Properties

Label 84.2.o.b.19.3
Level $84$
Weight $2$
Character 84.19
Analytic conductor $0.671$
Analytic rank $0$
Dimension $8$
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] = [84,2,Mod(19,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 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("84.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.o (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: \(0.670743376979\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.562828176.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) 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 19.3
Root \(1.40376 + 0.171630i\) of defining polynomial
Character \(\chi\) \(=\) 84.19
Dual form 84.2.o.b.31.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.553244 - 1.30151i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.38784 - 1.44010i) q^{4} +(0.834598 + 0.481855i) q^{5} +(1.40376 - 0.171630i) q^{6} +(1.20103 - 2.35744i) q^{7} +(-2.64212 + 1.00956i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.553244 - 1.30151i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.38784 - 1.44010i) q^{4} +(0.834598 + 0.481855i) q^{5} +(1.40376 - 0.171630i) q^{6} +(1.20103 - 2.35744i) q^{7} +(-2.64212 + 1.00956i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.08887 - 0.819652i) q^{10} +(-4.74861 + 2.74161i) q^{11} +(0.553244 - 1.92196i) q^{12} +3.75117i q^{13} +(-2.40376 - 2.86739i) q^{14} +0.963711i q^{15} +(-0.147789 + 3.99727i) q^{16} +(-0.594545 + 0.343260i) q^{17} +(0.850516 + 1.12988i) q^{18} +(2.44109 - 4.22809i) q^{19} +(-0.464369 - 1.87065i) q^{20} +(2.64212 - 0.138595i) q^{21} +(0.941086 + 7.69713i) q^{22} +(1.07465 + 0.620450i) q^{23} +(-2.19536 - 1.78336i) q^{24} +(-2.03563 - 3.52582i) q^{25} +(4.88217 + 2.07531i) q^{26} -1.00000 q^{27} +(-5.06180 + 1.54214i) q^{28} -2.48011 q^{29} +(1.25428 + 0.533167i) q^{30} +(2.41401 + 4.18119i) q^{31} +(5.12071 + 2.40381i) q^{32} +(-4.74861 - 2.74161i) q^{33} +(0.117828 + 0.963711i) q^{34} +(2.13832 - 1.38879i) q^{35} +(1.94109 - 0.481855i) q^{36} +(1.36643 - 2.36673i) q^{37} +(-4.15237 - 5.51625i) q^{38} +(-3.24861 + 1.87558i) q^{39} +(-2.69157 - 0.430544i) q^{40} -9.42976i q^{41} +(1.28135 - 3.51541i) q^{42} -5.97437i q^{43} +(10.5385 + 3.03356i) q^{44} +(-0.834598 + 0.481855i) q^{45} +(1.40207 - 1.05541i) q^{46} +(1.80752 - 3.13072i) q^{47} +(-3.53563 + 1.87065i) q^{48} +(-4.11504 - 5.66272i) q^{49} +(-5.71508 + 0.698752i) q^{50} +(-0.594545 - 0.343260i) q^{51} +(5.40207 - 5.20603i) q^{52} +(2.04757 + 3.54650i) q^{53} +(-0.553244 + 1.30151i) q^{54} -5.28424 q^{55} +(-0.793298 + 7.44115i) q^{56} +4.88217 q^{57} +(-1.37210 + 3.22788i) q^{58} +(6.34315 + 10.9867i) q^{59} +(1.38784 - 1.33748i) q^{60} +(9.01711 + 5.20603i) q^{61} +(6.77738 - 0.828634i) q^{62} +(1.44109 + 2.21884i) q^{63} +(5.96158 - 5.33475i) q^{64} +(-1.80752 + 3.13072i) q^{65} +(-6.19536 + 4.66357i) q^{66} +(-8.17396 + 4.71924i) q^{67} +(1.31946 + 0.379814i) q^{68} +1.24090i q^{69} +(-0.624505 - 3.55138i) q^{70} -10.1163i q^{71} +(0.446756 - 2.79292i) q^{72} +(-5.76850 + 3.33044i) q^{73} +(-2.32435 - 3.08781i) q^{74} +(2.03563 - 3.52582i) q^{75} +(-9.47672 + 2.35250i) q^{76} +(0.759946 + 14.4873i) q^{77} +(0.643814 + 5.26574i) q^{78} +(-1.22492 - 0.707208i) q^{79} +(-2.04945 + 3.26490i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-12.2729 - 5.21696i) q^{82} -0.543780 q^{83} +(-3.86643 - 3.61257i) q^{84} -0.661608 q^{85} +(-7.77568 - 3.30528i) q^{86} +(-1.24005 - 2.14784i) q^{87} +(9.77857 - 12.0377i) q^{88} +(0.480107 + 0.277190i) q^{89} +(0.165402 + 1.35282i) q^{90} +(8.84315 + 4.50528i) q^{91} +(-0.597935 - 2.40870i) q^{92} +(-2.41401 + 4.18119i) q^{93} +(-3.07465 - 4.08455i) q^{94} +(4.07465 - 2.35250i) q^{95} +(0.478592 + 5.63657i) q^{96} +10.8747i q^{97} +(-9.64670 + 2.22289i) q^{98} -5.48322i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9} - 13 q^{10} - 6 q^{11} + q^{12} - 10 q^{14} + 7 q^{16} + q^{18} + 6 q^{19} - 22 q^{20} - 4 q^{21} - 6 q^{22} + 11 q^{24} + 2 q^{25} + 12 q^{26} - 8 q^{27} - 7 q^{28} - 16 q^{29} - 5 q^{30} - 6 q^{31} + 21 q^{32} - 6 q^{33} + 28 q^{34} + 12 q^{35} + 2 q^{36} + 6 q^{37} + 8 q^{38} + 6 q^{39} - 13 q^{40} + 7 q^{42} + 19 q^{44} - 12 q^{46} - 4 q^{47} - 10 q^{48} + 4 q^{49} + 2 q^{50} + 20 q^{52} - 4 q^{53} - q^{54} + 8 q^{55} - q^{56} + 12 q^{57} - 23 q^{58} + 14 q^{59} + q^{60} + 12 q^{61} + 48 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{65} - 21 q^{66} - 42 q^{67} - 10 q^{68} + 35 q^{70} + 7 q^{72} - 18 q^{73} - 28 q^{74} - 2 q^{75} - 44 q^{76} + 8 q^{77} - 6 q^{78} + 6 q^{79} - 33 q^{80} - 4 q^{81} - 14 q^{82} - 4 q^{83} - 26 q^{84} - 32 q^{85} - 42 q^{86} - 8 q^{87} + 11 q^{88} + 8 q^{90} + 34 q^{91} - 28 q^{92} + 6 q^{93} - 16 q^{94} + 24 q^{95} + 9 q^{96} - 19 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.553244 1.30151i 0.391203 0.920305i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.38784 1.44010i −0.693921 0.720051i
\(5\) 0.834598 + 0.481855i 0.373244 + 0.215492i 0.674875 0.737932i \(-0.264198\pi\)
−0.301631 + 0.953425i \(0.597531\pi\)
\(6\) 1.40376 0.171630i 0.573083 0.0700677i
\(7\) 1.20103 2.35744i 0.453948 0.891028i
\(8\) −2.64212 + 1.00956i −0.934130 + 0.356933i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.08887 0.819652i 0.344332 0.259197i
\(11\) −4.74861 + 2.74161i −1.43176 + 0.826626i −0.997255 0.0740437i \(-0.976410\pi\)
−0.434504 + 0.900670i \(0.643076\pi\)
\(12\) 0.553244 1.92196i 0.159708 0.554821i
\(13\) 3.75117i 1.04039i 0.854048 + 0.520193i \(0.174140\pi\)
−0.854048 + 0.520193i \(0.825860\pi\)
\(14\) −2.40376 2.86739i −0.642432 0.766343i
\(15\) 0.963711i 0.248829i
\(16\) −0.147789 + 3.99727i −0.0369471 + 0.999317i
\(17\) −0.594545 + 0.343260i −0.144198 + 0.0832529i −0.570363 0.821393i \(-0.693198\pi\)
0.426165 + 0.904645i \(0.359864\pi\)
\(18\) 0.850516 + 1.12988i 0.200469 + 0.266315i
\(19\) 2.44109 4.22809i 0.560024 0.969989i −0.437470 0.899233i \(-0.644125\pi\)
0.997494 0.0707563i \(-0.0225413\pi\)
\(20\) −0.464369 1.87065i −0.103836 0.418289i
\(21\) 2.64212 0.138595i 0.576558 0.0302439i
\(22\) 0.941086 + 7.69713i 0.200640 + 1.64103i
\(23\) 1.07465 + 0.620450i 0.224080 + 0.129373i 0.607838 0.794061i \(-0.292037\pi\)
−0.383758 + 0.923434i \(0.625370\pi\)
\(24\) −2.19536 1.78336i −0.448127 0.364027i
\(25\) −2.03563 3.52582i −0.407126 0.705163i
\(26\) 4.88217 + 2.07531i 0.957473 + 0.407002i
\(27\) −1.00000 −0.192450
\(28\) −5.06180 + 1.54214i −0.956590 + 0.291438i
\(29\) −2.48011 −0.460544 −0.230272 0.973126i \(-0.573962\pi\)
−0.230272 + 0.973126i \(0.573962\pi\)
\(30\) 1.25428 + 0.533167i 0.228999 + 0.0973426i
\(31\) 2.41401 + 4.18119i 0.433569 + 0.750963i 0.997178 0.0750787i \(-0.0239208\pi\)
−0.563609 + 0.826042i \(0.690587\pi\)
\(32\) 5.12071 + 2.40381i 0.905222 + 0.424938i
\(33\) −4.74861 2.74161i −0.826626 0.477253i
\(34\) 0.117828 + 0.963711i 0.0202073 + 0.165275i
\(35\) 2.13832 1.38879i 0.361443 0.234748i
\(36\) 1.94109 0.481855i 0.323514 0.0803092i
\(37\) 1.36643 2.36673i 0.224640 0.389089i −0.731571 0.681765i \(-0.761213\pi\)
0.956212 + 0.292677i \(0.0945459\pi\)
\(38\) −4.15237 5.51625i −0.673603 0.894855i
\(39\) −3.24861 + 1.87558i −0.520193 + 0.300334i
\(40\) −2.69157 0.430544i −0.425574 0.0680749i
\(41\) 9.42976i 1.47268i −0.676611 0.736340i \(-0.736552\pi\)
0.676611 0.736340i \(-0.263448\pi\)
\(42\) 1.28135 3.51541i 0.197717 0.542440i
\(43\) 5.97437i 0.911083i −0.890215 0.455541i \(-0.849446\pi\)
0.890215 0.455541i \(-0.150554\pi\)
\(44\) 10.5385 + 3.03356i 1.58874 + 0.457326i
\(45\) −0.834598 + 0.481855i −0.124415 + 0.0718308i
\(46\) 1.40207 1.05541i 0.206723 0.155611i
\(47\) 1.80752 3.13072i 0.263654 0.456662i −0.703556 0.710640i \(-0.748406\pi\)
0.967210 + 0.253978i \(0.0817390\pi\)
\(48\) −3.53563 + 1.87065i −0.510324 + 0.270004i
\(49\) −4.11504 5.66272i −0.587863 0.808960i
\(50\) −5.71508 + 0.698752i −0.808234 + 0.0988184i
\(51\) −0.594545 0.343260i −0.0832529 0.0480661i
\(52\) 5.40207 5.20603i 0.749132 0.721946i
\(53\) 2.04757 + 3.54650i 0.281256 + 0.487150i 0.971694 0.236242i \(-0.0759157\pi\)
−0.690438 + 0.723391i \(0.742582\pi\)
\(54\) −0.553244 + 1.30151i −0.0752870 + 0.177113i
\(55\) −5.28424 −0.712526
\(56\) −0.793298 + 7.44115i −0.106009 + 0.994365i
\(57\) 4.88217 0.646660
\(58\) −1.37210 + 3.22788i −0.180166 + 0.423841i
\(59\) 6.34315 + 10.9867i 0.825808 + 1.43034i 0.901300 + 0.433195i \(0.142614\pi\)
−0.0754923 + 0.997146i \(0.524053\pi\)
\(60\) 1.38784 1.33748i 0.179170 0.172668i
\(61\) 9.01711 + 5.20603i 1.15452 + 0.666564i 0.949985 0.312295i \(-0.101098\pi\)
0.204537 + 0.978859i \(0.434431\pi\)
\(62\) 6.77738 0.828634i 0.860728 0.105237i
\(63\) 1.44109 + 2.21884i 0.181560 + 0.279548i
\(64\) 5.96158 5.33475i 0.745198 0.666843i
\(65\) −1.80752 + 3.13072i −0.224195 + 0.388318i
\(66\) −6.19536 + 4.66357i −0.762596 + 0.574045i
\(67\) −8.17396 + 4.71924i −0.998608 + 0.576546i −0.907836 0.419325i \(-0.862267\pi\)
−0.0907716 + 0.995872i \(0.528933\pi\)
\(68\) 1.31946 + 0.379814i 0.160009 + 0.0460592i
\(69\) 1.24090i 0.149387i
\(70\) −0.624505 3.55138i −0.0746427 0.424472i
\(71\) 10.1163i 1.20058i −0.799782 0.600291i \(-0.795052\pi\)
0.799782 0.600291i \(-0.204948\pi\)
\(72\) 0.446756 2.79292i 0.0526507 0.329149i
\(73\) −5.76850 + 3.33044i −0.675152 + 0.389799i −0.798026 0.602623i \(-0.794122\pi\)
0.122874 + 0.992422i \(0.460789\pi\)
\(74\) −2.32435 3.08781i −0.270200 0.358950i
\(75\) 2.03563 3.52582i 0.235054 0.407126i
\(76\) −9.47672 + 2.35250i −1.08705 + 0.269850i
\(77\) 0.759946 + 14.4873i 0.0866039 + 1.65098i
\(78\) 0.643814 + 5.26574i 0.0728976 + 0.596228i
\(79\) −1.22492 0.707208i −0.137814 0.0795671i 0.429508 0.903063i \(-0.358687\pi\)
−0.567322 + 0.823496i \(0.692020\pi\)
\(80\) −2.04945 + 3.26490i −0.229135 + 0.365027i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −12.2729 5.21696i −1.35531 0.576117i
\(83\) −0.543780 −0.0596876 −0.0298438 0.999555i \(-0.509501\pi\)
−0.0298438 + 0.999555i \(0.509501\pi\)
\(84\) −3.86643 3.61257i −0.421863 0.394164i
\(85\) −0.661608 −0.0717614
\(86\) −7.77568 3.30528i −0.838474 0.356418i
\(87\) −1.24005 2.14784i −0.132948 0.230272i
\(88\) 9.77857 12.0377i 1.04240 1.28322i
\(89\) 0.480107 + 0.277190i 0.0508912 + 0.0293821i 0.525230 0.850960i \(-0.323979\pi\)
−0.474339 + 0.880343i \(0.657313\pi\)
\(90\) 0.165402 + 1.35282i 0.0174349 + 0.142600i
\(91\) 8.84315 + 4.50528i 0.927014 + 0.472281i
\(92\) −0.597935 2.40870i −0.0623390 0.251124i
\(93\) −2.41401 + 4.18119i −0.250321 + 0.433569i
\(94\) −3.07465 4.08455i −0.317126 0.421289i
\(95\) 4.07465 2.35250i 0.418050 0.241362i
\(96\) 0.478592 + 5.63657i 0.0488461 + 0.575280i
\(97\) 10.8747i 1.10416i 0.833790 + 0.552081i \(0.186166\pi\)
−0.833790 + 0.552081i \(0.813834\pi\)
\(98\) −9.64670 + 2.22289i −0.974464 + 0.224546i
\(99\) 5.48322i 0.551084i
\(100\) −2.25240 + 7.82479i −0.225240 + 0.782479i
\(101\) 12.4972 7.21527i 1.24352 0.717946i 0.273710 0.961812i \(-0.411749\pi\)
0.969809 + 0.243866i \(0.0784157\pi\)
\(102\) −0.775684 + 0.583897i −0.0768042 + 0.0578144i
\(103\) −7.51235 + 13.0118i −0.740214 + 1.28209i 0.212184 + 0.977230i \(0.431942\pi\)
−0.952398 + 0.304858i \(0.901391\pi\)
\(104\) −3.78702 9.91103i −0.371348 0.971857i
\(105\) 2.27189 + 1.15745i 0.221714 + 0.112955i
\(106\) 5.74861 0.702851i 0.558354 0.0682669i
\(107\) −10.4925 6.05782i −1.01434 0.585632i −0.101883 0.994796i \(-0.532487\pi\)
−0.912461 + 0.409165i \(0.865820\pi\)
\(108\) 1.38784 + 1.44010i 0.133545 + 0.138574i
\(109\) 3.03563 + 5.25787i 0.290761 + 0.503612i 0.973990 0.226592i \(-0.0727583\pi\)
−0.683229 + 0.730204i \(0.739425\pi\)
\(110\) −2.92347 + 6.87747i −0.278742 + 0.655741i
\(111\) 2.73287 0.259392
\(112\) 9.24582 + 5.14925i 0.873648 + 0.486559i
\(113\) −7.37939 −0.694194 −0.347097 0.937829i \(-0.612833\pi\)
−0.347097 + 0.937829i \(0.612833\pi\)
\(114\) 2.70103 6.35418i 0.252975 0.595124i
\(115\) 0.597935 + 1.03565i 0.0557577 + 0.0965752i
\(116\) 3.44200 + 3.57161i 0.319581 + 0.331615i
\(117\) −3.24861 1.87558i −0.300334 0.173398i
\(118\) 17.8085 2.17735i 1.63941 0.200442i
\(119\) 0.0951483 + 1.81387i 0.00872223 + 0.166277i
\(120\) −0.972923 2.54624i −0.0888153 0.232439i
\(121\) 9.53284 16.5114i 0.866622 1.50103i
\(122\) 11.7643 8.85562i 1.06509 0.801751i
\(123\) 8.16641 4.71488i 0.736340 0.425126i
\(124\) 2.67107 9.27924i 0.239869 0.833301i
\(125\) 8.74207i 0.781915i
\(126\) 3.68511 0.648022i 0.328296 0.0577303i
\(127\) 11.6431i 1.03316i 0.856240 + 0.516578i \(0.172794\pi\)
−0.856240 + 0.516578i \(0.827206\pi\)
\(128\) −3.64500 10.7105i −0.322176 0.946680i
\(129\) 5.17396 2.98718i 0.455541 0.263007i
\(130\) 3.07465 + 4.08455i 0.269665 + 0.358239i
\(131\) −4.63078 + 8.02074i −0.404593 + 0.700776i −0.994274 0.106861i \(-0.965920\pi\)
0.589681 + 0.807636i \(0.299253\pi\)
\(132\) 2.64212 + 10.6434i 0.229967 + 0.926389i
\(133\) −7.03563 10.8328i −0.610067 0.939321i
\(134\) 1.61993 + 13.2494i 0.139940 + 1.14457i
\(135\) −0.834598 0.481855i −0.0718308 0.0414715i
\(136\) 1.22432 1.50716i 0.104984 0.129238i
\(137\) −3.61504 6.26144i −0.308854 0.534951i 0.669258 0.743030i \(-0.266612\pi\)
−0.978112 + 0.208080i \(0.933279\pi\)
\(138\) 1.61504 + 0.686521i 0.137481 + 0.0584405i
\(139\) 5.30812 0.450229 0.225115 0.974332i \(-0.427724\pi\)
0.225115 + 0.974332i \(0.427724\pi\)
\(140\) −4.96766 1.15198i −0.419844 0.0973604i
\(141\) 3.61504 0.304441
\(142\) −13.1664 5.59677i −1.10490 0.469671i
\(143\) −10.2842 17.8128i −0.860011 1.48958i
\(144\) −3.38784 2.12662i −0.282320 0.177219i
\(145\) −2.06989 1.19505i −0.171895 0.0992438i
\(146\) 1.14321 + 9.35029i 0.0946127 + 0.773836i
\(147\) 2.84654 6.39509i 0.234779 0.527458i
\(148\) −5.30473 + 1.31685i −0.436046 + 0.108244i
\(149\) −2.33080 + 4.03707i −0.190947 + 0.330730i −0.945564 0.325435i \(-0.894489\pi\)
0.754617 + 0.656165i \(0.227822\pi\)
\(150\) −3.46267 4.60002i −0.282726 0.375590i
\(151\) 10.5709 6.10309i 0.860244 0.496662i −0.00384988 0.999993i \(-0.501225\pi\)
0.864094 + 0.503330i \(0.167892\pi\)
\(152\) −2.18114 + 13.6355i −0.176914 + 1.10599i
\(153\) 0.686521i 0.0555019i
\(154\) 19.2758 + 7.02594i 1.55329 + 0.566167i
\(155\) 4.65281i 0.373723i
\(156\) 7.20959 + 2.07531i 0.577229 + 0.166158i
\(157\) −18.9944 + 10.9664i −1.51592 + 0.875217i −0.516095 + 0.856531i \(0.672615\pi\)
−0.999825 + 0.0186856i \(0.994052\pi\)
\(158\) −1.59812 + 1.20298i −0.127139 + 0.0957042i
\(159\) −2.04757 + 3.54650i −0.162383 + 0.281256i
\(160\) 3.11545 + 4.47366i 0.246298 + 0.353674i
\(161\) 2.75337 1.78824i 0.216996 0.140933i
\(162\) −1.40376 + 0.171630i −0.110290 + 0.0134845i
\(163\) −3.48011 2.00924i −0.272583 0.157376i 0.357478 0.933922i \(-0.383637\pi\)
−0.630061 + 0.776546i \(0.716970\pi\)
\(164\) −13.5798 + 13.0870i −1.06041 + 1.02192i
\(165\) −2.64212 4.57628i −0.205689 0.356263i
\(166\) −0.300843 + 0.707734i −0.0233499 + 0.0549308i
\(167\) 14.7178 1.13890 0.569448 0.822027i \(-0.307157\pi\)
0.569448 + 0.822027i \(0.307157\pi\)
\(168\) −6.84087 + 3.03356i −0.527785 + 0.234044i
\(169\) −1.07126 −0.0824047
\(170\) −0.366030 + 0.861087i −0.0280733 + 0.0660424i
\(171\) 2.44109 + 4.22809i 0.186675 + 0.323330i
\(172\) −8.60370 + 8.29148i −0.656026 + 0.632219i
\(173\) −10.0918 5.82648i −0.767262 0.442979i 0.0646349 0.997909i \(-0.479412\pi\)
−0.831897 + 0.554930i \(0.812745\pi\)
\(174\) −3.48148 + 0.425661i −0.263930 + 0.0322693i
\(175\) −10.7568 + 0.564256i −0.813134 + 0.0426538i
\(176\) −10.2572 19.3866i −0.773163 1.46132i
\(177\) −6.34315 + 10.9867i −0.476780 + 0.825808i
\(178\) 0.626381 0.471509i 0.0469492 0.0353411i
\(179\) −2.24663 + 1.29709i −0.167921 + 0.0969494i −0.581605 0.813471i \(-0.697575\pi\)
0.413684 + 0.910421i \(0.364242\pi\)
\(180\) 1.85221 + 0.533167i 0.138056 + 0.0397399i
\(181\) 9.53343i 0.708615i −0.935129 0.354307i \(-0.884717\pi\)
0.935129 0.354307i \(-0.115283\pi\)
\(182\) 10.7561 9.01691i 0.797293 0.668378i
\(183\) 10.4121i 0.769681i
\(184\) −3.46574 0.554380i −0.255498 0.0408694i
\(185\) 2.28085 1.31685i 0.167691 0.0968166i
\(186\) 4.10631 + 5.45507i 0.301089 + 0.399985i
\(187\) 1.88217 3.26002i 0.137638 0.238396i
\(188\) −7.01711 + 1.74193i −0.511775 + 0.127043i
\(189\) −1.20103 + 2.35744i −0.0873623 + 0.171478i
\(190\) −0.807521 6.60470i −0.0585837 0.479155i
\(191\) 7.21637 + 4.16637i 0.522158 + 0.301468i 0.737817 0.675001i \(-0.235857\pi\)
−0.215659 + 0.976469i \(0.569190\pi\)
\(192\) 7.60082 + 2.49551i 0.548542 + 0.180098i
\(193\) 6.18630 + 10.7150i 0.445300 + 0.771282i 0.998073 0.0620498i \(-0.0197638\pi\)
−0.552773 + 0.833332i \(0.686430\pi\)
\(194\) 14.1536 + 6.01639i 1.01617 + 0.431951i
\(195\) −3.61504 −0.258878
\(196\) −2.44387 + 13.7850i −0.174562 + 0.984646i
\(197\) 3.23686 0.230617 0.115308 0.993330i \(-0.463214\pi\)
0.115308 + 0.993330i \(0.463214\pi\)
\(198\) −7.13645 3.03356i −0.507165 0.215586i
\(199\) −9.61504 16.6537i −0.681592 1.18055i −0.974495 0.224410i \(-0.927955\pi\)
0.292903 0.956142i \(-0.405379\pi\)
\(200\) 8.93790 + 7.26054i 0.632005 + 0.513397i
\(201\) −8.17396 4.71924i −0.576546 0.332869i
\(202\) −2.47672 20.2570i −0.174261 1.42528i
\(203\) −2.97869 + 5.84670i −0.209063 + 0.410358i
\(204\) 0.330804 + 1.33260i 0.0231609 + 0.0933004i
\(205\) 4.54378 7.87006i 0.317351 0.549669i
\(206\) 12.7787 + 16.9761i 0.890338 + 1.18278i
\(207\) −1.07465 + 0.620450i −0.0746934 + 0.0431243i
\(208\) −14.9944 0.554380i −1.03968 0.0384393i
\(209\) 26.7700i 1.85172i
\(210\) 2.76334 2.31653i 0.190688 0.159856i
\(211\) 9.24637i 0.636546i −0.947999 0.318273i \(-0.896897\pi\)
0.947999 0.318273i \(-0.103103\pi\)
\(212\) 2.26562 7.87070i 0.155603 0.540562i
\(213\) 8.76095 5.05814i 0.600291 0.346578i
\(214\) −13.6892 + 10.3046i −0.935773 + 0.704405i
\(215\) 2.87878 4.98620i 0.196331 0.340056i
\(216\) 2.64212 1.00956i 0.179773 0.0686918i
\(217\) 12.7562 0.669139i 0.865947 0.0454241i
\(218\) 8.52260 1.04201i 0.577223 0.0705740i
\(219\) −5.76850 3.33044i −0.389799 0.225051i
\(220\) 7.33369 + 7.60984i 0.494437 + 0.513055i
\(221\) −1.28763 2.23024i −0.0866152 0.150022i
\(222\) 1.51194 3.55685i 0.101475 0.238720i
\(223\) 1.94585 0.130303 0.0651517 0.997875i \(-0.479247\pi\)
0.0651517 + 0.997875i \(0.479247\pi\)
\(224\) 11.8170 9.18471i 0.789556 0.613679i
\(225\) 4.07126 0.271417
\(226\) −4.08260 + 9.60432i −0.271571 + 0.638870i
\(227\) 4.32265 + 7.48706i 0.286905 + 0.496933i 0.973069 0.230513i \(-0.0740404\pi\)
−0.686165 + 0.727446i \(0.740707\pi\)
\(228\) −6.77568 7.03083i −0.448731 0.465628i
\(229\) 14.5396 + 8.39446i 0.960805 + 0.554721i 0.896421 0.443204i \(-0.146158\pi\)
0.0643846 + 0.997925i \(0.479492\pi\)
\(230\) 1.67871 0.205247i 0.110691 0.0135336i
\(231\) −12.1664 + 7.90179i −0.800491 + 0.519900i
\(232\) 6.55274 2.50381i 0.430208 0.164383i
\(233\) 0.523283 0.906353i 0.0342814 0.0593772i −0.848376 0.529395i \(-0.822419\pi\)
0.882657 + 0.470018i \(0.155752\pi\)
\(234\) −4.23836 + 3.19043i −0.277070 + 0.208565i
\(235\) 3.01711 1.74193i 0.196814 0.113631i
\(236\) 7.01862 24.3825i 0.456873 1.58717i
\(237\) 1.41442i 0.0918761i
\(238\) 2.41340 + 0.879676i 0.156438 + 0.0570210i
\(239\) 19.2479i 1.24505i 0.782602 + 0.622523i \(0.213892\pi\)
−0.782602 + 0.622523i \(0.786108\pi\)
\(240\) −3.85221 0.142425i −0.248659 0.00919352i
\(241\) −2.38754 + 1.37844i −0.153795 + 0.0887934i −0.574922 0.818208i \(-0.694968\pi\)
0.421128 + 0.907001i \(0.361634\pi\)
\(242\) −16.2157 21.5419i −1.04238 1.38476i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.01711 20.2107i −0.321187 1.29386i
\(245\) −0.705792 6.70895i −0.0450914 0.428619i
\(246\) −1.61843 13.2371i −0.103187 0.843968i
\(247\) 15.8603 + 9.15692i 1.00916 + 0.582641i
\(248\) −10.5992 8.61011i −0.673053 0.546742i
\(249\) −0.271890 0.470927i −0.0172303 0.0298438i
\(250\) −11.3779 4.83650i −0.719600 0.305887i
\(251\) −20.7493 −1.30968 −0.654841 0.755767i \(-0.727264\pi\)
−0.654841 + 0.755767i \(0.727264\pi\)
\(252\) 1.19536 5.15472i 0.0753008 0.324717i
\(253\) −6.80413 −0.427772
\(254\) 15.1536 + 6.44147i 0.950819 + 0.404173i
\(255\) −0.330804 0.572969i −0.0207157 0.0358807i
\(256\) −15.9563 1.18150i −0.997270 0.0738438i
\(257\) 6.45283 + 3.72554i 0.402516 + 0.232393i 0.687569 0.726119i \(-0.258678\pi\)
−0.285053 + 0.958512i \(0.592011\pi\)
\(258\) −1.02538 8.38658i −0.0638375 0.522126i
\(259\) −3.93830 6.06381i −0.244714 0.376787i
\(260\) 7.01711 1.74193i 0.435182 0.108030i
\(261\) 1.24005 2.14784i 0.0767574 0.132948i
\(262\) 7.87711 + 10.4644i 0.486649 + 0.646494i
\(263\) 25.7034 14.8399i 1.58494 0.915066i 0.590818 0.806805i \(-0.298805\pi\)
0.994123 0.108260i \(-0.0345280\pi\)
\(264\) 15.3142 + 2.44966i 0.942524 + 0.150766i
\(265\) 3.94654i 0.242434i
\(266\) −17.9914 + 3.16375i −1.10312 + 0.193982i
\(267\) 0.554380i 0.0339275i
\(268\) 18.1403 + 5.22178i 1.10810 + 0.318971i
\(269\) −3.73727 + 2.15771i −0.227865 + 0.131558i −0.609587 0.792719i \(-0.708665\pi\)
0.381722 + 0.924277i \(0.375331\pi\)
\(270\) −1.08887 + 0.819652i −0.0662668 + 0.0498824i
\(271\) 6.79142 11.7631i 0.412550 0.714557i −0.582618 0.812746i \(-0.697972\pi\)
0.995168 + 0.0981892i \(0.0313050\pi\)
\(272\) −1.28424 2.42728i −0.0778683 0.147176i
\(273\) 0.519893 + 9.91103i 0.0314654 + 0.599843i
\(274\) −10.1493 + 1.24090i −0.613142 + 0.0749656i
\(275\) 19.3328 + 11.1618i 1.16581 + 0.673082i
\(276\) 1.78702 1.72217i 0.107566 0.103663i
\(277\) −1.03563 1.79376i −0.0622250 0.107777i 0.833235 0.552920i \(-0.186486\pi\)
−0.895460 + 0.445143i \(0.853153\pi\)
\(278\) 2.93669 6.90856i 0.176131 0.414348i
\(279\) −4.82802 −0.289046
\(280\) −4.24764 + 5.82811i −0.253845 + 0.348296i
\(281\) 23.7122 1.41455 0.707276 0.706938i \(-0.249924\pi\)
0.707276 + 0.706938i \(0.249924\pi\)
\(282\) 2.00000 4.70500i 0.119098 0.280179i
\(283\) −6.12739 10.6129i −0.364235 0.630874i 0.624418 0.781091i \(-0.285336\pi\)
−0.988653 + 0.150216i \(0.952003\pi\)
\(284\) −14.5685 + 14.0398i −0.864480 + 0.833109i
\(285\) 4.07465 + 2.35250i 0.241362 + 0.139350i
\(286\) −28.8732 + 3.53017i −1.70731 + 0.208743i
\(287\) −22.2301 11.3254i −1.31220 0.668520i
\(288\) −4.64212 + 3.23276i −0.273539 + 0.190492i
\(289\) −8.26434 + 14.3143i −0.486138 + 0.842016i
\(290\) −2.70053 + 2.03282i −0.158580 + 0.119372i
\(291\) −9.41780 + 5.43737i −0.552081 + 0.318744i
\(292\) 12.8019 + 3.68510i 0.749177 + 0.215654i
\(293\) 10.7090i 0.625626i −0.949815 0.312813i \(-0.898729\pi\)
0.949815 0.312813i \(-0.101271\pi\)
\(294\) −6.74843 7.24284i −0.393576 0.422411i
\(295\) 12.2259i 0.711821i
\(296\) −1.22093 + 7.63269i −0.0709649 + 0.443641i
\(297\) 4.74861 2.74161i 0.275542 0.159084i
\(298\) 3.96477 + 5.26704i 0.229673 + 0.305112i
\(299\) −2.32741 + 4.03120i −0.134598 + 0.233130i
\(300\) −7.90267 + 1.96176i −0.456261 + 0.113262i
\(301\) −14.0842 7.17541i −0.811801 0.413584i
\(302\) −2.09495 17.1345i −0.120551 0.985982i
\(303\) 12.4972 + 7.21527i 0.717946 + 0.414506i
\(304\) 16.5400 + 10.3825i 0.948636 + 0.595480i
\(305\) 5.01711 + 8.68988i 0.287279 + 0.497581i
\(306\) −0.893512 0.379814i −0.0510787 0.0217125i
\(307\) 4.22056 0.240880 0.120440 0.992721i \(-0.461569\pi\)
0.120440 + 0.992721i \(0.461569\pi\)
\(308\) 19.8085 21.2005i 1.12870 1.20801i
\(309\) −15.0247 −0.854725
\(310\) 6.05567 + 2.57414i 0.343939 + 0.146201i
\(311\) −4.85070 8.40165i −0.275058 0.476414i 0.695092 0.718921i \(-0.255364\pi\)
−0.970150 + 0.242507i \(0.922030\pi\)
\(312\) 6.68969 8.23517i 0.378729 0.466225i
\(313\) 11.8328 + 6.83168i 0.668831 + 0.386149i 0.795633 0.605778i \(-0.207138\pi\)
−0.126803 + 0.991928i \(0.540472\pi\)
\(314\) 3.76434 + 30.7885i 0.212434 + 1.73750i
\(315\) 0.133565 + 2.54624i 0.00752556 + 0.143464i
\(316\) 0.681544 + 2.74550i 0.0383398 + 0.154447i
\(317\) −10.0442 + 17.3970i −0.564138 + 0.977115i 0.432992 + 0.901398i \(0.357458\pi\)
−0.997129 + 0.0757171i \(0.975875\pi\)
\(318\) 3.48299 + 4.62701i 0.195316 + 0.259470i
\(319\) 11.7771 6.79948i 0.659388 0.380698i
\(320\) 7.54610 1.57975i 0.421840 0.0883106i
\(321\) 12.1156i 0.676229i
\(322\) −0.804130 4.57286i −0.0448124 0.254836i
\(323\) 3.35171i 0.186494i
\(324\) −0.553244 + 1.92196i −0.0307358 + 0.106775i
\(325\) 13.2259 7.63599i 0.733642 0.423569i
\(326\) −4.54039 + 3.41778i −0.251469 + 0.189294i
\(327\) −3.03563 + 5.25787i −0.167871 + 0.290761i
\(328\) 9.51989 + 24.9145i 0.525648 + 1.37568i
\(329\) −5.20959 8.02121i −0.287214 0.442224i
\(330\) −7.41780 + 0.906935i −0.408337 + 0.0499251i
\(331\) 8.15886 + 4.71052i 0.448452 + 0.258914i 0.707176 0.707037i \(-0.249969\pi\)
−0.258724 + 0.965951i \(0.583302\pi\)
\(332\) 0.754681 + 0.783099i 0.0414185 + 0.0429781i
\(333\) 1.36643 + 2.36673i 0.0748802 + 0.129696i
\(334\) 8.14252 19.1553i 0.445539 1.04813i
\(335\) −9.09596 −0.496965
\(336\) 0.163526 + 10.5817i 0.00892109 + 0.577281i
\(337\) −13.4411 −0.732185 −0.366092 0.930578i \(-0.619305\pi\)
−0.366092 + 0.930578i \(0.619305\pi\)
\(338\) −0.592669 + 1.39425i −0.0322369 + 0.0758374i
\(339\) −3.68969 6.39074i −0.200397 0.347097i
\(340\) 0.918207 + 0.952783i 0.0497968 + 0.0516719i
\(341\) −22.9264 13.2365i −1.24153 0.716799i
\(342\) 6.85340 0.837928i 0.370589 0.0453100i
\(343\) −18.2918 + 2.89985i −0.987666 + 0.156577i
\(344\) 6.03148 + 15.7850i 0.325195 + 0.851070i
\(345\) −0.597935 + 1.03565i −0.0321917 + 0.0557577i
\(346\) −13.1664 + 9.91103i −0.707831 + 0.532820i
\(347\) −19.5890 + 11.3097i −1.05159 + 0.607136i −0.923094 0.384574i \(-0.874349\pi\)
−0.128497 + 0.991710i \(0.541015\pi\)
\(348\) −1.37210 + 4.76666i −0.0735525 + 0.255520i
\(349\) 2.48180i 0.132848i −0.997791 0.0664239i \(-0.978841\pi\)
0.997791 0.0664239i \(-0.0211590\pi\)
\(350\) −5.21673 + 14.3122i −0.278846 + 0.765018i
\(351\) 3.75117i 0.200223i
\(352\) −30.9066 + 2.62423i −1.64733 + 0.139872i
\(353\) −7.89315 + 4.55711i −0.420110 + 0.242551i −0.695124 0.718889i \(-0.744651\pi\)
0.275014 + 0.961440i \(0.411317\pi\)
\(354\) 10.7899 + 14.3340i 0.573477 + 0.761841i
\(355\) 4.87458 8.44303i 0.258716 0.448109i
\(356\) −0.267131 1.07610i −0.0141579 0.0570331i
\(357\) −1.52328 + 0.989336i −0.0806207 + 0.0523612i
\(358\) 0.445241 + 3.64162i 0.0235317 + 0.192466i
\(359\) −6.00000 3.46410i −0.316668 0.182828i 0.333238 0.942843i \(-0.391859\pi\)
−0.649906 + 0.760014i \(0.725192\pi\)
\(360\) 1.71865 2.11569i 0.0905806 0.111507i
\(361\) −2.41780 4.18776i −0.127253 0.220408i
\(362\) −12.4078 5.27431i −0.652141 0.277212i
\(363\) 19.0657 1.00069
\(364\) −5.78484 18.9877i −0.303208 0.995223i
\(365\) −6.41917 −0.335995
\(366\) 13.5514 + 5.76041i 0.708341 + 0.301101i
\(367\) −1.91680 3.31999i −0.100056 0.173302i 0.811652 0.584142i \(-0.198569\pi\)
−0.911707 + 0.410840i \(0.865235\pi\)
\(368\) −2.63893 + 4.20398i −0.137564 + 0.219147i
\(369\) 8.16641 + 4.71488i 0.425126 + 0.245447i
\(370\) −0.452022 3.69708i −0.0234995 0.192202i
\(371\) 10.8199 0.567567i 0.561740 0.0294666i
\(372\) 9.37160 2.32641i 0.485895 0.120619i
\(373\) 13.4150 23.2355i 0.694603 1.20309i −0.275711 0.961241i \(-0.588913\pi\)
0.970314 0.241848i \(-0.0777534\pi\)
\(374\) −3.20164 4.25325i −0.165553 0.219930i
\(375\) 7.57086 4.37104i 0.390957 0.225719i
\(376\) −1.61504 + 10.0965i −0.0832894 + 0.520689i
\(377\) 9.30330i 0.479144i
\(378\) 2.40376 + 2.86739i 0.123636 + 0.147483i
\(379\) 6.93692i 0.356325i −0.984001 0.178163i \(-0.942985\pi\)
0.984001 0.178163i \(-0.0570153\pi\)
\(380\) −9.04282 2.60301i −0.463887 0.133532i
\(381\) −10.0832 + 5.82154i −0.516578 + 0.298247i
\(382\) 9.41497 7.08713i 0.481712 0.362609i
\(383\) 1.12881 1.95515i 0.0576793 0.0999035i −0.835744 0.549119i \(-0.814963\pi\)
0.893423 + 0.449216i \(0.148297\pi\)
\(384\) 7.45303 8.51189i 0.380336 0.434371i
\(385\) −6.34654 + 12.4573i −0.323450 + 0.634881i
\(386\) 17.3682 2.12351i 0.884017 0.108084i
\(387\) 5.17396 + 2.98718i 0.263007 + 0.151847i
\(388\) 15.6607 15.0924i 0.795054 0.766202i
\(389\) −15.3047 26.5086i −0.775981 1.34404i −0.934242 0.356641i \(-0.883922\pi\)
0.158261 0.987397i \(-0.449411\pi\)
\(390\) −2.00000 + 4.70500i −0.101274 + 0.238247i
\(391\) −0.851904 −0.0430827
\(392\) 16.5893 + 10.8072i 0.837885 + 0.545847i
\(393\) −9.26156 −0.467184
\(394\) 1.79078 4.21280i 0.0902179 0.212238i
\(395\) −0.681544 1.18047i −0.0342922 0.0593958i
\(396\) −7.89640 + 7.60984i −0.396809 + 0.382409i
\(397\) −12.0368 6.94947i −0.604112 0.348784i 0.166546 0.986034i \(-0.446739\pi\)
−0.770657 + 0.637250i \(0.780072\pi\)
\(398\) −26.9944 + 3.30046i −1.35311 + 0.165437i
\(399\) 5.86365 11.5094i 0.293550 0.576192i
\(400\) 14.3945 7.61589i 0.719724 0.380794i
\(401\) 5.13832 8.89984i 0.256596 0.444437i −0.708732 0.705478i \(-0.750732\pi\)
0.965328 + 0.261041i \(0.0840658\pi\)
\(402\) −10.6643 + 8.02757i −0.531887 + 0.400379i
\(403\) −15.6843 + 9.05535i −0.781292 + 0.451079i
\(404\) −27.7349 7.98361i −1.37986 0.397199i
\(405\) 0.963711i 0.0478872i
\(406\) 5.96158 + 7.11144i 0.295868 + 0.352935i
\(407\) 14.9849i 0.742775i
\(408\) 1.91740 + 0.306707i 0.0949254 + 0.0151843i
\(409\) 10.5342 6.08193i 0.520883 0.300732i −0.216413 0.976302i \(-0.569436\pi\)
0.737296 + 0.675570i \(0.236102\pi\)
\(410\) −7.72912 10.2678i −0.381714 0.507092i
\(411\) 3.61504 6.26144i 0.178317 0.308854i
\(412\) 29.1642 7.23973i 1.43682 0.356676i
\(413\) 33.5187 1.75826i 1.64935 0.0865182i
\(414\) 0.212976 + 1.74193i 0.0104672 + 0.0856111i
\(415\) −0.453838 0.262023i −0.0222780 0.0128622i
\(416\) −9.01711 + 19.2086i −0.442100 + 0.941781i
\(417\) 2.65406 + 4.59697i 0.129970 + 0.225115i
\(418\) 34.8414 + 14.8104i 1.70415 + 0.724398i
\(419\) 16.2245 0.792619 0.396310 0.918117i \(-0.370291\pi\)
0.396310 + 0.918117i \(0.370291\pi\)
\(420\) −1.48618 4.87811i −0.0725182 0.238027i
\(421\) −9.58477 −0.467133 −0.233567 0.972341i \(-0.575040\pi\)
−0.233567 + 0.972341i \(0.575040\pi\)
\(422\) −12.0342 5.11550i −0.585816 0.249019i
\(423\) 1.80752 + 3.13072i 0.0878847 + 0.152221i
\(424\) −8.99034 7.30313i −0.436609 0.354672i
\(425\) 2.42055 + 1.39750i 0.117414 + 0.0677889i
\(426\) −1.73626 14.2008i −0.0841220 0.688032i
\(427\) 23.1027 15.0047i 1.11802 0.726127i
\(428\) 5.83799 + 23.5175i 0.282190 + 1.13676i
\(429\) 10.2842 17.8128i 0.496528 0.860011i
\(430\) −4.89690 6.50534i −0.236150 0.313715i
\(431\) −0.131544 + 0.0759470i −0.00633626 + 0.00365824i −0.503165 0.864190i \(-0.667831\pi\)
0.496829 + 0.867849i \(0.334498\pi\)
\(432\) 0.147789 3.99727i 0.00711048 0.192319i
\(433\) 9.46997i 0.455098i −0.973767 0.227549i \(-0.926929\pi\)
0.973767 0.227549i \(-0.0730711\pi\)
\(434\) 6.18640 16.9725i 0.296957 0.814705i
\(435\) 2.39011i 0.114597i
\(436\) 3.35889 11.6687i 0.160862 0.558830i
\(437\) 5.24663 3.02915i 0.250981 0.144904i
\(438\) −7.52599 + 5.66520i −0.359606 + 0.270694i
\(439\) −16.7373 + 28.9898i −0.798826 + 1.38361i 0.121555 + 0.992585i \(0.461212\pi\)
−0.920381 + 0.391023i \(0.872121\pi\)
\(440\) 13.9616 5.33475i 0.665592 0.254324i
\(441\) 6.96158 0.732369i 0.331504 0.0348747i
\(442\) −3.61504 + 0.441992i −0.171950 + 0.0210234i
\(443\) −22.6513 13.0777i −1.07619 0.621341i −0.146327 0.989236i \(-0.546745\pi\)
−0.929867 + 0.367895i \(0.880079\pi\)
\(444\) −3.79279 3.93561i −0.179998 0.186776i
\(445\) 0.267131 + 0.462684i 0.0126632 + 0.0219333i
\(446\) 1.07653 2.53253i 0.0509750 0.119919i
\(447\) −4.66161 −0.220486
\(448\) −5.41629 20.4613i −0.255896 0.966704i
\(449\) 10.2918 0.485701 0.242851 0.970064i \(-0.421918\pi\)
0.242851 + 0.970064i \(0.421918\pi\)
\(450\) 2.25240 5.29878i 0.106179 0.249787i
\(451\) 25.8527 + 44.7782i 1.21736 + 2.10852i
\(452\) 10.2414 + 10.6271i 0.481716 + 0.499855i
\(453\) 10.5709 + 6.10309i 0.496662 + 0.286748i
\(454\) 12.1359 1.48380i 0.569568 0.0696380i
\(455\) 5.20959 + 8.02121i 0.244229 + 0.376040i
\(456\) −12.8993 + 4.92884i −0.604064 + 0.230814i
\(457\) −5.96574 + 10.3330i −0.279065 + 0.483356i −0.971153 0.238458i \(-0.923358\pi\)
0.692087 + 0.721814i \(0.256691\pi\)
\(458\) 18.9694 14.2792i 0.886382 0.667225i
\(459\) 0.594545 0.343260i 0.0277510 0.0160220i
\(460\) 0.661608 2.29841i 0.0308476 0.107164i
\(461\) 30.0093i 1.39767i 0.715281 + 0.698837i \(0.246299\pi\)
−0.715281 + 0.698837i \(0.753701\pi\)
\(462\) 3.55324 + 20.2063i 0.165312 + 0.940082i
\(463\) 13.2736i 0.616875i 0.951245 + 0.308437i \(0.0998060\pi\)
−0.951245 + 0.308437i \(0.900194\pi\)
\(464\) 0.366532 9.91365i 0.0170158 0.460230i
\(465\) −4.02945 + 2.32641i −0.186861 + 0.107885i
\(466\) −0.890122 1.18249i −0.0412341 0.0547778i
\(467\) 14.8246 25.6770i 0.686002 1.18819i −0.287119 0.957895i \(-0.592697\pi\)
0.973121 0.230295i \(-0.0739692\pi\)
\(468\) 1.80752 + 7.28134i 0.0835527 + 0.336580i
\(469\) 1.30812 + 24.9376i 0.0604036 + 1.15151i
\(470\) −0.597935 4.89050i −0.0275807 0.225582i
\(471\) −18.9944 10.9664i −0.875217 0.505307i
\(472\) −27.8510 22.6243i −1.28195 1.04137i
\(473\) 16.3794 + 28.3699i 0.753125 + 1.30445i
\(474\) −1.84087 0.782517i −0.0845540 0.0359422i
\(475\) −19.8766 −0.912001
\(476\) 2.48011 2.65439i 0.113676 0.121664i
\(477\) −4.09515 −0.187504
\(478\) 25.0513 + 10.6488i 1.14582 + 0.487065i
\(479\) −5.76773 9.99001i −0.263535 0.456455i 0.703644 0.710553i \(-0.251555\pi\)
−0.967179 + 0.254097i \(0.918222\pi\)
\(480\) −2.31658 + 4.93488i −0.105737 + 0.225246i
\(481\) 8.87802 + 5.12573i 0.404803 + 0.233713i
\(482\) 0.473165 + 3.87001i 0.0215521 + 0.176274i
\(483\) 2.92535 + 1.49036i 0.133108 + 0.0678138i
\(484\) −37.0081 + 9.18691i −1.68219 + 0.417587i
\(485\) −5.24005 + 9.07604i −0.237939 + 0.412122i
\(486\) −0.850516 1.12988i −0.0385802 0.0512523i
\(487\) −8.44822 + 4.87758i −0.382825 + 0.221024i −0.679047 0.734095i \(-0.737607\pi\)
0.296221 + 0.955119i \(0.404273\pi\)
\(488\) −29.0801 4.65165i −1.31639 0.210570i
\(489\) 4.01848i 0.181722i
\(490\) −9.12223 2.79310i −0.412100 0.126179i
\(491\) 40.4736i 1.82655i −0.407346 0.913274i \(-0.633546\pi\)
0.407346 0.913274i \(-0.366454\pi\)
\(492\) −18.1236 5.21696i −0.817075 0.235199i
\(493\) 1.47453 0.851323i 0.0664097 0.0383416i
\(494\) 20.6924 15.5762i 0.930995 0.700808i
\(495\) 2.64212 4.57628i 0.118754 0.205689i
\(496\) −17.0701 + 9.03151i −0.766470 + 0.405527i
\(497\) −23.8485 12.1500i −1.06975 0.545001i
\(498\) −0.763337 + 0.0933291i −0.0342059 + 0.00418218i
\(499\) −27.6827 15.9826i −1.23925 0.715480i −0.270307 0.962774i \(-0.587125\pi\)
−0.968941 + 0.247294i \(0.920459\pi\)
\(500\) −12.5895 + 12.1326i −0.563019 + 0.542587i
\(501\) 7.35889 + 12.7460i 0.328771 + 0.569448i
\(502\) −11.4794 + 27.0053i −0.512351 + 1.20531i
\(503\) 22.7110 1.01263 0.506317 0.862348i \(-0.331007\pi\)
0.506317 + 0.862348i \(0.331007\pi\)
\(504\) −6.04757 4.40759i −0.269380 0.196330i
\(505\) 13.9069 0.618847
\(506\) −3.76434 + 8.85562i −0.167346 + 0.393681i
\(507\) −0.535631 0.927740i −0.0237882 0.0412024i
\(508\) 16.7672 16.1588i 0.743925 0.716929i
\(509\) −1.98947 1.14862i −0.0881819 0.0509118i 0.455261 0.890358i \(-0.349546\pi\)
−0.543443 + 0.839446i \(0.682879\pi\)
\(510\) −0.928739 + 0.113552i −0.0411252 + 0.00502816i
\(511\) 0.923166 + 17.5989i 0.0408384 + 0.778528i
\(512\) −10.3655 + 20.1136i −0.458093 + 0.888904i
\(513\) −2.44109 + 4.22809i −0.107777 + 0.186675i
\(514\) 8.41881 6.33727i 0.371338 0.279525i
\(515\) −12.5396 + 7.23973i −0.552560 + 0.319021i
\(516\) −11.4825 3.30528i −0.505488 0.145507i
\(517\) 19.8221i 0.871773i
\(518\) −10.0709 + 1.77096i −0.442491 + 0.0778114i
\(519\) 11.6530i 0.511508i
\(520\) 1.61504 10.0965i 0.0708242 0.442762i
\(521\) −32.5712 + 18.8050i −1.42697 + 0.823862i −0.996881 0.0789240i \(-0.974852\pi\)
−0.430090 + 0.902786i \(0.641518\pi\)
\(522\) −2.10937 2.80222i −0.0923247 0.122650i
\(523\) −17.8444 + 30.9073i −0.780279 + 1.35148i 0.151500 + 0.988457i \(0.451590\pi\)
−0.931779 + 0.363026i \(0.881744\pi\)
\(524\) 17.9775 4.46273i 0.785350 0.194955i
\(525\) −5.86704 9.03350i −0.256059 0.394254i
\(526\) −5.09394 41.6632i −0.222106 1.81660i
\(527\) −2.87047 1.65727i −0.125040 0.0721917i
\(528\) 11.6607 18.5763i 0.507469 0.808429i
\(529\) −10.7301 18.5850i −0.466525 0.808046i
\(530\) 5.13645 + 2.18340i 0.223113 + 0.0948408i
\(531\) −12.6863 −0.550539
\(532\) −5.83597 + 25.1662i −0.253021 + 1.09109i
\(533\) 35.3726 1.53216
\(534\) 0.721529 + 0.306707i 0.0312236 + 0.0132725i
\(535\) −5.83799 10.1117i −0.252398 0.437167i
\(536\) 16.8322 20.7209i 0.727041 0.895005i
\(537\) −2.24663 1.29709i −0.0969494 0.0559738i
\(538\) 0.740657 + 6.05782i 0.0319320 + 0.261171i
\(539\) 35.0657 + 15.6082i 1.51039 + 0.672293i
\(540\) 0.464369 + 1.87065i 0.0199833 + 0.0804998i
\(541\) −18.5102 + 32.0605i −0.795814 + 1.37839i 0.126507 + 0.991966i \(0.459623\pi\)
−0.922321 + 0.386425i \(0.873710\pi\)
\(542\) −11.5524 15.3469i −0.496219 0.659208i
\(543\) 8.25620 4.76672i 0.354307 0.204559i
\(544\) −3.86963 + 0.328564i −0.165909 + 0.0140871i
\(545\) 5.85094i 0.250627i
\(546\) 13.1869 + 4.80657i 0.564347 + 0.205702i
\(547\) 2.09106i 0.0894073i −0.999000 0.0447036i \(-0.985766\pi\)
0.999000 0.0447036i \(-0.0142344\pi\)
\(548\) −4.00000 + 13.8959i −0.170872 + 0.593604i
\(549\) −9.01711 + 5.20603i −0.384841 + 0.222188i
\(550\) 25.2229 18.9866i 1.07551 0.809591i
\(551\) −6.05415 + 10.4861i −0.257916 + 0.446723i
\(552\) −1.25276 3.27861i −0.0533211 0.139547i
\(553\) −3.13837 + 2.03829i −0.133457 + 0.0866771i
\(554\) −2.90755 + 0.355491i −0.123530 + 0.0151034i
\(555\) 2.28085 + 1.31685i 0.0968166 + 0.0558971i
\(556\) −7.36684 7.64424i −0.312424 0.324188i
\(557\) 8.39887 + 14.5473i 0.355872 + 0.616388i 0.987267 0.159073i \(-0.0508507\pi\)
−0.631395 + 0.775461i \(0.717517\pi\)
\(558\) −2.67107 + 6.28370i −0.113075 + 0.266010i
\(559\) 22.4109 0.947878
\(560\) 5.23535 + 8.75271i 0.221234 + 0.369869i
\(561\) 3.76434 0.158931
\(562\) 13.1186 30.8616i 0.553376 1.30182i
\(563\) 8.69784 + 15.0651i 0.366570 + 0.634918i 0.989027 0.147736i \(-0.0471986\pi\)
−0.622456 + 0.782654i \(0.713865\pi\)
\(564\) −5.01711 5.20603i −0.211258 0.219213i
\(565\) −6.15882 3.55580i −0.259104 0.149594i
\(566\) −17.2028 + 2.10329i −0.723086 + 0.0884079i
\(567\) −2.64212 + 0.138595i −0.110959 + 0.00582044i
\(568\) 10.2130 + 26.7284i 0.428527 + 1.12150i
\(569\) 17.1425 29.6917i 0.718652 1.24474i −0.242882 0.970056i \(-0.578093\pi\)
0.961534 0.274686i \(-0.0885739\pi\)
\(570\) 5.31607 4.00168i 0.222666 0.167612i
\(571\) 5.14176 2.96860i 0.215176 0.124232i −0.388539 0.921432i \(-0.627020\pi\)
0.603715 + 0.797201i \(0.293687\pi\)
\(572\) −11.3794 + 39.5317i −0.475796 + 1.65290i
\(573\) 8.33274i 0.348105i
\(574\) −27.0388 + 22.6669i −1.12858 + 0.946097i
\(575\) 5.05203i 0.210684i
\(576\) 1.63924 + 7.83026i 0.0683015 + 0.326261i
\(577\) 33.7930 19.5104i 1.40682 0.812229i 0.411742 0.911300i \(-0.364920\pi\)
0.995080 + 0.0990712i \(0.0315871\pi\)
\(578\) 14.0579 + 18.6754i 0.584732 + 0.776794i
\(579\) −6.18630 + 10.7150i −0.257094 + 0.445300i
\(580\) 1.15169 + 4.63940i 0.0478211 + 0.192641i
\(581\) −0.653097 + 1.28193i −0.0270950 + 0.0531833i
\(582\) 1.86643 + 15.2655i 0.0773662 + 0.632777i
\(583\) −19.4462 11.2273i −0.805381 0.464987i
\(584\) 11.8788 14.6231i 0.491547 0.605107i
\(585\) −1.80752 3.13072i −0.0747318 0.129439i
\(586\) −13.9378 5.92469i −0.575767 0.244747i
\(587\) −7.71931 −0.318610 −0.159305 0.987229i \(-0.550925\pi\)
−0.159305 + 0.987229i \(0.550925\pi\)
\(588\) −13.1601 + 4.77607i −0.542715 + 0.196962i
\(589\) 23.5712 0.971235
\(590\) 15.9121 + 6.76392i 0.655092 + 0.278466i
\(591\) 1.61843 + 2.80321i 0.0665734 + 0.115308i
\(592\) 9.25853 + 5.81178i 0.380523 + 0.238863i
\(593\) 0.336377 + 0.194207i 0.0138133 + 0.00797513i 0.506891 0.862010i \(-0.330795\pi\)
−0.493077 + 0.869985i \(0.664128\pi\)
\(594\) −0.941086 7.69713i −0.0386132 0.315817i
\(595\) −0.794612 + 1.55970i −0.0325759 + 0.0639415i
\(596\) 9.04858 2.24622i 0.370644 0.0920088i
\(597\) 9.61504 16.6537i 0.393517 0.681592i
\(598\) 3.95901 + 5.25938i 0.161896 + 0.215072i
\(599\) 18.0000 10.3923i 0.735460 0.424618i −0.0849563 0.996385i \(-0.527075\pi\)
0.820416 + 0.571767i \(0.193742\pi\)
\(600\) −1.81886 + 11.3707i −0.0742547 + 0.464207i
\(601\) 26.4110i 1.07733i −0.842521 0.538664i \(-0.818929\pi\)
0.842521 0.538664i \(-0.181071\pi\)
\(602\) −17.1309 + 14.3610i −0.698202 + 0.585309i
\(603\) 9.43847i 0.384364i
\(604\) −23.4598 6.75299i −0.954564 0.274775i
\(605\) 15.9122 9.18691i 0.646922 0.373501i
\(606\) 16.3047 12.2734i 0.662335 0.498573i
\(607\) 20.3531 35.2526i 0.826106 1.43086i −0.0749655 0.997186i \(-0.523885\pi\)
0.901071 0.433671i \(-0.142782\pi\)
\(608\) 22.6636 15.7829i 0.919131 0.640081i
\(609\) −6.55274 + 0.343730i −0.265530 + 0.0139287i
\(610\) 14.0856 1.72217i 0.570310 0.0697288i
\(611\) 11.7438 + 6.78031i 0.475105 + 0.274302i
\(612\) −0.988660 + 0.952783i −0.0399642 + 0.0385140i
\(613\) −8.66920 15.0155i −0.350146 0.606470i 0.636129 0.771583i \(-0.280535\pi\)
−0.986275 + 0.165113i \(0.947201\pi\)
\(614\) 2.33500 5.49310i 0.0942330 0.221683i
\(615\) 9.08756 0.366446
\(616\) −16.6337 37.5100i −0.670189 1.51132i
\(617\) −46.4753 −1.87103 −0.935513 0.353291i \(-0.885062\pi\)
−0.935513 + 0.353291i \(0.885062\pi\)
\(618\) −8.31232 + 19.5547i −0.334371 + 0.786607i
\(619\) 13.1911 + 22.8476i 0.530194 + 0.918322i 0.999379 + 0.0352227i \(0.0112141\pi\)
−0.469186 + 0.883099i \(0.655453\pi\)
\(620\) 6.70053 6.45737i 0.269100 0.259334i
\(621\) −1.07465 0.620450i −0.0431243 0.0248978i
\(622\) −13.6184 + 1.66505i −0.546049 + 0.0667625i
\(623\) 1.23008 0.798909i 0.0492822 0.0320076i
\(624\) −7.01711 13.2627i −0.280909 0.530935i
\(625\) −5.96574 + 10.3330i −0.238630 + 0.413318i
\(626\) 15.4379 11.6209i 0.617023 0.464465i
\(627\) −23.1835 + 13.3850i −0.925860 + 0.534546i
\(628\) 42.1541 + 12.1342i 1.68213 + 0.484209i
\(629\) 1.87617i 0.0748079i
\(630\) 3.38784 + 1.23485i 0.134975 + 0.0491978i
\(631\) 41.0696i 1.63495i −0.575961 0.817477i \(-0.695372\pi\)
0.575961 0.817477i \(-0.304628\pi\)
\(632\) 3.95035 + 0.631898i 0.157137 + 0.0251356i
\(633\) 8.00759 4.62318i 0.318273 0.183755i
\(634\) 17.0855 + 22.6974i 0.678551 + 0.901428i
\(635\) −5.61028 + 9.71729i −0.222637 + 0.385619i
\(636\) 7.94904 1.97327i 0.315200 0.0782452i
\(637\) 21.2418 15.4362i 0.841632 0.611605i
\(638\) −2.33399 19.0897i −0.0924037 0.755768i
\(639\) 8.76095 + 5.05814i 0.346578 + 0.200097i
\(640\) 2.11878 10.6953i 0.0837522 0.422769i
\(641\) −22.7239 39.3590i −0.897540 1.55459i −0.830629 0.556827i \(-0.812019\pi\)
−0.0669115 0.997759i \(-0.521315\pi\)
\(642\) −15.7686 6.70291i −0.622337 0.264543i
\(643\) −30.5534 −1.20491 −0.602454 0.798154i \(-0.705810\pi\)
−0.602454 + 0.798154i \(0.705810\pi\)
\(644\) −6.39649 1.48333i −0.252057 0.0584513i
\(645\) 5.75756 0.226704
\(646\) 4.36228 + 1.85432i 0.171632 + 0.0729571i
\(647\) 18.0896 + 31.3321i 0.711175 + 1.23179i 0.964417 + 0.264388i \(0.0851698\pi\)
−0.253242 + 0.967403i \(0.581497\pi\)
\(648\) 2.19536 + 1.78336i 0.0862420 + 0.0700571i
\(649\) −60.2423 34.7809i −2.36472 1.36527i
\(650\) −2.62113 21.4382i −0.102809 0.840876i
\(651\) 6.95759 + 10.7126i 0.272689 + 0.419861i
\(652\) 1.93633 + 7.80022i 0.0758324 + 0.305480i
\(653\) 4.11545 7.12816i 0.161050 0.278946i −0.774196 0.632946i \(-0.781845\pi\)
0.935245 + 0.354000i \(0.115179\pi\)
\(654\) 5.16371 + 6.85978i 0.201917 + 0.268239i
\(655\) −7.72968 + 4.46273i −0.302024 + 0.174373i
\(656\) 37.6933 + 1.39361i 1.47168 + 0.0544114i
\(657\) 6.66089i 0.259866i
\(658\) −13.3218 + 2.34262i −0.519339 + 0.0913250i
\(659\) 22.8837i 0.891422i −0.895177 0.445711i \(-0.852951\pi\)
0.895177 0.445711i \(-0.147049\pi\)
\(660\) −2.92347 + 10.1561i −0.113796 + 0.395325i
\(661\) −17.7212 + 10.2313i −0.689275 + 0.397953i −0.803340 0.595520i \(-0.796946\pi\)
0.114065 + 0.993473i \(0.463613\pi\)
\(662\) 10.6446 8.01275i 0.413715 0.311424i
\(663\) 1.28763 2.23024i 0.0500073 0.0866152i
\(664\) 1.43673 0.548978i 0.0557560 0.0213045i
\(665\) −0.652090 12.4312i −0.0252870 0.482060i
\(666\) 3.83629 0.469043i 0.148653 0.0181750i
\(667\) −2.66525 1.53878i −0.103199 0.0595819i
\(668\) −20.4260 21.1951i −0.790304 0.820063i
\(669\) 0.972923 + 1.68515i 0.0376154 + 0.0651517i
\(670\) −5.03228 + 11.8385i −0.194414 + 0.457359i
\(671\) −57.0916 −2.20400
\(672\) 13.8627 + 5.64145i 0.534765 + 0.217624i
\(673\) 4.23008 0.163058 0.0815289 0.996671i \(-0.474020\pi\)
0.0815289 + 0.996671i \(0.474020\pi\)
\(674\) −7.43622 + 17.4937i −0.286433 + 0.673833i
\(675\) 2.03563 + 3.52582i 0.0783515 + 0.135709i
\(676\) 1.48674 + 1.54273i 0.0571824 + 0.0593356i
\(677\) 20.7962 + 12.0067i 0.799262 + 0.461454i 0.843213 0.537580i \(-0.180661\pi\)
−0.0439511 + 0.999034i \(0.513995\pi\)
\(678\) −10.3589 + 1.26653i −0.397831 + 0.0486406i
\(679\) 25.6365 + 13.0609i 0.983840 + 0.501232i
\(680\) 1.74805 0.667932i 0.0670345 0.0256140i
\(681\) −4.32265 + 7.48706i −0.165644 + 0.286905i
\(682\) −29.9113 + 22.5158i −1.14536 + 0.862174i
\(683\) −7.09951 + 4.09890i −0.271655 + 0.156840i −0.629640 0.776887i \(-0.716797\pi\)
0.357984 + 0.933728i \(0.383464\pi\)
\(684\) 2.70103 9.38333i 0.103277 0.358781i
\(685\) 6.96771i 0.266222i
\(686\) −6.34567 + 25.4113i −0.242279 + 0.970207i
\(687\) 16.7889i 0.640537i
\(688\) 23.8812 + 0.882944i 0.910461 + 0.0336619i
\(689\) −13.3035 + 7.68079i −0.506824 + 0.292615i
\(690\) 1.01711 + 1.35119i 0.0387206 + 0.0514388i
\(691\) 17.9925 31.1638i 0.684465 1.18553i −0.289139 0.957287i \(-0.593369\pi\)
0.973605 0.228242i \(-0.0732976\pi\)
\(692\) 5.61504 + 22.6194i 0.213452 + 0.859860i
\(693\) −12.9264 6.58552i −0.491032 0.250163i
\(694\) 3.88217 + 31.7522i 0.147365 + 1.20530i
\(695\) 4.43015 + 2.55775i 0.168045 + 0.0970209i
\(696\) 5.44473 + 4.42293i 0.206382 + 0.167651i
\(697\) 3.23686 + 5.60641i 0.122605 + 0.212358i
\(698\) −3.23008 1.37304i −0.122260 0.0519704i
\(699\) 1.04657 0.0395848
\(700\) 15.7413 + 14.7077i 0.594964 + 0.555900i
\(701\) −12.9471 −0.489003 −0.244502 0.969649i \(-0.578624\pi\)
−0.244502 + 0.969649i \(0.578624\pi\)
\(702\) −4.88217 2.07531i −0.184266 0.0783276i
\(703\) −6.67117 11.5548i −0.251608 0.435798i
\(704\) −13.6834 + 41.6769i −0.515713 + 1.57076i
\(705\) 3.01711 + 1.74193i 0.113631 + 0.0656048i
\(706\) 1.56428 + 12.7942i 0.0588723 + 0.481516i
\(707\) −2.00000 38.1272i −0.0752177 1.43392i
\(708\) 24.6252 6.11296i 0.925472 0.229739i
\(709\) −6.65603 + 11.5286i −0.249973 + 0.432965i −0.963518 0.267644i \(-0.913755\pi\)
0.713545 + 0.700609i \(0.247088\pi\)
\(710\) −8.29183 11.0154i −0.311187 0.413399i
\(711\) 1.22492 0.707208i 0.0459381 0.0265224i
\(712\) −1.54834 0.247673i −0.0580265 0.00928192i
\(713\) 5.99109i 0.224368i
\(714\) 0.444880 + 2.52991i 0.0166492 + 0.0946794i
\(715\) 19.8221i 0.741303i
\(716\) 4.98592 + 1.43522i 0.186333 + 0.0536367i
\(717\) −16.6692 + 9.62396i −0.622523 + 0.359414i
\(718\) −7.82802 + 5.89255i −0.292139 + 0.219908i
\(719\) −23.7520 + 41.1397i −0.885800 + 1.53425i −0.0410056 + 0.999159i \(0.513056\pi\)
−0.844794 + 0.535091i \(0.820277\pi\)
\(720\) −1.80276 3.40733i −0.0671850 0.126984i
\(721\) 21.6519 + 33.3375i 0.806358 + 1.24155i
\(722\) −6.78803 + 0.829936i −0.252624 + 0.0308870i
\(723\) −2.38754 1.37844i −0.0887934 0.0512649i
\(724\) −13.7291 + 13.2309i −0.510239 + 0.491723i
\(725\) 5.04858 + 8.74440i 0.187500 + 0.324759i
\(726\) 10.5480 24.8141i 0.391472 0.920939i
\(727\) 24.3567 0.903340 0.451670 0.892185i \(-0.350828\pi\)
0.451670 + 0.892185i \(0.350828\pi\)
\(728\) −27.9130 2.97579i −1.03452 0.110290i
\(729\) 1.00000 0.0370370
\(730\) −3.55137 + 8.35460i −0.131442 + 0.309218i
\(731\) 2.05076 + 3.55203i 0.0758503 + 0.131377i
\(732\) 14.9944 14.4503i 0.554210 0.534098i
\(733\) 3.35812 + 1.93881i 0.124035 + 0.0716117i 0.560734 0.827996i \(-0.310519\pi\)
−0.436699 + 0.899608i \(0.643852\pi\)
\(734\) −5.38144 + 0.657960i −0.198633 + 0.0242857i
\(735\) 5.45723 3.96571i 0.201293 0.146277i
\(736\) 4.01153 + 5.76041i 0.147867 + 0.212331i
\(737\) 25.8766 44.8196i 0.953177 1.65095i
\(738\) 10.6545 8.02016i 0.392196 0.295226i
\(739\) −7.46497 + 4.30990i −0.274603 + 0.158542i −0.630978 0.775801i \(-0.717346\pi\)
0.356374 + 0.934343i \(0.384013\pi\)
\(740\) −5.06185 1.45708i −0.186077 0.0535632i
\(741\) 18.3138i 0.672776i
\(742\) 5.24733 14.3961i 0.192636 0.528499i
\(743\) 6.12929i 0.224862i 0.993660 + 0.112431i \(0.0358637\pi\)
−0.993660 + 0.112431i \(0.964136\pi\)
\(744\) 2.15695 13.4843i 0.0790775 0.494357i
\(745\) −3.89057 + 2.24622i −0.142539 + 0.0822952i
\(746\) −22.8194 30.3146i −0.835477 1.10990i
\(747\) 0.271890 0.470927i 0.00994793 0.0172303i
\(748\) −7.30692 + 1.81387i −0.267167 + 0.0663216i
\(749\) −26.8827 + 17.4597i −0.982273 + 0.637963i
\(750\) −1.50040 12.2718i −0.0547870 0.448102i
\(751\) 30.7146 + 17.7331i 1.12079 + 0.647090i 0.941603 0.336725i \(-0.109319\pi\)
0.179190 + 0.983815i \(0.442652\pi\)
\(752\) 12.2472 + 7.68783i 0.446609 + 0.280346i
\(753\) −10.3746 17.9694i −0.378072 0.654841i
\(754\) −12.1083 5.14699i −0.440959 0.187442i
\(755\) 11.7632 0.428108
\(756\) 5.06180 1.54214i 0.184096 0.0560872i
\(757\) 29.4204 1.06930 0.534651 0.845073i \(-0.320443\pi\)
0.534651 + 0.845073i \(0.320443\pi\)
\(758\) −9.02845 3.83781i −0.327928 0.139395i
\(759\) −3.40207 5.89255i −0.123487 0.213886i
\(760\) −8.39073 + 10.3292i −0.304364 + 0.374679i
\(761\) 43.5568 + 25.1475i 1.57893 + 0.911597i 0.995009 + 0.0997877i \(0.0318164\pi\)
0.583923 + 0.811809i \(0.301517\pi\)
\(762\) 1.99830 + 16.3441i 0.0723909 + 0.592084i
\(763\) 16.0410 0.841446i 0.580723 0.0304624i
\(764\) −4.01518 16.1746i −0.145264 0.585175i
\(765\) 0.330804 0.572969i 0.0119602 0.0207157i
\(766\) −1.92014 2.55082i −0.0693774 0.0921650i
\(767\) −41.2128 + 23.7942i −1.48811 + 0.859160i
\(768\) −6.95495 14.4093i −0.250965 0.519952i
\(769\) 20.2817i 0.731377i −0.930737 0.365689i \(-0.880833\pi\)
0.930737 0.365689i \(-0.119167\pi\)
\(770\) 12.7020 + 15.1520i 0.457750 + 0.546039i
\(771\) 7.45109i 0.268344i
\(772\) 6.84507 23.7796i 0.246359 0.855847i
\(773\) −18.8149 + 10.8628i −0.676723 + 0.390706i −0.798619 0.601836i \(-0.794436\pi\)
0.121896 + 0.992543i \(0.461103\pi\)
\(774\) 6.75030 5.08130i 0.242635 0.182643i
\(775\) 9.82806 17.0227i 0.353034 0.611473i
\(776\) −10.9787 28.7324i −0.394112 1.03143i
\(777\) 3.28226 6.44257i 0.117751 0.231126i
\(778\) −42.9684 + 5.25351i −1.54049 + 0.188347i
\(779\) −39.8698 23.0189i −1.42848 0.824736i
\(780\) 5.01711 + 5.20603i 0.179641 + 0.186406i
\(781\) 27.7349 + 48.0382i 0.992432 + 1.71894i
\(782\) −0.471311 + 1.10876i −0.0168540 + 0.0396492i
\(783\) 2.48011 0.0886318
\(784\) 23.2436 15.6120i 0.830128 0.557573i
\(785\) −21.1369 −0.754410
\(786\) −5.12390 + 12.0540i −0.182764 + 0.429951i
\(787\) 0.299328 + 0.518452i 0.0106699 + 0.0184808i 0.871311 0.490731i \(-0.163270\pi\)
−0.860641 + 0.509212i \(0.829937\pi\)
\(788\) −4.49225 4.66141i −0.160030 0.166056i
\(789\) 25.7034 + 14.8399i 0.915066 + 0.528313i
\(790\) −1.91345 + 0.233947i −0.0680774 + 0.00832346i
\(791\) −8.86288 + 17.3965i −0.315128 + 0.618547i
\(792\) 5.53563 + 14.4873i 0.196700 + 0.514784i
\(793\) −19.5287 + 33.8247i −0.693484 + 1.20115i
\(794\) −15.7041 + 11.8213i −0.557318 + 0.419521i
\(795\) −3.41780 + 1.97327i −0.121217 + 0.0699847i
\(796\) −10.6389 + 36.9594i −0.377087 + 1.30999i
\(797\) 36.1789i 1.28152i −0.767741 0.640760i \(-0.778619\pi\)
0.767741 0.640760i \(-0.221381\pi\)
\(798\) −11.7356 13.9991i −0.415435 0.495563i
\(799\) 2.48180i 0.0877998i
\(800\) −1.94847 22.9480i −0.0688890 0.811333i
\(801\) −0.480107 + 0.277190i −0.0169637 + 0.00979402i
\(802\) −8.74046 11.6113i −0.308636 0.410011i
\(803\) 18.2616 31.6299i 0.644436 1.11620i
\(804\) 4.54798 + 18.3209i 0.160395 + 0.646128i
\(805\) 3.15963 0.165741i 0.111362 0.00584162i
\(806\) 3.10834 + 25.4231i 0.109487 + 0.895490i
\(807\) −3.73727 2.15771i −0.131558 0.0759551i
\(808\) −25.7349 + 31.6803i −0.905350 + 1.11451i
\(809\) 15.0603 + 26.0852i 0.529491 + 0.917106i 0.999408 + 0.0343953i \(0.0109505\pi\)
−0.469917 + 0.882711i \(0.655716\pi\)
\(810\) −1.25428 0.533167i −0.0440708 0.0187336i
\(811\) 21.5947 0.758292 0.379146 0.925337i \(-0.376218\pi\)
0.379146 + 0.925337i \(0.376218\pi\)
\(812\) 12.5538 3.82468i 0.440552 0.134220i
\(813\) 13.5828 0.476371
\(814\) 19.5030 + 8.29032i 0.683579 + 0.290575i
\(815\) −1.93633 3.35382i −0.0678266 0.117479i
\(816\) 1.45997 2.32582i 0.0511092 0.0814201i
\(817\) −25.2601 14.5839i −0.883740 0.510228i
\(818\) −2.08769 17.0751i −0.0729942 0.597018i
\(819\) −8.32326 + 5.40576i −0.290838 + 0.188892i
\(820\) −17.6397 + 4.37889i −0.616006 + 0.152917i
\(821\) −25.1264 + 43.5202i −0.876918 + 1.51887i −0.0222131 + 0.999753i \(0.507071\pi\)
−0.854705 + 0.519114i \(0.826262\pi\)
\(822\) −6.14930 8.16910i −0.214482 0.284930i
\(823\) 2.87338 1.65894i 0.100160 0.0578272i −0.449084 0.893490i \(-0.648249\pi\)
0.549243 + 0.835663i \(0.314916\pi\)
\(824\) 6.71237 41.9628i 0.233837 1.46184i
\(825\) 22.3236i 0.777209i
\(826\) 16.2556 44.5976i 0.565606 1.55175i
\(827\) 29.3948i 1.02216i 0.859534 + 0.511078i \(0.170754\pi\)
−0.859534 + 0.511078i \(0.829246\pi\)
\(828\) 2.38496 + 0.686521i 0.0828830 + 0.0238583i
\(829\) 28.2980 16.3379i 0.982830 0.567437i 0.0797067 0.996818i \(-0.474602\pi\)
0.903123 + 0.429381i \(0.141268\pi\)
\(830\) −0.592108 + 0.445710i −0.0205524 + 0.0154708i
\(831\) 1.03563 1.79376i 0.0359256 0.0622250i
\(832\) 20.0115 + 22.3629i 0.693775 + 0.775294i
\(833\) 4.39036 + 1.95421i 0.152117 + 0.0677094i
\(834\) 7.45133 0.911035i 0.258019 0.0315465i
\(835\) 12.2834 + 7.09184i 0.425086 + 0.245423i
\(836\) 38.5516 37.1526i 1.33333 1.28495i
\(837\) −2.41401 4.18119i −0.0834403 0.144523i
\(838\) 8.97611 21.1163i 0.310075 0.729451i
\(839\) 8.66161 0.299032 0.149516 0.988759i \(-0.452228\pi\)
0.149516 + 0.988759i \(0.452228\pi\)
\(840\) −7.17111 0.764509i −0.247427 0.0263781i
\(841\) −22.8491 −0.787899
\(842\) −5.30272 + 12.4747i −0.182744 + 0.429905i
\(843\) 11.8561 + 20.5354i 0.408346 + 0.707276i
\(844\) −13.3157 + 12.8325i −0.458346 + 0.441713i
\(845\) −0.894073 0.516193i −0.0307570 0.0177576i
\(846\) 5.07465 0.620450i 0.174470 0.0213315i
\(847\) −27.4753 42.3038i −0.944062 1.45358i
\(848\) −14.4789 + 7.66057i −0.497209 + 0.263065i
\(849\) 6.12739 10.6129i 0.210291 0.364235i
\(850\) 3.15801 2.37720i 0.108319 0.0815372i
\(851\) 2.93688 1.69561i 0.100675 0.0581248i
\(852\) −19.4431 5.59677i −0.666108 0.191742i
\(853\) 7.17809i 0.245773i 0.992421 + 0.122887i \(0.0392151\pi\)
−0.992421 + 0.122887i \(0.960785\pi\)
\(854\) −6.74724 38.3696i −0.230886 1.31298i
\(855\) 4.70500i 0.160908i
\(856\) 33.8380 + 5.41274i 1.15656 + 0.185004i
\(857\) 39.5334 22.8246i 1.35044 0.779675i 0.362126 0.932129i \(-0.382051\pi\)
0.988311 + 0.152454i \(0.0487176\pi\)
\(858\) −17.4938 23.2398i −0.597229 0.793395i
\(859\) −6.77944 + 11.7423i −0.231311 + 0.400643i −0.958194 0.286118i \(-0.907635\pi\)
0.726883 + 0.686761i \(0.240968\pi\)
\(860\) −11.1759 + 2.77431i −0.381096 + 0.0946033i
\(861\) −1.30692 24.9145i −0.0445396 0.849085i
\(862\) 0.0260696 + 0.213223i 0.000887934 + 0.00726240i
\(863\) 36.0550 + 20.8163i 1.22733 + 0.708597i 0.966470 0.256781i \(-0.0826620\pi\)
0.260856 + 0.965378i \(0.415995\pi\)
\(864\) −5.12071 2.40381i −0.174210 0.0817794i
\(865\) −5.61504 9.72554i −0.190917 0.330678i
\(866\) −12.3252 5.23920i −0.418828 0.178035i
\(867\) −16.5287 −0.561344
\(868\) −18.6672 17.4416i −0.633607 0.592005i
\(869\) 7.75555 0.263089
\(870\) −3.11074 1.32231i −0.105464 0.0448306i
\(871\) −17.7026 30.6619i −0.599831 1.03894i
\(872\) −13.3286 10.8273i −0.451364 0.366657i
\(873\) −9.41780 5.43737i −0.318744 0.184027i
\(874\) −1.03979 8.50439i −0.0351713 0.287665i
\(875\) −20.6089 10.4995i −0.696708 0.354948i
\(876\) 3.20959 + 12.9294i 0.108442 + 0.436843i
\(877\) 9.84239 17.0475i 0.332354 0.575654i −0.650619 0.759404i \(-0.725491\pi\)
0.982973 + 0.183751i \(0.0588239\pi\)
\(878\) 28.4706 + 37.8221i 0.960837 + 1.27643i
\(879\) 9.27427 5.35450i 0.312813 0.180603i
\(880\) 0.780950 21.1225i 0.0263258 0.712040i
\(881\) 7.24606i 0.244126i −0.992522 0.122063i \(-0.961049\pi\)
0.992522 0.122063i \(-0.0389510\pi\)
\(882\) 2.89827 9.46573i 0.0975899 0.318728i
\(883\) 35.4533i 1.19310i 0.802577 + 0.596549i \(0.203462\pi\)
−0.802577 + 0.596549i \(0.796538\pi\)
\(884\) −1.42474 + 4.94953i −0.0479193 + 0.166471i
\(885\) −10.5880 + 6.11296i −0.355911 + 0.205485i
\(886\) −29.5524 + 22.2456i −0.992833 + 0.747357i
\(887\) 8.98684 15.5657i 0.301749 0.522644i −0.674784 0.738016i \(-0.735763\pi\)
0.976532 + 0.215372i \(0.0690964\pi\)
\(888\) −7.22056 + 2.75899i −0.242306 + 0.0925857i
\(889\) 27.4479 + 13.9837i 0.920572 + 0.468999i
\(890\) 0.749976 0.0916955i 0.0251392 0.00307364i
\(891\) 4.74861 + 2.74161i 0.159084 + 0.0918474i
\(892\) −2.70053 2.80222i −0.0904203 0.0938251i
\(893\) −8.82463 15.2847i −0.295305 0.511483i
\(894\) −2.57901 + 6.06712i −0.0862549 + 0.202915i
\(895\) −2.50005 −0.0835674
\(896\) −29.6270 4.27074i −0.989770 0.142675i
\(897\) −4.65483 −0.155420
\(898\) 5.69389 13.3949i 0.190008 0.446993i
\(899\) −5.98700 10.3698i −0.199678 0.345852i
\(900\) −5.65027 5.86303i −0.188342 0.195434i
\(901\) −2.43475 1.40570i −0.0811132 0.0468307i
\(902\) 72.5820 8.87421i 2.41672 0.295479i
\(903\) −0.828017 15.7850i −0.0275547 0.525292i
\(904\) 19.4972 7.44992i 0.648468 0.247781i
\(905\) 4.59374 7.95658i 0.152701 0.264486i
\(906\) 13.7915 10.3816i 0.458191 0.344904i
\(907\) −7.60870 + 4.39289i −0.252643 + 0.145863i −0.620974 0.783831i \(-0.713263\pi\)
0.368331 + 0.929695i \(0.379929\pi\)
\(908\) 4.78297 16.6159i 0.158728 0.551419i
\(909\) 14.4305i 0.478631i
\(910\) 13.3218 2.34262i 0.441615 0.0776573i
\(911\) 21.5478i 0.713911i 0.934121 + 0.356955i \(0.116185\pi\)
−0.934121 + 0.356955i \(0.883815\pi\)
\(912\) −0.721529 + 19.5154i −0.0238922 + 0.646218i
\(913\) 2.58220 1.49083i 0.0854582 0.0493393i
\(914\) 10.1479 + 13.4811i 0.335663 + 0.445915i
\(915\) −5.01711 + 8.68988i −0.165860 + 0.287279i
\(916\) −8.08983 32.5887i −0.267295 1.07676i
\(917\) 13.3467 + 20.5500i 0.440747 + 0.678619i
\(918\) −0.117828 0.963711i −0.00388890 0.0318072i
\(919\) −27.5939 15.9314i −0.910240 0.525527i −0.0297316 0.999558i \(-0.509465\pi\)
−0.880508 + 0.474031i \(0.842799\pi\)
\(920\) −2.62537 2.13267i −0.0865558 0.0703120i
\(921\) 2.11028 + 3.65512i 0.0695362 + 0.120440i
\(922\) 39.0574 + 16.6025i 1.28629 + 0.546774i
\(923\) 37.9479 1.24907
\(924\) 28.2644 + 6.55444i 0.929832 + 0.215625i
\(925\) −11.1262 −0.365828
\(926\) 17.2756 + 7.34352i 0.567713 + 0.241323i
\(927\) −7.51235 13.0118i −0.246738 0.427363i
\(928\) −12.6999 5.96171i −0.416895 0.195703i
\(929\) 44.1750 + 25.5044i 1.44933 + 0.836773i 0.998442 0.0558058i \(-0.0177728\pi\)
0.450892 + 0.892579i \(0.351106\pi\)
\(930\) 0.798563 + 6.53143i 0.0261859 + 0.214174i
\(931\) −33.9876 + 3.57555i −1.11390 + 0.117184i
\(932\) −2.03148 + 0.504294i −0.0665432 + 0.0165187i
\(933\) 4.85070 8.40165i 0.158805 0.275058i
\(934\) −25.2172 33.5000i −0.825131 1.09615i
\(935\) 3.14171 1.81387i 0.102745 0.0593199i
\(936\) 10.4767 + 1.67586i 0.342442 + 0.0547771i
\(937\) 2.65742i 0.0868141i −0.999057 0.0434071i \(-0.986179\pi\)
0.999057 0.0434071i \(-0.0138212\pi\)
\(938\) 33.1801 + 12.0940i 1.08337 + 0.394884i
\(939\) 13.6634i 0.445887i
\(940\) −6.69582 1.92742i −0.218394 0.0628656i
\(941\) 26.2920 15.1797i 0.857096 0.494844i −0.00594304 0.999982i \(-0.501892\pi\)
0.863039 + 0.505138i \(0.168558\pi\)
\(942\) −24.7815 + 18.6543i −0.807423 + 0.607789i
\(943\) 5.85070 10.1337i 0.190525 0.329999i
\(944\) −44.8541 + 23.7316i −1.45988 + 0.772397i
\(945\) −2.13832 + 1.38879i −0.0695597 + 0.0451774i
\(946\) 45.9855 5.62240i 1.49512 0.182800i
\(947\) 37.6505 + 21.7375i 1.22348 + 0.706374i 0.965657 0.259819i \(-0.0836630\pi\)
0.257818 + 0.966193i \(0.416996\pi\)
\(948\) −2.03690 + 1.96299i −0.0661555 + 0.0637548i
\(949\) −12.4931 21.6386i −0.405542 0.702419i
\(950\) −10.9966 + 25.8695i −0.356777 + 0.839319i
\(951\) −20.0884 −0.651410
\(952\) −2.08260 4.69640i −0.0674975 0.152211i
\(953\) −53.8683 −1.74497 −0.872483 0.488645i \(-0.837491\pi\)
−0.872483 + 0.488645i \(0.837491\pi\)
\(954\) −2.26562 + 5.32987i −0.0733520 + 0.172561i
\(955\) 4.01518 + 6.95449i 0.129928 + 0.225042i
\(956\) 27.7190 26.7131i 0.896496 0.863963i
\(957\) 11.7771 + 6.79948i 0.380698 + 0.219796i
\(958\) −16.1930 + 1.97984i −0.523173 + 0.0639656i
\(959\) −19.1027 + 1.00205i −0.616860 + 0.0323580i
\(960\) 5.14115 + 5.74524i 0.165930 + 0.185427i
\(961\) 3.84512 6.65995i 0.124036 0.214837i
\(962\) 11.5829 8.71903i 0.373447 0.281113i
\(963\) 10.4925 6.05782i 0.338115 0.195211i
\(964\) 5.29862 + 1.52523i 0.170657 + 0.0491244i
\(965\) 11.9236i 0.383835i
\(966\) 3.55815 2.98283i 0.114482 0.0959709i
\(967\) 44.9529i 1.44559i 0.691064 + 0.722794i \(0.257142\pi\)
−0.691064 + 0.722794i \(0.742858\pi\)
\(968\) −8.51771 + 53.2490i −0.273770 + 1.71149i
\(969\) −2.90267 + 1.67586i −0.0932472 + 0.0538363i
\(970\) 8.91350 + 11.8412i 0.286195 + 0.380199i
\(971\) 0.641758 1.11156i 0.0205950 0.0356716i −0.855544 0.517730i \(-0.826777\pi\)
0.876139 + 0.482058i \(0.160111\pi\)
\(972\) −1.94109 + 0.481855i −0.0622604 + 0.0154555i
\(973\) 6.37523 12.5136i 0.204381 0.401167i
\(974\) 1.67428 + 13.6939i 0.0536474 + 0.438781i
\(975\) 13.2259 + 7.63599i 0.423569 + 0.244547i
\(976\) −22.1425 + 35.2744i −0.708765 + 1.12911i
\(977\) −9.67678 16.7607i −0.309588 0.536222i 0.668684 0.743546i \(-0.266858\pi\)
−0.978272 + 0.207325i \(0.933524\pi\)
\(978\) −5.23008 2.22320i −0.167240 0.0710901i
\(979\) −3.03979 −0.0971520
\(980\) −8.68205 + 10.3274i −0.277338 + 0.329896i
\(981\) −6.07126 −0.193840
\(982\) −52.6767 22.3918i −1.68098 0.714550i
\(983\) −4.21637 7.30296i −0.134481 0.232928i 0.790918 0.611922i \(-0.209603\pi\)
−0.925399 + 0.378994i \(0.876270\pi\)
\(984\) −16.8167 + 20.7017i −0.536096 + 0.659947i
\(985\) 2.70148 + 1.55970i 0.0860763 + 0.0496962i
\(986\) −0.292225 2.39011i −0.00930635 0.0761165i
\(987\) 4.34178 8.52224i 0.138200 0.271266i
\(988\) −8.82463 35.5488i −0.280749 1.13096i
\(989\) 3.70680 6.42036i 0.117869 0.204156i
\(990\) −4.49433 5.97054i −0.142839 0.189756i
\(991\) 21.1967 12.2379i 0.673334 0.388750i −0.124005 0.992282i \(-0.539574\pi\)
0.797339 + 0.603532i \(0.206240\pi\)
\(992\) 2.31065 + 27.2135i 0.0733633 + 0.864029i
\(993\) 9.42104i 0.298968i
\(994\) −29.0073 + 24.3171i −0.920057 + 0.771292i
\(995\) 18.5322i 0.587511i
\(996\) −0.300843 + 1.04512i −0.00953258 + 0.0331160i
\(997\) −29.0273 + 16.7589i −0.919304 + 0.530761i −0.883413 0.468595i \(-0.844760\pi\)
−0.0358914 + 0.999356i \(0.511427\pi\)
\(998\) −36.1168 + 27.1870i −1.14326 + 0.860588i
\(999\) −1.36643 + 2.36673i −0.0432321 + 0.0748802i
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 84.2.o.b.19.3 yes 8
3.2 odd 2 252.2.bf.f.19.2 8
4.3 odd 2 84.2.o.a.19.3 8
7.2 even 3 588.2.b.a.391.2 8
7.3 odd 6 84.2.o.a.31.3 yes 8
7.4 even 3 588.2.o.d.31.3 8
7.5 odd 6 588.2.b.b.391.2 8
7.6 odd 2 588.2.o.b.19.3 8
8.3 odd 2 1344.2.bl.j.1279.2 8
8.5 even 2 1344.2.bl.i.1279.2 8
12.11 even 2 252.2.bf.g.19.2 8
21.2 odd 6 1764.2.b.j.1567.7 8
21.5 even 6 1764.2.b.i.1567.7 8
21.17 even 6 252.2.bf.g.199.2 8
28.3 even 6 inner 84.2.o.b.31.3 yes 8
28.11 odd 6 588.2.o.b.31.3 8
28.19 even 6 588.2.b.a.391.1 8
28.23 odd 6 588.2.b.b.391.1 8
28.27 even 2 588.2.o.d.19.3 8
56.3 even 6 1344.2.bl.i.703.2 8
56.45 odd 6 1344.2.bl.j.703.2 8
84.23 even 6 1764.2.b.i.1567.8 8
84.47 odd 6 1764.2.b.j.1567.8 8
84.59 odd 6 252.2.bf.f.199.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.o.a.19.3 8 4.3 odd 2
84.2.o.a.31.3 yes 8 7.3 odd 6
84.2.o.b.19.3 yes 8 1.1 even 1 trivial
84.2.o.b.31.3 yes 8 28.3 even 6 inner
252.2.bf.f.19.2 8 3.2 odd 2
252.2.bf.f.199.2 8 84.59 odd 6
252.2.bf.g.19.2 8 12.11 even 2
252.2.bf.g.199.2 8 21.17 even 6
588.2.b.a.391.1 8 28.19 even 6
588.2.b.a.391.2 8 7.2 even 3
588.2.b.b.391.1 8 28.23 odd 6
588.2.b.b.391.2 8 7.5 odd 6
588.2.o.b.19.3 8 7.6 odd 2
588.2.o.b.31.3 8 28.11 odd 6
588.2.o.d.19.3 8 28.27 even 2
588.2.o.d.31.3 8 7.4 even 3
1344.2.bl.i.703.2 8 56.3 even 6
1344.2.bl.i.1279.2 8 8.5 even 2
1344.2.bl.j.703.2 8 56.45 odd 6
1344.2.bl.j.1279.2 8 8.3 odd 2
1764.2.b.i.1567.7 8 21.5 even 6
1764.2.b.i.1567.8 8 84.23 even 6
1764.2.b.j.1567.7 8 21.2 odd 6
1764.2.b.j.1567.8 8 84.47 odd 6