Properties

Label 475.2.j.c.49.4
Level $475$
Weight $2$
Character 475.49
Analytic conductor $3.793$
Analytic rank $0$
Dimension $16$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(49,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.1387535264013605949997056.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.4
Root \(1.19454 - 0.689667i\) of defining polynomial
Character \(\chi\) \(=\) 475.49
Dual form 475.2.j.c.349.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.950409 - 0.548719i) q^{2} +(-0.328513 - 0.189667i) q^{3} +(-0.397815 - 0.689035i) q^{4} +(0.208148 + 0.360522i) q^{6} +1.89307i q^{7} +3.06803i q^{8} +(-1.42805 - 2.47346i) q^{9} +O(q^{10})\) \(q+(-0.950409 - 0.548719i) q^{2} +(-0.328513 - 0.189667i) q^{3} +(-0.397815 - 0.689035i) q^{4} +(0.208148 + 0.360522i) q^{6} +1.89307i q^{7} +3.06803i q^{8} +(-1.42805 - 2.47346i) q^{9} +0.134400 q^{11} +0.301809i q^{12} +(-3.04298 + 1.75687i) q^{13} +(1.03876 - 1.79919i) q^{14} +(0.887858 - 1.53781i) q^{16} +(1.43867 + 0.830615i) q^{17} +3.13440i q^{18} +(-2.10596 + 3.81640i) q^{19} +(0.359052 - 0.621897i) q^{21} +(-0.127735 - 0.0737478i) q^{22} +(-4.65042 + 2.68492i) q^{23} +(0.581904 - 1.00789i) q^{24} +3.85611 q^{26} +2.22142i q^{27} +(1.30439 - 0.753090i) q^{28} +(2.48530 + 4.30466i) q^{29} +6.56472 q^{31} +(3.62633 - 2.09366i) q^{32} +(-0.0441521 - 0.0254912i) q^{33} +(-0.911548 - 1.57885i) q^{34} +(-1.13620 + 1.96796i) q^{36} -1.69819i q^{37} +(4.09566 - 2.47156i) q^{38} +1.33288 q^{39} +(-5.31637 + 9.20823i) q^{41} +(-0.682493 + 0.394038i) q^{42} +(7.36801 + 4.25392i) q^{43} +(-0.0534662 - 0.0926063i) q^{44} +5.89307 q^{46} +(-9.62623 + 5.55771i) q^{47} +(-0.583345 + 0.336794i) q^{48} +3.41630 q^{49} +(-0.315080 - 0.545735i) q^{51} +(2.42109 + 1.39781i) q^{52} +(0.229365 - 0.132424i) q^{53} +(1.21894 - 2.11126i) q^{54} -5.80799 q^{56} +(1.41568 - 0.854305i) q^{57} -5.45492i q^{58} +(-3.44833 + 5.97269i) q^{59} +(-4.58794 - 7.94655i) q^{61} +(-6.23917 - 3.60219i) q^{62} +(4.68243 - 2.70340i) q^{63} -8.14676 q^{64} +(0.0279750 + 0.0484542i) q^{66} +(-2.55784 + 1.47677i) q^{67} -1.32172i q^{68} +2.03696 q^{69} +(-0.664176 + 1.15039i) q^{71} +(7.58865 - 4.38131i) q^{72} +(-5.49266 - 3.17119i) q^{73} +(-0.931830 + 1.61398i) q^{74} +(3.46742 - 0.0671384i) q^{76} +0.254428i q^{77} +(-1.26678 - 0.731376i) q^{78} +(-0.733639 + 1.27070i) q^{79} +(-3.86283 + 6.69062i) q^{81} +(10.1055 - 5.83439i) q^{82} -7.44736i q^{83} -0.571345 q^{84} +(-4.66842 - 8.08593i) q^{86} -1.88551i q^{87} +0.412343i q^{88} +(4.86804 + 8.43169i) q^{89} +(-3.32587 - 5.76057i) q^{91} +(3.70001 + 2.13620i) q^{92} +(-2.15659 - 1.24511i) q^{93} +12.1985 q^{94} -1.58839 q^{96} +(-15.1285 - 8.73447i) q^{97} +(-3.24688 - 1.87459i) q^{98} +(-0.191930 - 0.332433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49} - 44 q^{51} - 68 q^{54} - 164 q^{56} - 10 q^{59} - 224 q^{64} + 62 q^{66} + 36 q^{69} - 40 q^{71} + 50 q^{74} + 126 q^{76} + 34 q^{79} - 24 q^{81} + 80 q^{84} - 16 q^{86} + 22 q^{89} - 12 q^{91} + 124 q^{94} + 84 q^{96} + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.950409 0.548719i −0.672041 0.388003i 0.124809 0.992181i \(-0.460168\pi\)
−0.796850 + 0.604178i \(0.793502\pi\)
\(3\) −0.328513 0.189667i −0.189667 0.109504i 0.402160 0.915570i \(-0.368260\pi\)
−0.591827 + 0.806065i \(0.701593\pi\)
\(4\) −0.397815 0.689035i −0.198907 0.344518i
\(5\) 0 0
\(6\) 0.208148 + 0.360522i 0.0849759 + 0.147183i
\(7\) 1.89307i 0.715512i 0.933815 + 0.357756i \(0.116458\pi\)
−0.933815 + 0.357756i \(0.883542\pi\)
\(8\) 3.06803i 1.08471i
\(9\) −1.42805 2.47346i −0.476018 0.824487i
\(10\) 0 0
\(11\) 0.134400 0.0405231 0.0202615 0.999795i \(-0.493550\pi\)
0.0202615 + 0.999795i \(0.493550\pi\)
\(12\) 0.301809i 0.0871248i
\(13\) −3.04298 + 1.75687i −0.843972 + 0.487267i −0.858612 0.512626i \(-0.828673\pi\)
0.0146407 + 0.999893i \(0.495340\pi\)
\(14\) 1.03876 1.79919i 0.277621 0.480854i
\(15\) 0 0
\(16\) 0.887858 1.53781i 0.221964 0.384454i
\(17\) 1.43867 + 0.830615i 0.348928 + 0.201454i 0.664213 0.747543i \(-0.268767\pi\)
−0.315285 + 0.948997i \(0.602100\pi\)
\(18\) 3.13440i 0.738785i
\(19\) −2.10596 + 3.81640i −0.483141 + 0.875543i
\(20\) 0 0
\(21\) 0.359052 0.621897i 0.0783516 0.135709i
\(22\) −0.127735 0.0737478i −0.0272332 0.0157231i
\(23\) −4.65042 + 2.68492i −0.969679 + 0.559844i −0.899138 0.437664i \(-0.855806\pi\)
−0.0705407 + 0.997509i \(0.522472\pi\)
\(24\) 0.581904 1.00789i 0.118781 0.205734i
\(25\) 0 0
\(26\) 3.85611 0.756245
\(27\) 2.22142i 0.427512i
\(28\) 1.30439 0.753090i 0.246507 0.142321i
\(29\) 2.48530 + 4.30466i 0.461508 + 0.799355i 0.999036 0.0438905i \(-0.0139753\pi\)
−0.537528 + 0.843246i \(0.680642\pi\)
\(30\) 0 0
\(31\) 6.56472 1.17906 0.589529 0.807747i \(-0.299313\pi\)
0.589529 + 0.807747i \(0.299313\pi\)
\(32\) 3.62633 2.09366i 0.641050 0.370111i
\(33\) −0.0441521 0.0254912i −0.00768589 0.00443745i
\(34\) −0.911548 1.57885i −0.156329 0.270770i
\(35\) 0 0
\(36\) −1.13620 + 1.96796i −0.189367 + 0.327993i
\(37\) 1.69819i 0.279181i −0.990209 0.139590i \(-0.955421\pi\)
0.990209 0.139590i \(-0.0445786\pi\)
\(38\) 4.09566 2.47156i 0.664404 0.400940i
\(39\) 1.33288 0.213431
\(40\) 0 0
\(41\) −5.31637 + 9.20823i −0.830278 + 1.43808i 0.0675398 + 0.997717i \(0.478485\pi\)
−0.897818 + 0.440367i \(0.854848\pi\)
\(42\) −0.682493 + 0.394038i −0.105311 + 0.0608013i
\(43\) 7.36801 + 4.25392i 1.12361 + 0.648717i 0.942320 0.334713i \(-0.108639\pi\)
0.181290 + 0.983430i \(0.441973\pi\)
\(44\) −0.0534662 0.0926063i −0.00806034 0.0139609i
\(45\) 0 0
\(46\) 5.89307 0.868885
\(47\) −9.62623 + 5.55771i −1.40413 + 0.810675i −0.994813 0.101718i \(-0.967566\pi\)
−0.409316 + 0.912392i \(0.634233\pi\)
\(48\) −0.583345 + 0.336794i −0.0841986 + 0.0486121i
\(49\) 3.41630 0.488042
\(50\) 0 0
\(51\) −0.315080 0.545735i −0.0441201 0.0764182i
\(52\) 2.42109 + 1.39781i 0.335744 + 0.193842i
\(53\) 0.229365 0.132424i 0.0315057 0.0181898i −0.484164 0.874977i \(-0.660876\pi\)
0.515670 + 0.856787i \(0.327543\pi\)
\(54\) 1.21894 2.11126i 0.165876 0.287306i
\(55\) 0 0
\(56\) −5.80799 −0.776125
\(57\) 1.41568 0.854305i 0.187511 0.113155i
\(58\) 5.45492i 0.716266i
\(59\) −3.44833 + 5.97269i −0.448935 + 0.777578i −0.998317 0.0579932i \(-0.981530\pi\)
0.549382 + 0.835571i \(0.314863\pi\)
\(60\) 0 0
\(61\) −4.58794 7.94655i −0.587426 1.01745i −0.994568 0.104087i \(-0.966808\pi\)
0.407142 0.913365i \(-0.366525\pi\)
\(62\) −6.23917 3.60219i −0.792375 0.457478i
\(63\) 4.68243 2.70340i 0.589930 0.340596i
\(64\) −8.14676 −1.01834
\(65\) 0 0
\(66\) 0.0279750 + 0.0484542i 0.00344349 + 0.00596430i
\(67\) −2.55784 + 1.47677i −0.312490 + 0.180416i −0.648040 0.761606i \(-0.724411\pi\)
0.335550 + 0.942022i \(0.391078\pi\)
\(68\) 1.32172i 0.160282i
\(69\) 2.03696 0.245221
\(70\) 0 0
\(71\) −0.664176 + 1.15039i −0.0788232 + 0.136526i −0.902742 0.430181i \(-0.858450\pi\)
0.823919 + 0.566707i \(0.191783\pi\)
\(72\) 7.58865 4.38131i 0.894331 0.516342i
\(73\) −5.49266 3.17119i −0.642867 0.371159i 0.142851 0.989744i \(-0.454373\pi\)
−0.785718 + 0.618585i \(0.787706\pi\)
\(74\) −0.931830 + 1.61398i −0.108323 + 0.187621i
\(75\) 0 0
\(76\) 3.46742 0.0671384i 0.397740 0.00770130i
\(77\) 0.254428i 0.0289948i
\(78\) −1.26678 0.731376i −0.143435 0.0828120i
\(79\) −0.733639 + 1.27070i −0.0825408 + 0.142965i −0.904341 0.426811i \(-0.859637\pi\)
0.821800 + 0.569776i \(0.192970\pi\)
\(80\) 0 0
\(81\) −3.86283 + 6.69062i −0.429203 + 0.743402i
\(82\) 10.1055 5.83439i 1.11596 0.644301i
\(83\) 7.44736i 0.817454i −0.912657 0.408727i \(-0.865973\pi\)
0.912657 0.408727i \(-0.134027\pi\)
\(84\) −0.571345 −0.0623388
\(85\) 0 0
\(86\) −4.66842 8.08593i −0.503408 0.871929i
\(87\) 1.88551i 0.202148i
\(88\) 0.412343i 0.0439559i
\(89\) 4.86804 + 8.43169i 0.516011 + 0.893757i 0.999827 + 0.0185878i \(0.00591701\pi\)
−0.483816 + 0.875170i \(0.660750\pi\)
\(90\) 0 0
\(91\) −3.32587 5.76057i −0.348646 0.603872i
\(92\) 3.70001 + 2.13620i 0.385753 + 0.222714i
\(93\) −2.15659 1.24511i −0.223628 0.129112i
\(94\) 12.1985 1.25818
\(95\) 0 0
\(96\) −1.58839 −0.162115
\(97\) −15.1285 8.73447i −1.53607 0.886851i −0.999063 0.0432737i \(-0.986221\pi\)
−0.537008 0.843577i \(-0.680445\pi\)
\(98\) −3.24688 1.87459i −0.327984 0.189362i
\(99\) −0.191930 0.332433i −0.0192897 0.0334108i
\(100\) 0 0
\(101\) −2.69865 4.67420i −0.268526 0.465101i 0.699955 0.714187i \(-0.253203\pi\)
−0.968481 + 0.249086i \(0.919870\pi\)
\(102\) 0.691562i 0.0684749i
\(103\) 2.14750i 0.211599i −0.994387 0.105800i \(-0.966260\pi\)
0.994387 0.105800i \(-0.0337402\pi\)
\(104\) −5.39012 9.33596i −0.528545 0.915467i
\(105\) 0 0
\(106\) −0.290654 −0.0282308
\(107\) 1.00093i 0.0967631i −0.998829 0.0483815i \(-0.984594\pi\)
0.998829 0.0483815i \(-0.0154063\pi\)
\(108\) 1.53064 0.883713i 0.147285 0.0850353i
\(109\) 8.13145 14.0841i 0.778852 1.34901i −0.153752 0.988109i \(-0.549136\pi\)
0.932604 0.360902i \(-0.117531\pi\)
\(110\) 0 0
\(111\) −0.322091 + 0.557877i −0.0305715 + 0.0529514i
\(112\) 2.91119 + 1.68077i 0.275081 + 0.158818i
\(113\) 0.843010i 0.0793037i −0.999214 0.0396519i \(-0.987375\pi\)
0.999214 0.0396519i \(-0.0126249\pi\)
\(114\) −1.81425 + 0.0351287i −0.169920 + 0.00329010i
\(115\) 0 0
\(116\) 1.97737 3.42491i 0.183595 0.317995i
\(117\) 8.69108 + 5.01780i 0.803491 + 0.463896i
\(118\) 6.55466 3.78433i 0.603405 0.348376i
\(119\) −1.57241 + 2.72349i −0.144143 + 0.249662i
\(120\) 0 0
\(121\) −10.9819 −0.998358
\(122\) 10.0700i 0.911692i
\(123\) 3.49299 2.01668i 0.314953 0.181838i
\(124\) −2.61154 4.52332i −0.234523 0.406206i
\(125\) 0 0
\(126\) −5.93363 −0.528610
\(127\) 16.2290 9.36984i 1.44009 0.831439i 0.442239 0.896897i \(-0.354184\pi\)
0.997855 + 0.0654584i \(0.0208510\pi\)
\(128\) 0.490101 + 0.282960i 0.0433193 + 0.0250104i
\(129\) −1.61366 2.79493i −0.142074 0.246080i
\(130\) 0 0
\(131\) −1.44322 + 2.49973i −0.126095 + 0.218402i −0.922160 0.386808i \(-0.873578\pi\)
0.796066 + 0.605210i \(0.206911\pi\)
\(132\) 0.0405631i 0.00353057i
\(133\) −7.22471 3.98673i −0.626461 0.345693i
\(134\) 3.24133 0.280008
\(135\) 0 0
\(136\) −2.54835 + 4.41387i −0.218519 + 0.378487i
\(137\) −16.3086 + 9.41579i −1.39334 + 0.804445i −0.993683 0.112220i \(-0.964204\pi\)
−0.399656 + 0.916665i \(0.630871\pi\)
\(138\) −1.93595 1.11772i −0.164799 0.0951466i
\(139\) −9.08974 15.7439i −0.770982 1.33538i −0.937025 0.349262i \(-0.886432\pi\)
0.166043 0.986118i \(-0.446901\pi\)
\(140\) 0 0
\(141\) 4.21645 0.355089
\(142\) 1.26248 0.728892i 0.105945 0.0611672i
\(143\) −0.408977 + 0.236123i −0.0342003 + 0.0197456i
\(144\) −5.07163 −0.422636
\(145\) 0 0
\(146\) 3.48018 + 6.02785i 0.288022 + 0.498868i
\(147\) −1.12230 0.647958i −0.0925655 0.0534427i
\(148\) −1.17011 + 0.675565i −0.0961827 + 0.0555311i
\(149\) −11.1272 + 19.2728i −0.911573 + 1.57889i −0.0997308 + 0.995014i \(0.531798\pi\)
−0.811842 + 0.583877i \(0.801535\pi\)
\(150\) 0 0
\(151\) 3.33482 0.271384 0.135692 0.990751i \(-0.456674\pi\)
0.135692 + 0.990751i \(0.456674\pi\)
\(152\) −11.7088 6.46116i −0.949712 0.524069i
\(153\) 4.74465i 0.383582i
\(154\) 0.139610 0.241811i 0.0112501 0.0194857i
\(155\) 0 0
\(156\) −0.530238 0.918400i −0.0424530 0.0735308i
\(157\) −6.28986 3.63145i −0.501986 0.289822i 0.227548 0.973767i \(-0.426929\pi\)
−0.729533 + 0.683945i \(0.760263\pi\)
\(158\) 1.39451 0.805123i 0.110942 0.0640522i
\(159\) −0.100466 −0.00796744
\(160\) 0 0
\(161\) −5.08273 8.80355i −0.400576 0.693817i
\(162\) 7.34254 4.23922i 0.576884 0.333064i
\(163\) 19.7783i 1.54916i 0.632478 + 0.774578i \(0.282038\pi\)
−0.632478 + 0.774578i \(0.717962\pi\)
\(164\) 8.45972 0.660593
\(165\) 0 0
\(166\) −4.08651 + 7.07805i −0.317175 + 0.549363i
\(167\) −2.94726 + 1.70160i −0.228066 + 0.131674i −0.609679 0.792648i \(-0.708702\pi\)
0.381614 + 0.924322i \(0.375368\pi\)
\(168\) 1.90800 + 1.10158i 0.147205 + 0.0849890i
\(169\) −0.326838 + 0.566100i −0.0251414 + 0.0435461i
\(170\) 0 0
\(171\) 12.4471 0.241010i 0.951857 0.0184305i
\(172\) 6.76909i 0.516138i
\(173\) −9.16750 5.29286i −0.696992 0.402409i 0.109234 0.994016i \(-0.465160\pi\)
−0.806226 + 0.591607i \(0.798494\pi\)
\(174\) −1.03462 + 1.79201i −0.0784341 + 0.135852i
\(175\) 0 0
\(176\) 0.119328 0.206682i 0.00899469 0.0155793i
\(177\) 2.26564 1.30807i 0.170296 0.0983205i
\(178\) 10.6847i 0.800855i
\(179\) 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 0.949141 0.314851i \(-0.101955\pi\)
−0.747240 + 0.664555i \(0.768621\pi\)
\(182\) 7.29987i 0.541102i
\(183\) 3.48072i 0.257303i
\(184\) −8.23742 14.2676i −0.607270 1.05182i
\(185\) 0 0
\(186\) 1.36643 + 2.36673i 0.100192 + 0.173537i
\(187\) 0.193357 + 0.111635i 0.0141396 + 0.00816353i
\(188\) 7.65891 + 4.42187i 0.558583 + 0.322498i
\(189\) −4.20530 −0.305890
\(190\) 0 0
\(191\) 20.4758 1.48157 0.740787 0.671740i \(-0.234453\pi\)
0.740787 + 0.671740i \(0.234453\pi\)
\(192\) 2.67631 + 1.54517i 0.193146 + 0.111513i
\(193\) 9.54664 + 5.51176i 0.687182 + 0.396745i 0.802556 0.596577i \(-0.203473\pi\)
−0.115373 + 0.993322i \(0.536806\pi\)
\(194\) 9.58554 + 16.6026i 0.688202 + 1.19200i
\(195\) 0 0
\(196\) −1.35905 2.35395i −0.0970752 0.168139i
\(197\) 19.8532i 1.41448i −0.706971 0.707242i \(-0.749939\pi\)
0.706971 0.707242i \(-0.250061\pi\)
\(198\) 0.421263i 0.0299379i
\(199\) 10.5013 + 18.1888i 0.744417 + 1.28937i 0.950467 + 0.310826i \(0.100606\pi\)
−0.206050 + 0.978542i \(0.566061\pi\)
\(200\) 0 0
\(201\) 1.12038 0.0790254
\(202\) 5.92321i 0.416756i
\(203\) −8.14901 + 4.70483i −0.571948 + 0.330215i
\(204\) −0.250687 + 0.434203i −0.0175516 + 0.0304003i
\(205\) 0 0
\(206\) −1.17837 + 2.04100i −0.0821011 + 0.142203i
\(207\) 13.2821 + 7.66842i 0.923169 + 0.532992i
\(208\) 6.23939i 0.432624i
\(209\) −0.283041 + 0.512924i −0.0195784 + 0.0354797i
\(210\) 0 0
\(211\) 6.41284 11.1074i 0.441478 0.764663i −0.556321 0.830967i \(-0.687788\pi\)
0.997799 + 0.0663046i \(0.0211209\pi\)
\(212\) −0.182489 0.105360i −0.0125334 0.00723617i
\(213\) 0.436380 0.251944i 0.0299003 0.0172629i
\(214\) −0.549227 + 0.951289i −0.0375444 + 0.0650288i
\(215\) 0 0
\(216\) −6.81538 −0.463728
\(217\) 12.4275i 0.843630i
\(218\) −15.4564 + 8.92377i −1.04684 + 0.604394i
\(219\) 1.20294 + 2.08355i 0.0812870 + 0.140793i
\(220\) 0 0
\(221\) −5.83712 −0.392647
\(222\) 0.612236 0.353475i 0.0410906 0.0237237i
\(223\) 17.6621 + 10.1972i 1.18274 + 0.682856i 0.956647 0.291249i \(-0.0940708\pi\)
0.226095 + 0.974105i \(0.427404\pi\)
\(224\) 3.96344 + 6.86488i 0.264819 + 0.458679i
\(225\) 0 0
\(226\) −0.462576 + 0.801205i −0.0307701 + 0.0532954i
\(227\) 25.4172i 1.68700i 0.537129 + 0.843500i \(0.319509\pi\)
−0.537129 + 0.843500i \(0.680491\pi\)
\(228\) −1.15182 0.635598i −0.0762814 0.0420935i
\(229\) −2.21553 −0.146406 −0.0732030 0.997317i \(-0.523322\pi\)
−0.0732030 + 0.997317i \(0.523322\pi\)
\(230\) 0 0
\(231\) 0.0482566 0.0835829i 0.00317505 0.00549935i
\(232\) −13.2068 + 7.62496i −0.867071 + 0.500603i
\(233\) −12.2609 7.07882i −0.803236 0.463749i 0.0413652 0.999144i \(-0.486829\pi\)
−0.844602 + 0.535395i \(0.820163\pi\)
\(234\) −5.50672 9.53792i −0.359986 0.623514i
\(235\) 0 0
\(236\) 5.48719 0.357186
\(237\) 0.482019 0.278294i 0.0313105 0.0180771i
\(238\) 2.98887 1.72562i 0.193739 0.111855i
\(239\) −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 0.939781 + 0.341776i \(0.111028\pi\)
−0.173904 + 0.984763i \(0.555638\pi\)
\(242\) 10.4373 + 6.02600i 0.670937 + 0.387366i
\(243\) 8.30939 4.79743i 0.533048 0.307755i
\(244\) −3.65030 + 6.32251i −0.233687 + 0.404757i
\(245\) 0 0
\(246\) −4.42636 −0.282215
\(247\) −0.296503 15.3131i −0.0188660 0.974352i
\(248\) 20.1407i 1.27894i
\(249\) −1.41252 + 2.44655i −0.0895147 + 0.155044i
\(250\) 0 0
\(251\) −8.59495 14.8869i −0.542509 0.939653i −0.998759 0.0498012i \(-0.984141\pi\)
0.456250 0.889851i \(-0.349192\pi\)
\(252\) −3.72548 2.15090i −0.234683 0.135494i
\(253\) −0.625016 + 0.360853i −0.0392944 + 0.0226866i
\(254\) −20.5656 −1.29040
\(255\) 0 0
\(256\) 7.83623 + 13.5727i 0.489764 + 0.848297i
\(257\) −16.9246 + 9.77143i −1.05573 + 0.609525i −0.924248 0.381794i \(-0.875307\pi\)
−0.131481 + 0.991319i \(0.541973\pi\)
\(258\) 3.54178i 0.220501i
\(259\) 3.21479 0.199757
\(260\) 0 0
\(261\) 7.09827 12.2946i 0.439372 0.761014i
\(262\) 2.74330 1.58384i 0.169482 0.0978502i
\(263\) 7.63280 + 4.40680i 0.470659 + 0.271735i 0.716515 0.697571i \(-0.245736\pi\)
−0.245857 + 0.969306i \(0.579069\pi\)
\(264\) 0.0782078 0.135460i 0.00481336 0.00833698i
\(265\) 0 0
\(266\) 4.67883 + 7.75336i 0.286878 + 0.475389i
\(267\) 3.69322i 0.226022i
\(268\) 2.03510 + 1.17496i 0.124313 + 0.0717723i
\(269\) 0.144181 0.249729i 0.00879088 0.0152263i −0.861596 0.507594i \(-0.830535\pi\)
0.870387 + 0.492368i \(0.163868\pi\)
\(270\) 0 0
\(271\) 12.4356 21.5391i 0.755409 1.30841i −0.189761 0.981830i \(-0.560771\pi\)
0.945171 0.326577i \(-0.105895\pi\)
\(272\) 2.55466 1.47494i 0.154899 0.0894311i
\(273\) 2.52323i 0.152713i
\(274\) 20.6665 1.24851
\(275\) 0 0
\(276\) −0.810333 1.40354i −0.0487763 0.0844831i
\(277\) 4.40486i 0.264662i −0.991206 0.132331i \(-0.957754\pi\)
0.991206 0.132331i \(-0.0422463\pi\)
\(278\) 19.9509i 1.19657i
\(279\) −9.37476 16.2376i −0.561252 0.972118i
\(280\) 0 0
\(281\) 16.3607 + 28.3376i 0.975998 + 1.69048i 0.676600 + 0.736350i \(0.263452\pi\)
0.299398 + 0.954128i \(0.403214\pi\)
\(282\) −4.00736 2.31365i −0.238635 0.137776i
\(283\) −1.15088 0.664463i −0.0684129 0.0394982i 0.465403 0.885099i \(-0.345909\pi\)
−0.533816 + 0.845600i \(0.679243\pi\)
\(284\) 1.05688 0.0627140
\(285\) 0 0
\(286\) 0.518260 0.0306454
\(287\) −17.4318 10.0643i −1.02897 0.594074i
\(288\) −10.3572 5.97972i −0.610302 0.352358i
\(289\) −7.12016 12.3325i −0.418833 0.725440i
\(290\) 0 0
\(291\) 3.31328 + 5.73877i 0.194228 + 0.336413i
\(292\) 5.04618i 0.295305i
\(293\) 7.72365i 0.451220i 0.974218 + 0.225610i \(0.0724375\pi\)
−0.974218 + 0.225610i \(0.927562\pi\)
\(294\) 0.711094 + 1.23165i 0.0414718 + 0.0718313i
\(295\) 0 0
\(296\) 5.21010 0.302831
\(297\) 0.298558i 0.0173241i
\(298\) 21.1507 12.2114i 1.22523 0.707386i
\(299\) 9.43409 16.3403i 0.545588 0.944986i
\(300\) 0 0
\(301\) −8.05296 + 13.9481i −0.464165 + 0.803957i
\(302\) −3.16944 1.82988i −0.182381 0.105298i
\(303\) 2.04738i 0.117619i
\(304\) 3.99912 + 6.62700i 0.229366 + 0.380085i
\(305\) 0 0
\(306\) −2.60348 + 4.50936i −0.148831 + 0.257783i
\(307\) 7.88085 + 4.55001i 0.449784 + 0.259683i 0.707739 0.706474i \(-0.249715\pi\)
−0.257955 + 0.966157i \(0.583049\pi\)
\(308\) 0.175310 0.101215i 0.00998921 0.00576727i
\(309\) −0.407309 + 0.705480i −0.0231710 + 0.0401333i
\(310\) 0 0
\(311\) −12.4569 −0.706364 −0.353182 0.935555i \(-0.614900\pi\)
−0.353182 + 0.935555i \(0.614900\pi\)
\(312\) 4.08931i 0.231512i
\(313\) −1.77148 + 1.02277i −0.100130 + 0.0578101i −0.549229 0.835672i \(-0.685078\pi\)
0.449099 + 0.893482i \(0.351745\pi\)
\(314\) 3.98530 + 6.90274i 0.224903 + 0.389544i
\(315\) 0 0
\(316\) 1.16741 0.0656719
\(317\) 20.4133 11.7856i 1.14653 0.661947i 0.198487 0.980103i \(-0.436397\pi\)
0.948038 + 0.318157i \(0.103064\pi\)
\(318\) 0.0954834 + 0.0551274i 0.00535445 + 0.00309139i
\(319\) 0.334024 + 0.578546i 0.0187017 + 0.0323923i
\(320\) 0 0
\(321\) −0.189842 + 0.328817i −0.0105960 + 0.0183528i
\(322\) 11.1560i 0.621698i
\(323\) −6.19974 + 3.74129i −0.344963 + 0.208171i
\(324\) 6.14676 0.341487
\(325\) 0 0
\(326\) 10.8527 18.7975i 0.601077 1.04110i
\(327\) −5.34257 + 3.08454i −0.295445 + 0.170575i
\(328\) −28.2511 16.3108i −1.55991 0.900613i
\(329\) −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 \(0.671986\pi\)
\(332\) −5.13150 + 2.96267i −0.281627 + 0.162598i
\(333\) −4.20041 + 2.42511i −0.230181 + 0.132895i
\(334\) 3.73480 0.204359
\(335\) 0 0
\(336\) −0.637575 1.10431i −0.0347826 0.0602451i
\(337\) 28.3087 + 16.3440i 1.54207 + 0.890316i 0.998708 + 0.0508197i \(0.0161834\pi\)
0.543365 + 0.839497i \(0.317150\pi\)
\(338\) 0.621259 0.358684i 0.0337921 0.0195098i
\(339\) −0.159891 + 0.276940i −0.00868409 + 0.0150413i
\(340\) 0 0
\(341\) 0.882297 0.0477791
\(342\) −11.9621 6.60093i −0.646838 0.356937i
\(343\) 19.7188i 1.06471i
\(344\) −13.0512 + 22.6053i −0.703671 + 1.21879i
\(345\) 0 0
\(346\) 5.80859 + 10.0608i 0.312271 + 0.540870i
\(347\) 2.22279 + 1.28333i 0.119326 + 0.0688927i 0.558475 0.829521i \(-0.311387\pi\)
−0.439149 + 0.898414i \(0.644720\pi\)
\(348\) −1.29919 + 0.750085i −0.0696436 + 0.0402088i
\(349\) −16.6195 −0.889619 −0.444810 0.895625i \(-0.646729\pi\)
−0.444810 + 0.895625i \(0.646729\pi\)
\(350\) 0 0
\(351\) −3.90274 6.75974i −0.208313 0.360808i
\(352\) 0.487378 0.281388i 0.0259773 0.0149980i
\(353\) 28.3629i 1.50961i −0.655951 0.754803i \(-0.727732\pi\)
0.655951 0.754803i \(-0.272268\pi\)
\(354\) −2.87105 −0.152595
\(355\) 0 0
\(356\) 3.87315 6.70850i 0.205277 0.355550i
\(357\) 1.03311 0.596468i 0.0546781 0.0315684i
\(358\) −13.8783 8.01262i −0.733489 0.423480i
\(359\) 8.69427 15.0589i 0.458866 0.794780i −0.540035 0.841643i \(-0.681589\pi\)
0.998901 + 0.0468628i \(0.0149224\pi\)
\(360\) 0 0
\(361\) −10.1298 16.0744i −0.533150 0.846021i
\(362\) 5.96195i 0.313353i
\(363\) 3.60771 + 2.08291i 0.189355 + 0.109324i
\(364\) −2.64616 + 4.58328i −0.138696 + 0.240229i
\(365\) 0 0
\(366\) 1.90994 3.30811i 0.0998342 0.172918i
\(367\) 22.3477 12.9024i 1.16654 0.673501i 0.213676 0.976905i \(-0.431456\pi\)
0.952862 + 0.303404i \(0.0981231\pi\)
\(368\) 9.53531i 0.497062i
\(369\) 30.3683 1.58091
\(370\) 0 0
\(371\) 0.250687 + 0.434203i 0.0130150 + 0.0225427i
\(372\) 1.98129i 0.102725i
\(373\) 27.0663i 1.40144i −0.713437 0.700719i \(-0.752862\pi\)
0.713437 0.700719i \(-0.247138\pi\)
\(374\) −0.122512 0.212197i −0.00633495 0.0109724i
\(375\) 0 0
\(376\) −17.0512 29.5336i −0.879349 1.52308i
\(377\) −15.1254 8.73267i −0.778999 0.449755i
\(378\) 3.99675 + 2.30753i 0.205571 + 0.118686i
\(379\) −12.4028 −0.637092 −0.318546 0.947907i \(-0.603194\pi\)
−0.318546 + 0.947907i \(0.603194\pi\)
\(380\) 0 0
\(381\) −7.10859 −0.364184
\(382\) −19.4604 11.2354i −0.995678 0.574855i
\(383\) −4.64139 2.67971i −0.237164 0.136927i 0.376709 0.926332i \(-0.377056\pi\)
−0.613873 + 0.789405i \(0.710389\pi\)
\(384\) −0.107336 0.185912i −0.00547749 0.00948728i
\(385\) 0 0
\(386\) −6.04881 10.4769i −0.307877 0.533258i
\(387\) 24.2993i 1.23520i
\(388\) 13.8988i 0.705605i
\(389\) 4.28467 + 7.42126i 0.217241 + 0.376273i 0.953964 0.299923i \(-0.0969608\pi\)
−0.736722 + 0.676195i \(0.763628\pi\)
\(390\) 0 0
\(391\) −8.92053 −0.451131
\(392\) 10.4813i 0.529386i
\(393\) 0.948232 0.547462i 0.0478320 0.0276158i
\(394\) −10.8939 + 18.8687i −0.548824 + 0.950592i
\(395\) 0 0
\(396\) −0.152705 + 0.264493i −0.00767373 + 0.0132913i
\(397\) 9.21844 + 5.32227i 0.462660 + 0.267117i 0.713162 0.700999i \(-0.247262\pi\)
−0.250502 + 0.968116i \(0.580596\pi\)
\(398\) 23.0490i 1.15534i
\(399\) 1.61726 + 2.67998i 0.0809641 + 0.134167i
\(400\) 0 0
\(401\) −3.82604 + 6.62690i −0.191063 + 0.330932i −0.945603 0.325323i \(-0.894527\pi\)
0.754539 + 0.656255i \(0.227860\pi\)
\(402\) −1.06482 0.614773i −0.0531083 0.0306621i
\(403\) −19.9763 + 11.5333i −0.995091 + 0.574516i
\(404\) −2.14713 + 3.71893i −0.106824 + 0.185024i
\(405\) 0 0
\(406\) 10.3265 0.512497
\(407\) 0.228237i 0.0113133i
\(408\) 1.67433 0.966676i 0.0828918 0.0478576i
\(409\) −8.84435 15.3189i −0.437325 0.757469i 0.560157 0.828386i \(-0.310741\pi\)
−0.997482 + 0.0709173i \(0.977407\pi\)
\(410\) 0 0
\(411\) 7.14345 0.352361
\(412\) −1.47970 + 0.854305i −0.0728996 + 0.0420886i
\(413\) −11.3067 6.52793i −0.556367 0.321218i
\(414\) −8.41561 14.5763i −0.413605 0.716384i
\(415\) 0 0
\(416\) −7.35657 + 12.7420i −0.360685 + 0.624726i
\(417\) 6.89609i 0.337703i
\(418\) 0.550456 0.332178i 0.0269237 0.0162473i
\(419\) −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 0.0975661 + 0.995229i \(0.468894\pi\)
−0.910677 + 0.413120i \(0.864439\pi\)
\(422\) −12.1896 + 7.03770i −0.593383 + 0.342590i
\(423\) 27.4935 + 15.8734i 1.33678 + 0.771791i
\(424\) 0.406280 + 0.703698i 0.0197307 + 0.0341746i
\(425\) 0 0
\(426\) −0.552987 −0.0267923
\(427\) 15.0434 8.68529i 0.727999 0.420311i
\(428\) −0.689673 + 0.398183i −0.0333366 + 0.0192469i
\(429\) 0.179139 0.00864890
\(430\) 0 0
\(431\) 3.08799 + 5.34855i 0.148743 + 0.257631i 0.930763 0.365623i \(-0.119144\pi\)
−0.782020 + 0.623253i \(0.785811\pi\)
\(432\) 3.41613 + 1.97230i 0.164359 + 0.0948925i
\(433\) 16.0693 9.27761i 0.772241 0.445854i −0.0614325 0.998111i \(-0.519567\pi\)
0.833673 + 0.552258i \(0.186234\pi\)
\(434\) 6.81918 11.8112i 0.327331 0.566954i
\(435\) 0 0
\(436\) −12.9392 −0.619677
\(437\) −0.453129 23.4022i −0.0216761 1.11948i
\(438\) 2.64030i 0.126158i
\(439\) −0.113656 + 0.196858i −0.00542450 + 0.00939550i −0.868725 0.495295i \(-0.835060\pi\)
0.863300 + 0.504690i \(0.168393\pi\)
\(440\) 0 0
\(441\) −4.87865 8.45007i −0.232317 0.402384i
\(442\) 5.54765 + 3.20294i 0.263875 + 0.152348i
\(443\) 30.2959 17.4913i 1.43940 0.831038i 0.441593 0.897216i \(-0.354414\pi\)
0.997808 + 0.0661770i \(0.0210802\pi\)
\(444\) 0.512529 0.0243236
\(445\) 0 0
\(446\) −11.1908 19.3831i −0.529901 0.917815i
\(447\) 7.31083 4.22091i 0.345791 0.199642i
\(448\) 15.4224i 0.728638i
\(449\) 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
\(452\) −0.580864 + 0.335362i −0.0273215 + 0.0157741i
\(453\) −1.09553 0.632505i −0.0514725 0.0297177i
\(454\) 13.9469 24.1568i 0.654561 1.13373i
\(455\) 0 0
\(456\) 2.62103 + 4.34335i 0.122741 + 0.203396i
\(457\) 1.60241i 0.0749578i 0.999297 + 0.0374789i \(0.0119327\pi\)
−0.999297 + 0.0374789i \(0.988067\pi\)
\(458\) 2.10566 + 1.21570i 0.0983909 + 0.0568060i
\(459\) −1.84514 + 3.19588i −0.0861239 + 0.149171i
\(460\) 0 0
\(461\) 4.37081 7.57046i 0.203569 0.352592i −0.746107 0.665826i \(-0.768079\pi\)
0.949676 + 0.313234i \(0.101413\pi\)
\(462\) −0.0917270 + 0.0529586i −0.00426753 + 0.00246386i
\(463\) 21.1886i 0.984718i −0.870392 0.492359i \(-0.836135\pi\)
0.870392 0.492359i \(-0.163865\pi\)
\(464\) 8.82636 0.409753
\(465\) 0 0
\(466\) 7.76857 + 13.4556i 0.359872 + 0.623316i
\(467\) 20.4516i 0.946388i 0.880958 + 0.473194i \(0.156899\pi\)
−0.880958 + 0.473194i \(0.843101\pi\)
\(468\) 7.98461i 0.369089i
\(469\) −2.79563 4.84217i −0.129090 0.223591i
\(470\) 0 0
\(471\) 1.37753 + 2.38596i 0.0634734 + 0.109939i
\(472\) −18.3244 10.5796i −0.843449 0.486965i
\(473\) 0.990259 + 0.571727i 0.0455322 + 0.0262880i
\(474\) −0.610821 −0.0280559
\(475\) 0 0
\(476\) 2.50211 0.114684
\(477\) −0.655090 0.378216i −0.0299945 0.0173173i
\(478\) 2.86525 + 1.65425i 0.131054 + 0.0756639i
\(479\) 11.7746 + 20.3942i 0.537994 + 0.931833i 0.999012 + 0.0444419i \(0.0141510\pi\)
−0.461018 + 0.887391i \(0.652516\pi\)
\(480\) 0 0
\(481\) 2.98350 + 5.16757i 0.136036 + 0.235621i
\(482\) 26.0962i 1.18865i
\(483\) 3.85611i 0.175459i
\(484\) 4.36877 + 7.56694i 0.198581 + 0.343952i
\(485\) 0 0
\(486\) −10.5298 −0.477640
\(487\) 36.0392i 1.63309i 0.577280 + 0.816546i \(0.304114\pi\)
−0.577280 + 0.816546i \(0.695886\pi\)
\(488\) 24.3803 14.0760i 1.10364 0.637188i
\(489\) 3.75129 6.49742i 0.169639 0.293824i
\(490\) 0 0
\(491\) −10.0297 + 17.3720i −0.452635 + 0.783988i −0.998549 0.0538541i \(-0.982849\pi\)
0.545913 + 0.837842i \(0.316183\pi\)
\(492\) −2.77913 1.60453i −0.125293 0.0723378i
\(493\) 8.25729i 0.371890i
\(494\) −8.12081 + 14.7164i −0.365373 + 0.662124i
\(495\) 0 0
\(496\) 5.82853 10.0953i 0.261709 0.453293i
\(497\) −2.17776 1.25733i −0.0976858 0.0563989i
\(498\) 2.68494 1.55015i 0.120315 0.0694640i
\(499\) −18.4364 + 31.9328i −0.825328 + 1.42951i 0.0763399 + 0.997082i \(0.475677\pi\)
−0.901668 + 0.432429i \(0.857657\pi\)
\(500\) 0 0
\(501\) 1.29095 0.0576753
\(502\) 18.8649i 0.841980i
\(503\) 18.7483 10.8244i 0.835947 0.482634i −0.0199377 0.999801i \(-0.506347\pi\)
0.855884 + 0.517167i \(0.173013\pi\)
\(504\) 8.29412 + 14.3658i 0.369449 + 0.639905i
\(505\) 0 0
\(506\) 0.792028 0.0352099
\(507\) 0.214741 0.123981i 0.00953697 0.00550617i
\(508\) −12.9123 7.45492i −0.572891 0.330759i
\(509\) −18.2279 31.5717i −0.807938 1.39939i −0.914289 0.405062i \(-0.867250\pi\)
0.106351 0.994329i \(-0.466083\pi\)
\(510\) 0 0
\(511\) 6.00327 10.3980i 0.265569 0.459979i
\(512\) 18.3314i 0.810141i
\(513\) −8.47783 4.67822i −0.374305 0.206549i
\(514\) 21.4471 0.945990
\(515\) 0 0
\(516\) −1.28387 + 2.22373i −0.0565193 + 0.0978943i
\(517\) −1.29376 + 0.746955i −0.0568997 + 0.0328511i
\(518\) −3.05537 1.76402i −0.134245 0.0775065i
\(519\) 2.00776 + 3.47754i 0.0881309 + 0.152647i
\(520\) 0 0
\(521\) −22.6092 −0.990528 −0.495264 0.868742i \(-0.664929\pi\)
−0.495264 + 0.868742i \(0.664929\pi\)
\(522\) −13.4925 + 7.78991i −0.590552 + 0.340955i
\(523\) −0.461515 + 0.266456i −0.0201806 + 0.0116513i −0.510056 0.860141i \(-0.670375\pi\)
0.489876 + 0.871792i \(0.337042\pi\)
\(524\) 2.29654 0.100325
\(525\) 0 0
\(526\) −4.83619 8.37653i −0.210868 0.365234i
\(527\) 9.44444 + 5.45275i 0.411406 + 0.237525i
\(528\) −0.0784015 + 0.0452651i −0.00341199 + 0.00196991i
\(529\) 2.91759 5.05341i 0.126852 0.219714i
\(530\) 0 0
\(531\) 19.6976 0.854804
\(532\) 0.127098 + 6.56406i 0.00551038 + 0.284588i
\(533\) 37.3606i 1.61827i
\(534\) −2.02654 + 3.51007i −0.0876971 + 0.151896i
\(535\) 0 0
\(536\) −4.53078 7.84754i −0.195700 0.338962i
\(537\) −4.79708 2.76959i −0.207009 0.119517i
\(538\) −0.274062 + 0.158230i −0.0118157 + 0.00682178i
\(539\) 0.459150 0.0197770
\(540\) 0 0
\(541\) −2.50820 4.34433i −0.107836 0.186777i 0.807057 0.590473i \(-0.201059\pi\)
−0.914893 + 0.403696i \(0.867725\pi\)
\(542\) −23.6378 + 13.6473i −1.01533 + 0.586202i
\(543\) 2.06077i 0.0884362i
\(544\) 6.95610 0.298240
\(545\) 0 0
\(546\) 1.38454 2.39810i 0.0592530 0.102629i
\(547\) 19.5981 11.3149i 0.837952 0.483792i −0.0186154 0.999827i \(-0.505926\pi\)
0.856568 + 0.516035i \(0.172592\pi\)
\(548\) 12.9756 + 7.49148i 0.554291 + 0.320020i
\(549\) −13.1037 + 22.6962i −0.559250 + 0.968650i
\(550\) 0 0
\(551\) −21.6622 + 0.419439i −0.922843 + 0.0178687i
\(552\) 6.24946i 0.265995i
\(553\) −2.40552 1.38883i −0.102293 0.0590590i
\(554\) −2.41703 + 4.18642i −0.102690 + 0.177864i
\(555\) 0 0
\(556\) −7.23207 + 12.5263i −0.306708 + 0.531234i
\(557\) 30.5321 17.6277i 1.29369 0.746910i 0.314381 0.949297i \(-0.398203\pi\)
0.979306 + 0.202387i \(0.0648698\pi\)
\(558\) 20.5764i 0.871070i
\(559\) −29.8943 −1.26439
\(560\) 0 0
\(561\) −0.0423468 0.0733467i −0.00178788 0.00309670i
\(562\) 35.9097i 1.51476i
\(563\) 24.6295i 1.03801i 0.854771 + 0.519005i \(0.173698\pi\)
−0.854771 + 0.519005i \(0.826302\pi\)
\(564\) −1.67737 2.90528i −0.0706298 0.122334i
\(565\) 0 0
\(566\) 0.729207 + 1.26302i 0.0306509 + 0.0530888i
\(567\) −12.6658 7.31260i −0.531913 0.307100i
\(568\) −3.52942 2.03771i −0.148091 0.0855005i
\(569\) 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 \(0.613002\pi\)
\(572\) 0.325394 + 0.187866i 0.0136054 + 0.00785508i
\(573\) −6.72655 3.88357i −0.281006 0.162239i
\(574\) 11.0449 + 19.1303i 0.461005 + 0.798484i
\(575\) 0 0
\(576\) 11.6340 + 20.1507i 0.484750 + 0.839612i
\(577\) 12.4486i 0.518244i 0.965845 + 0.259122i \(0.0834331\pi\)
−0.965845 + 0.259122i \(0.916567\pi\)
\(578\) 15.6279i 0.650034i
\(579\) −2.09080 3.62136i −0.0868905 0.150499i
\(580\) 0 0
\(581\) 14.0984 0.584899
\(582\) 7.27224i 0.301444i
\(583\) 0.0308266 0.0177977i 0.00127671 0.000737107i
\(584\) 9.72930 16.8516i 0.402601 0.697326i
\(585\) 0 0
\(586\) 4.23811 7.34063i 0.175075 0.303238i
\(587\) −3.90702 2.25572i −0.161260 0.0931036i 0.417198 0.908816i \(-0.363012\pi\)
−0.578458 + 0.815712i \(0.696345\pi\)
\(588\) 1.03107i 0.0425206i
\(589\) −13.8250 + 25.0536i −0.569651 + 1.03232i
\(590\) 0 0
\(591\) −3.76550 + 6.52204i −0.154892 + 0.268281i
\(592\) −2.61150 1.50775i −0.107332 0.0619682i
\(593\) −16.9812 + 9.80411i −0.697335 + 0.402606i −0.806354 0.591433i \(-0.798562\pi\)
0.109019 + 0.994040i \(0.465229\pi\)
\(594\) 0.163825 0.283753i 0.00672181 0.0116425i
\(595\) 0 0
\(596\) 17.7062 0.725274
\(597\) 7.96699i 0.326067i
\(598\) −17.9325 + 10.3533i −0.733315 + 0.423379i
\(599\) 5.38795 + 9.33221i 0.220146 + 0.381304i 0.954852 0.297082i \(-0.0960134\pi\)
−0.734706 + 0.678385i \(0.762680\pi\)
\(600\) 0 0
\(601\) 15.0244 0.612860 0.306430 0.951893i \(-0.400866\pi\)
0.306430 + 0.951893i \(0.400866\pi\)
\(602\) 15.3072 8.83763i 0.623876 0.360195i
\(603\) 7.30547 + 4.21782i 0.297502 + 0.171763i
\(604\) −1.32664 2.29781i −0.0539802 0.0934964i
\(605\) 0 0
\(606\) 1.12344 1.94585i 0.0456365 0.0790448i
\(607\) 25.1901i 1.02243i 0.859452 + 0.511217i \(0.170805\pi\)
−0.859452 + 0.511217i \(0.829195\pi\)
\(608\) 0.353343 + 18.2487i 0.0143300 + 0.740082i
\(609\) 3.56940 0.144640
\(610\) 0 0
\(611\) 19.5283 33.8240i 0.790030 1.36837i
\(612\) −3.26923 + 1.88749i −0.132151 + 0.0762973i
\(613\) 14.0600 + 8.11753i 0.567877 + 0.327864i 0.756301 0.654224i \(-0.227005\pi\)
−0.188424 + 0.982088i \(0.560338\pi\)
\(614\) −4.99336 8.64875i −0.201516 0.349035i
\(615\) 0 0
\(616\) −0.780593 −0.0314510
\(617\) 5.64498 3.25913i 0.227258 0.131208i −0.382048 0.924142i \(-0.624781\pi\)
0.609307 + 0.792935i \(0.291448\pi\)
\(618\) 0.774220 0.446996i 0.0311437 0.0179808i
\(619\) 4.39112 0.176494 0.0882470 0.996099i \(-0.471874\pi\)
0.0882470 + 0.996099i \(0.471874\pi\)
\(620\) 0 0
\(621\) −5.96433 10.3305i −0.239340 0.414550i
\(622\) 11.8391 + 6.83532i 0.474705 + 0.274071i
\(623\) −15.9618 + 9.21553i −0.639494 + 0.369212i
\(624\) 1.18341 2.04972i 0.0473742 0.0820545i
\(625\) 0 0
\(626\) 2.24484 0.0897220
\(627\) 0.190267 0.114819i 0.00759855 0.00458541i
\(628\) 5.77858i 0.230590i
\(629\) 1.41054 2.44313i 0.0562420 0.0974140i
\(630\) 0 0
\(631\) 17.3104 + 29.9826i 0.689118 + 1.19359i 0.972124 + 0.234469i \(0.0753350\pi\)
−0.283006 + 0.959118i \(0.591332\pi\)
\(632\) −3.89855 2.25083i −0.155076 0.0895331i
\(633\) −4.21340 + 2.43261i −0.167468 + 0.0966875i
\(634\) −25.8680 −1.02735
\(635\) 0 0
\(636\) 0.0399667 + 0.0692243i 0.00158478 + 0.00274492i
\(637\) −10.3957 + 6.00198i −0.411894 + 0.237807i
\(638\) 0.733141i 0.0290253i
\(639\) 3.79391 0.150085
\(640\) 0 0
\(641\) −3.70621 + 6.41934i −0.146386 + 0.253549i −0.929889 0.367839i \(-0.880098\pi\)
0.783503 + 0.621388i \(0.213431\pi\)
\(642\) 0.360856 0.208340i 0.0142418 0.00822253i
\(643\) −14.3292 8.27294i −0.565087 0.326253i 0.190098 0.981765i \(-0.439120\pi\)
−0.755185 + 0.655512i \(0.772453\pi\)
\(644\) −4.04397 + 7.00437i −0.159355 + 0.276011i
\(645\) 0 0
\(646\) 7.94520 0.153840i 0.312600 0.00605276i
\(647\) 29.4822i 1.15907i 0.814949 + 0.579533i \(0.196765\pi\)
−0.814949 + 0.579533i \(0.803235\pi\)
\(648\) −20.5270 11.8513i −0.806377 0.465562i
\(649\) −0.463456 + 0.802729i −0.0181922 + 0.0315099i
\(650\) 0 0
\(651\) 2.35708 4.08258i 0.0923811 0.160009i
\(652\) 13.6279 7.86810i 0.533712 0.308138i
\(653\) 6.57421i 0.257269i −0.991692 0.128634i \(-0.958941\pi\)
0.991692 0.128634i \(-0.0410594\pi\)
\(654\) 6.77017 0.264735
\(655\) 0 0
\(656\) 9.44037 + 16.3512i 0.368584 + 0.638407i
\(657\) 18.1145i 0.706713i
\(658\) 23.0925i 0.900241i
\(659\) −13.1685 22.8085i −0.512972 0.888494i −0.999887 0.0150445i \(-0.995211\pi\)
0.486915 0.873450i \(-0.338122\pi\)
\(660\) 0 0
\(661\) −1.89210 3.27721i −0.0735941 0.127469i 0.826880 0.562378i \(-0.190114\pi\)
−0.900474 + 0.434910i \(0.856780\pi\)
\(662\) 17.7893 + 10.2706i 0.691399 + 0.399180i
\(663\) 1.91757 + 1.10711i 0.0744721 + 0.0429965i
\(664\) 22.8487 0.886703
\(665\) 0 0
\(666\) 5.32281 0.206255
\(667\) −23.1153 13.3456i −0.895029 0.516745i
\(668\) 2.34492 + 1.35384i 0.0907278 + 0.0523817i
\(669\) −3.86815 6.69983i −0.149551 0.259031i
\(670\) 0 0
\(671\) −0.616619 1.06802i −0.0238043 0.0412303i
\(672\) 3.00694i 0.115995i
\(673\) 21.0431i 0.811150i 0.914062 + 0.405575i \(0.132929\pi\)
−0.914062 + 0.405575i \(0.867071\pi\)
\(674\) −17.9366 31.0670i −0.690891 1.19666i
\(675\) 0 0
\(676\) 0.520083 0.0200032
\(677\) 15.2744i 0.587043i −0.955952 0.293522i \(-0.905173\pi\)
0.955952 0.293522i \(-0.0948273\pi\)
\(678\) 0.303924 0.175471i 0.0116721 0.00673891i
\(679\) 16.5349 28.6394i 0.634553 1.09908i
\(680\) 0 0
\(681\) 4.82081 8.34988i 0.184734 0.319968i
\(682\) −0.838544 0.484133i −0.0321095 0.0185384i
\(683\) 8.60225i 0.329156i 0.986364 + 0.164578i \(0.0526262\pi\)
−0.986364 + 0.164578i \(0.947374\pi\)
\(684\) −5.11772 8.48064i −0.195681 0.324265i
\(685\) 0 0
\(686\) 10.8201 18.7409i 0.413112 0.715530i
\(687\) 0.727828 + 0.420212i 0.0277684 + 0.0160321i
\(688\) 13.0835 7.55375i 0.498803 0.287984i
\(689\) −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 \(0.275286\pi\)
\(692\) 8.42231i 0.320168i
\(693\) 0.629318 0.363337i 0.0239058 0.0138020i
\(694\) −1.40837 2.43937i −0.0534611 0.0925974i
\(695\) 0 0
\(696\) 5.78481 0.219273
\(697\) −15.2970 + 8.83172i −0.579414 + 0.334525i
\(698\) 15.7953 + 9.11942i 0.597861 + 0.345175i
\(699\) 2.68523 + 4.65096i 0.101565 + 0.175916i
\(700\) 0 0
\(701\) −5.36463 + 9.29181i −0.202619 + 0.350947i −0.949372 0.314155i \(-0.898279\pi\)
0.746752 + 0.665102i \(0.231612\pi\)
\(702\) 8.56603i 0.323304i
\(703\) 6.48098 + 3.57633i 0.244435 + 0.134884i
\(704\) −1.09492 −0.0412665
\(705\) 0 0
\(706\) −15.5633 + 26.9564i −0.585732 + 1.01452i
\(707\) 8.84859 5.10873i 0.332785 0.192134i
\(708\) −1.80261 1.04074i −0.0677463 0.0391134i
\(709\) −14.4238 24.9828i −0.541697 0.938247i −0.998807 0.0488369i \(-0.984449\pi\)
0.457109 0.889410i \(-0.348885\pi\)
\(710\) 0 0
\(711\) 4.19070 0.157164
\(712\) −25.8687 + 14.9353i −0.969470 + 0.559724i
\(713\) −30.5287 + 17.6257i −1.14331 + 0.660089i
\(714\) −1.30917 −0.0489946
\(715\) 0 0
\(716\) −5.80905 10.0616i −0.217095 0.376019i
\(717\) 0.990386 + 0.571800i 0.0369866 + 0.0213542i
\(718\) −16.5262 + 9.54143i −0.616754 + 0.356083i
\(719\) −10.0278 + 17.3686i −0.373972 + 0.647739i −0.990173 0.139851i \(-0.955338\pi\)
0.616200 + 0.787589i \(0.288671\pi\)
\(720\) 0 0
\(721\) 4.06535 0.151402
\(722\) 0.807171 + 20.8357i 0.0300398 + 0.775424i
\(723\) 9.02026i 0.335467i
\(724\) 2.16117 3.74326i 0.0803193 0.139117i
\(725\) 0 0
\(726\) −2.28587 3.95923i −0.0848364 0.146941i
\(727\) 0.675951 + 0.390261i 0.0250697 + 0.0144740i 0.512482 0.858698i \(-0.328726\pi\)
−0.487413 + 0.873172i \(0.662059\pi\)
\(728\) 17.6736 10.2039i 0.655028 0.378180i
\(729\) 19.5373 0.723604
\(730\) 0 0
\(731\) 7.06674 + 12.2399i 0.261373 + 0.452711i
\(732\) 2.39834 1.38468i 0.0886452 0.0511794i
\(733\) 26.8391i 0.991326i 0.868515 + 0.495663i \(0.165075\pi\)
−0.868515 + 0.495663i \(0.834925\pi\)
\(734\) −28.3192 −1.04528
\(735\) 0 0
\(736\) −11.2426 + 19.4728i −0.414409 + 0.717777i
\(737\) −0.343774 + 0.198478i −0.0126631 + 0.00731103i
\(738\) −28.8623 16.6636i −1.06243 0.613397i
\(739\) 10.3265 17.8861i 0.379867 0.657949i −0.611175 0.791495i \(-0.709303\pi\)
0.991043 + 0.133546i \(0.0426363\pi\)
\(740\) 0 0
\(741\) −2.80699 + 5.08680i −0.103117 + 0.186868i
\(742\) 0.550227i 0.0201995i
\(743\) 1.27580 + 0.736585i 0.0468047 + 0.0270227i 0.523220 0.852198i \(-0.324731\pi\)
−0.476415 + 0.879220i \(0.658064\pi\)
\(744\) 3.82003 6.61649i 0.140049 0.242572i
\(745\) 0 0
\(746\) −14.8518 + 25.7240i −0.543762 + 0.941824i
\(747\) −18.4208 + 10.6352i −0.673980 + 0.389123i
\(748\) 0.177639i 0.00649514i
\(749\) 1.89482 0.0692352
\(750\) 0 0
\(751\) −7.78121 13.4775i −0.283940 0.491799i 0.688411 0.725321i \(-0.258308\pi\)
−0.972352 + 0.233521i \(0.924975\pi\)
\(752\) 19.7378i 0.719764i
\(753\) 6.52071i 0.237628i
\(754\) 9.58356 + 16.5992i 0.349013 + 0.604508i
\(755\) 0 0
\(756\) 1.67293 + 2.89760i 0.0608438 + 0.105385i
\(757\) −17.4726 10.0878i −0.635052 0.366647i 0.147654 0.989039i \(-0.452828\pi\)
−0.782706 + 0.622392i \(0.786161\pi\)
\(758\) 11.7878 + 6.80568i 0.428152 + 0.247193i
\(759\) 0.273767 0.00993713
\(760\) 0 0
\(761\) −15.1076 −0.547649 −0.273825 0.961780i \(-0.588289\pi\)
−0.273825 + 0.961780i \(0.588289\pi\)
\(762\) 6.75607 + 3.90062i 0.244747 + 0.141305i
\(763\) 26.6621 + 15.3934i 0.965234 + 0.557278i
\(764\) −8.14556 14.1085i −0.294696 0.510428i
\(765\) 0 0
\(766\) 2.94082 + 5.09364i 0.106256 + 0.184041i
\(767\) 24.2331i 0.875005i
\(768\) 5.94509i 0.214525i
\(769\) 25.8290 + 44.7372i 0.931418 + 1.61326i 0.780900 + 0.624656i \(0.214761\pi\)
0.150518 + 0.988607i \(0.451906\pi\)
\(770\) 0 0
\(771\) 7.41327 0.266982
\(772\) 8.77063i 0.315662i
\(773\) −26.1157 + 15.0779i −0.939316 + 0.542314i −0.889746 0.456457i \(-0.849118\pi\)
−0.0495699 + 0.998771i \(0.515785\pi\)
\(774\) −13.3335 + 23.0943i −0.479262 + 0.830107i
\(775\) 0 0
\(776\) 26.7976 46.4148i 0.961978 1.66620i
\(777\) −1.05610 0.609739i −0.0378874 0.0218743i
\(778\)