Properties

Label 637.2.q.f.589.1
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
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] = [637,2,Mod(491,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.491");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - x^{2} - 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 589.1
Root \(1.39564 - 0.228425i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.f.491.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.395644 - 0.228425i) q^{2} +(1.39564 - 2.41733i) q^{3} +(-0.895644 - 1.55130i) q^{4} -0.456850i q^{5} +(-1.10436 + 0.637600i) q^{6} +1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})\) \(q+(-0.395644 - 0.228425i) q^{2} +(1.39564 - 2.41733i) q^{3} +(-0.895644 - 1.55130i) q^{4} -0.456850i q^{5} +(-1.10436 + 0.637600i) q^{6} +1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +(-0.104356 + 0.180750i) q^{10} +(-3.39564 - 1.96048i) q^{11} -5.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} +(-1.10436 - 0.637600i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(1.50000 + 2.59808i) q^{17} +2.18890i q^{18} +(-1.18693 + 0.685275i) q^{19} +(-0.708712 + 0.409175i) q^{20} +(0.895644 + 1.55130i) q^{22} +(0.791288 - 1.37055i) q^{23} +(4.18693 + 2.41733i) q^{24} +4.79129 q^{25} +(1.58258 + 0.456850i) q^{26} -5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} +(0.291288 + 0.504525i) q^{30} -8.66025i q^{31} +(4.10436 - 2.36965i) q^{32} +(-9.47822 + 5.47225i) q^{33} -1.37055i q^{34} +(-4.29129 + 7.43273i) q^{36} +(6.00000 + 3.46410i) q^{37} +0.626136 q^{38} +(-2.79129 + 9.66930i) q^{39} +0.791288 q^{40} +(-6.79129 - 3.92095i) q^{41} +(-4.68693 - 8.11800i) q^{43} +7.02355i q^{44} +(-1.89564 + 1.09445i) q^{45} +(-0.626136 + 0.361500i) q^{46} +9.57395i q^{47} +(3.89564 + 6.74745i) q^{48} +(-1.89564 - 1.09445i) q^{50} +8.37386 q^{51} +(4.47822 + 4.65390i) q^{52} +6.16515 q^{53} +(1.97822 + 1.14213i) q^{54} +(-0.895644 + 1.55130i) q^{55} +3.82560i q^{57} +(-2.68693 + 1.55130i) q^{58} +(-10.6652 + 6.15753i) q^{59} +2.28425i q^{60} +(-7.37386 - 12.7719i) q^{61} +(-1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(0.395644 + 1.59898i) q^{65} +5.00000 q^{66} +(-3.87386 - 2.23658i) q^{67} +(2.68693 - 4.65390i) q^{68} +(-2.20871 - 3.82560i) q^{69} +(3.79129 - 2.18890i) q^{71} +(7.18693 - 4.14938i) q^{72} +3.46410i q^{73} +(-1.58258 - 2.74110i) q^{74} +(6.68693 - 11.5821i) q^{75} +(2.12614 + 1.22753i) q^{76} +(3.31307 - 3.18800i) q^{78} -6.00000 q^{79} +(1.10436 + 0.637600i) q^{80} +(0.208712 - 0.361500i) q^{81} +(1.79129 + 3.10260i) q^{82} +7.02355i q^{83} +(1.18693 - 0.685275i) q^{85} +4.28245i q^{86} +(-9.47822 - 16.4168i) q^{87} +(3.39564 - 5.88143i) q^{88} +(13.9782 + 8.07033i) q^{89} +1.00000 q^{90} -2.83485 q^{92} +(-20.9347 - 12.0866i) q^{93} +(2.18693 - 3.78788i) q^{94} +(0.313068 + 0.542250i) q^{95} -13.2288i q^{96} +(6.31307 - 3.64485i) q^{97} +18.7864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + q^{3} + q^{4} - 9 q^{6} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} + q^{3} + q^{4} - 9 q^{6} - 5 q^{9} - 5 q^{10} - 9 q^{11} - 20 q^{12} - 14 q^{13} - 9 q^{15} - q^{16} + 6 q^{17} + 9 q^{19} - 12 q^{20} - q^{22} - 6 q^{23} + 3 q^{24} + 10 q^{25} - 12 q^{26} - 20 q^{27} + 9 q^{29} - 8 q^{30} + 21 q^{32} - 15 q^{33} - 8 q^{36} + 24 q^{37} + 30 q^{38} - 2 q^{39} - 6 q^{40} - 18 q^{41} - 5 q^{43} - 3 q^{45} - 30 q^{46} + 11 q^{48} - 3 q^{50} + 6 q^{51} - 5 q^{52} - 12 q^{53} - 15 q^{54} + q^{55} + 3 q^{58} - 6 q^{59} - 2 q^{61} + 15 q^{62} + 32 q^{64} - 3 q^{65} + 20 q^{66} + 12 q^{67} - 3 q^{68} - 18 q^{69} + 6 q^{71} + 15 q^{72} + 12 q^{74} + 13 q^{75} + 36 q^{76} + 27 q^{78} - 24 q^{79} + 9 q^{80} + 10 q^{81} - 2 q^{82} - 9 q^{85} - 15 q^{87} + 9 q^{88} + 33 q^{89} + 4 q^{90} - 48 q^{92} - 15 q^{93} - 5 q^{94} + 15 q^{95} + 39 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.395644 0.228425i −0.279763 0.161521i 0.353553 0.935414i \(-0.384973\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 1.39564 2.41733i 0.805775 1.39564i −0.109991 0.993933i \(-0.535082\pi\)
0.915766 0.401711i \(-0.131584\pi\)
\(4\) −0.895644 1.55130i −0.447822 0.775650i
\(5\) 0.456850i 0.204310i −0.994769 0.102155i \(-0.967426\pi\)
0.994769 0.102155i \(-0.0325737\pi\)
\(6\) −1.10436 + 0.637600i −0.450851 + 0.260299i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) −2.39564 4.14938i −0.798548 1.38313i
\(10\) −0.104356 + 0.180750i −0.0330003 + 0.0571582i
\(11\) −3.39564 1.96048i −1.02383 0.591106i −0.108616 0.994084i \(-0.534642\pi\)
−0.915210 + 0.402978i \(0.867975\pi\)
\(12\) −5.00000 −1.44338
\(13\) −3.50000 + 0.866025i −0.970725 + 0.240192i
\(14\) 0 0
\(15\) −1.10436 0.637600i −0.285144 0.164628i
\(16\) −1.39564 + 2.41733i −0.348911 + 0.604332i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 2.18890i 0.515929i
\(19\) −1.18693 + 0.685275i −0.272301 + 0.157213i −0.629933 0.776650i \(-0.716918\pi\)
0.357632 + 0.933863i \(0.383584\pi\)
\(20\) −0.708712 + 0.409175i −0.158473 + 0.0914943i
\(21\) 0 0
\(22\) 0.895644 + 1.55130i 0.190952 + 0.330738i
\(23\) 0.791288 1.37055i 0.164995 0.285780i −0.771659 0.636037i \(-0.780573\pi\)
0.936653 + 0.350257i \(0.113906\pi\)
\(24\) 4.18693 + 2.41733i 0.854654 + 0.493435i
\(25\) 4.79129 0.958258
\(26\) 1.58258 + 0.456850i 0.310369 + 0.0895957i
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 3.39564 5.88143i 0.630555 1.09215i −0.356883 0.934149i \(-0.616161\pi\)
0.987438 0.158005i \(-0.0505061\pi\)
\(30\) 0.291288 + 0.504525i 0.0531816 + 0.0921133i
\(31\) 8.66025i 1.55543i −0.628619 0.777714i \(-0.716379\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) 4.10436 2.36965i 0.725555 0.418899i
\(33\) −9.47822 + 5.47225i −1.64995 + 0.952597i
\(34\) 1.37055i 0.235048i
\(35\) 0 0
\(36\) −4.29129 + 7.43273i −0.715215 + 1.23879i
\(37\) 6.00000 + 3.46410i 0.986394 + 0.569495i 0.904194 0.427121i \(-0.140472\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0.626136 0.101573
\(39\) −2.79129 + 9.66930i −0.446964 + 1.54833i
\(40\) 0.791288 0.125114
\(41\) −6.79129 3.92095i −1.06062 0.612350i −0.135017 0.990843i \(-0.543109\pi\)
−0.925604 + 0.378493i \(0.876442\pi\)
\(42\) 0 0
\(43\) −4.68693 8.11800i −0.714750 1.23798i −0.963056 0.269302i \(-0.913207\pi\)
0.248305 0.968682i \(-0.420126\pi\)
\(44\) 7.02355i 1.05884i
\(45\) −1.89564 + 1.09445i −0.282586 + 0.163151i
\(46\) −0.626136 + 0.361500i −0.0923188 + 0.0533003i
\(47\) 9.57395i 1.39650i 0.715852 + 0.698252i \(0.246039\pi\)
−0.715852 + 0.698252i \(0.753961\pi\)
\(48\) 3.89564 + 6.74745i 0.562288 + 0.973911i
\(49\) 0 0
\(50\) −1.89564 1.09445i −0.268085 0.154779i
\(51\) 8.37386 1.17258
\(52\) 4.47822 + 4.65390i 0.621017 + 0.645380i
\(53\) 6.16515 0.846849 0.423424 0.905931i \(-0.360828\pi\)
0.423424 + 0.905931i \(0.360828\pi\)
\(54\) 1.97822 + 1.14213i 0.269202 + 0.155424i
\(55\) −0.895644 + 1.55130i −0.120769 + 0.209177i
\(56\) 0 0
\(57\) 3.82560i 0.506713i
\(58\) −2.68693 + 1.55130i −0.352811 + 0.203696i
\(59\) −10.6652 + 6.15753i −1.38848 + 0.801642i −0.993145 0.116893i \(-0.962707\pi\)
−0.395340 + 0.918535i \(0.629373\pi\)
\(60\) 2.28425i 0.294896i
\(61\) −7.37386 12.7719i −0.944126 1.63528i −0.757491 0.652846i \(-0.773575\pi\)
−0.186636 0.982429i \(-0.559758\pi\)
\(62\) −1.97822 + 3.42638i −0.251234 + 0.435150i
\(63\) 0 0
\(64\) 3.41742 0.427178
\(65\) 0.395644 + 1.59898i 0.0490736 + 0.198329i
\(66\) 5.00000 0.615457
\(67\) −3.87386 2.23658i −0.473268 0.273241i 0.244339 0.969690i \(-0.421429\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 2.68693 4.65390i 0.325838 0.564369i
\(69\) −2.20871 3.82560i −0.265898 0.460548i
\(70\) 0 0
\(71\) 3.79129 2.18890i 0.449943 0.259775i −0.257863 0.966181i \(-0.583018\pi\)
0.707806 + 0.706407i \(0.249685\pi\)
\(72\) 7.18693 4.14938i 0.846988 0.489009i
\(73\) 3.46410i 0.405442i 0.979236 + 0.202721i \(0.0649785\pi\)
−0.979236 + 0.202721i \(0.935021\pi\)
\(74\) −1.58258 2.74110i −0.183971 0.318647i
\(75\) 6.68693 11.5821i 0.772140 1.33739i
\(76\) 2.12614 + 1.22753i 0.243885 + 0.140807i
\(77\) 0 0
\(78\) 3.31307 3.18800i 0.375131 0.360970i
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) 1.10436 + 0.637600i 0.123471 + 0.0712859i
\(81\) 0.208712 0.361500i 0.0231902 0.0401667i
\(82\) 1.79129 + 3.10260i 0.197815 + 0.342625i
\(83\) 7.02355i 0.770935i 0.922721 + 0.385468i \(0.125960\pi\)
−0.922721 + 0.385468i \(0.874040\pi\)
\(84\) 0 0
\(85\) 1.18693 0.685275i 0.128741 0.0743286i
\(86\) 4.28245i 0.461789i
\(87\) −9.47822 16.4168i −1.01617 1.76006i
\(88\) 3.39564 5.88143i 0.361977 0.626962i
\(89\) 13.9782 + 8.07033i 1.48169 + 0.855453i 0.999784 0.0207708i \(-0.00661204\pi\)
0.481904 + 0.876224i \(0.339945\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) −2.83485 −0.295553
\(93\) −20.9347 12.0866i −2.17082 1.25333i
\(94\) 2.18693 3.78788i 0.225565 0.390690i
\(95\) 0.313068 + 0.542250i 0.0321201 + 0.0556337i
\(96\) 13.2288i 1.35015i
\(97\) 6.31307 3.64485i 0.640995 0.370079i −0.144003 0.989577i \(-0.545997\pi\)
0.784998 + 0.619499i \(0.212664\pi\)
\(98\) 0 0
\(99\) 18.7864i 1.88811i
\(100\) −4.29129 7.43273i −0.429129 0.743273i
\(101\) 2.60436 4.51088i 0.259143 0.448849i −0.706869 0.707344i \(-0.749893\pi\)
0.966013 + 0.258495i \(0.0832265\pi\)
\(102\) −3.31307 1.91280i −0.328043 0.189396i
\(103\) −4.58258 −0.451535 −0.225767 0.974181i \(-0.572489\pi\)
−0.225767 + 0.974181i \(0.572489\pi\)
\(104\) −1.50000 6.06218i −0.147087 0.594445i
\(105\) 0 0
\(106\) −2.43920 1.40828i −0.236917 0.136784i
\(107\) 2.60436 4.51088i 0.251773 0.436083i −0.712241 0.701935i \(-0.752320\pi\)
0.964014 + 0.265852i \(0.0856532\pi\)
\(108\) 4.47822 + 7.75650i 0.430917 + 0.746370i
\(109\) 7.93725i 0.760251i −0.924935 0.380126i \(-0.875881\pi\)
0.924935 0.380126i \(-0.124119\pi\)
\(110\) 0.708712 0.409175i 0.0675731 0.0390133i
\(111\) 16.7477 9.66930i 1.58962 0.917770i
\(112\) 0 0
\(113\) −5.29129 9.16478i −0.497762 0.862150i 0.502234 0.864732i \(-0.332512\pi\)
−0.999997 + 0.00258173i \(0.999178\pi\)
\(114\) 0.873864 1.51358i 0.0818448 0.141759i
\(115\) −0.626136 0.361500i −0.0583875 0.0337101i
\(116\) −12.1652 −1.12951
\(117\) 11.9782 + 12.4481i 1.10739 + 1.15083i
\(118\) 5.62614 0.517928
\(119\) 0 0
\(120\) 1.10436 1.91280i 0.100813 0.174614i
\(121\) 2.18693 + 3.78788i 0.198812 + 0.344352i
\(122\) 6.73750i 0.609985i
\(123\) −18.9564 + 10.9445i −1.70924 + 0.986833i
\(124\) −13.4347 + 7.75650i −1.20647 + 0.696555i
\(125\) 4.47315i 0.400091i
\(126\) 0 0
\(127\) −3.47822 + 6.02445i −0.308642 + 0.534584i −0.978066 0.208297i \(-0.933208\pi\)
0.669423 + 0.742881i \(0.266541\pi\)
\(128\) −9.56080 5.51993i −0.845063 0.487897i
\(129\) −26.1652 −2.30371
\(130\) 0.208712 0.723000i 0.0183053 0.0634113i
\(131\) 17.3739 1.51796 0.758981 0.651113i \(-0.225698\pi\)
0.758981 + 0.651113i \(0.225698\pi\)
\(132\) 16.9782 + 9.80238i 1.47776 + 0.853188i
\(133\) 0 0
\(134\) 1.02178 + 1.76978i 0.0882684 + 0.152885i
\(135\) 2.28425i 0.196597i
\(136\) −4.50000 + 2.59808i −0.385872 + 0.222783i
\(137\) 10.3521 5.97678i 0.884438 0.510631i 0.0123190 0.999924i \(-0.496079\pi\)
0.872119 + 0.489294i \(0.162745\pi\)
\(138\) 2.01810i 0.171792i
\(139\) 1.89564 + 3.28335i 0.160786 + 0.278490i 0.935151 0.354249i \(-0.115264\pi\)
−0.774365 + 0.632740i \(0.781930\pi\)
\(140\) 0 0
\(141\) 23.1434 + 13.3618i 1.94902 + 1.12527i
\(142\) −2.00000 −0.167836
\(143\) 13.5826 + 3.92095i 1.13583 + 0.327886i
\(144\) 13.3739 1.11449
\(145\) −2.68693 1.55130i −0.223138 0.128829i
\(146\) 0.791288 1.37055i 0.0654874 0.113428i
\(147\) 0 0
\(148\) 12.4104i 1.02013i
\(149\) −0.395644 + 0.228425i −0.0324124 + 0.0187133i −0.516119 0.856517i \(-0.672624\pi\)
0.483706 + 0.875230i \(0.339290\pi\)
\(150\) −5.29129 + 3.05493i −0.432032 + 0.249434i
\(151\) 12.1244i 0.986666i −0.869841 0.493333i \(-0.835778\pi\)
0.869841 0.493333i \(-0.164222\pi\)
\(152\) −1.18693 2.05583i −0.0962729 0.166750i
\(153\) 7.18693 12.4481i 0.581029 1.00637i
\(154\) 0 0
\(155\) −3.95644 −0.317789
\(156\) 17.5000 4.33013i 1.40112 0.346688i
\(157\) 0.956439 0.0763322 0.0381661 0.999271i \(-0.487848\pi\)
0.0381661 + 0.999271i \(0.487848\pi\)
\(158\) 2.37386 + 1.37055i 0.188854 + 0.109035i
\(159\) 8.60436 14.9032i 0.682370 1.18190i
\(160\) −1.08258 1.87508i −0.0855851 0.148238i
\(161\) 0 0
\(162\) −0.165151 + 0.0953502i −0.0129755 + 0.00749142i
\(163\) 6.00000 3.46410i 0.469956 0.271329i −0.246265 0.969202i \(-0.579203\pi\)
0.716221 + 0.697873i \(0.245870\pi\)
\(164\) 14.0471i 1.09689i
\(165\) 2.50000 + 4.33013i 0.194625 + 0.337100i
\(166\) 1.60436 2.77883i 0.124522 0.215679i
\(167\) −12.7087 7.33738i −0.983430 0.567783i −0.0801258 0.996785i \(-0.525532\pi\)
−0.903304 + 0.429001i \(0.858866\pi\)
\(168\) 0 0
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) −0.626136 −0.0480225
\(171\) 5.68693 + 3.28335i 0.434891 + 0.251084i
\(172\) −8.39564 + 14.5417i −0.640162 + 1.10879i
\(173\) 9.87386 + 17.1020i 0.750696 + 1.30024i 0.947486 + 0.319798i \(0.103615\pi\)
−0.196790 + 0.980446i \(0.563052\pi\)
\(174\) 8.66025i 0.656532i
\(175\) 0 0
\(176\) 9.47822 5.47225i 0.714448 0.412487i
\(177\) 34.3749i 2.58377i
\(178\) −3.68693 6.38595i −0.276347 0.478647i
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) 3.39564 + 1.96048i 0.253096 + 0.146125i
\(181\) 9.16515 0.681240 0.340620 0.940201i \(-0.389363\pi\)
0.340620 + 0.940201i \(0.389363\pi\)
\(182\) 0 0
\(183\) −41.1652 −3.04302
\(184\) 2.37386 + 1.37055i 0.175004 + 0.101038i
\(185\) 1.58258 2.74110i 0.116353 0.201530i
\(186\) 5.52178 + 9.56400i 0.404877 + 0.701267i
\(187\) 11.7629i 0.860185i
\(188\) 14.8521 8.57485i 1.08320 0.625386i
\(189\) 0 0
\(190\) 0.286051i 0.0207523i
\(191\) 7.18693 + 12.4481i 0.520028 + 0.900715i 0.999729 + 0.0232830i \(0.00741188\pi\)
−0.479701 + 0.877432i \(0.659255\pi\)
\(192\) 4.76951 8.26103i 0.344210 0.596188i
\(193\) 16.7477 + 9.66930i 1.20553 + 0.696012i 0.961779 0.273827i \(-0.0882895\pi\)
0.243749 + 0.969838i \(0.421623\pi\)
\(194\) −3.33030 −0.239102
\(195\) 4.41742 + 1.27520i 0.316338 + 0.0913190i
\(196\) 0 0
\(197\) 1.97822 + 1.14213i 0.140942 + 0.0813731i 0.568813 0.822467i \(-0.307403\pi\)
−0.427871 + 0.903840i \(0.640736\pi\)
\(198\) 4.29129 7.43273i 0.304969 0.528221i
\(199\) −5.50000 9.52628i −0.389885 0.675300i 0.602549 0.798082i \(-0.294152\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 8.29875i 0.586811i
\(201\) −10.8131 + 6.24293i −0.762695 + 0.440342i
\(202\) −2.06080 + 1.18980i −0.144997 + 0.0837141i
\(203\) 0 0
\(204\) −7.50000 12.9904i −0.525105 0.909509i
\(205\) −1.79129 + 3.10260i −0.125109 + 0.216695i
\(206\) 1.81307 + 1.04678i 0.126322 + 0.0729323i
\(207\) −7.58258 −0.527025
\(208\) 2.79129 9.66930i 0.193541 0.670446i
\(209\) 5.37386 0.371718
\(210\) 0 0
\(211\) −5.29129 + 9.16478i −0.364267 + 0.630929i −0.988658 0.150183i \(-0.952014\pi\)
0.624391 + 0.781112i \(0.285347\pi\)
\(212\) −5.52178 9.56400i −0.379237 0.656859i
\(213\) 12.2197i 0.837280i
\(214\) −2.06080 + 1.18980i −0.140873 + 0.0813331i
\(215\) −3.70871 + 2.14123i −0.252932 + 0.146030i
\(216\) 8.66025i 0.589256i
\(217\) 0 0
\(218\) −1.81307 + 3.14033i −0.122796 + 0.212690i
\(219\) 8.37386 + 4.83465i 0.565853 + 0.326696i
\(220\) 3.20871 0.216331
\(221\) −7.50000 7.79423i −0.504505 0.524297i
\(222\) −8.83485 −0.592956
\(223\) −16.4347 9.48855i −1.10055 0.635401i −0.164182 0.986430i \(-0.552498\pi\)
−0.936364 + 0.351029i \(0.885832\pi\)
\(224\) 0 0
\(225\) −11.4782 19.8809i −0.765215 1.32539i
\(226\) 4.83465i 0.321596i
\(227\) 7.66515 4.42548i 0.508754 0.293729i −0.223567 0.974688i \(-0.571770\pi\)
0.732321 + 0.680959i \(0.238437\pi\)
\(228\) 5.93466 3.42638i 0.393032 0.226917i
\(229\) 6.92820i 0.457829i 0.973447 + 0.228914i \(0.0735176\pi\)
−0.973447 + 0.228914i \(0.926482\pi\)
\(230\) 0.165151 + 0.286051i 0.0108898 + 0.0188616i
\(231\) 0 0
\(232\) 10.1869 + 5.88143i 0.668805 + 0.386135i
\(233\) 15.9564 1.04534 0.522671 0.852535i \(-0.324936\pi\)
0.522671 + 0.852535i \(0.324936\pi\)
\(234\) −1.89564 7.66115i −0.123922 0.500825i
\(235\) 4.37386 0.285319
\(236\) 19.1044 + 11.0299i 1.24359 + 0.717986i
\(237\) −8.37386 + 14.5040i −0.543941 + 0.942133i
\(238\) 0 0
\(239\) 13.2288i 0.855697i 0.903850 + 0.427849i \(0.140728\pi\)
−0.903850 + 0.427849i \(0.859272\pi\)
\(240\) 3.08258 1.77973i 0.198979 0.114881i
\(241\) −17.0608 + 9.85005i −1.09898 + 0.634498i −0.935954 0.352123i \(-0.885460\pi\)
−0.163029 + 0.986621i \(0.552126\pi\)
\(242\) 1.99820i 0.128449i
\(243\) −8.08258 13.9994i −0.518497 0.898064i
\(244\) −13.2087 + 22.8782i −0.845601 + 1.46462i
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) 3.56080 3.42638i 0.226568 0.218015i
\(248\) 15.0000 0.952501
\(249\) 16.9782 + 9.80238i 1.07595 + 0.621201i
\(250\) −1.02178 + 1.76978i −0.0646231 + 0.111930i
\(251\) 1.41742 + 2.45505i 0.0894670 + 0.154961i 0.907286 0.420514i \(-0.138150\pi\)
−0.817819 + 0.575476i \(0.804817\pi\)
\(252\) 0 0
\(253\) −5.37386 + 3.10260i −0.337852 + 0.195059i
\(254\) 2.75227 1.58903i 0.172693 0.0997043i
\(255\) 3.82560i 0.239568i
\(256\) −0.895644 1.55130i −0.0559777 0.0969563i
\(257\) −2.52178 + 4.36785i −0.157304 + 0.272459i −0.933896 0.357546i \(-0.883614\pi\)
0.776591 + 0.630005i \(0.216947\pi\)
\(258\) 10.3521 + 5.97678i 0.644493 + 0.372098i
\(259\) 0 0
\(260\) 2.12614 2.04588i 0.131857 0.126880i
\(261\) −32.5390 −2.01411
\(262\) −6.87386 3.96863i −0.424669 0.245183i
\(263\) −4.66515 + 8.08028i −0.287666 + 0.498251i −0.973252 0.229740i \(-0.926212\pi\)
0.685587 + 0.727991i \(0.259546\pi\)
\(264\) −9.47822 16.4168i −0.583344 1.01038i
\(265\) 2.81655i 0.173019i
\(266\) 0 0
\(267\) 39.0172 22.5266i 2.38782 1.37861i
\(268\) 8.01270i 0.489454i
\(269\) 7.89564 + 13.6757i 0.481406 + 0.833819i 0.999772 0.0213391i \(-0.00679298\pi\)
−0.518366 + 0.855159i \(0.673460\pi\)
\(270\) 0.521780 0.903750i 0.0317545 0.0550005i
\(271\) −11.1261 6.42368i −0.675865 0.390211i 0.122430 0.992477i \(-0.460931\pi\)
−0.798295 + 0.602266i \(0.794264\pi\)
\(272\) −8.37386 −0.507740
\(273\) 0 0
\(274\) −5.46099 −0.329910
\(275\) −16.2695 9.39320i −0.981088 0.566432i
\(276\) −3.95644 + 6.85275i −0.238150 + 0.412487i
\(277\) −5.87386 10.1738i −0.352926 0.611286i 0.633835 0.773469i \(-0.281480\pi\)
−0.986761 + 0.162182i \(0.948147\pi\)
\(278\) 1.73205i 0.103882i
\(279\) −35.9347 + 20.7469i −2.15135 + 1.24208i
\(280\) 0 0
\(281\) 30.6446i 1.82810i 0.405597 + 0.914052i \(0.367064\pi\)
−0.405597 + 0.914052i \(0.632936\pi\)
\(282\) −6.10436 10.5731i −0.363509 0.629616i
\(283\) −1.37386 + 2.37960i −0.0816677 + 0.141453i −0.903966 0.427603i \(-0.859358\pi\)
0.822299 + 0.569056i \(0.192691\pi\)
\(284\) −6.79129 3.92095i −0.402989 0.232666i
\(285\) 1.74773 0.103526
\(286\) −4.47822 4.65390i −0.264803 0.275191i
\(287\) 0 0
\(288\) −19.6652 11.3537i −1.15878 0.669022i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0.708712 + 1.22753i 0.0416170 + 0.0720828i
\(291\) 20.3477i 1.19280i
\(292\) 5.37386 3.10260i 0.314482 0.181566i
\(293\) 2.20871 1.27520i 0.129034 0.0744980i −0.434093 0.900868i \(-0.642931\pi\)
0.563128 + 0.826370i \(0.309598\pi\)
\(294\) 0 0
\(295\) 2.81307 + 4.87238i 0.163783 + 0.283681i
\(296\) −6.00000 + 10.3923i −0.348743 + 0.604040i
\(297\) 16.9782 + 9.80238i 0.985176 + 0.568792i
\(298\) 0.208712 0.0120904
\(299\) −1.58258 + 5.48220i −0.0915227 + 0.317044i
\(300\) −23.9564 −1.38313
\(301\) 0 0
\(302\) −2.76951 + 4.79693i −0.159367 + 0.276032i
\(303\) −7.26951 12.5912i −0.417622 0.723343i
\(304\) 3.82560i 0.219413i
\(305\) −5.83485 + 3.36875i −0.334102 + 0.192894i
\(306\) −5.68693 + 3.28335i −0.325100 + 0.187697i
\(307\) 15.5130i 0.885374i 0.896676 + 0.442687i \(0.145975\pi\)
−0.896676 + 0.442687i \(0.854025\pi\)
\(308\) 0 0
\(309\) −6.39564 + 11.0776i −0.363835 + 0.630182i
\(310\) 1.56534 + 0.903750i 0.0889054 + 0.0513296i
\(311\) 26.5390 1.50489 0.752445 0.658655i \(-0.228874\pi\)
0.752445 + 0.658655i \(0.228874\pi\)
\(312\) −16.7477 4.83465i −0.948153 0.273708i
\(313\) −6.74773 −0.381404 −0.190702 0.981648i \(-0.561076\pi\)
−0.190702 + 0.981648i \(0.561076\pi\)
\(314\) −0.378409 0.218475i −0.0213549 0.0123292i
\(315\) 0 0
\(316\) 5.37386 + 9.30780i 0.302303 + 0.523605i
\(317\) 18.5203i 1.04020i −0.854105 0.520101i \(-0.825894\pi\)
0.854105 0.520101i \(-0.174106\pi\)
\(318\) −6.80852 + 3.93090i −0.381803 + 0.220434i
\(319\) −23.0608 + 13.3142i −1.29116 + 0.745450i
\(320\) 1.56125i 0.0872766i
\(321\) −7.26951 12.5912i −0.405744 0.702770i
\(322\) 0 0
\(323\) −3.56080 2.05583i −0.198128 0.114389i
\(324\) −0.747727 −0.0415404
\(325\) −16.7695 + 4.14938i −0.930205 + 0.230166i
\(326\) −3.16515 −0.175302
\(327\) −19.1869 11.0776i −1.06104 0.612592i
\(328\) 6.79129 11.7629i 0.374986 0.649495i
\(329\) 0 0
\(330\) 2.28425i 0.125744i
\(331\) 21.5608 12.4481i 1.18509 0.684211i 0.227902 0.973684i \(-0.426813\pi\)
0.957186 + 0.289473i \(0.0934800\pi\)
\(332\) 10.8956 6.29060i 0.597976 0.345242i
\(333\) 33.1950i 1.81908i
\(334\) 3.35208 + 5.80598i 0.183418 + 0.317689i
\(335\) −1.02178 + 1.76978i −0.0558258 + 0.0966932i
\(336\) 0 0
\(337\) 9.95644 0.542362 0.271181 0.962528i \(-0.412586\pi\)
0.271181 + 0.962528i \(0.412586\pi\)
\(338\) −5.93466 0.228425i −0.322803 0.0124247i
\(339\) −29.5390 −1.60434
\(340\) −2.12614 1.22753i −0.115306 0.0665719i
\(341\) −16.9782 + 29.4071i −0.919422 + 1.59249i
\(342\) −1.50000 2.59808i −0.0811107 0.140488i
\(343\) 0 0
\(344\) 14.0608 8.11800i 0.758107 0.437693i
\(345\) −1.74773 + 1.00905i −0.0940945 + 0.0543255i
\(346\) 9.02175i 0.485013i
\(347\) 6.79129 + 11.7629i 0.364575 + 0.631463i 0.988708 0.149855i \(-0.0478808\pi\)
−0.624132 + 0.781319i \(0.714547\pi\)
\(348\) −16.9782 + 29.4071i −0.910128 + 1.57639i
\(349\) −18.2477 10.5353i −0.976778 0.563943i −0.0754825 0.997147i \(-0.524050\pi\)
−0.901296 + 0.433204i \(0.857383\pi\)
\(350\) 0 0
\(351\) 17.5000 4.33013i 0.934081 0.231125i
\(352\) −18.5826 −0.990455
\(353\) 15.7259 + 9.07938i 0.837008 + 0.483247i 0.856246 0.516568i \(-0.172791\pi\)
−0.0192383 + 0.999815i \(0.506124\pi\)
\(354\) 7.85208 13.6002i 0.417334 0.722843i
\(355\) −1.00000 1.73205i −0.0530745 0.0919277i
\(356\) 28.9126i 1.53236i
\(357\) 0 0
\(358\) −3.56080 + 2.05583i −0.188194 + 0.108654i
\(359\) 0.552200i 0.0291440i −0.999894 0.0145720i \(-0.995361\pi\)
0.999894 0.0145720i \(-0.00463858\pi\)
\(360\) −1.89564 3.28335i −0.0999092 0.173048i
\(361\) −8.56080 + 14.8277i −0.450568 + 0.780407i
\(362\) −3.62614 2.09355i −0.190586 0.110035i
\(363\) 12.2087 0.640791
\(364\) 0 0
\(365\) 1.58258 0.0828358
\(366\) 16.2867 + 9.40315i 0.851322 + 0.491511i
\(367\) 9.00000 15.5885i 0.469796 0.813711i −0.529607 0.848243i \(-0.677661\pi\)
0.999404 + 0.0345320i \(0.0109941\pi\)
\(368\) 2.20871 + 3.82560i 0.115137 + 0.199423i
\(369\) 37.5728i 1.95596i
\(370\) −1.25227 + 0.723000i −0.0651026 + 0.0375870i
\(371\) 0 0
\(372\) 43.3013i 2.24507i
\(373\) −16.1044 27.8936i −0.833852 1.44427i −0.894962 0.446143i \(-0.852797\pi\)
0.0611098 0.998131i \(-0.480536\pi\)
\(374\) −2.68693 + 4.65390i −0.138938 + 0.240648i
\(375\) −10.8131 6.24293i −0.558384 0.322383i
\(376\) −16.5826 −0.855181
\(377\) −6.79129 + 23.5257i −0.349769 + 1.21164i
\(378\) 0 0
\(379\) −24.5608 14.1802i −1.26160 0.728387i −0.288219 0.957565i \(-0.593063\pi\)
−0.973385 + 0.229178i \(0.926396\pi\)
\(380\) 0.560795 0.971326i 0.0287682 0.0498280i
\(381\) 9.70871 + 16.8160i 0.497392 + 0.861509i
\(382\) 6.56670i 0.335982i
\(383\) 1.10436 0.637600i 0.0564300 0.0325799i −0.471520 0.881856i \(-0.656294\pi\)
0.527950 + 0.849276i \(0.322961\pi\)
\(384\) −26.6869 + 15.4077i −1.36186 + 0.786271i
\(385\) 0 0
\(386\) −4.41742 7.65120i −0.224841 0.389436i
\(387\) −22.4564 + 38.8957i −1.14152 + 1.97718i
\(388\) −11.3085 6.52898i −0.574103 0.331459i
\(389\) −0.330303 −0.0167470 −0.00837351 0.999965i \(-0.502665\pi\)
−0.00837351 + 0.999965i \(0.502665\pi\)
\(390\) −1.45644 1.51358i −0.0737497 0.0766429i
\(391\) 4.74773 0.240103
\(392\) 0 0
\(393\) 24.2477 41.9983i 1.22314 2.11853i
\(394\) −0.521780 0.903750i −0.0262869 0.0455303i
\(395\) 2.74110i 0.137920i
\(396\) 29.1434 16.8259i 1.46451 0.845535i
\(397\) 28.1216 16.2360i 1.41138 0.814862i 0.415864 0.909427i \(-0.363479\pi\)
0.995519 + 0.0945652i \(0.0301461\pi\)
\(398\) 5.02535i 0.251898i
\(399\) 0 0
\(400\) −6.68693 + 11.5821i −0.334347 + 0.579105i
\(401\) 27.0998 + 15.6461i 1.35330 + 0.781328i 0.988710 0.149840i \(-0.0478759\pi\)
0.364590 + 0.931168i \(0.381209\pi\)
\(402\) 5.70417 0.284498
\(403\) 7.50000 + 30.3109i 0.373602 + 1.50989i
\(404\) −9.33030 −0.464200
\(405\) −0.165151 0.0953502i −0.00820644 0.00473799i
\(406\) 0 0
\(407\) −13.5826 23.5257i −0.673263 1.16613i
\(408\) 14.5040i 0.718053i
\(409\) 7.18693 4.14938i 0.355371 0.205173i −0.311677 0.950188i \(-0.600891\pi\)
0.667048 + 0.745015i \(0.267557\pi\)
\(410\) 1.41742 0.818350i 0.0700016 0.0404154i
\(411\) 33.3658i 1.64581i
\(412\) 4.10436 + 7.10895i 0.202207 + 0.350233i
\(413\) 0 0
\(414\) 3.00000 + 1.73205i 0.147442 + 0.0851257i
\(415\) 3.20871 0.157509
\(416\) −12.3131 + 11.8483i −0.603698 + 0.580909i
\(417\) 10.5826 0.518231
\(418\) −2.12614 1.22753i −0.103993 0.0600402i
\(419\) 0.873864 1.51358i 0.0426910 0.0739430i −0.843890 0.536516i \(-0.819740\pi\)
0.886581 + 0.462573i \(0.153074\pi\)
\(420\) 0 0
\(421\) 4.18710i 0.204067i 0.994781 + 0.102033i \(0.0325349\pi\)
−0.994781 + 0.102033i \(0.967465\pi\)
\(422\) 4.18693 2.41733i 0.203817 0.117674i
\(423\) 39.7259 22.9358i 1.93154 1.11518i
\(424\) 10.6784i 0.518587i
\(425\) 7.18693 + 12.4481i 0.348617 + 0.603823i
\(426\) −2.79129 + 4.83465i −0.135238 + 0.234240i
\(427\) 0 0
\(428\) −9.33030 −0.450997
\(429\) 28.4347 27.3613i 1.37284 1.32101i
\(430\) 1.95644 0.0943479
\(431\) 30.0172 + 17.3305i 1.44588 + 0.834779i 0.998232 0.0594316i \(-0.0189288\pi\)
0.447647 + 0.894210i \(0.352262\pi\)
\(432\) 6.97822 12.0866i 0.335740 0.581518i
\(433\) 16.2477 + 28.1419i 0.780816 + 1.35241i 0.931467 + 0.363826i \(0.118530\pi\)
−0.150651 + 0.988587i \(0.548137\pi\)
\(434\) 0 0
\(435\) −7.50000 + 4.33013i −0.359597 + 0.207614i
\(436\) −12.3131 + 7.10895i −0.589689 + 0.340457i
\(437\) 2.16900i 0.103757i
\(438\) −2.20871 3.82560i −0.105536 0.182794i
\(439\) 10.2695 17.7873i 0.490137 0.848942i −0.509799 0.860294i \(-0.670280\pi\)
0.999936 + 0.0113518i \(0.00361346\pi\)
\(440\) −2.68693 1.55130i −0.128094 0.0739554i
\(441\) 0 0
\(442\) 1.18693 + 4.79693i 0.0564566 + 0.228167i
\(443\) −15.1652 −0.720518 −0.360259 0.932852i \(-0.617312\pi\)
−0.360259 + 0.932852i \(0.617312\pi\)
\(444\) −30.0000 17.3205i −1.42374 0.821995i
\(445\) 3.68693 6.38595i 0.174777 0.302723i
\(446\) 4.33485 + 7.50818i 0.205261 + 0.355523i
\(447\) 1.27520i 0.0603149i
\(448\) 0 0
\(449\) −21.7913 + 12.5812i −1.02839 + 0.593744i −0.916524 0.399979i \(-0.869017\pi\)
−0.111870 + 0.993723i \(0.535684\pi\)
\(450\) 10.4877i 0.494393i
\(451\) 15.3739 + 26.6283i 0.723927 + 1.25388i
\(452\) −9.47822 + 16.4168i −0.445818 + 0.772179i
\(453\) −29.3085 16.9213i −1.37703 0.795031i
\(454\) −4.04356 −0.189774
\(455\) 0 0
\(456\) −6.62614 −0.310297
\(457\) 19.7477 + 11.4014i 0.923760 + 0.533333i 0.884833 0.465909i \(-0.154273\pi\)
0.0389271 + 0.999242i \(0.487606\pi\)
\(458\) 1.58258 2.74110i 0.0739489 0.128083i
\(459\) −7.50000 12.9904i −0.350070 0.606339i
\(460\) 1.29510i 0.0603844i
\(461\) 4.02178 2.32198i 0.187313 0.108145i −0.403411 0.915019i \(-0.632176\pi\)
0.590724 + 0.806874i \(0.298842\pi\)
\(462\) 0 0
\(463\) 7.93725i 0.368875i 0.982844 + 0.184438i \(0.0590464\pi\)
−0.982844 + 0.184438i \(0.940954\pi\)
\(464\) 9.47822 + 16.4168i 0.440015 + 0.762129i
\(465\) −5.52178 + 9.56400i −0.256066 + 0.443520i
\(466\) −6.31307 3.64485i −0.292447 0.168844i
\(467\) 30.1652 1.39588 0.697938 0.716158i \(-0.254101\pi\)
0.697938 + 0.716158i \(0.254101\pi\)
\(468\) 8.58258 29.7309i 0.396730 1.37431i
\(469\) 0 0
\(470\) −1.73049 0.999100i −0.0798217 0.0460851i
\(471\) 1.33485 2.31203i 0.0615066 0.106533i
\(472\) −10.6652 18.4726i −0.490903 0.850270i
\(473\) 36.7545i 1.68997i
\(474\) 6.62614 3.82560i 0.304349 0.175716i
\(475\) −5.68693 + 3.28335i −0.260934 + 0.150651i
\(476\) 0 0
\(477\) −14.7695 25.5815i −0.676249 1.17130i
\(478\) 3.02178 5.23388i 0.138213 0.239392i
\(479\) −16.3521 9.44088i −0.747146 0.431365i 0.0775159 0.996991i \(-0.475301\pi\)
−0.824662 + 0.565626i \(0.808634\pi\)
\(480\) −6.04356 −0.275850
\(481\) −24.0000 6.92820i −1.09431 0.315899i
\(482\) 9.00000 0.409939
\(483\) 0 0
\(484\) 3.91742 6.78518i 0.178065 0.308417i
\(485\) −1.66515 2.88413i −0.0756106 0.130961i
\(486\) 7.38505i 0.334993i
\(487\) 25.4347 14.6847i 1.15255 0.665428i 0.203046 0.979169i \(-0.434916\pi\)
0.949508 + 0.313742i \(0.101583\pi\)
\(488\) 22.1216 12.7719i 1.00140 0.578157i
\(489\) 19.3386i 0.874522i
\(490\) 0 0
\(491\) 2.06080 3.56940i 0.0930024 0.161085i −0.815771 0.578375i \(-0.803687\pi\)
0.908773 + 0.417291i \(0.137020\pi\)
\(492\) 33.9564 + 19.6048i 1.53087 + 0.883851i
\(493\) 20.3739 0.917593
\(494\) −2.19148 + 0.542250i −0.0985992 + 0.0243970i
\(495\) 8.58258 0.385758
\(496\) 20.9347 + 12.0866i 0.939994 + 0.542706i
\(497\) 0 0
\(498\) −4.47822 7.75650i −0.200674 0.347577i
\(499\) 18.4050i 0.823921i 0.911202 + 0.411961i \(0.135156\pi\)
−0.911202 + 0.411961i \(0.864844\pi\)
\(500\) −6.93920 + 4.00635i −0.310331 + 0.179169i
\(501\) −35.4737 + 20.4807i −1.58485 + 0.915012i
\(502\) 1.29510i 0.0578032i
\(503\) −9.56080 16.5598i −0.426295 0.738364i 0.570246 0.821474i \(-0.306848\pi\)
−0.996540 + 0.0831100i \(0.973515\pi\)
\(504\) 0 0
\(505\) −2.06080 1.18980i −0.0917042 0.0529454i
\(506\) 2.83485 0.126024
\(507\) 1.39564 36.2599i 0.0619827 1.61036i
\(508\) 12.4610 0.552867
\(509\) −13.0390 7.52808i −0.577944 0.333676i 0.182372 0.983230i \(-0.441623\pi\)
−0.760316 + 0.649553i \(0.774956\pi\)
\(510\) −0.873864 + 1.51358i −0.0386953 + 0.0670223i
\(511\) 0 0
\(512\) 22.8981i 1.01196i
\(513\) 5.93466 3.42638i 0.262022 0.151278i
\(514\) 1.99545 1.15208i 0.0880157 0.0508159i
\(515\) 2.09355i 0.0922529i
\(516\) 23.4347 + 40.5900i 1.03165 + 1.78688i
\(517\) 18.7695 32.5097i 0.825482 1.42978i
\(518\) 0 0
\(519\) 55.1216 2.41957
\(520\) −2.76951 + 0.685275i −0.121451 + 0.0300513i
\(521\) 16.4174 0.719260 0.359630 0.933095i \(-0.382903\pi\)
0.359630 + 0.933095i \(0.382903\pi\)
\(522\) 12.8739 + 7.43273i 0.563474 + 0.325322i
\(523\) −12.1652 + 21.0707i −0.531945 + 0.921356i 0.467360 + 0.884067i \(0.345205\pi\)
−0.999305 + 0.0372883i \(0.988128\pi\)
\(524\) −15.5608 26.9521i −0.679776 1.17741i
\(525\) 0 0
\(526\) 3.69148 2.13128i 0.160956 0.0929280i
\(527\) 22.5000 12.9904i 0.980115 0.565870i
\(528\) 30.5493i 1.32949i
\(529\) 10.2477 + 17.7496i 0.445553 + 0.771721i
\(530\) −0.643371 + 1.11435i −0.0279463 + 0.0484043i
\(531\) 51.0998 + 29.5025i 2.21754 + 1.28030i
\(532\) 0 0
\(533\) 27.1652 + 7.84190i 1.17665 + 0.339671i
\(534\) −20.5826 −0.890695
\(535\) −2.06080 1.18980i −0.0890960 0.0514396i
\(536\) 3.87386 6.70973i 0.167325 0.289816i
\(537\) −12.5608 21.7559i −0.542038 0.938838i
\(538\) 7.21425i 0.311029i
\(539\) 0 0
\(540\) 3.54356 2.04588i 0.152491 0.0880405i
\(541\) 6.28065i 0.270026i 0.990844 + 0.135013i \(0.0431077\pi\)
−0.990844 + 0.135013i \(0.956892\pi\)
\(542\) 2.93466 + 5.08298i 0.126054 + 0.218333i
\(543\) 12.7913 22.1552i 0.548927 0.950769i
\(544\) 12.3131 + 7.10895i 0.527918 + 0.304794i
\(545\) −3.62614 −0.155327
\(546\) 0 0
\(547\) −11.7477 −0.502297 −0.251148 0.967949i \(-0.580808\pi\)
−0.251148 + 0.967949i \(0.580808\pi\)
\(548\) −18.5436 10.7061i −0.792142 0.457343i
\(549\) −35.3303 + 61.1939i −1.50786 + 2.61169i
\(550\) 4.29129 + 7.43273i 0.182981 + 0.316933i
\(551\) 9.30780i 0.396526i
\(552\) 6.62614 3.82560i 0.282027 0.162828i
\(553\) 0 0
\(554\) 5.36695i 0.228020i
\(555\) −4.41742 7.65120i −0.187509 0.324775i
\(556\) 3.39564 5.88143i 0.144007 0.249428i
\(557\) −28.5998 16.5121i −1.21181 0.699640i −0.248659 0.968591i \(-0.579990\pi\)
−0.963154 + 0.268951i \(0.913323\pi\)
\(558\) 18.9564 0.802490
\(559\) 23.4347 + 24.3540i 0.991180 + 1.03006i
\(560\) 0 0
\(561\) −28.4347 16.4168i −1.20051 0.693116i
\(562\) 7.00000 12.1244i 0.295277 0.511435i
\(563\) −18.1652 31.4630i −0.765570 1.32601i −0.939945 0.341327i \(-0.889124\pi\)
0.174375 0.984679i \(-0.444210\pi\)
\(564\) 47.8698i 2.01568i
\(565\) −4.18693 + 2.41733i −0.176146 + 0.101698i
\(566\) 1.08712 0.627650i 0.0456951 0.0263821i
\(567\) 0 0
\(568\) 3.79129 + 6.56670i 0.159079 + 0.275533i
\(569\) −8.37386 + 14.5040i −0.351051 + 0.608038i −0.986434 0.164159i \(-0.947509\pi\)
0.635383 + 0.772197i \(0.280842\pi\)
\(570\) −0.691478 0.399225i −0.0289628 0.0167217i
\(571\) −2.04356 −0.0855204 −0.0427602 0.999085i \(-0.513615\pi\)
−0.0427602 + 0.999085i \(0.513615\pi\)
\(572\) −6.08258 24.5824i −0.254325 1.02784i
\(573\) 40.1216 1.67610
\(574\) 0 0
\(575\) 3.79129 6.56670i 0.158108 0.273850i
\(576\) −8.18693 14.1802i −0.341122 0.590841i
\(577\) 35.6501i 1.48413i 0.670327 + 0.742066i \(0.266154\pi\)
−0.670327 + 0.742066i \(0.733846\pi\)
\(578\) −3.16515 + 1.82740i −0.131653 + 0.0760099i
\(579\) 46.7477 26.9898i 1.94277 1.12166i
\(580\) 5.55765i 0.230769i
\(581\) 0 0
\(582\) −4.64792 + 8.05043i −0.192662 + 0.333701i
\(583\) −20.9347 12.0866i −0.867025 0.500577i
\(584\) −6.00000 −0.248282
\(585\) 5.68693 5.47225i 0.235126 0.226250i
\(586\) −1.16515 −0.0481320
\(587\) −8.22595 4.74925i −0.339521 0.196023i 0.320539 0.947235i \(-0.396136\pi\)
−0.660060 + 0.751213i \(0.729469\pi\)
\(588\) 0 0
\(589\) 5.93466 + 10.2791i 0.244533 + 0.423544i
\(590\) 2.57030i 0.105818i
\(591\) 5.52178 3.18800i 0.227136 0.131137i
\(592\) −16.7477 + 9.66930i −0.688327 + 0.397406i
\(593\) 6.37600i 0.261831i 0.991394 + 0.130916i \(0.0417917\pi\)
−0.991394 + 0.130916i \(0.958208\pi\)
\(594\) −4.47822 7.75650i −0.183744 0.318253i
\(595\) 0 0
\(596\) 0.708712 + 0.409175i 0.0290300 + 0.0167605i
\(597\) −30.7042 −1.25664
\(598\) 1.87841 1.80750i 0.0768139 0.0739142i
\(599\) −6.62614 −0.270737 −0.135368 0.990795i \(-0.543222\pi\)
−0.135368 + 0.990795i \(0.543222\pi\)
\(600\) 20.0608 + 11.5821i 0.818979 + 0.472837i
\(601\) 6.18693 10.7161i 0.252370 0.437118i −0.711808 0.702374i \(-0.752123\pi\)
0.964178 + 0.265256i \(0.0854566\pi\)
\(602\) 0 0
\(603\) 21.4322i 0.872785i
\(604\) −18.8085 + 10.8591i −0.765308 + 0.441851i
\(605\) 1.73049 0.999100i 0.0703545 0.0406192i
\(606\) 6.64215i 0.269819i
\(607\) 9.87386 + 17.1020i 0.400768 + 0.694150i 0.993819 0.111015i \(-0.0354101\pi\)
−0.593051 + 0.805165i \(0.702077\pi\)
\(608\) −3.24773 + 5.62523i −0.131713 + 0.228133i
\(609\) 0 0
\(610\) 3.07803 0.124626
\(611\) −8.29129 33.5088i −0.335430 1.35562i
\(612\) −25.7477 −1.04079
\(613\) −15.8085 9.12705i −0.638500 0.368638i 0.145536 0.989353i \(-0.453509\pi\)
−0.784037 + 0.620715i \(0.786843\pi\)
\(614\) 3.54356 6.13763i 0.143006 0.247694i
\(615\) 5.00000 + 8.66025i 0.201619 + 0.349215i
\(616\) 0 0
\(617\) −14.9174 + 8.61258i −0.600553 + 0.346729i −0.769259 0.638937i \(-0.779374\pi\)
0.168706 + 0.985666i \(0.446041\pi\)
\(618\) 5.06080 2.92185i 0.203575 0.117534i
\(619\) 19.3386i 0.777284i 0.921389 + 0.388642i \(0.127056\pi\)
−0.921389 + 0.388642i \(0.872944\pi\)
\(620\) 3.54356 + 6.13763i 0.142313 + 0.246493i
\(621\) −3.95644 + 6.85275i −0.158766 + 0.274992i
\(622\) −10.5000 6.06218i −0.421012 0.243071i
\(623\) 0 0
\(624\) −19.4782 20.2424i −0.779753 0.810343i
\(625\) 21.9129 0.876515
\(626\) 2.66970 + 1.54135i 0.106703 + 0.0616048i
\(627\) 7.50000 12.9904i 0.299521 0.518786i
\(628\) −0.856629 1.48372i −0.0341832 0.0592071i
\(629\) 20.7846i 0.828737i
\(630\) 0 0
\(631\) 23.9347 13.8187i 0.952824 0.550113i 0.0588668 0.998266i \(-0.481251\pi\)
0.893957 + 0.448153i \(0.147918\pi\)
\(632\) 10.3923i 0.413384i
\(633\) 14.7695 + 25.5815i 0.587035 + 1.01677i
\(634\) −4.23049 + 7.32743i −0.168014 + 0.291009i
\(635\) 2.75227 + 1.58903i 0.109221 + 0.0630586i
\(636\) −30.8258 −1.22232
\(637\) 0 0
\(638\) 12.1652 0.481623
\(639\) −18.1652 10.4877i −0.718602 0.414885i
\(640\) −2.52178 + 4.36785i −0.0996821 + 0.172654i
\(641\) −14.6869 25.4385i −0.580099 1.00476i −0.995467 0.0951074i \(-0.969681\pi\)
0.415368 0.909653i \(-0.363653\pi\)
\(642\) 6.64215i 0.262145i
\(643\) 39.2477 22.6597i 1.54778 0.893611i 0.549468 0.835515i \(-0.314830\pi\)
0.998311 0.0580962i \(-0.0185030\pi\)
\(644\) 0 0
\(645\) 11.9536i 0.470671i
\(646\) 0.939205 + 1.62675i 0.0369525 + 0.0640036i
\(647\) −17.5390 + 30.3785i −0.689530 + 1.19430i 0.282460 + 0.959279i \(0.408849\pi\)
−0.971990 + 0.235022i \(0.924484\pi\)
\(648\) 0.626136 + 0.361500i 0.0245970 + 0.0142011i
\(649\) 48.2867 1.89542
\(650\) 7.58258 + 2.18890i 0.297413 + 0.0858558i
\(651\) 0 0
\(652\) −10.7477 6.20520i −0.420913 0.243015i
\(653\) −7.89564 + 13.6757i −0.308980 + 0.535170i −0.978140 0.207949i \(-0.933321\pi\)
0.669159 + 0.743119i \(0.266654\pi\)
\(654\) 5.06080 + 8.76555i 0.197893 + 0.342760i
\(655\) 7.93725i 0.310134i
\(656\) 18.9564 10.9445i 0.740125 0.427311i
\(657\) 14.3739 8.29875i 0.560778 0.323765i
\(658\) 0 0
\(659\) −3.00000 5.19615i −0.116863 0.202413i 0.801660 0.597781i \(-0.203951\pi\)
−0.918523 + 0.395367i \(0.870617\pi\)
\(660\) 4.47822 7.75650i 0.174314 0.301922i
\(661\) −43.7477 25.2578i −1.70159 0.982413i −0.944155 0.329502i \(-0.893119\pi\)
−0.757434 0.652911i \(-0.773547\pi\)
\(662\) −11.3739 −0.442058
\(663\) −29.3085 + 7.25198i −1.13825 + 0.281644i
\(664\) −12.1652 −0.472099
\(665\) 0 0
\(666\) −7.58258 + 13.1334i −0.293819 + 0.508909i
\(667\) −5.37386 9.30780i −0.208077 0.360400i
\(668\) 26.2867i 1.01706i
\(669\) −45.8739 + 26.4853i −1.77359 + 1.02398i
\(670\) 0.808522 0.466801i 0.0312359 0.0180341i
\(671\) 57.8251i 2.23231i
\(672\) 0 0
\(673\) −13.2477 + 22.9457i −0.510662 + 0.884493i 0.489261 + 0.872137i \(0.337266\pi\)
−0.999924 + 0.0123559i \(0.996067\pi\)
\(674\) −3.93920 2.27430i −0.151732 0.0876028i
\(675\) −23.9564 −0.922084
\(676\) −19.7042 12.4104i −0.757853 0.477323i
\(677\) −29.2087 −1.12258 −0.561291 0.827619i \(-0.689695\pi\)
−0.561291 + 0.827619i \(0.689695\pi\)
\(678\) 11.6869 + 6.74745i 0.448834 + 0.259134i
\(679\) 0 0
\(680\) 1.18693 + 2.05583i 0.0455168 + 0.0788373i
\(681\) 24.7056i 0.946719i
\(682\) 13.4347 7.75650i 0.514440 0.297012i
\(683\) 26.2913 15.1793i 1.00601 0.580819i 0.0959878 0.995383i \(-0.469399\pi\)
0.910020 + 0.414563i \(0.136066\pi\)
\(684\) 11.7629i 0.449764i
\(685\) −2.73049 4.72935i −0.104327 0.180699i
\(686\) 0 0
\(687\) 16.7477 + 9.66930i 0.638966 + 0.368907i
\(688\) 26.1652 0.997537
\(689\) −21.5780 + 5.33918i −0.822057 + 0.203406i
\(690\) 0.921970 0.0350988
\(691\) −8.93466 5.15843i −0.339890 0.196236i 0.320333 0.947305i \(-0.396205\pi\)
−0.660224 + 0.751069i \(0.729538\pi\)
\(692\) 17.6869 30.6347i 0.672356 1.16456i
\(693\) 0 0
\(694\) 6.20520i 0.235546i
\(695\) 1.50000 0.866025i 0.0568982 0.0328502i
\(696\) 28.4347 16.4168i 1.07781 0.622276i
\(697\) 23.5257i 0.891100i
\(698\) 4.81307 + 8.33648i 0.182177 + 0.315540i
\(699\) 22.2695 38.5719i 0.842310 1.45892i
\(700\) 0 0
\(701\) −13.9129 −0.525482 −0.262741 0.964866i \(-0.584627\pi\)
−0.262741 + 0.964866i \(0.584627\pi\)
\(702\) −7.91288 2.28425i −0.298652 0.0862135i
\(703\) −9.49545 −0.358128
\(704\) −11.6044 6.69978i −0.437356 0.252507i
\(705\) 6.10436 10.5731i 0.229903 0.398204i
\(706\) −4.14792 7.18440i −0.156109 0.270389i
\(707\) 0 0
\(708\) 53.3258 30.7876i 2.00410 1.15707i
\(709\) −13.1869 + 7.61348i −0.495246 + 0.285930i −0.726748 0.686904i \(-0.758969\pi\)
0.231502 + 0.972834i \(0.425636\pi\)
\(710\) 0.913701i 0.0342906i
\(711\) 14.3739 + 24.8963i 0.539062 + 0.933683i
\(712\) −13.9782 + 24.2110i −0.523856 + 0.907345i
\(713\) −11.8693 6.85275i −0.444509 0.256638i
\(714\) 0 0
\(715\) 1.79129 6.20520i 0.0669904 0.232061i
\(716\) −16.1216 −0.602492
\(717\) 31.9782 + 18.4626i 1.19425 + 0.689500i
\(718\) −0.126136 + 0.218475i −0.00470737 + 0.00815341i
\(719\) −12.0826 20.9276i −0.450604 0.780469i 0.547820 0.836597i \(-0.315458\pi\)
−0.998424 + 0.0561274i \(0.982125\pi\)
\(720\) 6.10985i 0.227701i
\(721\) 0 0
\(722\) 6.77405 3.91100i 0.252104 0.145552i
\(723\) 54.9887i 2.04505i
\(724\) −8.20871 14.2179i −0.305074 0.528404i
\(725\) 16.2695 28.1796i 0.604234 1.04656i
\(726\) −4.83030 2.78878i −0.179269 0.103501i
\(727\) −0.252273 −0.00935628 −0.00467814 0.999989i \(-0.501489\pi\)
−0.00467814 + 0.999989i \(0.501489\pi\)
\(728\) 0 0
\(729\) −43.8693 −1.62479
\(730\) −0.626136 0.361500i −0.0231744 0.0133797i
\(731\) 14.0608 24.3540i 0.520057 0.900766i
\(732\) 36.8693 + 63.8595i 1.36273 + 2.36032i
\(733\) 16.9590i 0.626395i 0.949688 + 0.313198i \(0.101400\pi\)
−0.949688 + 0.313198i \(0.898600\pi\)
\(734\) −7.12159 + 4.11165i −0.262863 + 0.151764i
\(735\) 0 0
\(736\) 7.50030i 0.276465i
\(737\) 8.76951 + 15.1892i 0.323029 + 0.559503i
\(738\) 8.58258 14.8655i 0.315929 0.547205i
\(739\) 16.7477 + 9.66930i 0.616075 + 0.355691i 0.775339 0.631545i \(-0.217579\pi\)
−0.159264 + 0.987236i \(0.550912\pi\)
\(740\) −5.66970 −0.208422
\(741\) −3.31307 13.3896i −0.121709 0.491879i
\(742\) 0 0
\(743\) 29.8521 + 17.2351i 1.09517 + 0.632295i 0.934947 0.354787i \(-0.115446\pi\)
0.160219 + 0.987081i \(0.448780\pi\)
\(744\) 20.9347 36.2599i 0.767502 1.32935i
\(745\) 0.104356 + 0.180750i 0.00382331 + 0.00662217i
\(746\) 14.7146i 0.538738i
\(747\) 29.1434 16.8259i 1.06630 0.615629i
\(748\) −18.2477 + 10.5353i −0.667203 + 0.385210i
\(749\) 0 0
\(750\) 2.85208 + 4.93995i 0.104143 + 0.180382i
\(751\) −11.8739 + 20.5661i −0.433283 + 0.750469i −0.997154 0.0753944i \(-0.975978\pi\)
0.563870 + 0.825863i \(0.309312\pi\)
\(752\) −23.1434 13.3618i −0.843952 0.487256i
\(753\) 7.91288 0.288361
\(754\) 8.06080 7.75650i 0.293557 0.282475i
\(755\) −5.53901 −0.201585
\(756\) 0 0
\(757\) −3.00000 + 5.19615i −0.109037 + 0.188857i −0.915380 0.402590i \(-0.868110\pi\)
0.806343 + 0.591448i \(0.201443\pi\)
\(758\) 6.47822 + 11.2206i 0.235300 + 0.407551i
\(759\) 17.3205i 0.628695i
\(760\) −0.939205 + 0.542250i −0.0340685 + 0.0196695i
\(761\) 11.2259 6.48130i 0.406940 0.234947i −0.282534 0.959257i \(-0.591175\pi\)
0.689474 + 0.724310i \(0.257842\pi\)
\(762\) 8.87086i 0.321357i
\(763\) 0 0
\(764\) 12.8739 22.2982i 0.465760 0.806720i
\(765\) −5.68693 3.28335i −0.205611 0.118710i
\(766\) −0.582576 −0.0210493
\(767\) 31.9955 30.7876i 1.15529 1.11168i
\(768\) −5.00000 −0.180422
\(769\) −8.12614 4.69163i −0.293036 0.169184i 0.346274 0.938133i \(-0.387447\pi\)
−0.639310 + 0.768949i \(0.720780\pi\)
\(770\) 0 0
\(771\) 7.03901 + 12.1919i 0.253504 + 0.439082i
\(772\) 34.6410i 1.24676i
\(773\) 16.8303 9.71698i 0.605344 0.349495i −0.165797 0.986160i \(-0.553020\pi\)
0.771141 + 0.636664i \(0.219686\pi\)
\(774\) 17.7695 10.2592i 0.638712 0.368760i
\(775\) 41.4938i 1.49050i
\(776\) 6.31307 + 10.9346i 0.226626 + 0.392528i
\(777\) 0 0
\(778\) 0.130682 + 0.0754495i 0.00468519 + 0.00270499i
\(779\) 10.7477 0.385077
\(780\) −1.97822 7.99488i −0.0708316 0.286263i
\(781\) −17.1652 −0.614217
\(782\) −1.87841 1.08450i −0.0671718 0.0387816i
\(783\) −16.9782 + 29.4071i −0.606752 + 1.05093i
\(784\) 0 0
\(785\) 0.436950i 0.0155954i
\(786\) −19.1869 + 11.0776i −0.684375 + 0.395124i
\(787\) 22.7477 13.1334i 0.810869 0.468155i −0.0363886 0.999338i \(-0.511585\pi\)
0.847258 + 0.531182i \(0.178252\pi\)
\(788\) 4.09175i 0.145763i
\(789\) 13.0218 + 22.5544i 0.463588 + 0.802957i
\(790\) 0.626136 1.08450i 0.0222769 0.0385848i
\(791\) 0 0
\(792\) −32.5390 −1.15622
\(793\) 36.8693 + 38.3157i 1.30927 + 1.36063i
\(794\) −14.8348 −0.526469
\(795\) −6.80852 3.93090i −0.241473 0.139415i
\(796\) −9.85208 + 17.0643i −0.349198 + 0.604828i
\(797\) 6.00000 + 10.3923i 0.212531 + 0.368114i 0.952506 0.304520i \(-0.0984960\pi\)
−0.739975 + 0.672634i \(0.765163\pi\)
\(798\) 0 0
\(799\) −24.8739 + 14.3609i −0.879974 + 0.508053i
\(800\) 19.6652 11.3537i 0.695268 0.401413i
\(801\) 77.3345i 2.73248i
\(802\) −7.14792 12.3806i −0.252402 0.437173i
\(803\) 6.79129 11.7629i 0.239659 0.415102i
\(804\) 19.3693 + 11.1829i 0.683103 + 0.394390i
\(805\) 0 0
\(806\) 3.95644 13.7055i 0.139360 0.482756i
\(807\) 44.0780 1.55162
\(808\) 7.81307 + 4.51088i 0.274863 + 0.158692i
\(809\) −26.6216 + 46.1099i −0.935965 + 1.62114i −0.163062 + 0.986616i \(0.552137\pi\)
−0.772904 + 0.634524i \(0.781196\pi\)
\(810\) 0.0435608 + 0.0754495i 0.00153057 + 0.00265102i
\(811\) 27.6374i 0.970479i 0.874381 + 0.485240i \(0.161268\pi\)
−0.874381 + 0.485240i \(0.838732\pi\)
\(812\) 0 0
\(813\) −31.0562 + 17.9303i −1.08919 + 0.628844i
\(814\) 12.4104i 0.434985i
\(815\) −1.58258 2.74110i −0.0554352 0.0960166i
\(816\) −11.6869 + 20.2424i −0.409124 + 0.708624i
\(817\) 11.1261 + 6.42368i 0.389254 + 0.224736i
\(818\) −3.79129 −0.132559
\(819\) 0 0
\(820\) 6.41742 0.224106
\(821\) 10.9610 + 6.32833i 0.382541 + 0.220860i 0.678923 0.734209i \(-0.262447\pi\)
−0.296382 + 0.955069i \(0.595780\pi\)
\(822\) −7.62159 + 13.2010i −0.265834 + 0.460437i
\(823\) 11.2477 + 19.4816i 0.392071 + 0.679087i 0.992723 0.120424i \(-0.0384254\pi\)
−0.600651 + 0.799511i \(0.705092\pi\)
\(824\) 7.93725i 0.276507i
\(825\) −45.4129 + 26.2191i −1.58107 + 0.912833i
\(826\) 0 0
\(827\) 35.3839i 1.23042i −0.788364 0.615210i \(-0.789071\pi\)
0.788364 0.615210i \(-0.210929\pi\)
\(828\) 6.79129 + 11.7629i 0.236014 + 0.408787i
\(829\) −17.1869 + 29.7686i −0.596927 + 1.03391i 0.396345 + 0.918102i \(0.370278\pi\)
−0.993272 + 0.115806i \(0.963055\pi\)
\(830\) −1.26951 0.732950i −0.0440652 0.0254411i
\(831\) −32.7913 −1.13752
\(832\) −11.9610 + 2.95958i −0.414673 + 0.102605i
\(833\) 0 0
\(834\) −4.18693 2.41733i −0.144982 0.0837052i
\(835\) −3.35208 + 5.80598i −0.116004 + 0.200924i
\(836\) −4.81307 8.33648i −0.166463 0.288323i
\(837\) 43.3013i 1.49671i
\(838\) −0.691478 + 0.399225i −0.0238867 + 0.0137910i
\(839\) −24.2305 + 13.9895i −0.836530 + 0.482971i −0.856083 0.516838i \(-0.827109\pi\)
0.0195536 + 0.999809i \(0.493776\pi\)
\(840\) 0 0
\(841\) −8.56080 14.8277i −0.295200 0.511301i
\(842\) 0.956439 1.65660i 0.0329611 0.0570903i
\(843\) 74.0780 + 42.7690i 2.55138 + 1.47304i
\(844\) 18.9564 0.652508
\(845\) −2.76951 5.25378i −0.0952740 0.180735i
\(846\) −20.9564 −0.720497
\(847\) 0 0
\(848\) −8.60436 + 14.9032i −0.295475 + 0.511777i
\(849\) 3.83485 + 6.64215i 0.131612 + 0.227958i
\(850\) 6.56670i 0.225236i
\(851\) 9.49545 5.48220i 0.325500 0.187927i
\(852\) −18.9564 + 10.9445i −0.649437 + 0.374953i
\(853\) 14.1425i 0.484229i −0.970248 0.242114i \(-0.922159\pi\)
0.970248 0.242114i \(-0.0778409\pi\)
\(854\) 0 0
\(855\) 1.50000 2.59808i 0.0512989 0.0888523i
\(856\) 7.81307 + 4.51088i 0.267045 + 0.154179i
\(857\) 15.4610 0.528137 0.264069 0.964504i \(-0.414935\pi\)
0.264069 + 0.964504i \(0.414935\pi\)
\(858\) −17.5000 + 4.33013i −0.597440 + 0.147828i
\(859\) −14.0000 −0.477674 −0.238837 0.971060i \(-0.576766\pi\)
−0.238837 + 0.971060i \(0.576766\pi\)
\(860\) 6.64337 + 3.83555i 0.226537 + 0.130791i
\(861\) 0 0
\(862\) −7.91742 13.7134i −0.269669 0.467080i
\(863\) 45.4147i 1.54594i 0.634446 + 0.772968i \(0.281228\pi\)
−0.634446 + 0.772968i \(0.718772\pi\)
\(864\) −20.5218 + 11.8483i −0.698165 + 0.403086i
\(865\) 7.81307 4.51088i 0.265652 0.153374i
\(866\) 14.8456i 0.504473i
\(867\) −11.1652 19.3386i −0.379188 0.656774i
\(868\) 0 0
\(869\) 20.3739 + 11.7629i 0.691136 + 0.399028i
\(870\) 3.95644 0.134136
\(871\) 15.4955 + 4.47315i 0.525043 + 0.151567i
\(872\) 13.7477 0.465557
\(873\) −30.2477 17.4635i −1.02373 0.591051i
\(874\) 0.495454 0.858152i 0.0167590 0.0290274i
\(875\) 0 0
\(876\) 17.3205i 0.585206i
\(877\) 2.75227 1.58903i 0.0929377 0.0536576i −0.452811 0.891607i \(-0.649579\pi\)
0.545749 + 0.837949i \(0.316245\pi\)
\(878\) −8.12614 + 4.69163i −0.274244 + 0.158335i
\(879\) 7.11890i 0.240115i
\(880\) −2.50000 4.33013i −0.0842750 0.145969i
\(881\) −8.29129 + 14.3609i −0.279341 + 0.483832i −0.971221 0.238180i \(-0.923449\pi\)
0.691880 + 0.722012i \(0.256783\pi\)
\(882\) 0 0
\(883\) 29.2432 0.984111 0.492056 0.870564i \(-0.336246\pi\)
0.492056 + 0.870564i \(0.336246\pi\)
\(884\) −5.37386 + 18.6156i −0.180743 + 0.626111i
\(885\) 15.7042 0.527890
\(886\) 6.00000 + 3.46410i 0.201574 + 0.116379i
\(887\) −11.2087 + 19.4141i −0.376352 + 0.651860i −0.990528 0.137308i \(-0.956155\pi\)
0.614177 + 0.789169i \(0.289488\pi\)
\(888\) 16.7477 + 29.0079i 0.562017 + 0.973442i
\(889\) 0 0
\(890\) −2.91742 + 1.68438i −0.0977923 + 0.0564604i
\(891\) −1.41742 + 0.818350i −0.0474855 + 0.0274158i
\(892\) 33.9935i 1.13819i
\(893\) −6.56080 11.3636i −0.219549 0.380269i
\(894\) 0.291288 0.504525i 0.00974212 0.0168739i
\(895\) −3.56080 2.05583i −0.119024 0.0687187i
\(896\) 0 0
\(897\) 11.0436 + 11.4768i 0.368734 + 0.383199i
\(898\) 11.4955 0.383608
\(899\) −50.9347 29.4071i −1.69877 0.980783i
\(900\) −20.5608 + 35.6123i −0.685360 + 1.18708i
\(901\) 9.24773 + 16.0175i 0.308086 + 0.533621i
\(902\) 14.0471i 0.467717i
\(903\) 0 0
\(904\) 15.8739 9.16478i 0.527957 0.304816i
\(905\) 4.18710i 0.139184i
\(906\) 7.73049 + 13.3896i 0.256828 + 0.444840i
\(907\) 20.5390 35.5746i 0.681987 1.18124i −0.292387 0.956300i \(-0.594449\pi\)
0.974374 0.224936i \(-0.0722172\pi\)
\(908\) −13.7305 7.92730i −0.455662 0.263077i
\(909\) −24.9564 −0.827753
\(910\) 0 0
\(911\) −43.1216 −1.42868 −0.714341 0.699798i \(-0.753273\pi\)
−0.714341 + 0.699798i \(0.753273\pi\)
\(912\) −9.24773 5.33918i −0.306223 0.176798i
\(913\) 13.7695 23.8495i 0.455704 0.789303i
\(914\) −5.20871 9.02175i −0.172289 0.298413i
\(915\) 18.8063i 0.621717i
\(916\) 10.7477 6.20520i 0.355115 0.205026i
\(917\) 0 0
\(918\) 6.85275i 0.226175i
\(919\) −12.9564 22.4412i −0.427393 0.740267i 0.569247 0.822166i \(-0.307235\pi\)
−0.996641 + 0.0818992i \(0.973901\pi\)
\(920\) 0.626136 1.08450i 0.0206431 0.0357549i
\(921\) 37.5000 + 21.6506i 1.23567 + 0.713413i
\(922\) −2.12159 −0.0698709
\(923\) −11.3739 + 10.9445i −0.374375 + 0.360243i
\(924\) 0 0
\(925\) 28.7477 + 16.5975i 0.945219 + 0.545723i
\(926\) 1.81307 3.14033i 0.0595811 0.103198i
\(927\) 10.9782 + 19.0148i 0.360572 + 0.624529i
\(928\) 32.1860i 1.05656i
\(929\) −50.1606 + 28.9602i −1.64572 + 0.950155i −0.666969 + 0.745086i \(0.732408\pi\)
−0.978748 + 0.205069i \(0.934258\pi\)
\(930\) 4.36932 2.52263i 0.143276 0.0827202i
\(931\) 0 0
\(932\) −14.2913 24.7532i −0.468127 0.810819i
\(933\) 37.0390 64.1535i 1.21260 2.10029i
\(934\) −11.9347 6.89048i −0.390514 0.225463i
\(935\) −5.37386 −0.175744
\(936\) −21.5608 + 20.7469i −0.704737 + 0.678133i
\(937\) 20.4955 0.669557 0.334779 0.942297i \(-0.391338\pi\)
0.334779 + 0.942297i \(0.391338\pi\)
\(938\) 0 0
\(939\) −9.41742 + 16.3115i −0.307326 + 0.532304i
\(940\) −3.91742 6.78518i −0.127772 0.221308i
\(941\) 39.3049i 1.28130i −0.767832 0.640651i \(-0.778665\pi\)
0.767832 0.640651i \(-0.221335\pi\)
\(942\) −1.05625 + 0.609826i −0.0344145 + 0.0198692i
\(943\) −10.7477 + 6.20520i −0.349994 + 0.202069i
\(944\) 34.3749i 1.11881i
\(945\) 0 0
\(946\) 8.39564 14.5417i 0.272966 0.472791i
\(947\) −33.2305 19.1856i −1.07985 0.623449i −0.148991 0.988839i \(-0.547603\pi\)
−0.930855 + 0.365389i \(0.880936\pi\)
\(948\) 30.0000 0.974355
\(949\) −3.00000 12.1244i −0.0973841 0.393573i
\(950\) 3.00000 0.0973329
\(951\) −44.7695 25.8477i −1.45175 0.838169i
\(952\) 0 0
\(953\) 7.50000 + 12.9904i 0.242949 + 0.420800i 0.961553 0.274620i \(-0.0885520\pi\)
−0.718604 + 0.695419i \(0.755219\pi\)
\(954\) 13.4949i 0.436914i
\(955\) 5.68693 3.28335i 0.184025 0.106247i
\(956\) 20.5218 11.8483i 0.663722 0.383200i
\(957\) 74.3273i 2.40266i
\(958\) 4.31307 + 7.47045i 0.139349 + 0.241359i
\(959\) 0 0
\(960\) −3.77405 2.17895i −0.121807 0.0703253i
\(961\) −44.0000 −1.41935
\(962\) 7.91288 + 8.22330i 0.255121 + 0.265130i
\(963\) −24.9564 −0.804210
\(964\) 30.5608 + 17.6443i 0.984297 + 0.568284i
\(965\) 4.41742 7.65120i 0.142202 0.246301i
\(966\) 0 0
\(967\) 23.8118i 0.765735i −0.923803 0.382867i \(-0.874937\pi\)
0.923803 0.382867i \(-0.125063\pi\)
\(968\) −6.56080 + 3.78788i −0.210872 + 0.121747i
\(969\) −9.93920 + 5.73840i −0.319293 + 0.184344i
\(970\) 1.52145i 0.0488508i
\(971\) −11.1261 19.2710i −0.357055 0.618437i 0.630413 0.776260i \(-0.282886\pi\)
−0.987467 + 0.157823i \(0.949552\pi\)
\(972\) −14.4782 + 25.0770i −0.464389 + 0.804346i
\(973\) 0 0
\(974\) −13.4174 −0.429922
\(975\) −13.3739 + 46.3284i −0.428306 + 1.48370i
\(976\) 41.1652 1.31766
\(977\) −1.20417 0.695226i −0.0385247 0.0222422i 0.480614 0.876932i \(-0.340414\pi\)
−0.519139 + 0.854690i \(0.673747\pi\)
\(978\) −4.41742 + 7.65120i −0.141254 + 0.244659i
\(979\) −31.6434 54.8079i −1.01133 1.75167i
\(980\) 0 0
\(981\) −32.9347 + 19.0148i −1.05152 + 0.607097i
\(982\) −1.63068 + 0.941475i −0.0520372 + 0.0300437i
\(983\) 19.8908i 0.634418i 0.948356 + 0.317209i \(0.102746\pi\)
−0.948356 + 0.317209i \(0.897254\pi\)
\(984\) −18.9564 32.8335i −0.604309 1.04669i
\(985\) 0.521780 0.903750i 0.0166253 0.0287959i
\(986\) −8.06080 4.65390i −0.256708 0.148210i
\(987\) 0 0
\(988\) −8.50455 2.45505i −0.270566 0.0781056i
\(989\) −14.8348 −0.471721
\(990\) −3.39564 1.96048i −0.107921 0.0623080i
\(991\) 20.1869 34.9648i 0.641259 1.11069i −0.343893 0.939009i \(-0.611746\pi\)
0.985152 0.171684i \(-0.0549209\pi\)
\(992\) −20.5218 35.5448i −0.651567 1.12855i
\(993\) 69.4926i 2.20528i
\(994\) 0 0
\(995\) −4.35208 + 2.51268i −0.137970 + 0.0796572i
\(996\) 35.1178i 1.11275i
\(997\) 7.03901 + 12.1919i 0.222928 + 0.386122i 0.955696 0.294356i \(-0.0951052\pi\)
−0.732768 + 0.680479i \(0.761772\pi\)
\(998\) 4.20417 7.28183i 0.133081 0.230502i
\(999\) −30.0000 17.3205i −0.949158 0.547997i
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 637.2.q.f.589.1 yes 4
7.2 even 3 637.2.k.f.459.2 4
7.3 odd 6 637.2.u.e.30.2 4
7.4 even 3 637.2.u.d.30.2 4
7.5 odd 6 637.2.k.d.459.2 4
7.6 odd 2 637.2.q.e.589.1 yes 4
13.6 odd 12 8281.2.a.bq.1.3 4
13.7 odd 12 8281.2.a.bq.1.2 4
13.10 even 6 inner 637.2.q.f.491.1 yes 4
91.6 even 12 8281.2.a.bs.1.3 4
91.10 odd 6 637.2.k.d.569.1 4
91.20 even 12 8281.2.a.bs.1.2 4
91.23 even 6 637.2.u.d.361.2 4
91.62 odd 6 637.2.q.e.491.1 4
91.75 odd 6 637.2.u.e.361.2 4
91.88 even 6 637.2.k.f.569.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.k.d.459.2 4 7.5 odd 6
637.2.k.d.569.1 4 91.10 odd 6
637.2.k.f.459.2 4 7.2 even 3
637.2.k.f.569.1 4 91.88 even 6
637.2.q.e.491.1 4 91.62 odd 6
637.2.q.e.589.1 yes 4 7.6 odd 2
637.2.q.f.491.1 yes 4 13.10 even 6 inner
637.2.q.f.589.1 yes 4 1.1 even 1 trivial
637.2.u.d.30.2 4 7.4 even 3
637.2.u.d.361.2 4 91.23 even 6
637.2.u.e.30.2 4 7.3 odd 6
637.2.u.e.361.2 4 91.75 odd 6
8281.2.a.bq.1.2 4 13.7 odd 12
8281.2.a.bq.1.3 4 13.6 odd 12
8281.2.a.bs.1.2 4 91.20 even 12
8281.2.a.bs.1.3 4 91.6 even 12