Properties

Label 189.2.f.a.64.1
Level $189$
Weight $2$
Character 189.64
Analytic conductor $1.509$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(64,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 64.1
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 189.64
Dual form 189.2.f.a.127.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(0.500000 + 0.866025i) q^{7} +5.05408 q^{8} +O(q^{10})\) \(q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(0.500000 + 0.866025i) q^{7} +5.05408 q^{8} +6.38151 q^{10} +(2.25729 + 3.90975i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.23025 - 2.13086i) q^{14} +(-2.16372 - 3.74766i) q^{16} +0.945916 q^{17} -4.05408 q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +2.46050 q^{26} -4.05408 q^{28} +(1.23025 + 2.13086i) q^{29} +(-1.16372 + 2.01561i) q^{31} +(-0.269748 + 0.467216i) q^{32} +(-1.16372 - 2.01561i) q^{34} -2.59358 q^{35} +1.78074 q^{37} +(4.98755 + 8.63868i) q^{38} +(-6.55408 + 11.3520i) q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} -18.3025 q^{44} +0.672570 q^{46} +(-6.08113 - 10.5328i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.12422 + 3.67926i) q^{50} +(-2.02704 - 3.51094i) q^{52} +6.27335 q^{53} -11.7089 q^{55} +(2.52704 + 4.37697i) q^{56} +(3.02704 - 5.24299i) q^{58} +(-1.36333 + 2.36135i) q^{59} +(1.13667 + 1.96878i) q^{61} +5.72665 q^{62} -7.32743 q^{64} +(-1.29679 - 2.24611i) q^{65} +(7.90856 - 13.6980i) q^{67} +(-1.91741 + 3.32105i) q^{68} +(3.19076 + 5.52655i) q^{70} -3.27335 q^{71} -1.50739 q^{73} +(-2.19076 - 3.79450i) q^{74} +(8.21780 - 14.2336i) q^{76} +(-2.25729 + 3.90975i) q^{77} +(-7.35447 - 12.7383i) q^{79} +11.2235 q^{80} +15.7630 q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(12.8384 - 22.2368i) q^{86} +(11.4086 + 19.7602i) q^{88} +14.3566 q^{89} -1.00000 q^{91} +(-0.554084 - 0.959702i) q^{92} +(-14.9626 + 25.9161i) q^{94} +(5.25729 - 9.10590i) q^{95} +(5.74484 + 9.95036i) q^{97} +2.46050 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} - 10 q^{35} - 6 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} - 9 q^{47} - 3 q^{49} + 10 q^{50} - 3 q^{52} + 36 q^{53} - 12 q^{55} + 6 q^{56} + 9 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} + 6 q^{68} - 18 q^{71} + 6 q^{73} + 6 q^{74} + 21 q^{76} + 2 q^{77} - 15 q^{79} - 22 q^{80} + 18 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 4 q^{89} - 6 q^{91} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23025 2.13086i −0.869920 1.50675i −0.862078 0.506776i \(-0.830837\pi\)
−0.00784213 0.999969i \(-0.502496\pi\)
\(3\) 0 0
\(4\) −2.02704 + 3.51094i −1.01352 + 1.75547i
\(5\) −1.29679 + 2.24611i −0.579942 + 1.00449i 0.415543 + 0.909573i \(0.363591\pi\)
−0.995485 + 0.0949156i \(0.969742\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 5.05408 1.78689
\(9\) 0 0
\(10\) 6.38151 2.01801
\(11\) 2.25729 + 3.90975i 0.680600 + 1.17883i 0.974798 + 0.223089i \(0.0716141\pi\)
−0.294198 + 0.955744i \(0.595053\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 1.23025 2.13086i 0.328799 0.569496i
\(15\) 0 0
\(16\) −2.16372 3.74766i −0.540929 0.936916i
\(17\) 0.945916 0.229418 0.114709 0.993399i \(-0.463406\pi\)
0.114709 + 0.993399i \(0.463406\pi\)
\(18\) 0 0
\(19\) −4.05408 −0.930071 −0.465035 0.885292i \(-0.653958\pi\)
−0.465035 + 0.885292i \(0.653958\pi\)
\(20\) −5.25729 9.10590i −1.17557 2.03614i
\(21\) 0 0
\(22\) 5.55408 9.61996i 1.18413 2.05098i
\(23\) −0.136673 + 0.236725i −0.0284983 + 0.0493605i −0.879923 0.475117i \(-0.842406\pi\)
0.851425 + 0.524477i \(0.175739\pi\)
\(24\) 0 0
\(25\) −0.863327 1.49533i −0.172665 0.299065i
\(26\) 2.46050 0.482545
\(27\) 0 0
\(28\) −4.05408 −0.766150
\(29\) 1.23025 + 2.13086i 0.228452 + 0.395691i 0.957350 0.288932i \(-0.0933002\pi\)
−0.728897 + 0.684623i \(0.759967\pi\)
\(30\) 0 0
\(31\) −1.16372 + 2.01561i −0.209009 + 0.362015i −0.951403 0.307949i \(-0.900357\pi\)
0.742393 + 0.669964i \(0.233691\pi\)
\(32\) −0.269748 + 0.467216i −0.0476851 + 0.0825930i
\(33\) 0 0
\(34\) −1.16372 2.01561i −0.199576 0.345675i
\(35\) −2.59358 −0.438395
\(36\) 0 0
\(37\) 1.78074 0.292752 0.146376 0.989229i \(-0.453239\pi\)
0.146376 + 0.989229i \(0.453239\pi\)
\(38\) 4.98755 + 8.63868i 0.809087 + 1.40138i
\(39\) 0 0
\(40\) −6.55408 + 11.3520i −1.03629 + 1.79491i
\(41\) −3.20321 + 5.54812i −0.500257 + 0.866471i 0.499743 + 0.866174i \(0.333428\pi\)
−1.00000 0.000297253i \(0.999905\pi\)
\(42\) 0 0
\(43\) 5.21780 + 9.03749i 0.795707 + 1.37820i 0.922389 + 0.386262i \(0.126234\pi\)
−0.126682 + 0.991943i \(0.540433\pi\)
\(44\) −18.3025 −2.75921
\(45\) 0 0
\(46\) 0.672570 0.0991650
\(47\) −6.08113 10.5328i −0.887023 1.53637i −0.843377 0.537323i \(-0.819436\pi\)
−0.0436467 0.999047i \(-0.513898\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −2.12422 + 3.67926i −0.300410 + 0.520326i
\(51\) 0 0
\(52\) −2.02704 3.51094i −0.281100 0.486880i
\(53\) 6.27335 0.861710 0.430855 0.902421i \(-0.358212\pi\)
0.430855 + 0.902421i \(0.358212\pi\)
\(54\) 0 0
\(55\) −11.7089 −1.57883
\(56\) 2.52704 + 4.37697i 0.337690 + 0.584897i
\(57\) 0 0
\(58\) 3.02704 5.24299i 0.397470 0.688438i
\(59\) −1.36333 + 2.36135i −0.177490 + 0.307422i −0.941020 0.338350i \(-0.890131\pi\)
0.763530 + 0.645772i \(0.223464\pi\)
\(60\) 0 0
\(61\) 1.13667 + 1.96878i 0.145536 + 0.252076i 0.929573 0.368639i \(-0.120176\pi\)
−0.784037 + 0.620714i \(0.786843\pi\)
\(62\) 5.72665 0.727286
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) −1.29679 2.24611i −0.160847 0.278595i
\(66\) 0 0
\(67\) 7.90856 13.6980i 0.966184 1.67348i 0.259784 0.965667i \(-0.416349\pi\)
0.706400 0.707813i \(-0.250318\pi\)
\(68\) −1.91741 + 3.32105i −0.232520 + 0.402737i
\(69\) 0 0
\(70\) 3.19076 + 5.52655i 0.381368 + 0.660550i
\(71\) −3.27335 −0.388475 −0.194237 0.980955i \(-0.562223\pi\)
−0.194237 + 0.980955i \(0.562223\pi\)
\(72\) 0 0
\(73\) −1.50739 −0.176427 −0.0882134 0.996102i \(-0.528116\pi\)
−0.0882134 + 0.996102i \(0.528116\pi\)
\(74\) −2.19076 3.79450i −0.254670 0.441102i
\(75\) 0 0
\(76\) 8.21780 14.2336i 0.942646 1.63271i
\(77\) −2.25729 + 3.90975i −0.257243 + 0.445557i
\(78\) 0 0
\(79\) −7.35447 12.7383i −0.827443 1.43317i −0.900038 0.435811i \(-0.856461\pi\)
0.0725952 0.997361i \(-0.476872\pi\)
\(80\) 11.2235 1.25483
\(81\) 0 0
\(82\) 15.7630 1.74074
\(83\) −0.472958 0.819187i −0.0519139 0.0899175i 0.838901 0.544285i \(-0.183199\pi\)
−0.890815 + 0.454367i \(0.849865\pi\)
\(84\) 0 0
\(85\) −1.22665 + 2.12463i −0.133049 + 0.230448i
\(86\) 12.8384 22.2368i 1.38440 2.39786i
\(87\) 0 0
\(88\) 11.4086 + 19.7602i 1.21616 + 2.10644i
\(89\) 14.3566 1.52180 0.760899 0.648871i \(-0.224758\pi\)
0.760899 + 0.648871i \(0.224758\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) −0.554084 0.959702i −0.0577673 0.100056i
\(93\) 0 0
\(94\) −14.9626 + 25.9161i −1.54328 + 2.67304i
\(95\) 5.25729 9.10590i 0.539387 0.934246i
\(96\) 0 0
\(97\) 5.74484 + 9.95036i 0.583300 + 1.01031i 0.995085 + 0.0990246i \(0.0315722\pi\)
−0.411785 + 0.911281i \(0.635094\pi\)
\(98\) 2.46050 0.248549
\(99\) 0 0
\(100\) 7.00000 0.700000
\(101\) −1.83988 3.18677i −0.183075 0.317096i 0.759851 0.650097i \(-0.225272\pi\)
−0.942926 + 0.333002i \(0.891939\pi\)
\(102\) 0 0
\(103\) 4.86333 8.42353i 0.479198 0.829995i −0.520518 0.853851i \(-0.674261\pi\)
0.999715 + 0.0238560i \(0.00759431\pi\)
\(104\) −2.52704 + 4.37697i −0.247797 + 0.429197i
\(105\) 0 0
\(106\) −7.71780 13.3676i −0.749619 1.29838i
\(107\) 1.37432 0.132860 0.0664301 0.997791i \(-0.478839\pi\)
0.0664301 + 0.997791i \(0.478839\pi\)
\(108\) 0 0
\(109\) −3.39922 −0.325587 −0.162793 0.986660i \(-0.552050\pi\)
−0.162793 + 0.986660i \(0.552050\pi\)
\(110\) 14.4050 + 24.9501i 1.37346 + 2.37890i
\(111\) 0 0
\(112\) 2.16372 3.74766i 0.204452 0.354121i
\(113\) 5.19436 8.99689i 0.488644 0.846356i −0.511271 0.859420i \(-0.670825\pi\)
0.999915 + 0.0130636i \(0.00415840\pi\)
\(114\) 0 0
\(115\) −0.354473 0.613964i −0.0330547 0.0572525i
\(116\) −9.97509 −0.926164
\(117\) 0 0
\(118\) 6.70895 0.617608
\(119\) 0.472958 + 0.819187i 0.0433560 + 0.0750948i
\(120\) 0 0
\(121\) −4.69076 + 8.12463i −0.426432 + 0.738603i
\(122\) 2.79679 4.84418i 0.253209 0.438572i
\(123\) 0 0
\(124\) −4.71780 8.17147i −0.423671 0.733820i
\(125\) −8.48968 −0.759340
\(126\) 0 0
\(127\) 0.672570 0.0596809 0.0298405 0.999555i \(-0.490500\pi\)
0.0298405 + 0.999555i \(0.490500\pi\)
\(128\) 9.55408 + 16.5482i 0.844470 + 1.46266i
\(129\) 0 0
\(130\) −3.19076 + 5.52655i −0.279848 + 0.484711i
\(131\) 3.95691 6.85356i 0.345717 0.598799i −0.639767 0.768569i \(-0.720969\pi\)
0.985484 + 0.169770i \(0.0543026\pi\)
\(132\) 0 0
\(133\) −2.02704 3.51094i −0.175767 0.304437i
\(134\) −38.9181 −3.36201
\(135\) 0 0
\(136\) 4.78074 0.409945
\(137\) −1.83628 3.18054i −0.156884 0.271732i 0.776859 0.629674i \(-0.216812\pi\)
−0.933744 + 0.357943i \(0.883478\pi\)
\(138\) 0 0
\(139\) 1.02704 1.77889i 0.0871126 0.150883i −0.819177 0.573541i \(-0.805569\pi\)
0.906289 + 0.422658i \(0.138903\pi\)
\(140\) 5.25729 9.10590i 0.444322 0.769589i
\(141\) 0 0
\(142\) 4.02704 + 6.97504i 0.337942 + 0.585332i
\(143\) −4.51459 −0.377529
\(144\) 0 0
\(145\) −6.38151 −0.529956
\(146\) 1.85447 + 3.21204i 0.153477 + 0.265830i
\(147\) 0 0
\(148\) −3.60963 + 6.25206i −0.296710 + 0.513917i
\(149\) −6.77188 + 11.7292i −0.554774 + 0.960897i 0.443147 + 0.896449i \(0.353862\pi\)
−0.997921 + 0.0644482i \(0.979471\pi\)
\(150\) 0 0
\(151\) −4.96410 8.59808i −0.403973 0.699702i 0.590228 0.807236i \(-0.299038\pi\)
−0.994201 + 0.107535i \(0.965704\pi\)
\(152\) −20.4897 −1.66193
\(153\) 0 0
\(154\) 11.1082 0.895122
\(155\) −3.01819 5.22765i −0.242427 0.419895i
\(156\) 0 0
\(157\) −3.02704 + 5.24299i −0.241584 + 0.418436i −0.961166 0.275972i \(-0.911000\pi\)
0.719581 + 0.694408i \(0.244334\pi\)
\(158\) −18.0957 + 31.3427i −1.43962 + 2.49349i
\(159\) 0 0
\(160\) −0.699612 1.21176i −0.0553092 0.0957983i
\(161\) −0.273346 −0.0215427
\(162\) 0 0
\(163\) 17.8171 1.39554 0.697772 0.716320i \(-0.254175\pi\)
0.697772 + 0.716320i \(0.254175\pi\)
\(164\) −12.9861 22.4926i −1.01404 1.75637i
\(165\) 0 0
\(166\) −1.16372 + 2.01561i −0.0903218 + 0.156442i
\(167\) −4.23385 + 7.33325i −0.327625 + 0.567464i −0.982040 0.188672i \(-0.939582\pi\)
0.654415 + 0.756136i \(0.272915\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 6.03638 0.462969
\(171\) 0 0
\(172\) −42.3068 −3.22586
\(173\) 8.67830 + 15.0313i 0.659799 + 1.14281i 0.980667 + 0.195682i \(0.0626920\pi\)
−0.320868 + 0.947124i \(0.603975\pi\)
\(174\) 0 0
\(175\) 0.863327 1.49533i 0.0652614 0.113036i
\(176\) 9.76829 16.9192i 0.736312 1.27533i
\(177\) 0 0
\(178\) −17.6623 30.5919i −1.32384 2.29296i
\(179\) 11.3494 0.848295 0.424147 0.905593i \(-0.360574\pi\)
0.424147 + 0.905593i \(0.360574\pi\)
\(180\) 0 0
\(181\) 21.8889 1.62699 0.813495 0.581572i \(-0.197562\pi\)
0.813495 + 0.581572i \(0.197562\pi\)
\(182\) 1.23025 + 2.13086i 0.0911924 + 0.157950i
\(183\) 0 0
\(184\) −0.690757 + 1.19643i −0.0509233 + 0.0882018i
\(185\) −2.30924 + 3.99973i −0.169779 + 0.294066i
\(186\) 0 0
\(187\) 2.13521 + 3.69829i 0.156142 + 0.270446i
\(188\) 49.3068 3.59607
\(189\) 0 0
\(190\) −25.8712 −1.87689
\(191\) −0.350874 0.607731i −0.0253883 0.0439739i 0.853052 0.521826i \(-0.174749\pi\)
−0.878440 + 0.477852i \(0.841416\pi\)
\(192\) 0 0
\(193\) −6.07227 + 10.5175i −0.437092 + 0.757065i −0.997464 0.0711760i \(-0.977325\pi\)
0.560372 + 0.828241i \(0.310658\pi\)
\(194\) 14.1352 24.4829i 1.01485 1.75777i
\(195\) 0 0
\(196\) −2.02704 3.51094i −0.144789 0.250781i
\(197\) 16.4107 1.16921 0.584607 0.811317i \(-0.301249\pi\)
0.584607 + 0.811317i \(0.301249\pi\)
\(198\) 0 0
\(199\) 22.7060 1.60959 0.804794 0.593555i \(-0.202276\pi\)
0.804794 + 0.593555i \(0.202276\pi\)
\(200\) −4.36333 7.55750i −0.308534 0.534396i
\(201\) 0 0
\(202\) −4.52704 + 7.84107i −0.318522 + 0.551696i
\(203\) −1.23025 + 2.13086i −0.0863468 + 0.149557i
\(204\) 0 0
\(205\) −8.30778 14.3895i −0.580241 1.00501i
\(206\) −23.9325 −1.66745
\(207\) 0 0
\(208\) 4.32743 0.300053
\(209\) −9.15126 15.8505i −0.633006 1.09640i
\(210\) 0 0
\(211\) −2.28074 + 3.95035i −0.157012 + 0.271954i −0.933790 0.357822i \(-0.883520\pi\)
0.776778 + 0.629775i \(0.216853\pi\)
\(212\) −12.7163 + 22.0253i −0.873362 + 1.51271i
\(213\) 0 0
\(214\) −1.69076 2.92848i −0.115578 0.200187i
\(215\) −27.0656 −1.84586
\(216\) 0 0
\(217\) −2.32743 −0.157996
\(218\) 4.18190 + 7.24327i 0.283234 + 0.490576i
\(219\) 0 0
\(220\) 23.7345 41.1094i 1.60018 2.77160i
\(221\) −0.472958 + 0.819187i −0.0318146 + 0.0551045i
\(222\) 0 0
\(223\) −6.66225 11.5394i −0.446137 0.772733i 0.551993 0.833849i \(-0.313867\pi\)
−0.998131 + 0.0611159i \(0.980534\pi\)
\(224\) −0.539495 −0.0360465
\(225\) 0 0
\(226\) −25.5615 −1.70032
\(227\) 0.690757 + 1.19643i 0.0458472 + 0.0794096i 0.888038 0.459769i \(-0.152068\pi\)
−0.842191 + 0.539179i \(0.818735\pi\)
\(228\) 0 0
\(229\) 8.98968 15.5706i 0.594055 1.02893i −0.399625 0.916679i \(-0.630859\pi\)
0.993679 0.112254i \(-0.0358072\pi\)
\(230\) −0.872181 + 1.51066i −0.0575099 + 0.0996101i
\(231\) 0 0
\(232\) 6.21780 + 10.7695i 0.408219 + 0.707055i
\(233\) 18.9823 1.24357 0.621786 0.783187i \(-0.286408\pi\)
0.621786 + 0.783187i \(0.286408\pi\)
\(234\) 0 0
\(235\) 31.5438 2.05769
\(236\) −5.52704 9.57312i −0.359780 0.623157i
\(237\) 0 0
\(238\) 1.16372 2.01561i 0.0754325 0.130653i
\(239\) 2.44592 4.23645i 0.158213 0.274033i −0.776011 0.630719i \(-0.782760\pi\)
0.934224 + 0.356686i \(0.116093\pi\)
\(240\) 0 0
\(241\) 13.0797 + 22.6546i 0.842535 + 1.45931i 0.887745 + 0.460336i \(0.152271\pi\)
−0.0452094 + 0.998978i \(0.514396\pi\)
\(242\) 23.0833 1.48385
\(243\) 0 0
\(244\) −9.21634 −0.590016
\(245\) −1.29679 2.24611i −0.0828489 0.143498i
\(246\) 0 0
\(247\) 2.02704 3.51094i 0.128978 0.223396i
\(248\) −5.88151 + 10.1871i −0.373477 + 0.646880i
\(249\) 0 0
\(250\) 10.4445 + 18.0903i 0.660565 + 1.14413i
\(251\) −18.4576 −1.16503 −0.582516 0.812819i \(-0.697932\pi\)
−0.582516 + 0.812819i \(0.697932\pi\)
\(252\) 0 0
\(253\) −1.23405 −0.0775838
\(254\) −0.827430 1.43315i −0.0519176 0.0899239i
\(255\) 0 0
\(256\) 16.1804 28.0253i 1.01128 1.75158i
\(257\) −5.86693 + 10.1618i −0.365969 + 0.633876i −0.988931 0.148375i \(-0.952596\pi\)
0.622962 + 0.782252i \(0.285929\pi\)
\(258\) 0 0
\(259\) 0.890369 + 1.54216i 0.0553248 + 0.0958254i
\(260\) 10.5146 0.652087
\(261\) 0 0
\(262\) −19.4720 −1.20298
\(263\) −3.76089 6.51406i −0.231907 0.401674i 0.726463 0.687206i \(-0.241163\pi\)
−0.958369 + 0.285532i \(0.907830\pi\)
\(264\) 0 0
\(265\) −8.13521 + 14.0906i −0.499742 + 0.865579i
\(266\) −4.98755 + 8.63868i −0.305806 + 0.529672i
\(267\) 0 0
\(268\) 32.0620 + 55.5329i 1.95850 + 3.39221i
\(269\) 18.8348 1.14838 0.574190 0.818722i \(-0.305317\pi\)
0.574190 + 0.818722i \(0.305317\pi\)
\(270\) 0 0
\(271\) −23.9823 −1.45682 −0.728410 0.685141i \(-0.759740\pi\)
−0.728410 + 0.685141i \(0.759740\pi\)
\(272\) −2.04669 3.54498i −0.124099 0.214946i
\(273\) 0 0
\(274\) −4.51819 + 7.82573i −0.272954 + 0.472770i
\(275\) 3.89757 6.75078i 0.235032 0.407088i
\(276\) 0 0
\(277\) −3.58113 6.20269i −0.215169 0.372684i 0.738156 0.674630i \(-0.235697\pi\)
−0.953325 + 0.301947i \(0.902364\pi\)
\(278\) −5.05408 −0.303124
\(279\) 0 0
\(280\) −13.1082 −0.783363
\(281\) 7.44085 + 12.8879i 0.443884 + 0.768830i 0.997974 0.0636271i \(-0.0202668\pi\)
−0.554090 + 0.832457i \(0.686933\pi\)
\(282\) 0 0
\(283\) −9.99854 + 17.3180i −0.594351 + 1.02945i 0.399287 + 0.916826i \(0.369258\pi\)
−0.993638 + 0.112621i \(0.964076\pi\)
\(284\) 6.63521 11.4925i 0.393727 0.681956i
\(285\) 0 0
\(286\) 5.55408 + 9.61996i 0.328420 + 0.568840i
\(287\) −6.40642 −0.378159
\(288\) 0 0
\(289\) −16.1052 −0.947367
\(290\) 7.85087 + 13.5981i 0.461019 + 0.798509i
\(291\) 0 0
\(292\) 3.05555 5.29236i 0.178812 0.309712i
\(293\) 7.53278 13.0472i 0.440070 0.762223i −0.557625 0.830093i \(-0.688287\pi\)
0.997694 + 0.0678705i \(0.0216205\pi\)
\(294\) 0 0
\(295\) −3.53590 6.12435i −0.205868 0.356574i
\(296\) 9.00000 0.523114
\(297\) 0 0
\(298\) 33.3245 1.93044
\(299\) −0.136673 0.236725i −0.00790401 0.0136901i
\(300\) 0 0
\(301\) −5.21780 + 9.03749i −0.300749 + 0.520912i
\(302\) −12.2142 + 21.1556i −0.702848 + 1.21737i
\(303\) 0 0
\(304\) 8.77188 + 15.1933i 0.503102 + 0.871398i
\(305\) −5.89610 −0.337610
\(306\) 0 0
\(307\) −27.2704 −1.55641 −0.778203 0.628013i \(-0.783868\pi\)
−0.778203 + 0.628013i \(0.783868\pi\)
\(308\) −9.15126 15.8505i −0.521442 0.903163i
\(309\) 0 0
\(310\) −7.42627 + 12.8627i −0.421784 + 0.730551i
\(311\) −7.99115 + 13.8411i −0.453136 + 0.784855i −0.998579 0.0532931i \(-0.983028\pi\)
0.545443 + 0.838148i \(0.316362\pi\)
\(312\) 0 0
\(313\) −5.79893 10.0440i −0.327775 0.567722i 0.654295 0.756239i \(-0.272965\pi\)
−0.982070 + 0.188517i \(0.939632\pi\)
\(314\) 14.8961 0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) −1.00885 1.74739i −0.0566629 0.0981430i 0.836303 0.548268i \(-0.184713\pi\)
−0.892965 + 0.450125i \(0.851379\pi\)
\(318\) 0 0
\(319\) −5.55408 + 9.61996i −0.310969 + 0.538614i
\(320\) 9.50214 16.4582i 0.531186 0.920040i
\(321\) 0 0
\(322\) 0.336285 + 0.582462i 0.0187404 + 0.0324594i
\(323\) −3.83482 −0.213375
\(324\) 0 0
\(325\) 1.72665 0.0957775
\(326\) −21.9195 37.9658i −1.21401 2.10273i
\(327\) 0 0
\(328\) −16.1893 + 28.0407i −0.893904 + 1.54829i
\(329\) 6.08113 10.5328i 0.335263 0.580693i
\(330\) 0 0
\(331\) 9.85447 + 17.0684i 0.541651 + 0.938167i 0.998809 + 0.0487815i \(0.0155338\pi\)
−0.457159 + 0.889385i \(0.651133\pi\)
\(332\) 3.83482 0.210463
\(333\) 0 0
\(334\) 20.8348 1.14003
\(335\) 20.5115 + 35.5269i 1.12066 + 1.94104i
\(336\) 0 0
\(337\) 14.5256 25.1590i 0.791259 1.37050i −0.133929 0.990991i \(-0.542759\pi\)
0.925188 0.379509i \(-0.123907\pi\)
\(338\) 14.7630 25.5703i 0.803003 1.39084i
\(339\) 0 0
\(340\) −4.97296 8.61342i −0.269697 0.467128i
\(341\) −10.5074 −0.569007
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 26.3712 + 45.6763i 1.42184 + 2.46270i
\(345\) 0 0
\(346\) 21.3530 36.9845i 1.14794 1.98830i
\(347\) 14.5416 25.1868i 0.780636 1.35210i −0.150936 0.988544i \(-0.548229\pi\)
0.931572 0.363557i \(-0.118438\pi\)
\(348\) 0 0
\(349\) −12.3815 21.4454i −0.662767 1.14795i −0.979885 0.199561i \(-0.936049\pi\)
0.317118 0.948386i \(-0.397285\pi\)
\(350\) −4.24844 −0.227089
\(351\) 0 0
\(352\) −2.43560 −0.129818
\(353\) −16.6513 28.8408i −0.886257 1.53504i −0.844266 0.535925i \(-0.819963\pi\)
−0.0419914 0.999118i \(-0.513370\pi\)
\(354\) 0 0
\(355\) 4.24484 7.35228i 0.225293 0.390219i
\(356\) −29.1015 + 50.4052i −1.54237 + 2.67147i
\(357\) 0 0
\(358\) −13.9626 24.1840i −0.737949 1.27816i
\(359\) −25.5366 −1.34777 −0.673884 0.738837i \(-0.735375\pi\)
−0.673884 + 0.738837i \(0.735375\pi\)
\(360\) 0 0
\(361\) −2.56440 −0.134968
\(362\) −26.9289 46.6422i −1.41535 2.45146i
\(363\) 0 0
\(364\) 2.02704 3.51094i 0.106246 0.184023i
\(365\) 1.95477 3.38576i 0.102317 0.177219i
\(366\) 0 0
\(367\) −13.7252 23.7727i −0.716449 1.24093i −0.962398 0.271644i \(-0.912433\pi\)
0.245949 0.969283i \(-0.420900\pi\)
\(368\) 1.18289 0.0616622
\(369\) 0 0
\(370\) 11.3638 0.590776
\(371\) 3.13667 + 5.43288i 0.162848 + 0.282061i
\(372\) 0 0
\(373\) −8.16372 + 14.1400i −0.422701 + 0.732140i −0.996203 0.0870646i \(-0.972251\pi\)
0.573502 + 0.819204i \(0.305585\pi\)
\(374\) 5.25370 9.09967i 0.271662 0.470533i
\(375\) 0 0
\(376\) −30.7345 53.2338i −1.58501 2.74532i
\(377\) −2.46050 −0.126722
\(378\) 0 0
\(379\) 12.0364 0.618267 0.309134 0.951019i \(-0.399961\pi\)
0.309134 + 0.951019i \(0.399961\pi\)
\(380\) 21.3135 + 36.9161i 1.09336 + 1.89376i
\(381\) 0 0
\(382\) −0.863327 + 1.49533i −0.0441716 + 0.0765075i
\(383\) −6.21780 + 10.7695i −0.317715 + 0.550298i −0.980011 0.198944i \(-0.936249\pi\)
0.662296 + 0.749242i \(0.269582\pi\)
\(384\) 0 0
\(385\) −5.85447 10.1402i −0.298372 0.516795i
\(386\) 29.8817 1.52094
\(387\) 0 0
\(388\) −46.5801 −2.36475
\(389\) 10.3004 + 17.8408i 0.522250 + 0.904564i 0.999665 + 0.0258860i \(0.00824070\pi\)
−0.477414 + 0.878678i \(0.658426\pi\)
\(390\) 0 0
\(391\) −0.129281 + 0.223922i −0.00653803 + 0.0113242i
\(392\) −2.52704 + 4.37697i −0.127635 + 0.221070i
\(393\) 0 0
\(394\) −20.1893 34.9689i −1.01712 1.76171i
\(395\) 38.1488 1.91948
\(396\) 0 0
\(397\) −23.6372 −1.18631 −0.593157 0.805087i \(-0.702119\pi\)
−0.593157 + 0.805087i \(0.702119\pi\)
\(398\) −27.9341 48.3833i −1.40021 2.42524i
\(399\) 0 0
\(400\) −3.73599 + 6.47092i −0.186799 + 0.323546i
\(401\) −1.28220 + 2.22084i −0.0640300 + 0.110903i −0.896263 0.443522i \(-0.853729\pi\)
0.832233 + 0.554426i \(0.187062\pi\)
\(402\) 0 0
\(403\) −1.16372 2.01561i −0.0579688 0.100405i
\(404\) 14.9181 0.742202
\(405\) 0 0
\(406\) 6.05408 0.300459
\(407\) 4.01965 + 6.96224i 0.199247 + 0.345105i
\(408\) 0 0
\(409\) 17.1623 29.7259i 0.848619 1.46985i −0.0338223 0.999428i \(-0.510768\pi\)
0.882441 0.470423i \(-0.155899\pi\)
\(410\) −20.4413 + 35.4054i −1.00953 + 1.74855i
\(411\) 0 0
\(412\) 19.7163 + 34.1497i 0.971354 + 1.68243i
\(413\) −2.72665 −0.134170
\(414\) 0 0
\(415\) 2.45331 0.120428
\(416\) −0.269748 0.467216i −0.0132255 0.0229072i
\(417\) 0 0
\(418\) −22.5167 + 39.0001i −1.10133 + 1.90756i
\(419\) 2.02850 3.51347i 0.0990989 0.171644i −0.812213 0.583361i \(-0.801737\pi\)
0.911312 + 0.411717i \(0.135071\pi\)
\(420\) 0 0
\(421\) 10.5344 + 18.2462i 0.513417 + 0.889264i 0.999879 + 0.0155624i \(0.00495387\pi\)
−0.486462 + 0.873702i \(0.661713\pi\)
\(422\) 11.2235 0.546353
\(423\) 0 0
\(424\) 31.7060 1.53978
\(425\) −0.816635 1.41445i −0.0396126 0.0686110i
\(426\) 0 0
\(427\) −1.13667 + 1.96878i −0.0550075 + 0.0952757i
\(428\) −2.78580 + 4.82515i −0.134657 + 0.233232i
\(429\) 0 0
\(430\) 33.2975 + 57.6729i 1.60575 + 2.78123i
\(431\) −22.6185 −1.08949 −0.544747 0.838600i \(-0.683374\pi\)
−0.544747 + 0.838600i \(0.683374\pi\)
\(432\) 0 0
\(433\) 2.41789 0.116196 0.0580982 0.998311i \(-0.481496\pi\)
0.0580982 + 0.998311i \(0.481496\pi\)
\(434\) 2.86333 + 4.95943i 0.137444 + 0.238060i
\(435\) 0 0
\(436\) 6.89037 11.9345i 0.329989 0.571557i
\(437\) 0.554084 0.959702i 0.0265054 0.0459088i
\(438\) 0 0
\(439\) 11.7448 + 20.3427i 0.560551 + 0.970902i 0.997448 + 0.0713911i \(0.0227438\pi\)
−0.436898 + 0.899511i \(0.643923\pi\)
\(440\) −59.1780 −2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) −6.70895 11.6202i −0.318752 0.552094i 0.661476 0.749966i \(-0.269930\pi\)
−0.980228 + 0.197872i \(0.936597\pi\)
\(444\) 0 0
\(445\) −18.6175 + 32.2465i −0.882554 + 1.52863i
\(446\) −16.3925 + 28.3927i −0.776208 + 1.34443i
\(447\) 0 0
\(448\) −3.66372 6.34574i −0.173094 0.299808i
\(449\) 9.16225 0.432393 0.216197 0.976350i \(-0.430635\pi\)
0.216197 + 0.976350i \(0.430635\pi\)
\(450\) 0 0
\(451\) −28.9224 −1.36190
\(452\) 21.0584 + 36.4741i 0.990502 + 1.71560i
\(453\) 0 0
\(454\) 1.69961 2.94381i 0.0797667 0.138160i
\(455\) 1.29679 2.24611i 0.0607944 0.105299i
\(456\) 0 0
\(457\) −4.40856 7.63584i −0.206224 0.357190i 0.744298 0.667847i \(-0.232784\pi\)
−0.950522 + 0.310658i \(0.899451\pi\)
\(458\) −44.2383 −2.06712
\(459\) 0 0
\(460\) 2.87412 0.134007
\(461\) −2.82957 4.90095i −0.131786 0.228260i 0.792579 0.609769i \(-0.208738\pi\)
−0.924365 + 0.381509i \(0.875405\pi\)
\(462\) 0 0
\(463\) −7.86333 + 13.6197i −0.365440 + 0.632960i −0.988847 0.148937i \(-0.952415\pi\)
0.623407 + 0.781898i \(0.285748\pi\)
\(464\) 5.32383 9.22115i 0.247153 0.428081i
\(465\) 0 0
\(466\) −23.3530 40.4486i −1.08181 1.87375i
\(467\) 21.9971 1.01790 0.508952 0.860795i \(-0.330033\pi\)
0.508952 + 0.860795i \(0.330033\pi\)
\(468\) 0 0
\(469\) 15.8171 0.730366
\(470\) −38.8068 67.2153i −1.79002 3.10041i
\(471\) 0 0
\(472\) −6.89037 + 11.9345i −0.317155 + 0.549328i
\(473\) −23.5562 + 40.8006i −1.08312 + 1.87601i
\(474\) 0 0
\(475\) 3.50000 + 6.06218i 0.160591 + 0.278152i
\(476\) −3.83482 −0.175769
\(477\) 0 0
\(478\) −12.0364 −0.550531
\(479\) 12.4875 + 21.6291i 0.570571 + 0.988257i 0.996507 + 0.0835043i \(0.0266112\pi\)
−0.425937 + 0.904753i \(0.640055\pi\)
\(480\) 0 0
\(481\) −0.890369 + 1.54216i −0.0405973 + 0.0703166i
\(482\) 32.1826 55.7419i 1.46588 2.53897i
\(483\) 0 0
\(484\) −19.0167 32.9379i −0.864397 1.49718i
\(485\) −29.7994 −1.35312
\(486\) 0 0
\(487\) −17.5979 −0.797435 −0.398717 0.917074i \(-0.630545\pi\)
−0.398717 + 0.917074i \(0.630545\pi\)
\(488\) 5.74484 + 9.95036i 0.260057 + 0.450432i
\(489\) 0 0
\(490\) −3.19076 + 5.52655i −0.144144 + 0.249664i
\(491\) 6.89757 11.9469i 0.311283 0.539158i −0.667358 0.744737i \(-0.732575\pi\)
0.978640 + 0.205580i \(0.0659080\pi\)
\(492\) 0 0
\(493\) 1.16372 + 2.01561i 0.0524111 + 0.0907787i
\(494\) −9.97509 −0.448801
\(495\) 0 0
\(496\) 10.0718 0.452237
\(497\) −1.63667 2.83480i −0.0734148 0.127158i
\(498\) 0 0
\(499\) −6.54377 + 11.3341i −0.292939 + 0.507386i −0.974503 0.224373i \(-0.927967\pi\)
0.681564 + 0.731758i \(0.261300\pi\)
\(500\) 17.2089 29.8068i 0.769607 1.33300i
\(501\) 0 0
\(502\) 22.7075 + 39.3305i 1.01348 + 1.75541i
\(503\) 22.3068 0.994611 0.497305 0.867576i \(-0.334323\pi\)
0.497305 + 0.867576i \(0.334323\pi\)
\(504\) 0 0
\(505\) 9.54377 0.424692
\(506\) 1.51819 + 2.62958i 0.0674917 + 0.116899i
\(507\) 0 0
\(508\) −1.36333 + 2.36135i −0.0604879 + 0.104768i
\(509\) −7.94659 + 13.7639i −0.352226 + 0.610074i −0.986639 0.162920i \(-0.947909\pi\)
0.634413 + 0.772994i \(0.281242\pi\)
\(510\) 0 0
\(511\) −0.753696 1.30544i −0.0333415 0.0577492i
\(512\) −41.4078 −1.82998
\(513\) 0 0
\(514\) 28.8712 1.27345
\(515\) 12.6134 + 21.8471i 0.555814 + 0.962698i
\(516\) 0 0
\(517\) 27.4538 47.5514i 1.20742 2.09131i
\(518\) 2.19076 3.79450i 0.0962563 0.166721i
\(519\) 0 0
\(520\) −6.55408 11.3520i −0.287416 0.497818i
\(521\) −4.41789 −0.193551 −0.0967756 0.995306i \(-0.530853\pi\)
−0.0967756 + 0.995306i \(0.530853\pi\)
\(522\) 0 0
\(523\) 25.2733 1.10513 0.552563 0.833471i \(-0.313650\pi\)
0.552563 + 0.833471i \(0.313650\pi\)
\(524\) 16.0416 + 27.7849i 0.700782 + 1.21379i
\(525\) 0 0
\(526\) −9.25370 + 16.0279i −0.403480 + 0.698848i
\(527\) −1.10078 + 1.90660i −0.0479506 + 0.0830528i
\(528\) 0 0
\(529\) 11.4626 + 19.8539i 0.498376 + 0.863212i
\(530\) 40.0335 1.73894
\(531\) 0 0
\(532\) 16.4356 0.712574
\(533\) −3.20321 5.54812i −0.138746 0.240316i
\(534\) 0 0
\(535\) −1.78220 + 3.08686i −0.0770513 + 0.133457i
\(536\) 39.9705 69.2310i 1.72646 2.99032i
\(537\) 0 0
\(538\) −23.1716 40.1344i −0.998998 1.73032i
\(539\) −4.51459 −0.194457
\(540\) 0 0
\(541\) −3.43852 −0.147834 −0.0739168 0.997264i \(-0.523550\pi\)
−0.0739168 + 0.997264i \(0.523550\pi\)
\(542\) 29.5043 + 51.1029i 1.26732 + 2.19506i
\(543\) 0 0
\(544\) −0.255158 + 0.441947i −0.0109398 + 0.0189483i
\(545\) 4.40808 7.63501i 0.188821 0.327048i
\(546\) 0 0
\(547\) 3.46410 + 6.00000i 0.148114 + 0.256542i 0.930531 0.366214i \(-0.119346\pi\)
−0.782416 + 0.622756i \(0.786013\pi\)
\(548\) 14.8889 0.636023
\(549\) 0 0
\(550\) −19.1800 −0.817836
\(551\) −4.98755 8.63868i −0.212477 0.368020i
\(552\) 0 0
\(553\) 7.35447 12.7383i 0.312744 0.541688i
\(554\) −8.81138 + 15.2618i −0.374360 + 0.648410i
\(555\) 0 0
\(556\) 4.16372 + 7.21177i 0.176581 + 0.305847i
\(557\) −33.5835 −1.42298 −0.711488 0.702698i \(-0.751979\pi\)
−0.711488 + 0.702698i \(0.751979\pi\)
\(558\) 0 0
\(559\) −10.4356 −0.441379
\(560\) 5.61177 + 9.71987i 0.237140 + 0.410739i
\(561\) 0 0
\(562\) 18.3083 31.7108i 0.772287 1.33764i
\(563\) 21.2396 36.7880i 0.895142 1.55043i 0.0615128 0.998106i \(-0.480407\pi\)
0.833629 0.552325i \(-0.186259\pi\)
\(564\) 0 0
\(565\) 13.4720 + 23.3341i 0.566770 + 0.981675i
\(566\) 49.2029 2.06815
\(567\) 0 0
\(568\) −16.5438 −0.694161
\(569\) 5.20175 + 9.00969i 0.218069 + 0.377706i 0.954217 0.299114i \(-0.0966910\pi\)
−0.736149 + 0.676820i \(0.763358\pi\)
\(570\) 0 0
\(571\) −8.92480 + 15.4582i −0.373491 + 0.646906i −0.990100 0.140364i \(-0.955173\pi\)
0.616609 + 0.787270i \(0.288506\pi\)
\(572\) 9.15126 15.8505i 0.382633 0.662741i
\(573\) 0 0
\(574\) 7.88151 + 13.6512i 0.328968 + 0.569789i
\(575\) 0.471974 0.0196827
\(576\) 0 0
\(577\) 11.9430 0.497193 0.248597 0.968607i \(-0.420031\pi\)
0.248597 + 0.968607i \(0.420031\pi\)
\(578\) 19.8135 + 34.3180i 0.824134 + 1.42744i
\(579\) 0 0
\(580\) 12.9356 22.4051i 0.537122 0.930322i
\(581\) 0.472958 0.819187i 0.0196216 0.0339856i
\(582\) 0 0
\(583\) 14.1608 + 24.5272i 0.586480 + 1.01581i
\(584\) −7.61849 −0.315255
\(585\) 0 0
\(586\) −37.0689 −1.53130
\(587\) 11.9299 + 20.6631i 0.492398 + 0.852859i 0.999962 0.00875568i \(-0.00278706\pi\)
−0.507563 + 0.861614i \(0.669454\pi\)
\(588\) 0 0
\(589\) 4.71780 8.17147i 0.194394 0.336699i
\(590\) −8.70009 + 15.0690i −0.358177 + 0.620381i
\(591\) 0 0
\(592\) −3.85301 6.67361i −0.158358 0.274284i
\(593\) −19.5801 −0.804060 −0.402030 0.915626i \(-0.631695\pi\)
−0.402030 + 0.915626i \(0.631695\pi\)
\(594\) 0 0
\(595\) −2.45331 −0.100576
\(596\) −27.4538 47.5514i −1.12455 1.94778i
\(597\) 0 0
\(598\) −0.336285 + 0.582462i −0.0137517 + 0.0238187i
\(599\) 9.27335 16.0619i 0.378899 0.656272i −0.612004 0.790855i \(-0.709636\pi\)
0.990902 + 0.134583i \(0.0429696\pi\)
\(600\) 0 0
\(601\) 9.09931 + 15.7605i 0.371169 + 0.642883i 0.989746 0.142841i \(-0.0456238\pi\)
−0.618577 + 0.785724i \(0.712290\pi\)
\(602\) 25.6768 1.04651
\(603\) 0 0
\(604\) 40.2498 1.63774
\(605\) −12.1659 21.0719i −0.494612 0.856693i
\(606\) 0 0
\(607\) 11.1549 19.3208i 0.452762 0.784206i −0.545795 0.837919i \(-0.683772\pi\)
0.998556 + 0.0537125i \(0.0171055\pi\)
\(608\) 1.09358 1.89413i 0.0443505 0.0768173i
\(609\) 0 0
\(610\) 7.25370 + 12.5638i 0.293694 + 0.508692i
\(611\) 12.1623 0.492032
\(612\) 0 0
\(613\) 10.2370 0.413467 0.206734 0.978397i \(-0.433717\pi\)
0.206734 + 0.978397i \(0.433717\pi\)
\(614\) 33.5495 + 58.1094i 1.35395 + 2.34511i
\(615\) 0 0
\(616\) −11.4086 + 19.7602i −0.459664 + 0.796161i
\(617\) −5.66372 + 9.80984i −0.228013 + 0.394929i −0.957219 0.289364i \(-0.906556\pi\)
0.729206 + 0.684294i \(0.239889\pi\)
\(618\) 0 0
\(619\) −4.31663 7.47663i −0.173500 0.300511i 0.766141 0.642672i \(-0.222174\pi\)
−0.939641 + 0.342161i \(0.888841\pi\)
\(620\) 24.4720 0.982818
\(621\) 0 0
\(622\) 39.3245 1.57677
\(623\) 7.17830 + 12.4332i 0.287593 + 0.498125i
\(624\) 0 0
\(625\) 15.3260 26.5454i 0.613039 1.06181i
\(626\) −14.2683 + 24.7134i −0.570275 + 0.987746i
\(627\) 0 0
\(628\) −12.2719 21.2555i −0.489701 0.848188i
\(629\) 1.68443 0.0671626
\(630\) 0 0
\(631\) −14.8535 −0.591308 −0.295654 0.955295i \(-0.595538\pi\)
−0.295654 + 0.955295i \(0.595538\pi\)
\(632\) −37.1701 64.3805i −1.47855 2.56092i
\(633\) 0 0
\(634\) −2.48229 + 4.29945i −0.0985844 + 0.170753i
\(635\) −0.872181 + 1.51066i −0.0346115 + 0.0599488i
\(636\) 0 0
\(637\) −0.500000 0.866025i −0.0198107 0.0343132i
\(638\) 27.3317 1.08207
\(639\) 0 0
\(640\) −49.5586 −1.95897
\(641\) −17.0797 29.5828i −0.674606 1.16845i −0.976584 0.215137i \(-0.930980\pi\)
0.301978 0.953315i \(-0.402353\pi\)
\(642\) 0 0
\(643\) 5.41741 9.38323i 0.213642 0.370039i −0.739210 0.673475i \(-0.764801\pi\)
0.952852 + 0.303437i \(0.0981341\pi\)
\(644\) 0.554084 0.959702i 0.0218340 0.0378176i
\(645\) 0 0
\(646\) 4.71780 + 8.17147i 0.185619 + 0.321502i
\(647\) −32.9692 −1.29615 −0.648077 0.761575i \(-0.724427\pi\)
−0.648077 + 0.761575i \(0.724427\pi\)
\(648\) 0 0
\(649\) −12.3097 −0.483199
\(650\) −2.12422 3.67926i −0.0833188 0.144312i
\(651\) 0 0
\(652\) −36.1160 + 62.5548i −1.41441 + 2.44984i
\(653\) −1.96557 + 3.40446i −0.0769185 + 0.133227i −0.901919 0.431905i \(-0.857841\pi\)
0.825000 + 0.565132i \(0.191175\pi\)
\(654\) 0 0
\(655\) 10.2626 + 17.7753i 0.400991 + 0.694537i
\(656\) 27.7233 1.08241
\(657\) 0 0
\(658\) −29.9253 −1.16661
\(659\) 8.40856 + 14.5640i 0.327551 + 0.567335i 0.982025 0.188749i \(-0.0604434\pi\)
−0.654474 + 0.756084i \(0.727110\pi\)
\(660\) 0 0
\(661\) 8.51080 14.7411i 0.331032 0.573364i −0.651683 0.758492i \(-0.725937\pi\)
0.982714 + 0.185128i \(0.0592700\pi\)
\(662\) 24.2470 41.9970i 0.942386 1.63226i
\(663\) 0 0
\(664\) −2.39037 4.14024i −0.0927643 0.160672i
\(665\) 10.5146 0.407738
\(666\) 0 0
\(667\) −0.672570 −0.0260420
\(668\) −17.1644 29.7296i −0.664110 1.15027i
\(669\) 0 0
\(670\) 50.4686 87.4141i 1.94977 3.37710i
\(671\) −5.13161 + 8.88821i −0.198104 + 0.343126i
\(672\) 0 0
\(673\) −14.3727 24.8942i −0.554025 0.959600i −0.997979 0.0635501i \(-0.979758\pi\)
0.443953 0.896050i \(-0.353576\pi\)
\(674\) −71.4805 −2.75333
\(675\) 0 0
\(676\) −48.6490 −1.87112
\(677\) −3.01819 5.22765i −0.115998 0.200915i 0.802180 0.597082i \(-0.203673\pi\)
−0.918178 + 0.396167i \(0.870340\pi\)
\(678\) 0 0
\(679\) −5.74484 + 9.95036i −0.220467 + 0.381860i
\(680\) −6.19961 + 10.7380i −0.237744 + 0.411785i
\(681\) 0 0
\(682\) 12.9267 + 22.3898i 0.494991 + 0.857349i
\(683\) −20.5113 −0.784842 −0.392421 0.919786i \(-0.628362\pi\)
−0.392421 + 0.919786i \(0.628362\pi\)
\(684\) 0 0
\(685\) 9.52510 0.363935
\(686\) 1.23025 + 2.13086i 0.0469713 + 0.0813566i
\(687\) 0 0
\(688\) 22.5797 39.1091i 0.860842 1.49102i
\(689\) −3.13667 + 5.43288i −0.119498 + 0.206976i
\(690\) 0 0
\(691\) 7.50146 + 12.9929i 0.285369 + 0.494274i 0.972699 0.232072i \(-0.0745505\pi\)
−0.687330 + 0.726346i \(0.741217\pi\)
\(692\) −70.3652 −2.67488
\(693\) 0 0
\(694\) −71.5595 −2.71636
\(695\) 2.66372 + 4.61369i 0.101040 + 0.175007i
\(696\) 0 0
\(697\) −3.02997 + 5.24806i −0.114768 + 0.198784i
\(698\) −30.4648 + 52.7665i −1.15311 + 1.99724i
\(699\) 0 0
\(700\) 3.50000 + 6.06218i 0.132288 + 0.229129i
\(701\) −38.5113 −1.45455 −0.727275 0.686346i \(-0.759214\pi\)
−0.727275 + 0.686346i \(0.759214\pi\)
\(702\) 0 0
\(703\) −7.21926 −0.272280
\(704\) −16.5402 28.6484i −0.623381 1.07973i
\(705\) 0 0
\(706\) −40.9705 + 70.9630i −1.54195 + 2.67073i
\(707\) 1.83988 3.18677i 0.0691959 0.119851i
\(708\) 0 0
\(709\) −3.82004 6.61650i −0.143465 0.248488i 0.785334 0.619072i \(-0.212491\pi\)
−0.928799 + 0.370584i \(0.879158\pi\)
\(710\) −20.8889 −0.783947
\(711\) 0 0
\(712\) 72.5595 2.71928
\(713\) −0.318097 0.550960i −0.0119128 0.0206336i
\(714\) 0 0
\(715\) 5.85447 10.1402i 0.218945 0.379224i
\(716\) −23.0057 + 39.8471i −0.859765 + 1.48916i
\(717\) 0 0
\(718\) 31.4164 + 54.4148i 1.17245 + 2.03074i
\(719\) 30.0364 1.12017 0.560084 0.828436i \(-0.310769\pi\)
0.560084 + 0.828436i \(0.310769\pi\)
\(720\) 0 0
\(721\) 9.72665 0.362240
\(722\) 3.15486 + 5.46438i 0.117412 + 0.203363i
\(723\) 0 0
\(724\) −44.3697 + 76.8506i −1.64899 + 2.85613i
\(725\) 2.12422 3.67926i 0.0788916 0.136644i
\(726\) 0 0
\(727\) −1.72812 2.99319i −0.0640923 0.111011i 0.832199 0.554478i \(-0.187082\pi\)
−0.896291 + 0.443466i \(0.853749\pi\)
\(728\) −5.05408 −0.187317
\(729\) 0 0
\(730\) −9.61944 −0.356032
\(731\) 4.93560 + 8.54871i 0.182550 + 0.316185i
\(732\) 0 0
\(733\) −19.2630 + 33.3645i −0.711496 + 1.23235i 0.252799 + 0.967519i \(0.418649\pi\)
−0.964295 + 0.264829i \(0.914685\pi\)
\(734\) −33.7709 + 58.4929i −1.24651 + 2.15901i
\(735\) 0 0
\(736\) −0.0737345 0.127712i −0.00271789 0.00470752i
\(737\) 71.4078 2.63034
\(738\) 0 0
\(739\) 45.1239 1.65991 0.829955 0.557830i \(-0.188366\pi\)
0.829955 + 0.557830i \(0.188366\pi\)
\(740\) −9.36186 16.2152i −0.344149 0.596084i
\(741\) 0 0
\(742\) 7.71780 13.3676i 0.283329 0.490741i
\(743\) 4.74338 8.21577i 0.174018 0.301407i −0.765803 0.643075i \(-0.777658\pi\)
0.939821 + 0.341668i \(0.110992\pi\)
\(744\) 0 0
\(745\) −17.5634 30.4207i −0.643474 1.11453i
\(746\) 40.1737 1.47086
\(747\) 0 0
\(748\) −17.3126 −0.633013
\(749\) 0.687159 + 1.19019i 0.0251082 + 0.0434887i
\(750\) 0 0
\(751\) 4.91595 8.51467i 0.179386 0.310705i −0.762285 0.647242i \(-0.775922\pi\)
0.941670 + 0.336537i \(0.109256\pi\)
\(752\) −26.3157 + 45.5800i −0.959633 + 1.66213i
\(753\) 0 0
\(754\) 3.02704 + 5.24299i 0.110238 + 0.190938i
\(755\) 25.7496 0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) −14.8078 25.6478i −0.537843 0.931571i
\(759\) 0 0
\(760\) 26.5708 46.0220i 0.963825 1.66939i
\(761\) 11.4897 19.9007i 0.416501 0.721400i −0.579084 0.815268i \(-0.696590\pi\)
0.995585 + 0.0938675i \(0.0299230\pi\)
\(762\) 0 0
\(763\) −1.69961 2.94381i −0.0615301 0.106573i
\(764\) 2.84494 0.102926
\(765\) 0 0
\(766\) 30.5979 1.10555
\(767\) −1.36333 2.36135i −0.0492269 0.0852635i
\(768\) 0 0
\(769\) −3.04329 + 5.27113i −0.109744 + 0.190082i −0.915666 0.401939i \(-0.868336\pi\)
0.805923 + 0.592021i \(0.201670\pi\)
\(770\) −14.4050 + 24.9501i −0.519119 + 0.899140i
\(771\) 0 0
\(772\) −24.6175 42.6388i −0.886003 1.53460i
\(773\) 41.8214 1.50421 0.752105 0.659043i \(-0.229038\pi\)
0.752105 + 0.659043i \(0.229038\pi\)
\(774\) 0 0
\(775\) 4.01867 0.144355
\(776\) 29.0349 + 50.2899i 1.04229 + 1.80530i
\(777\) 0 0
\(778\) 25.3442 43.8974i 0.908632 1.57380i
\(779\) 12.9861 22.4926i 0.465275 0.805880i
\(780\) 0 0
\(781\) −7.38891 12.7980i −0.264396 0.457947i
\(782\) 0.636194 0.0227503
\(783\) 0 0