0.198581 + 0.343952i
\(485\) 8.73447 15.1285i 0.396612 0.686952i
\(486\) 0 0
\(487\) 36.0392 1.63309 0.816546 0.577280i \(-0.195886\pi\)
0.816546 + 0.577280i \(0.195886\pi\)
\(488\) −14.0760 + 24.3803i −0.637188 + 1.10364i
\(489\) 0 0
\(490\) 1.87459 3.24688i 0.0846852 0.146679i
\(491\) 10.0297 + 17.3720i 0.452635 + 0.783988i 0.998549 0.0538541i \(-0.0171506\pi\)
−0.545913 + 0.837842i \(0.683817\pi\)
\(492\) 0 0
\(493\) −8.25729 −0.371890
\(494\) −8.12081 14.7164i −0.365373 0.662124i
\(495\) 0 0
\(496\) 5.82853 + 10.0953i 0.261709 + 0.453293i
\(497\) 1.25733 + 2.17776i 0.0563989 + 0.0976858i
\(498\) 0 0
\(499\) 18.4364 + 31.9328i 0.825328 + 1.42951i 0.901668 + 0.432429i \(0.142343\pi\)
−0.0763399 + 0.997082i \(0.524323\pi\)
\(500\) −0.397815 + 0.689035i −0.0177908 + 0.0308146i
\(501\) 0 0
\(502\) 18.8649 0.841980
\(503\) −10.8244 + 18.7483i −0.482634 + 0.835947i −0.999801 0.0199377i \(-0.993653\pi\)
0.517167 + 0.855884i \(0.326987\pi\)
\(504\) 0 0
\(505\) 5.39731 0.240177
\(506\) −0.792028 −0.0352099
\(507\) 0 0
\(508\) 7.45492 + 12.9123i 0.330759 + 0.572891i
\(509\) −18.2279 + 31.5717i −0.807938 + 1.39939i 0.106351 + 0.994329i \(0.466083\pi\)
−0.914289 + 0.405062i \(0.867250\pi\)
\(510\) 0 0
\(511\) 6.00327 + 10.3980i 0.265569 + 0.459979i
\(512\) 18.3314 0.810141
\(513\) 0 0
\(514\) −21.4471 −0.945990
\(515\) 1.07375 + 1.85979i 0.0473150 + 0.0819520i
\(516\) 0 0
\(517\) 0.746955 1.29376i 0.0328511 0.0568997i
\(518\) −1.76402 3.05537i −0.0775065 0.134245i
\(519\) 0 0
\(520\) −10.7802 −0.472745
\(521\) 22.6092 0.990528 0.495264 0.868742i \(-0.335071\pi\)
0.495264 + 0.868742i \(0.335071\pi\)
\(522\) 0 0
\(523\) −0.266456 + 0.461515i −0.0116513 + 0.0201806i −0.871792 0.489876i \(-0.837042\pi\)
0.860141 + 0.510056i \(0.170375\pi\)
\(524\) 2.29654 0.100325
\(525\) 0 0
\(526\) −4.83619 + 8.37653i −0.210868 + 0.365234i
\(527\) −5.45275 9.44444i −0.237525 0.411406i
\(528\) 0 0
\(529\) −2.91759 5.05341i −0.126852 0.219714i
\(530\) −0.145327 0.251713i −0.00631259 0.0109337i
\(531\) 0 0
\(532\) 6.56406 + 0.127098i 0.284588 + 0.00551038i
\(533\) −37.3606 −1.61827
\(534\) 0 0
\(535\) 0.500463 + 0.866827i 0.0216369 + 0.0374762i
\(536\) 4.53078 7.84754i 0.195700 0.338962i
\(537\) 0 0
\(538\) −0.158230 + 0.274062i −0.00682178 + 0.0118157i
\(539\) 0.459150 0.0197770
\(540\) 0 0
\(541\) −2.50820 + 4.34433i −0.107836 + 0.186777i −0.914893 0.403696i \(-0.867725\pi\)
0.807057 + 0.590473i \(0.201059\pi\)
\(542\) −13.6473 + 23.6378i −0.586202 + 1.01533i
\(543\) 0 0
\(544\) −6.95610 −0.298240
\(545\) 8.13145 14.0841i 0.348313 0.603296i
\(546\) 0 0
\(547\) −11.3149 + 19.5981i −0.483792 + 0.837952i −0.999827 0.0186154i \(-0.994074\pi\)
0.516035 + 0.856568i \(0.327408\pi\)
\(548\) 7.49148 + 12.9756i 0.320020 + 0.554291i
\(549\) 0 0
\(550\) 0.147496 0.00628923
\(551\) 21.6622 + 0.419439i 0.922843 + 0.0178687i
\(552\) 0 0
\(553\) 1.38883 + 2.40552i 0.0590590 + 0.102293i
\(554\) −2.41703 4.18642i −0.102690 0.177864i
\(555\) 0 0
\(556\) −7.23207 12.5263i −0.306708 0.531234i
\(557\) 17.6277 30.5321i 0.746910 1.29369i −0.202387 0.979306i \(-0.564870\pi\)
0.949297 0.314381i \(-0.101797\pi\)
\(558\) 0 0
\(559\) 29.8943 1.26439
\(560\) −1.68077 + 2.91119i −0.0710257 + 0.123020i
\(561\) 0 0
\(562\) −35.9097 −1.51476
\(563\) 24.6295 1.03801 0.519005 0.854771i \(-0.326302\pi\)
0.519005 + 0.854771i \(0.326302\pi\)
\(564\) 0 0
\(565\) −0.421505 0.730068i −0.0177329 0.0307142i
\(566\) −0.729207 + 1.26302i −0.0306509 + 0.0530888i
\(567\) 0 0
\(568\) 2.03771 + 3.52942i 0.0855005 + 0.148091i
\(569\) 20.0193 0.839252 0.419626 0.907697i \(-0.362161\pi\)
0.419626 + 0.907697i \(0.362161\pi\)
\(570\) 0 0
\(571\) −16.6121 −0.695195 −0.347597 0.937644i \(-0.613002\pi\)
−0.347597 + 0.937644i \(0.613002\pi\)
\(572\) −0.187866 0.325394i −0.00785508 0.0136054i
\(573\) 0 0
\(574\) −11.0449 + 19.1303i −0.461005 + 0.798484i
\(575\) 2.68492 + 4.65042i 0.111969 + 0.193936i
\(576\) 0 0
\(577\) 12.4486 0.518244 0.259122 0.965845i \(-0.416567\pi\)
0.259122 + 0.965845i \(0.416567\pi\)
\(578\) 15.6279 0.650034
\(579\) 0 0
\(580\) 1.97737 3.42491i 0.0821060 0.142212i
\(581\) −14.0984 −0.584899
\(582\) 0 0
\(583\) 0.0177977 0.0308266i 0.000737107 0.00127671i
\(584\) 9.72930 + 16.8516i 0.402601 + 0.697326i
\(585\) 0 0
\(586\) 4.23811 + 7.34063i 0.175075 + 0.303238i
\(587\) 2.25572 + 3.90702i 0.0931036 + 0.161260i 0.908816 0.417198i \(-0.136988\pi\)
−0.815712 + 0.578458i \(0.803655\pi\)
\(588\) 0 0
\(589\) 13.8250 + 25.0536i 0.569651 + 1.03232i
\(590\) 7.56867 0.311597
\(591\) 0 0
\(592\) −1.50775 2.61150i −0.0619682 0.107332i
\(593\) 9.80411 16.9812i 0.402606 0.697335i −0.591433 0.806354i \(-0.701438\pi\)
0.994040 + 0.109019i \(0.0347710\pi\)
\(594\) 0 0
\(595\) 1.57241 2.72349i 0.0644625 0.111652i
\(596\) −17.7062 −0.725274
\(597\) 0 0
\(598\) −10.3533 + 17.9325i −0.423379 + 0.733315i
\(599\) 5.38795 9.33221i 0.220146 0.381304i −0.734706 0.678385i \(-0.762680\pi\)
0.954852 + 0.297082i \(0.0960134\pi\)
\(600\) 0 0
\(601\) 15.0244 0.612860 0.306430 0.951893i \(-0.400866\pi\)
0.306430 + 0.951893i \(0.400866\pi\)
\(602\) 8.83763 15.3072i 0.360195 0.623876i
\(603\) 0 0
\(604\) 1.32664 2.29781i 0.0539802 0.0934964i
\(605\) −5.49097 9.51064i −0.223240 0.386662i
\(606\) 0 0
\(607\) 25.1901 1.02243 0.511217 0.859452i \(-0.329195\pi\)
0.511217 + 0.859452i \(0.329195\pi\)
\(608\) 18.2487 + 0.353343i 0.740082 + 0.0143300i
\(609\) 0 0
\(610\) −5.03499 8.72085i −0.203861 0.353097i
\(611\) −19.5283 33.8240i −0.790030 1.36837i
\(612\) 0 0
\(613\) −8.11753 14.0600i −0.327864 0.567877i 0.654224 0.756301i \(-0.272995\pi\)
−0.982088 + 0.188424i \(0.939662\pi\)
\(614\) −4.99336 + 8.64875i −0.201516 + 0.349035i
\(615\) 0 0
\(616\) −0.780593 −0.0314510
\(617\) 3.25913 5.64498i 0.131208 0.227258i −0.792935 0.609307i \(-0.791448\pi\)
0.924142 + 0.382048i \(0.124781\pi\)
\(618\) 0 0
\(619\) −4.39112 −0.176494 −0.0882470 0.996099i \(-0.528126\pi\)
−0.0882470 + 0.996099i \(0.528126\pi\)
\(620\) 5.22308 0.209764
\(621\) 0 0
\(622\) 6.83532 + 11.8391i 0.274071 + 0.474705i
\(623\) 9.21553 15.9618i 0.369212 0.639494i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −2.24484 −0.0897220
\(627\) 0 0
\(628\) −5.77858 −0.230590
\(629\) 1.41054 + 2.44313i 0.0562420 + 0.0974140i
\(630\) 0 0
\(631\) 17.3104 29.9826i 0.689118 1.19359i −0.283006 0.959118i \(-0.591332\pi\)
0.972124 0.234469i \(-0.0753350\pi\)
\(632\) 2.25083 + 3.89855i 0.0895331 + 0.155076i
\(633\) 0 0
\(634\) 25.8680 1.02735
\(635\) −18.7397 −0.743661
\(636\) 0 0
\(637\) 6.00198 10.3957i 0.237807 0.411894i
\(638\) −0.733141 −0.0290253
\(639\) 0 0
\(640\) −0.282960 + 0.490101i −0.0111850 + 0.0193730i
\(641\) 3.70621 + 6.41934i 0.146386 + 0.253549i 0.929889 0.367839i \(-0.119902\pi\)
−0.783503 + 0.621388i \(0.786569\pi\)
\(642\) 0 0
\(643\) 8.27294 + 14.3292i 0.326253 + 0.565087i 0.981765 0.190098i \(-0.0608805\pi\)
−0.655512 + 0.755185i \(0.727547\pi\)
\(644\) −4.04397 7.00437i −0.159355 0.276011i
\(645\) 0 0
\(646\) 7.94520 + 0.153840i 0.312600 + 0.00605276i
\(647\) −29.4822 −1.15907 −0.579533 0.814949i \(-0.696765\pi\)
−0.579533 + 0.814949i \(0.696765\pi\)
\(648\) 0 0
\(649\) 0.463456 + 0.802729i 0.0181922 + 0.0315099i
\(650\) 1.92805 3.33949i 0.0756245 0.130985i
\(651\) 0 0
\(652\) −7.86810 + 13.6279i −0.308138 + 0.533712i
\(653\) −6.57421 −0.257269 −0.128634 0.991692i \(-0.541059\pi\)
−0.128634 + 0.991692i \(0.541059\pi\)
\(654\) 0 0
\(655\) −1.44322 + 2.49973i −0.0563912 + 0.0976725i
\(656\) −9.44037 + 16.3512i −0.368584 + 0.638407i
\(657\) 0 0
\(658\) −23.0925 −0.900241
\(659\) −13.1685 + 22.8085i −0.512972 + 0.888494i 0.486915 + 0.873450i \(0.338122\pi\)
−0.999887 + 0.0150445i \(0.995211\pi\)
\(660\) 0 0
\(661\) −1.89210 + 3.27721i −0.0735941 + 0.127469i −0.900474 0.434910i \(-0.856780\pi\)
0.826880 + 0.562378i \(0.190114\pi\)
\(662\) −10.2706 17.7893i −0.399180 0.691399i
\(663\) 0 0
\(664\) −22.8487 −0.886703
\(665\) −4.26341 + 7.06496i −0.165328 + 0.273967i
\(666\) 0 0
\(667\) −13.3456 23.1153i −0.516745 0.895029i
\(668\) 1.35384 + 2.34492i 0.0523817 + 0.0907278i
\(669\) 0 0
\(670\) 1.62067 + 2.80708i 0.0626118 + 0.108447i
\(671\) 0.616619 1.06802i 0.0238043 0.0412303i
\(672\) 0 0
\(673\) −21.0431 −0.811150 −0.405575 0.914062i \(-0.632929\pi\)
−0.405575 + 0.914062i \(0.632929\pi\)
\(674\) −17.9366 + 31.0670i −0.690891 + 1.19666i
\(675\) 0 0
\(676\) 0.520083 0.0200032
\(677\) 15.2744 0.587043 0.293522 0.955952i \(-0.405173\pi\)
0.293522 + 0.955952i \(0.405173\pi\)
\(678\) 0 0
\(679\) −16.5349 28.6394i −0.634553 1.09908i
\(680\) 2.54835 4.41387i 0.0977248 0.169264i
\(681\) 0 0
\(682\) −0.484133 0.838544i −0.0185384 0.0321095i
\(683\) 8.60225 0.329156 0.164578 0.986364i \(-0.447374\pi\)
0.164578 + 0.986364i \(0.447374\pi\)
\(684\) 0 0
\(685\) −18.8316 −0.719518
\(686\) −10.8201 18.7409i −0.413112 0.715530i
\(687\) 0 0
\(688\) 7.55375 13.0835i 0.287984 0.498803i
\(689\) −0.465302 0.805926i −0.0177266 0.0307033i
\(690\) 0 0
\(691\) 34.1079 1.29753 0.648763 0.760990i \(-0.275286\pi\)
0.648763 + 0.760990i \(0.275286\pi\)
\(692\) −8.42231 −0.320168
\(693\) 0 0
\(694\) 1.40837 2.43937i 0.0534611 0.0925974i
\(695\) 18.1795 0.689587
\(696\) 0 0
\(697\) 8.83172 15.2970i 0.334525 0.579414i
\(698\) 9.11942 + 15.7953i 0.345175 + 0.597861i
\(699\) 0 0
\(700\) 0.753090 + 1.30439i 0.0284641 + 0.0493013i
\(701\) 5.36463 + 9.29181i 0.202619 + 0.350947i 0.949372 0.314155i \(-0.101721\pi\)
−0.746752 + 0.665102i \(0.768388\pi\)
\(702\) 0 0
\(703\) −3.57633 6.48098i −0.134884 0.244435i
\(704\) −1.09492 −0.0412665
\(705\) 0 0
\(706\) −15.5633 26.9564i −0.585732 1.01452i
\(707\) 5.10873 8.84859i 0.192134 0.332785i
\(708\) 0 0
\(709\) 14.4238 24.9828i 0.541697 0.938247i −0.457109 0.889410i \(-0.651115\pi\)
0.998807 0.0488369i \(-0.0155514\pi\)
\(710\) −1.45778 −0.0547096
\(711\) 0 0
\(712\) 14.9353 25.8687i 0.559724 0.969470i
\(713\) 17.6257 30.5287i 0.660089 1.14331i
\(714\) 0 0
\(715\) 0.472245 0.0176610
\(716\) 5.80905 10.0616i 0.217095 0.376019i
\(717\) 0 0
\(718\) −9.54143 + 16.5262i −0.356083 + 0.616754i
\(719\) −10.0278 17.3686i −0.373972 0.647739i 0.616200 0.787589i \(-0.288671\pi\)
−0.990173 + 0.139851i \(0.955338\pi\)
\(720\) 0 0
\(721\) 4.06535 0.151402
\(722\) −20.8357 0.807171i −0.775424 0.0300398i
\(723\) 0 0
\(724\) −2.16117 3.74326i −0.0803193 0.139117i
\(725\) 2.48530 + 4.30466i 0.0923016 + 0.159871i
\(726\) 0 0
\(727\) 0.390261 + 0.675951i 0.0144740 + 0.0250697i 0.873172 0.487413i \(-0.162059\pi\)
−0.858698 + 0.512482i \(0.828726\pi\)
\(728\) −10.2039 + 17.6736i −0.378180 + 0.655028i
\(729\) 0 0
\(730\) −6.96036 −0.257615
\(731\) −7.06674 + 12.2399i −0.261373 + 0.452711i
\(732\) 0 0
\(733\) −26.8391 −0.991326 −0.495663 0.868515i \(-0.665075\pi\)
−0.495663 + 0.868515i \(0.665075\pi\)
\(734\) −28.3192 −1.04528
\(735\) 0 0
\(736\) −11.2426 19.4728i −0.414409 0.717777i
\(737\) −0.198478 + 0.343774i −0.00731103 + 0.0126631i
\(738\) 0 0
\(739\) −10.3265 17.8861i −0.379867 0.657949i 0.611175 0.791495i \(-0.290697\pi\)
−0.991043 + 0.133546i \(0.957364\pi\)
\(740\) −1.35113 −0.0496685
\(741\) 0 0
\(742\) −0.550227 −0.0201995
\(743\) 0.736585 + 1.27580i 0.0270227 + 0.0468047i 0.879220 0.476415i \(-0.158064\pi\)
−0.852198 + 0.523220i \(0.824731\pi\)
\(744\) 0 0
\(745\) 11.1272 19.2728i 0.407668 0.706102i
\(746\) 14.8518 + 25.7240i 0.543762 + 0.941824i
\(747\) 0 0
\(748\) 0.177639 0.00649514
\(749\) 1.89482 0.0692352
\(750\) 0 0
\(751\) −7.78121 + 13.4775i −0.283940 + 0.491799i −0.972352 0.233521i \(-0.924975\pi\)
0.688411 + 0.725321i \(0.258308\pi\)
\(752\) −19.7378 −0.719764
\(753\) 0 0
\(754\) −9.58356 + 16.5992i −0.349013 + 0.604508i
\(755\) 1.66741 + 2.88804i 0.0606832 + 0.105106i
\(756\) 0 0
\(757\) −10.0878 17.4726i −0.366647 0.635052i 0.622392 0.782706i \(-0.286161\pi\)
−0.989039 + 0.147654i \(0.952828\pi\)
\(758\) 6.80568 + 11.7878i 0.247193 + 0.428152i
\(759\) 0 0
\(760\) −6.90957 + 11.4499i −0.250637 + 0.415333i
\(761\) 15.1076 0.547649 0.273825 0.961780i \(-0.411711\pi\)
0.273825 + 0.961780i \(0.411711\pi\)
\(762\) 0 0
\(763\) −15.3934 26.6621i −0.557278 0.965234i
\(764\) −8.14556 + 14.1085i −0.294696 + 0.510428i
\(765\) 0 0
\(766\) 2.94082 5.09364i 0.106256 0.184041i
\(767\) 24.2331 0.875005
\(768\) 0 0
\(769\) −25.8290 + 44.7372i −0.931418 + 1.61326i −0.150518 + 0.988607i \(0.548094\pi\)
−0.780900 + 0.624656i \(0.785239\pi\)
\(770\) 0.139610 0.241811i 0.00503118 0.00871426i
\(771\) 0 0
\(772\) −8.77063 −0.315662
\(773\) 15.0779 26.1157i 0.542314 0.939316i −0.456457 0.889746i \(-0.650882\pi\)
0.998771 0.0495699i \(-0.0157851\pi\)
\(774\) 0 0
\(775\) −3.28236 + 5.68521i −0.117906 + 0.204219i
\(776\) −26.7976 46.4148i −0.961978 1.66620i
\(777\) 0 0
\(778\) 9.40431 0.337161
\(779\) −23.9462 + 39.6816i −0.857962 + 1.42174i
\(780\) 0 0
\(781\) −0.0892652 0.154612i −0.00319416 0.00553244i
\(782\) −4.89487 8.47816i −0.175040 0.303178i
\(783\) 0