Properties

Label 189.2.f.a.127.1
Level $189$
Weight $2$
Character 189.127
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 127.1
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 189.127
Dual form 189.2.f.a.64.1

$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.00784213 + 0.999969i \(0.502496\pi\)
−0.862078 + 0.506776i \(0.830837\pi\)
\(3\) 0 0
\(4\) −2.02704 3.51094i −1.01352 1.75547i
\(5\) −1.29679 2.24611i −0.579942 1.00449i −0.995485 0.0949156i \(-0.969742\pi\)
0.415543 0.909573i \(-0.363591\pi\)
\(6\) 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 −0.294198 0.955744i \(-0.595053\pi\)
0.974798 0.223089i \(-0.0716141\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 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 0.851425 0.524477i \(-0.175739\pi\)
−0.879923 + 0.475117i \(0.842406\pi\)
\(24\) 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 −0.728897 0.684623i \(-0.759967\pi\)
0.957350 + 0.288932i \(0.0933002\pi\)
\(30\) 0 0
\(31\) −1.16372 2.01561i −0.209009 0.362015i 0.742393 0.669964i \(-0.233691\pi\)
−0.951403 + 0.307949i \(0.900357\pi\)
\(32\) −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 −1.00000 0.000297253i \(-0.999905\pi\)
0.499743 0.866174i \(-0.333428\pi\)
\(42\) 0 0
\(43\) 5.21780 9.03749i 0.795707 1.37820i −0.126682 0.991943i \(-0.540433\pi\)
0.922389 0.386262i \(-0.126234\pi\)
\(44\) −18.3025 −2.75921
\(45\) 0 0
\(46\) 0.672570 0.0991650
\(47\) −6.08113 + 10.5328i −0.887023 + 1.53637i −0.0436467 + 0.999047i \(0.513898\pi\)
−0.843377 + 0.537323i \(0.819436\pi\)
\(48\) 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 0.763530 0.645772i \(-0.223464\pi\)
−0.941020 + 0.338350i \(0.890131\pi\)
\(60\) 0 0
\(61\) 1.13667 1.96878i 0.145536 0.252076i −0.784037 0.620714i \(-0.786843\pi\)
0.929573 + 0.368639i \(0.120176\pi\)
\(62\) 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 0.706400 + 0.707813i \(0.250318\pi\)
0.259784 + 0.965667i \(0.416349\pi\)
\(68\) −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 0.0725952 + 0.997361i \(0.476872\pi\)
−0.900038 + 0.435811i \(0.856461\pi\)
\(80\) 11.2235 1.25483
\(81\) 0 0
\(82\) 15.7630 1.74074
\(83\) −0.472958 + 0.819187i −0.0519139 + 0.0899175i −0.890815 0.454367i \(-0.849865\pi\)
0.838901 + 0.544285i \(0.183199\pi\)
\(84\) 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 −0.411785 0.911281i \(-0.635094\pi\)
0.995085 0.0990246i \(-0.0315722\pi\)
\(98\) 2.46050 0.248549
\(99\) 0 0
\(100\) 7.00000 0.700000
\(101\) −1.83988 + 3.18677i −0.183075 + 0.317096i −0.942926 0.333002i \(-0.891939\pi\)
0.759851 + 0.650097i \(0.225272\pi\)
\(102\) 0 0
\(103\) 4.86333 + 8.42353i 0.479198 + 0.829995i 0.999715 0.0238560i \(-0.00759431\pi\)
−0.520518 + 0.853851i \(0.674261\pi\)
\(104\) −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 0.999915 0.0130636i \(-0.00415840\pi\)
−0.511271 + 0.859420i \(0.670825\pi\)
\(114\) 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 0.985484 0.169770i \(-0.0543026\pi\)
−0.639767 + 0.768569i \(0.720969\pi\)
\(132\) 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 −0.933744 0.357943i \(-0.883478\pi\)
0.776859 + 0.629674i \(0.216812\pi\)
\(138\) 0 0
\(139\) 1.02704 + 1.77889i 0.0871126 + 0.150883i 0.906289 0.422658i \(-0.138903\pi\)
−0.819177 + 0.573541i \(0.805569\pi\)
\(140\) 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 −0.997921 0.0644482i \(-0.979471\pi\)
0.443147 0.896449i \(-0.353862\pi\)
\(150\) 0 0
\(151\) −4.96410 + 8.59808i −0.403973 + 0.699702i −0.994201 0.107535i \(-0.965704\pi\)
0.590228 + 0.807236i \(0.299038\pi\)
\(152\) −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 0.719581 0.694408i \(-0.244334\pi\)
−0.961166 + 0.275972i \(0.911000\pi\)
\(158\) −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 0.654415 0.756136i \(-0.272915\pi\)
−0.982040 + 0.188672i \(0.939582\pi\)
\(168\) 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 −0.320868 0.947124i \(-0.603975\pi\)
0.980667 0.195682i \(-0.0626920\pi\)
\(174\) 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 −0.878440 0.477852i \(-0.841416\pi\)
0.853052 + 0.521826i \(0.174749\pi\)
\(192\) 0 0
\(193\) −6.07227 10.5175i −0.437092 0.757065i 0.560372 0.828241i \(-0.310658\pi\)
−0.997464 + 0.0711760i \(0.977325\pi\)
\(194\) 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 0.776778 0.629775i \(-0.216853\pi\)
−0.933790 + 0.357822i \(0.883520\pi\)
\(212\) −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 −0.998131 0.0611159i \(-0.980534\pi\)
0.551993 + 0.833849i \(0.313867\pi\)
\(224\) −0.539495 −0.0360465
\(225\) 0 0
\(226\) −25.5615 −1.70032
\(227\) 0.690757 1.19643i 0.0458472 0.0794096i −0.842191 0.539179i \(-0.818735\pi\)
0.888038 + 0.459769i \(0.152068\pi\)
\(228\) 0 0
\(229\) 8.98968 + 15.5706i 0.594055 + 1.02893i 0.993679 + 0.112254i \(0.0358072\pi\)
−0.399625 + 0.916679i \(0.630859\pi\)
\(230\) −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 0.934224 0.356686i \(-0.116093\pi\)
−0.776011 + 0.630719i \(0.782760\pi\)
\(240\) 0 0
\(241\) 13.0797 22.6546i 0.842535 1.45931i −0.0452094 0.998978i \(-0.514396\pi\)
0.887745 0.460336i \(-0.152271\pi\)
\(242\) 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 0.622962 0.782252i \(-0.285929\pi\)
−0.988931 + 0.148375i \(0.952596\pi\)
\(258\) 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 −0.958369 0.285532i \(-0.907830\pi\)
0.726463 + 0.687206i \(0.241163\pi\)
\(264\) 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 −0.953325 0.301947i \(-0.902364\pi\)
0.738156 + 0.674630i \(0.235697\pi\)
\(278\) −5.05408 −0.303124
\(279\) 0 0
\(280\) −13.1082 −0.783363
\(281\) 7.44085 12.8879i 0.443884 0.768830i −0.554090 0.832457i \(-0.686933\pi\)
0.997974 + 0.0636271i \(0.0202668\pi\)
\(282\) 0 0
\(283\) −9.99854 17.3180i −0.594351 1.02945i −0.993638 0.112621i \(-0.964076\pi\)
0.399287 0.916826i \(-0.369258\pi\)
\(284\) 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 0.997694 0.0678705i \(-0.0216205\pi\)
−0.557625 + 0.830093i \(0.688287\pi\)
\(294\) 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 0.545443 0.838148i \(-0.316362\pi\)
−0.998579 + 0.0532931i \(0.983028\pi\)
\(312\) 0 0
\(313\) −5.79893 + 10.0440i −0.327775 + 0.567722i −0.982070 0.188517i \(-0.939632\pi\)
0.654295 + 0.756239i \(0.272965\pi\)
\(314\) 14.8961 0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) −1.00885 + 1.74739i −0.0566629 + 0.0981430i −0.892965 0.450125i \(-0.851379\pi\)
0.836303 + 0.548268i \(0.184713\pi\)
\(318\) 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 −0.457159 0.889385i \(-0.651133\pi\)
0.998809 0.0487815i \(-0.0155338\pi\)
\(332\) 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 0.925188 + 0.379509i \(0.123907\pi\)
−0.133929 + 0.990991i \(0.542759\pi\)
\(338\) 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 0.931572 + 0.363557i \(0.118438\pi\)
−0.150936 + 0.988544i \(0.548229\pi\)
\(348\) 0 0
\(349\) −12.3815 + 21.4454i −0.662767 + 1.14795i 0.317118 + 0.948386i \(0.397285\pi\)
−0.979885 + 0.199561i \(0.936049\pi\)
\(350\) −4.24844 −0.227089
\(351\) 0 0
\(352\) −2.43560 −0.129818
\(353\) −16.6513 + 28.8408i −0.886257 + 1.53504i −0.0419914 + 0.999118i \(0.513370\pi\)
−0.844266 + 0.535925i \(0.819963\pi\)
\(354\) 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 0.245949 + 0.969283i \(0.420900\pi\)
−0.962398 + 0.271644i \(0.912433\pi\)
\(368\) 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 0.573502 0.819204i \(-0.305585\pi\)
−0.996203 + 0.0870646i \(0.972251\pi\)
\(374\) 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 0.662296 0.749242i \(-0.269582\pi\)
−0.980011 + 0.198944i \(0.936249\pi\)
\(384\) 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 −0.477414 0.878678i \(-0.658426\pi\)
0.999665 0.0258860i \(-0.00824070\pi\)
\(390\) 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 0.832233 0.554426i \(-0.187062\pi\)
−0.896263 + 0.443522i \(0.853729\pi\)
\(402\) 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 0.882441 + 0.470423i \(0.155899\pi\)
−0.0338223 + 0.999428i \(0.510768\pi\)
\(410\) −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 0.911312 0.411717i \(-0.135071\pi\)
−0.812213 + 0.583361i \(0.801737\pi\)
\(420\) 0 0
\(421\) 10.5344 18.2462i 0.513417 0.889264i −0.486462 0.873702i \(-0.661713\pi\)
0.999879 0.0155624i \(-0.00495387\pi\)
\(422\) 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 −0.436898 0.899511i \(-0.643923\pi\)
0.997448 0.0713911i \(-0.0227438\pi\)
\(440\) −59.1780 −2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) −6.70895 + 11.6202i −0.318752 + 0.552094i −0.980228 0.197872i \(-0.936597\pi\)
0.661476 + 0.749966i \(0.269930\pi\)
\(444\) 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 −0.950522 0.310658i \(-0.899451\pi\)
0.744298 + 0.667847i \(0.232784\pi\)
\(458\) −44.2383 −2.06712
\(459\) 0 0
\(460\) 2.87412 0.134007
\(461\) −2.82957 + 4.90095i −0.131786 + 0.228260i −0.924365 0.381509i \(-0.875405\pi\)
0.792579 + 0.609769i \(0.208738\pi\)
\(462\) 0 0
\(463\) −7.86333 13.6197i −0.365440 0.632960i 0.623407 0.781898i \(-0.285748\pi\)
−0.988847 + 0.148937i \(0.952415\pi\)
\(464\) 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 −0.425937 0.904753i \(-0.640055\pi\)
0.996507 0.0835043i \(-0.0266112\pi\)
\(480\) 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 0.978640 0.205580i \(-0.0659080\pi\)
−0.667358 + 0.744737i \(0.732575\pi\)
\(492\) 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 0.681564 0.731758i \(-0.261300\pi\)
−0.974503 + 0.224373i \(0.927967\pi\)
\(500\) 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 0.634413 0.772994i \(-0.281242\pi\)
−0.986639 + 0.162920i \(0.947909\pi\)
\(510\) 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 −0.782416 0.622756i \(-0.786013\pi\)
0.930531 + 0.366214i \(0.119346\pi\)
\(548\) 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 0.833629 + 0.552325i \(0.186259\pi\)
0.0615128 + 0.998106i \(0.480407\pi\)
\(564\) 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 −0.736149 0.676820i \(-0.763358\pi\)
0.954217 + 0.299114i \(0.0966910\pi\)
\(570\) 0 0
\(571\) −8.92480 15.4582i −0.373491 0.646906i 0.616609 0.787270i \(-0.288506\pi\)
−0.990100 + 0.140364i \(0.955173\pi\)
\(572\) 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 −0.507563 0.861614i \(-0.669454\pi\)
0.999962 + 0.00875568i \(0.00278706\pi\)
\(588\) 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 0.990902 0.134583i \(-0.0429696\pi\)
−0.612004 + 0.790855i \(0.709636\pi\)
\(600\) 0 0
\(601\) 9.09931 15.7605i 0.371169 0.642883i −0.618577 0.785724i \(-0.712290\pi\)
0.989746 + 0.142841i \(0.0456238\pi\)
\(602\) 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 0.998556 0.0537125i \(-0.0171055\pi\)
−0.545795 + 0.837919i \(0.683772\pi\)
\(608\) 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 0.729206 0.684294i \(-0.239889\pi\)
−0.957219 + 0.289364i \(0.906556\pi\)
\(618\) 0 0
\(619\) −4.31663 + 7.47663i −0.173500 + 0.300511i −0.939641 0.342161i \(-0.888841\pi\)
0.766141 + 0.642672i \(0.222174\pi\)
\(620\) 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 0.301978 + 0.953315i \(0.402353\pi\)
−0.976584 + 0.215137i \(0.930980\pi\)
\(642\) 0 0
\(643\) 5.41741 + 9.38323i 0.213642 + 0.370039i 0.952852 0.303437i \(-0.0981341\pi\)
−0.739210 + 0.673475i \(0.764801\pi\)
\(644\) 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 0.825000 0.565132i \(-0.191175\pi\)
−0.901919 + 0.431905i \(0.857841\pi\)
\(654\) 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 −0.654474 0.756084i \(-0.727110\pi\)
0.982025 + 0.188749i \(0.0604434\pi\)
\(660\) 0 0
\(661\) 8.51080 + 14.7411i 0.331032 + 0.573364i 0.982714 0.185128i \(-0.0592700\pi\)
−0.651683 + 0.758492i \(0.725937\pi\)
\(662\) 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 0.443953 + 0.896050i \(0.353576\pi\)
−0.997979 + 0.0635501i \(0.979758\pi\)
\(674\) −71.4805 −2.75333
\(675\) 0 0
\(676\) −48.6490 −1.87112
\(677\) −3.01819 + 5.22765i −0.115998 + 0.200915i −0.918178 0.396167i \(-0.870340\pi\)
0.802180 + 0.597082i \(0.203673\pi\)
\(678\) 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 −0.687330 0.726346i \(-0.741217\pi\)
0.972699 + 0.232072i \(0.0745505\pi\)
\(692\) −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 −0.928799 0.370584i \(-0.879158\pi\)
0.785334 + 0.619072i \(0.212491\pi\)
\(710\) −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 −0.896291 0.443466i \(-0.853749\pi\)
0.832199 + 0.554478i \(0.187082\pi\)
\(728\) −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 −0.964295 0.264829i \(-0.914685\pi\)
0.252799 0.967519i \(-0.418649\pi\)
\(734\) −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 0.939821 0.341668i \(-0.110992\pi\)
−0.765803 + 0.643075i \(0.777658\pi\)
\(744\) 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 0.941670 0.336537i \(-0.109256\pi\)
−0.762285 + 0.647242i \(0.775922\pi\)
\(752\) −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 0.995585 0.0938675i \(-0.0299230\pi\)
−0.579084 + 0.815268i \(0.696590\pi\)
\(762\) 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 0.805923 0.592021i \(-0.201670\pi\)
−0.915666 + 0.401939i \(0.868336\pi\)
\(770\) −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
\(784\) 4.32743 0.154551
\(785\) −7.85087 + 13.5981i −0.280210 + 0.485337i
\(786\) 0 0
\(787\) −16.1460 27.9657i −0.575543 0.996870i −0.995982 0.0895491i \(-0.971457\pi\)
0.420439 0.907321i \(-0.361876\pi\)
\(788\) −33.2652 57.6170i −1.18502 2.05252i
\(789\) 0 0
\(790\) −46.9327 + 81.2898i −1.66979 + 2.89216i
\(791\) 10.3887 0.369380
\(792\) 0 0
\(793\) −2.27335 −0.0807289
\(794\) 29.0797 50.3675i 1.03200 1.78747i
\(795\) 0 0
\(796\) −46.0261 79.7195i −1.63135 2.82558i
\(797\) 23.2829 + 40.3271i 0.824722 + 1.42846i 0.902132 + 0.431461i \(0.142002\pi\)
−0.0774101 + 0.996999i \(0.524665\pi\)
\(798\) 0 0
\(799\) −5.75223 + 9.96316i −0.203499 + 0.352471i
\(800\) 0.931521 0.0329343
\(801\) 0 0
\(802\) 6.30972 0.222804
\(803\) −3.40263 + 5.89352i −0.120076 + 0.207978i
\(804\) 0 0
\(805\) 0.354473 + 0.613964i 0.0124935 + 0.0216394i
\(806\) −2.86333 4.95943i −0.100856 0.174688i
\(807\) 0 0
\(808\) −9.29893 + 16.1062i −0.327135 + 0.566615i
\(809\) 10.8023 0.379790 0.189895 0.981804i \(-0.439185\pi\)
0.189895 + 0.981804i \(0.439185\pi\)
\(810\) 0 0
\(811\) 5.58307 0.196048 0.0980240 0.995184i \(-0.468748\pi\)
0.0980240 + 0.995184i \(0.468748\pi\)
\(812\) −4.98755 + 8.63868i −0.175029 + 0.303158i
\(813\) 0 0
\(814\) 9.89037 + 17.1306i 0.346657 + 0.600428i
\(815\) −23.1050 40.0191i −0.809335 1.40181i
\(816\) 0 0
\(817\) −21.1534 + 36.6388i −0.740064 + 1.28183i
\(818\) −84.4556 −2.95292
\(819\) 0 0
\(820\) 67.3609 2.35234
\(821\) −15.8940 + 27.5292i −0.554703 + 0.960774i 0.443223 + 0.896411i \(0.353835\pi\)
−0.997927 + 0.0643630i \(0.979498\pi\)
\(822\) 0 0
\(823\) 18.0000 + 31.1769i 0.627441 + 1.08676i 0.988063 + 0.154047i \(0.0492308\pi\)
−0.360623 + 0.932712i \(0.617436\pi\)
\(824\) 24.5797 + 42.5732i 0.856273 + 1.48311i
\(825\) 0 0
\(826\) 3.35447 5.81012i 0.116717 0.202160i
\(827\) −15.9224 −0.553675 −0.276837 0.960917i \(-0.589286\pi\)
−0.276837 + 0.960917i \(0.589286\pi\)
\(828\) 0 0
\(829\) 35.4720 1.23199 0.615996 0.787749i \(-0.288754\pi\)
0.615996 + 0.787749i \(0.288754\pi\)
\(830\) −3.01819 + 5.22765i −0.104763 + 0.181455i
\(831\) 0 0
\(832\) 3.66372 + 6.34574i 0.127016 + 0.219999i
\(833\) −0.472958 0.819187i −0.0163870 0.0283832i
\(834\) 0 0
\(835\) −10.9808 + 19.0194i −0.380007 + 0.658192i
\(836\) 74.2000 2.56626
\(837\) 0 0
\(838\) −9.98229 −0.344833
\(839\) −27.3391 + 47.3527i −0.943850 + 1.63480i −0.185814 + 0.982585i \(0.559492\pi\)
−0.758037 + 0.652212i \(0.773841\pi\)
\(840\) 0 0
\(841\) 11.4730 + 19.8717i 0.395619 + 0.685233i
\(842\) 25.9200 + 44.8948i 0.893263 + 1.54718i
\(843\) 0 0
\(844\) −9.24630 + 16.0151i −0.318271 + 0.551261i
\(845\) −31.1230 −1.07066
\(846\) 0 0
\(847\) −9.38151 −0.322353
\(848\) −13.5737 + 23.5104i −0.466124 + 0.807350i
\(849\) 0 0
\(850\) −2.00933 3.48027i −0.0689196 0.119372i
\(851\) −0.243379 0.421545i −0.00834292 0.0144504i
\(852\) 0 0
\(853\) 1.09884 1.90324i 0.0376234 0.0651656i −0.846601 0.532229i \(-0.821355\pi\)
0.884224 + 0.467063i \(0.154688\pi\)
\(854\) 5.59358 0.191408
\(855\) 0 0
\(856\) 6.94592 0.237407
\(857\) −7.88823 + 13.6628i −0.269457 + 0.466713i −0.968722 0.248150i \(-0.920178\pi\)
0.699265 + 0.714863i \(0.253511\pi\)
\(858\) 0 0
\(859\) −2.78813 4.82918i −0.0951298 0.164770i 0.814533 0.580117i \(-0.196993\pi\)
−0.909663 + 0.415348i \(0.863660\pi\)
\(860\) 54.8630 + 95.0255i 1.87081 + 3.24034i
\(861\) 0 0
\(862\) 27.8264 48.1968i 0.947773 1.64159i
\(863\) −23.1268 −0.787247 −0.393623 0.919272i \(-0.628779\pi\)
−0.393623 + 0.919272i \(0.628779\pi\)
\(864\) 0 0
\(865\) −45.0157 −1.53058
\(866\) −2.97462 + 5.15218i −0.101082 + 0.175078i
\(867\) 0 0
\(868\) 4.71780 + 8.17147i 0.160133 + 0.277358i
\(869\) 33.2024 + 57.5083i 1.12631 + 1.95083i
\(870\) 0 0
\(871\) 7.90856 13.6980i 0.267971 0.464140i
\(872\) −17.1800 −0.581787
\(873\) 0 0
\(874\) −2.72665 −0.0922304
\(875\) −4.24484 + 7.35228i −0.143502 + 0.248552i
\(876\) 0 0
\(877\) −1.96264 3.39939i −0.0662737 0.114789i 0.830985 0.556295i \(-0.187778\pi\)
−0.897258 + 0.441506i \(0.854444\pi\)
\(878\) 28.8982 + 50.0532i 0.975268 + 1.68921i
\(879\) 0 0
\(880\) 25.3348 43.8812i 0.854037 1.47923i
\(881\) −27.1986 −0.916345 −0.458173 0.888863i \(-0.651496\pi\)
−0.458173 + 0.888863i \(0.651496\pi\)
\(882\) 0 0
\(883\) 8.21341 0.276403 0.138202 0.990404i \(-0.455868\pi\)
0.138202 + 0.990404i \(0.455868\pi\)
\(884\) −1.91741 + 3.32105i −0.0644895 + 0.111699i
\(885\) 0 0
\(886\) −16.5074 28.5916i −0.554577 0.960555i
\(887\) −3.24057 5.61283i −0.108808 0.188460i 0.806480 0.591262i \(-0.201370\pi\)
−0.915287 + 0.402801i \(0.868037\pi\)
\(888\) 0 0
\(889\) 0.336285 0.582462i 0.0112786 0.0195352i
\(890\) 91.6169 3.07101
\(891\) 0 0
\(892\) 54.0187 1.80868
\(893\) 24.6534 42.7009i 0.824995 1.42893i
\(894\) 0 0
\(895\) −14.7178 25.4920i −0.491962 0.852103i
\(896\) −9.55408 16.5482i −0.319180 0.552835i
\(897\) 0 0
\(898\) −11.2719 + 19.5235i −0.376148 + 0.651507i
\(899\) −5.72665 −0.190995
\(900\) 0 0
\(901\) 5.93406 0.197692
\(902\) 35.5818 61.6295i 1.18474 2.05204i
\(903\) 0 0
\(904\) 26.2527 + 45.4710i 0.873152 + 1.51234i
\(905\) −28.3853 49.1648i −0.943560 1.63429i
\(906\) 0 0
\(907\) −5.06440 + 8.77180i −0.168161 + 0.291263i −0.937773 0.347248i \(-0.887116\pi\)
0.769613 + 0.638511i \(0.220449\pi\)
\(908\) −5.60078 −0.185868
\(909\) 0 0
\(910\) −6.38151 −0.211545
\(911\) 22.9612 39.7699i 0.760738 1.31764i −0.181733 0.983348i \(-0.558171\pi\)
0.942471 0.334289i \(-0.108496\pi\)
\(912\) 0 0
\(913\) 2.13521 + 3.69829i 0.0706652 + 0.122396i
\(914\) −10.8473 18.7880i −0.358796 0.621453i
\(915\) 0 0
\(916\) 36.4449 63.1245i 1.20417 2.08569i
\(917\) 7.91381 0.261337
\(918\) 0 0
\(919\) −4.92432 −0.162438 −0.0812192 0.996696i \(-0.525881\pi\)
−0.0812192 + 0.996696i \(0.525881\pi\)
\(920\) −1.79153 + 3.10303i −0.0590651 + 0.102304i
\(921\) 0 0
\(922\) −6.96216 12.0588i −0.229287 0.397136i
\(923\) 1.63667 + 2.83480i 0.0538718 + 0.0933086i
\(924\) 0 0
\(925\) −1.53736 + 2.66278i −0.0505481 + 0.0875518i
\(926\) 38.6955 1.27161
\(927\) 0 0
\(928\) −1.32743 −0.0435750
\(929\) 0.00379324 0.00657009i 0.000124452 0.000215558i −0.865963 0.500108i \(-0.833294\pi\)
0.866088 + 0.499892i \(0.166627\pi\)
\(930\) 0 0
\(931\) 2.02704 + 3.51094i 0.0664336 + 0.115066i
\(932\) −38.4779 66.6457i −1.26039 2.18305i
\(933\) 0 0
\(934\) −27.0620 + 46.8727i −0.885494 + 1.53372i
\(935\) −11.0757 −0.362213
\(936\) 0 0
\(937\) 21.1623 0.691341 0.345670 0.938356i \(-0.387652\pi\)
0.345670 + 0.938356i \(0.387652\pi\)
\(938\) −19.4590 + 33.7040i −0.635360 + 1.10048i
\(939\) 0 0
\(940\) −63.9405 110.748i −2.08551 3.61221i
\(941\) 2.27908 + 3.94748i 0.0742959 + 0.128684i 0.900780 0.434276i \(-0.142996\pi\)
−0.826484 + 0.562960i \(0.809662\pi\)
\(942\) 0 0
\(943\) −0.875585 + 1.51656i −0.0285130 + 0.0493859i
\(944\) 11.7994 0.384038
\(945\) 0 0
\(946\) 115.920 3.76890
\(947\) 6.86760 11.8950i 0.223167 0.386537i −0.732601 0.680658i \(-0.761694\pi\)
0.955768 + 0.294122i \(0.0950271\pi\)
\(948\) 0 0
\(949\) 0.753696 + 1.30544i 0.0244660 + 0.0423764i
\(950\) 8.61177 + 14.9160i 0.279403 + 0.483940i
\(951\) 0 0
\(952\) 2.39037 4.14024i 0.0774723 0.134186i
\(953\) −8.80699 −0.285286 −0.142643 0.989774i \(-0.545560\pi\)
−0.142643 + 0.989774i \(0.545560\pi\)
\(954\) 0 0
\(955\) 1.82004 0.0588951
\(956\) 9.91595 17.1749i 0.320705 0.555477i
\(957\) 0 0
\(958\) 30.7257 + 53.2184i 0.992701 + 1.71941i
\(959\) 1.83628 + 3.18054i 0.0592967 + 0.102705i
\(960\) 0 0
\(961\) 12.7915 22.1556i 0.412630 0.714696i
\(962\) 4.38151 0.141266
\(963\) 0 0
\(964\) −106.052 −3.41571
\(965\) −15.7489 + 27.2779i −0.506976 + 0.878108i
\(966\) 0 0
\(967\) −19.1642 33.1934i −0.616279 1.06743i −0.990159 0.139949i \(-0.955306\pi\)
0.373880 0.927477i \(-0.378027\pi\)
\(968\) −23.7075 41.0626i −0.761987 1.31980i
\(969\) 0 0
\(970\) 36.6608 63.4984i 1.17711 2.03881i
\(971\) 31.0187 0.995436 0.497718 0.867339i \(-0.334171\pi\)
0.497718 + 0.867339i \(0.334171\pi\)
\(972\) 0 0
\(973\) 2.05408 0.0658509
\(974\) 21.6498 37.4986i 0.693704 1.20153i
\(975\) 0 0
\(976\) 4.91887 + 8.51974i 0.157449 + 0.272710i
\(977\) −26.3712 45.6763i −0.843689 1.46131i −0.886755 0.462241i \(-0.847046\pi\)
0.0430652 0.999072i \(-0.486288\pi\)
\(978\) 0 0
\(979\) 32.4071 56.1307i 1.03574 1.79395i
\(980\) 10.5146 0.335876
\(981\) 0 0
\(982\) −33.9430 −1.08316
\(983\) −9.15146 + 15.8508i −0.291886 + 0.505562i −0.974256 0.225446i \(-0.927616\pi\)
0.682370 + 0.731007i \(0.260950\pi\)
\(984\) 0 0
\(985\) −21.2812 36.8601i −0.678076 1.17446i
\(986\) 2.86333 + 4.95943i 0.0911869 + 0.157940i
\(987\) 0 0
\(988\) 8.21780 14.2336i 0.261443 0.452833i
\(989\) −2.85253 −0.0907052
\(990\) 0 0
\(991\) −12.6008 −0.400277 −0.200138 0.979768i \(-0.564139\pi\)
−0.200138 + 0.979768i \(0.564139\pi\)
\(992\) −0.627819 + 1.08741i −0.0199333 + 0.0345254i
\(993\) 0 0
\(994\) −4.02704 6.97504i −0.127730 0.221235i
\(995\) −29.4449 51.0001i −0.933467 1.61681i
\(996\) 0 0
\(997\) −5.87120 + 10.1692i −0.185943 + 0.322062i −0.943894 0.330249i \(-0.892867\pi\)
0.757951 + 0.652311i \(0.226201\pi\)
\(998\) 32.2019 1.01933
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 189.2.f.a.127.1 6
3.2 odd 2 63.2.f.b.43.3 yes 6
4.3 odd 2 3024.2.r.g.2017.2 6
7.2 even 3 1323.2.h.d.802.3 6
7.3 odd 6 1323.2.g.b.667.1 6
7.4 even 3 1323.2.g.c.667.1 6
7.5 odd 6 1323.2.h.e.802.3 6
7.6 odd 2 1323.2.f.c.883.1 6
9.2 odd 6 567.2.a.d.1.1 3
9.4 even 3 inner 189.2.f.a.64.1 6
9.5 odd 6 63.2.f.b.22.3 6
9.7 even 3 567.2.a.g.1.3 3
12.11 even 2 1008.2.r.k.673.3 6
21.2 odd 6 441.2.h.c.214.1 6
21.5 even 6 441.2.h.b.214.1 6
21.11 odd 6 441.2.g.e.79.3 6
21.17 even 6 441.2.g.d.79.3 6
21.20 even 2 441.2.f.d.295.3 6
36.7 odd 6 9072.2.a.cd.1.2 3
36.11 even 6 9072.2.a.bq.1.2 3
36.23 even 6 1008.2.r.k.337.3 6
36.31 odd 6 3024.2.r.g.1009.2 6
63.4 even 3 1323.2.h.d.226.3 6
63.5 even 6 441.2.g.d.67.3 6
63.13 odd 6 1323.2.f.c.442.1 6
63.20 even 6 3969.2.a.m.1.1 3
63.23 odd 6 441.2.g.e.67.3 6
63.31 odd 6 1323.2.h.e.226.3 6
63.32 odd 6 441.2.h.c.373.1 6
63.34 odd 6 3969.2.a.p.1.3 3
63.40 odd 6 1323.2.g.b.361.1 6
63.41 even 6 441.2.f.d.148.3 6
63.58 even 3 1323.2.g.c.361.1 6
63.59 even 6 441.2.h.b.373.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.f.b.22.3 6 9.5 odd 6
63.2.f.b.43.3 yes 6 3.2 odd 2
189.2.f.a.64.1 6 9.4 even 3 inner
189.2.f.a.127.1 6 1.1 even 1 trivial
441.2.f.d.148.3 6 63.41 even 6
441.2.f.d.295.3 6 21.20 even 2
441.2.g.d.67.3 6 63.5 even 6
441.2.g.d.79.3 6 21.17 even 6
441.2.g.e.67.3 6 63.23 odd 6
441.2.g.e.79.3 6 21.11 odd 6
441.2.h.b.214.1 6 21.5 even 6
441.2.h.b.373.1 6 63.59 even 6
441.2.h.c.214.1 6 21.2 odd 6
441.2.h.c.373.1 6 63.32 odd 6
567.2.a.d.1.1 3 9.2 odd 6
567.2.a.g.1.3 3 9.7 even 3
1008.2.r.k.337.3 6 36.23 even 6
1008.2.r.k.673.3 6 12.11 even 2
1323.2.f.c.442.1 6 63.13 odd 6
1323.2.f.c.883.1 6 7.6 odd 2
1323.2.g.b.361.1 6 63.40 odd 6
1323.2.g.b.667.1 6 7.3 odd 6
1323.2.g.c.361.1 6 63.58 even 3
1323.2.g.c.667.1 6 7.4 even 3
1323.2.h.d.226.3 6 63.4 even 3
1323.2.h.d.802.3 6 7.2 even 3
1323.2.h.e.226.3 6 63.31 odd 6
1323.2.h.e.802.3 6 7.5 odd 6
3024.2.r.g.1009.2 6 36.31 odd 6
3024.2.r.g.2017.2 6 4.3 odd 2
3969.2.a.m.1.1 3 63.20 even 6
3969.2.a.p.1.3 3 63.34 odd 6
9072.2.a.bq.1.2 3 36.11 even 6
9072.2.a.cd.1.2 3 36.7 odd 6