Properties

Label 8.19.d.b.3.11
Level $8$
Weight $19$
Character 8.3
Analytic conductor $16.431$
Analytic rank $0$
Dimension $16$
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] = [8,19,Mod(3,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 19, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.3");
 
S:= CuspForms(chi, 19);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 8.d (of order \(2\), degree \(1\), 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: \(16.4308910168\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 5 x^{15} + 56971 x^{14} - 14457953 x^{13} + 5222713963 x^{12} - 1887111404561 x^{11} + 551417417640415 x^{10} + \cdots + 32\!\cdots\!30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{120}\cdot 3^{13}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.11
Root \(135.604 - 208.454i\) of defining polynomial
Character \(\chi\) \(=\) 8.3
Dual form 8.19.d.b.3.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(297.207 - 416.907i) q^{2} -25925.7 q^{3} +(-85479.4 - 247816. i) q^{4} +1.90314e6i q^{5} +(-7.70530e6 + 1.08086e7i) q^{6} +9.33592e6i q^{7} +(-1.28721e8 - 3.80157e7i) q^{8} +2.84720e8 q^{9} +O(q^{10})\) \(q+(297.207 - 416.907i) q^{2} -25925.7 q^{3} +(-85479.4 - 247816. i) q^{4} +1.90314e6i q^{5} +(-7.70530e6 + 1.08086e7i) q^{6} +9.33592e6i q^{7} +(-1.28721e8 - 3.80157e7i) q^{8} +2.84720e8 q^{9} +(7.93431e8 + 5.65626e8i) q^{10} +2.94305e9 q^{11} +(2.21611e9 + 6.42479e9i) q^{12} -7.67712e9i q^{13} +(3.89221e9 + 2.77470e9i) q^{14} -4.93401e10i q^{15} +(-5.41060e10 + 4.23663e10i) q^{16} -1.40802e10 q^{17} +(8.46209e10 - 1.18702e11i) q^{18} +5.59331e11 q^{19} +(4.71627e11 - 1.62679e11i) q^{20} -2.42040e11i q^{21} +(8.74698e11 - 1.22698e12i) q^{22} +2.61543e12i q^{23} +(3.33719e12 + 9.85583e11i) q^{24} +1.92773e11 q^{25} +(-3.20065e12 - 2.28170e12i) q^{26} +2.66258e12 q^{27} +(2.31359e12 - 7.98029e11i) q^{28} -1.91498e13i q^{29} +(-2.05702e13 - 1.46642e13i) q^{30} +3.57176e13i q^{31} +(1.58213e12 + 3.51488e13i) q^{32} -7.63007e13 q^{33} +(-4.18475e12 + 5.87015e12i) q^{34} -1.77675e13 q^{35} +(-2.43377e13 - 7.05581e13i) q^{36} +2.51975e14i q^{37} +(1.66237e14 - 2.33189e14i) q^{38} +1.99034e14i q^{39} +(7.23491e13 - 2.44974e14i) q^{40} +7.94564e13 q^{41} +(-1.00908e14 - 7.19361e13i) q^{42} -3.62991e14 q^{43} +(-2.51571e14 - 7.29336e14i) q^{44} +5.41861e14i q^{45} +(1.09039e15 + 7.77324e14i) q^{46} -2.20997e14i q^{47} +(1.40273e15 - 1.09838e15i) q^{48} +1.54125e15 q^{49} +(5.72935e13 - 8.03684e13i) q^{50} +3.65039e14 q^{51} +(-1.90251e15 + 6.56236e14i) q^{52} +1.22228e15i q^{53} +(7.91339e14 - 1.11005e15i) q^{54} +5.60103e15i q^{55} +(3.54912e14 - 1.20173e15i) q^{56} -1.45010e16 q^{57} +(-7.98371e15 - 5.69148e15i) q^{58} +2.66374e15 q^{59} +(-1.22273e16 + 4.21756e15i) q^{60} -2.02843e16i q^{61} +(1.48909e16 + 1.06155e16i) q^{62} +2.65812e15i q^{63} +(1.51240e16 + 9.78688e15i) q^{64} +1.46106e16 q^{65} +(-2.26771e16 + 3.18103e16i) q^{66} +3.97625e16 q^{67} +(1.20357e15 + 3.48930e15i) q^{68} -6.78067e16i q^{69} +(-5.28064e15 + 7.40741e15i) q^{70} -1.25349e16i q^{71} +(-3.66496e16 - 1.08238e16i) q^{72} +6.29849e15 q^{73} +(1.05050e17 + 7.48887e16i) q^{74} -4.99777e15 q^{75} +(-4.78113e16 - 1.38611e17i) q^{76} +2.74761e16i q^{77} +(8.29789e16 + 5.91545e16i) q^{78} +6.53764e16i q^{79} +(-8.06289e16 - 1.02971e17i) q^{80} -1.79336e17 q^{81} +(2.36150e16 - 3.31259e16i) q^{82} +1.09064e17 q^{83} +(-5.99813e16 + 2.06894e16i) q^{84} -2.67966e16i q^{85} +(-1.07883e17 + 1.51333e17i) q^{86} +4.96472e17i q^{87} +(-3.78834e17 - 1.11882e17i) q^{88} -3.14498e17 q^{89} +(2.25906e17 + 1.61045e17i) q^{90} +7.16729e16 q^{91} +(6.48144e17 - 2.23565e17i) q^{92} -9.26002e17i q^{93} +(-9.21354e16 - 6.56820e16i) q^{94} +1.06448e18i q^{95} +(-4.10178e16 - 9.11256e17i) q^{96} -5.54687e17 q^{97} +(4.58072e17 - 6.42560e17i) q^{98} +8.37946e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9} - 1569837600 q^{10} - 2471571264 q^{11} + 4764364056 q^{12} + 26163923904 q^{14} - 192320075504 q^{16} - 176439301344 q^{17} - 1044291511122 q^{18} - 833365634368 q^{19} + 1256486405760 q^{20} + 59927319356 q^{22} - 1968891910512 q^{24} - 15320509140080 q^{25} + 4184514840864 q^{26} + 11565649473408 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 141481742931936 q^{32} - 900457491648 q^{33} + 80653465357268 q^{34} + 20487495736320 q^{35} + 277183098847068 q^{36} + 493456694265564 q^{38} - 519930573603840 q^{40} - 594931562445024 q^{41} - 222362598288000 q^{42} - 25\!\cdots\!92 q^{43}+ \cdots - 81\!\cdots\!68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 297.207 416.907i 0.580483 0.814272i
\(3\) −25925.7 −1.31716 −0.658580 0.752510i \(-0.728843\pi\)
−0.658580 + 0.752510i \(0.728843\pi\)
\(4\) −85479.4 247816.i −0.326078 0.945343i
\(5\) 1.90314e6i 0.974405i 0.873289 + 0.487203i \(0.161983\pi\)
−0.873289 + 0.487203i \(0.838017\pi\)
\(6\) −7.70530e6 + 1.08086e7i −0.764590 + 1.07253i
\(7\) 9.33592e6i 0.231353i 0.993287 + 0.115676i \(0.0369035\pi\)
−0.993287 + 0.115676i \(0.963096\pi\)
\(8\) −1.28721e8 3.80157e7i −0.959049 0.283239i
\(9\) 2.84720e8 0.734912
\(10\) 7.93431e8 + 5.65626e8i 0.793431 + 0.565626i
\(11\) 2.94305e9 1.24814 0.624071 0.781367i \(-0.285477\pi\)
0.624071 + 0.781367i \(0.285477\pi\)
\(12\) 2.21611e9 + 6.42479e9i 0.429497 + 1.24517i
\(13\) 7.67712e9i 0.723949i −0.932188 0.361974i \(-0.882103\pi\)
0.932188 0.361974i \(-0.117897\pi\)
\(14\) 3.89221e9 + 2.77470e9i 0.188384 + 0.134296i
\(15\) 4.93401e10i 1.28345i
\(16\) −5.41060e10 + 4.23663e10i −0.787346 + 0.616511i
\(17\) −1.40802e10 −0.118732 −0.0593662 0.998236i \(-0.518908\pi\)
−0.0593662 + 0.998236i \(0.518908\pi\)
\(18\) 8.46209e10 1.18702e11i 0.426604 0.598418i
\(19\) 5.59331e11 1.73335 0.866676 0.498871i \(-0.166252\pi\)
0.866676 + 0.498871i \(0.166252\pi\)
\(20\) 4.71627e11 1.62679e11i 0.921147 0.317732i
\(21\) 2.42040e11i 0.304729i
\(22\) 8.74698e11 1.22698e12i 0.724526 1.01633i
\(23\) 2.61543e12i 1.45208i 0.687650 + 0.726042i \(0.258642\pi\)
−0.687650 + 0.726042i \(0.741358\pi\)
\(24\) 3.33719e12 + 9.85583e11i 1.26322 + 0.373072i
\(25\) 1.92773e11 0.0505343
\(26\) −3.20065e12 2.28170e12i −0.589491 0.420240i
\(27\) 2.66258e12 0.349164
\(28\) 2.31359e12 7.98029e11i 0.218708 0.0754391i
\(29\) 1.91498e13i 1.32003i −0.751253 0.660014i \(-0.770550\pi\)
0.751253 0.660014i \(-0.229450\pi\)
\(30\) −2.05702e13 1.46642e13i −1.04508 0.745020i
\(31\) 3.57176e13i 1.35091i 0.737401 + 0.675455i \(0.236053\pi\)
−0.737401 + 0.675455i \(0.763947\pi\)
\(32\) 1.58213e12 + 3.51488e13i 0.0449668 + 0.998988i
\(33\) −7.63007e13 −1.64400
\(34\) −4.18475e12 + 5.87015e12i −0.0689222 + 0.0966805i
\(35\) −1.77675e13 −0.225431
\(36\) −2.43377e13 7.05581e13i −0.239639 0.694744i
\(37\) 2.51975e14i 1.93884i 0.245414 + 0.969418i \(0.421076\pi\)
−0.245414 + 0.969418i \(0.578924\pi\)
\(38\) 1.66237e14 2.33189e14i 1.00618 1.41142i
\(39\) 1.99034e14i 0.953557i
\(40\) 7.23491e13 2.44974e14i 0.275990 0.934503i
\(41\) 7.94564e13 0.242702 0.121351 0.992610i \(-0.461277\pi\)
0.121351 + 0.992610i \(0.461277\pi\)
\(42\) −1.00908e14 7.19361e13i −0.248132 0.176890i
\(43\) −3.62991e14 −0.722236 −0.361118 0.932520i \(-0.617605\pi\)
−0.361118 + 0.932520i \(0.617605\pi\)
\(44\) −2.51571e14 7.29336e14i −0.406992 1.17992i
\(45\) 5.41861e14i 0.716102i
\(46\) 1.09039e15 + 7.77324e14i 1.18239 + 0.842911i
\(47\) 2.20997e14i 0.197472i −0.995114 0.0987361i \(-0.968520\pi\)
0.995114 0.0987361i \(-0.0314800\pi\)
\(48\) 1.40273e15 1.09838e15i 1.03706 0.812044i
\(49\) 1.54125e15 0.946476
\(50\) 5.72935e13 8.03684e13i 0.0293343 0.0411486i
\(51\) 3.65039e14 0.156390
\(52\) −1.90251e15 + 6.56236e14i −0.684380 + 0.236064i
\(53\) 1.22228e15i 0.370414i 0.982700 + 0.185207i \(0.0592956\pi\)
−0.982700 + 0.185207i \(0.940704\pi\)
\(54\) 7.91339e14 1.11005e15i 0.202684 0.284314i
\(55\) 5.60103e15i 1.21620i
\(56\) 3.54912e14 1.20173e15i 0.0655282 0.221879i
\(57\) −1.45010e16 −2.28310
\(58\) −7.98371e15 5.69148e15i −1.07486 0.766254i
\(59\) 2.66374e15 0.307485 0.153742 0.988111i \(-0.450867\pi\)
0.153742 + 0.988111i \(0.450867\pi\)
\(60\) −1.22273e16 + 4.21756e15i −1.21330 + 0.418505i
\(61\) 2.02843e16i 1.73457i −0.497816 0.867283i \(-0.665865\pi\)
0.497816 0.867283i \(-0.334135\pi\)
\(62\) 1.48909e16 + 1.06155e16i 1.10001 + 0.784181i
\(63\) 2.65812e15i 0.170024i
\(64\) 1.51240e16 + 9.78688e15i 0.839551 + 0.543281i
\(65\) 1.46106e16 0.705420
\(66\) −2.26771e16 + 3.18103e16i −0.954317 + 1.33867i
\(67\) 3.97625e16 1.46151 0.730753 0.682642i \(-0.239169\pi\)
0.730753 + 0.682642i \(0.239169\pi\)
\(68\) 1.20357e15 + 3.48930e15i 0.0387160 + 0.112243i
\(69\) 6.78067e16i 1.91263i
\(70\) −5.28064e15 + 7.40741e15i −0.130859 + 0.183562i
\(71\) 1.25349e16i 0.273398i −0.990613 0.136699i \(-0.956351\pi\)
0.990613 0.136699i \(-0.0436493\pi\)
\(72\) −3.66496e16 1.08238e16i −0.704817 0.208156i
\(73\) 6.29849e15 0.106987 0.0534934 0.998568i \(-0.482964\pi\)
0.0534934 + 0.998568i \(0.482964\pi\)
\(74\) 1.05050e17 + 7.48887e16i 1.57874 + 1.12546i
\(75\) −4.99777e15 −0.0665617
\(76\) −4.78113e16 1.38611e17i −0.565208 1.63861i
\(77\) 2.74761e16i 0.288761i
\(78\) 8.29789e16 + 5.91545e16i 0.776455 + 0.553524i
\(79\) 6.53764e16i 0.545478i 0.962088 + 0.272739i \(0.0879295\pi\)
−0.962088 + 0.272739i \(0.912070\pi\)
\(80\) −8.06289e16 1.02971e17i −0.600732 0.767194i
\(81\) −1.79336e17 −1.19482
\(82\) 2.36150e16 3.31259e16i 0.140885 0.197626i
\(83\) 1.09064e17 0.583416 0.291708 0.956507i \(-0.405776\pi\)
0.291708 + 0.956507i \(0.405776\pi\)
\(84\) −5.99813e16 + 2.06894e16i −0.288073 + 0.0993654i
\(85\) 2.67966e16i 0.115693i
\(86\) −1.07883e17 + 1.51333e17i −0.419246 + 0.588097i
\(87\) 4.96472e17i 1.73869i
\(88\) −3.78834e17 1.11882e17i −1.19703 0.353523i
\(89\) −3.14498e17 −0.897652 −0.448826 0.893619i \(-0.648158\pi\)
−0.448826 + 0.893619i \(0.648158\pi\)
\(90\) 2.25906e17 + 1.61045e17i 0.583102 + 0.415685i
\(91\) 7.16729e16 0.167488
\(92\) 6.48144e17 2.23565e17i 1.37272 0.473493i
\(93\) 9.26002e17i 1.77937i
\(94\) −9.21354e16 6.56820e16i −0.160796 0.114629i
\(95\) 1.06448e18i 1.68899i
\(96\) −4.10178e16 9.11256e17i −0.0592285 1.31583i
\(97\) −5.54687e17 −0.729629 −0.364815 0.931080i \(-0.618868\pi\)
−0.364815 + 0.931080i \(0.618868\pi\)
\(98\) 4.58072e17 6.42560e17i 0.549413 0.770689i
\(99\) 8.37946e17 0.917275
\(100\) −1.64781e16 4.77722e16i −0.0164781 0.0477722i
\(101\) 3.73907e17i 0.341878i 0.985282 + 0.170939i \(0.0546802\pi\)
−0.985282 + 0.170939i \(0.945320\pi\)
\(102\) 1.08492e17 1.52188e17i 0.0907816 0.127344i
\(103\) 1.07694e18i 0.825389i 0.910870 + 0.412694i \(0.135412\pi\)
−0.910870 + 0.412694i \(0.864588\pi\)
\(104\) −2.91851e17 + 9.88209e17i −0.205051 + 0.694303i
\(105\) 4.60635e17 0.296929
\(106\) 5.09577e17 + 3.63270e17i 0.301618 + 0.215019i
\(107\) 1.24459e18 0.676972 0.338486 0.940971i \(-0.390085\pi\)
0.338486 + 0.940971i \(0.390085\pi\)
\(108\) −2.27596e17 6.59830e17i −0.113855 0.330079i
\(109\) 1.91158e17i 0.0880146i −0.999031 0.0440073i \(-0.985988\pi\)
0.999031 0.0440073i \(-0.0140125\pi\)
\(110\) 2.33511e18 + 1.66467e18i 0.990315 + 0.705982i
\(111\) 6.53261e18i 2.55376i
\(112\) −3.95529e17 5.05129e17i −0.142632 0.182155i
\(113\) 4.88607e17 0.162650 0.0813249 0.996688i \(-0.474085\pi\)
0.0813249 + 0.996688i \(0.474085\pi\)
\(114\) −4.30982e18 + 6.04559e18i −1.32530 + 1.85907i
\(115\) −4.97751e18 −1.41492
\(116\) −4.74564e18 + 1.63692e18i −1.24788 + 0.430432i
\(117\) 2.18583e18i 0.532039i
\(118\) 7.91683e17 1.11053e18i 0.178490 0.250376i
\(119\) 1.31452e17i 0.0274691i
\(120\) −1.87570e18 + 6.35112e18i −0.363523 + 1.23089i
\(121\) 3.10165e18 0.557860
\(122\) −8.45666e18 6.02863e18i −1.41241 1.00689i
\(123\) −2.05996e18 −0.319678
\(124\) 8.85138e18 3.05312e18i 1.27707 0.440502i
\(125\) 7.62676e18i 1.02365i
\(126\) 1.10819e18 + 7.90014e17i 0.138446 + 0.0986960i
\(127\) 4.06004e18i 0.472386i −0.971706 0.236193i \(-0.924100\pi\)
0.971706 0.236193i \(-0.0758997\pi\)
\(128\) 8.57519e18 3.39658e18i 0.929724 0.368257i
\(129\) 9.41077e18 0.951301
\(130\) 4.34238e18 6.09126e18i 0.409484 0.574404i
\(131\) 4.83476e18 0.425533 0.212767 0.977103i \(-0.431753\pi\)
0.212767 + 0.977103i \(0.431753\pi\)
\(132\) 6.52214e18 + 1.89085e19i 0.536074 + 1.55415i
\(133\) 5.22187e18i 0.401016i
\(134\) 1.18177e19 1.65773e19i 0.848380 1.19006i
\(135\) 5.06725e18i 0.340227i
\(136\) 1.81243e18 + 5.35270e17i 0.113870 + 0.0336297i
\(137\) −2.02606e19 −1.19170 −0.595849 0.803096i \(-0.703184\pi\)
−0.595849 + 0.803096i \(0.703184\pi\)
\(138\) −2.82691e19 2.01526e19i −1.55740 1.11025i
\(139\) 1.28976e18 0.0665847 0.0332923 0.999446i \(-0.489401\pi\)
0.0332923 + 0.999446i \(0.489401\pi\)
\(140\) 1.51876e18 + 4.40307e18i 0.0735082 + 0.213110i
\(141\) 5.72950e18i 0.260103i
\(142\) −5.22589e18 3.72546e18i −0.222620 0.158703i
\(143\) 2.25942e19i 0.903591i
\(144\) −1.54051e19 + 1.20625e19i −0.578630 + 0.453082i
\(145\) 3.64447e19 1.28624
\(146\) 1.87196e18 2.62589e18i 0.0621041 0.0871164i
\(147\) −3.99581e19 −1.24666
\(148\) 6.24433e19 2.15386e19i 1.83287 0.632212i
\(149\) 6.12891e19i 1.69319i 0.532234 + 0.846597i \(0.321353\pi\)
−0.532234 + 0.846597i \(0.678647\pi\)
\(150\) −1.48537e18 + 2.08361e18i −0.0386380 + 0.0541994i
\(151\) 2.92476e19i 0.716635i 0.933600 + 0.358318i \(0.116650\pi\)
−0.933600 + 0.358318i \(0.883350\pi\)
\(152\) −7.19979e19 2.12634e19i −1.66237 0.490953i
\(153\) −4.00892e18 −0.0872579
\(154\) 1.14550e19 + 8.16611e18i 0.235130 + 0.167621i
\(155\) −6.79754e19 −1.31633
\(156\) 4.93239e19 1.70134e19i 0.901438 0.310934i
\(157\) 2.67899e19i 0.462248i 0.972924 + 0.231124i \(0.0742403\pi\)
−0.972924 + 0.231124i \(0.925760\pi\)
\(158\) 2.72559e19 + 1.94304e19i 0.444168 + 0.316641i
\(159\) 3.16884e19i 0.487895i
\(160\) −6.68929e19 + 3.01101e18i −0.973420 + 0.0438159i
\(161\) −2.44174e19 −0.335944
\(162\) −5.32999e19 + 7.47663e19i −0.693571 + 0.972906i
\(163\) 1.09227e20 1.34475 0.672377 0.740209i \(-0.265273\pi\)
0.672377 + 0.740209i \(0.265273\pi\)
\(164\) −6.79189e18 1.96906e19i −0.0791400 0.229437i
\(165\) 1.45210e20i 1.60193i
\(166\) 3.24146e19 4.54696e19i 0.338663 0.475060i
\(167\) 6.47127e19i 0.640533i −0.947327 0.320267i \(-0.896228\pi\)
0.947327 0.320267i \(-0.103772\pi\)
\(168\) −9.20132e18 + 3.11557e19i −0.0863111 + 0.292250i
\(169\) 5.35173e19 0.475898
\(170\) −1.11717e19 7.96414e18i −0.0942060 0.0671581i
\(171\) 1.59253e20 1.27386
\(172\) 3.10282e19 + 8.99548e19i 0.235505 + 0.682761i
\(173\) 1.74118e20i 1.25438i −0.778868 0.627188i \(-0.784206\pi\)
0.778868 0.627188i \(-0.215794\pi\)
\(174\) 2.06983e20 + 1.47555e20i 1.41577 + 1.00928i
\(175\) 1.79971e18i 0.0116912i
\(176\) −1.59237e20 + 1.24686e20i −0.982720 + 0.769494i
\(177\) −6.90592e19 −0.405007
\(178\) −9.34711e19 + 1.31117e20i −0.521072 + 0.730933i
\(179\) 1.12492e20 0.596272 0.298136 0.954523i \(-0.403635\pi\)
0.298136 + 0.954523i \(0.403635\pi\)
\(180\) 1.34282e20 4.63179e19i 0.676962 0.233505i
\(181\) 2.48283e20i 1.19080i −0.803428 0.595402i \(-0.796993\pi\)
0.803428 0.595402i \(-0.203007\pi\)
\(182\) 2.13017e19 2.98810e19i 0.0972237 0.136380i
\(183\) 5.25883e20i 2.28470i
\(184\) 9.94273e19 3.36661e20i 0.411287 1.39262i
\(185\) −4.79542e20 −1.88921
\(186\) −3.86057e20 2.75215e20i −1.44889 1.03289i
\(187\) −4.14389e19 −0.148195
\(188\) −5.47666e19 + 1.88907e19i −0.186679 + 0.0643914i
\(189\) 2.48576e19i 0.0807799i
\(190\) 4.43791e20 + 3.16372e20i 1.37530 + 0.980429i
\(191\) 3.36242e20i 0.993922i 0.867773 + 0.496961i \(0.165551\pi\)
−0.867773 + 0.496961i \(0.834449\pi\)
\(192\) −3.92100e20 2.53731e20i −1.10582 0.715588i
\(193\) 5.21758e20 1.40428 0.702139 0.712040i \(-0.252228\pi\)
0.702139 + 0.712040i \(0.252228\pi\)
\(194\) −1.64857e20 + 2.31253e20i −0.423538 + 0.594117i
\(195\) −3.78789e20 −0.929151
\(196\) −1.31746e20 3.81947e20i −0.308625 0.894744i
\(197\) 5.19244e20i 1.16192i 0.813933 + 0.580959i \(0.197322\pi\)
−0.813933 + 0.580959i \(0.802678\pi\)
\(198\) 2.49044e20 3.49346e20i 0.532463 0.746911i
\(199\) 8.49305e20i 1.73535i −0.497135 0.867673i \(-0.665615\pi\)
0.497135 0.867673i \(-0.334385\pi\)
\(200\) −2.48140e19 7.32840e18i −0.0484648 0.0143133i
\(201\) −1.03087e21 −1.92504
\(202\) 1.55885e20 + 1.11128e20i 0.278382 + 0.198455i
\(203\) 1.78781e20 0.305392
\(204\) −3.12034e19 9.04625e19i −0.0509953 0.147842i
\(205\) 1.51216e20i 0.236491i
\(206\) 4.48986e20 + 3.20076e20i 0.672091 + 0.479124i
\(207\) 7.44664e20i 1.06715i
\(208\) 3.25251e20 + 4.15378e20i 0.446323 + 0.569998i
\(209\) 1.64614e21 2.16347
\(210\) 1.36904e20 1.92042e20i 0.172362 0.241781i
\(211\) 4.10455e20 0.495135 0.247567 0.968871i \(-0.420369\pi\)
0.247567 + 0.968871i \(0.420369\pi\)
\(212\) 3.02900e20 1.04480e20i 0.350168 0.120784i
\(213\) 3.24975e20i 0.360109i
\(214\) 3.69900e20 5.18877e20i 0.392971 0.551239i
\(215\) 6.90820e20i 0.703751i
\(216\) −3.42731e20 1.01220e20i −0.334865 0.0988969i
\(217\) −3.33456e20 −0.312537
\(218\) −7.96953e19 5.68137e19i −0.0716678 0.0510910i
\(219\) −1.63293e20 −0.140919
\(220\) 1.38802e21 4.78773e20i 1.14972 0.396575i
\(221\) 1.08096e20i 0.0859562i
\(222\) −2.72349e21 1.94154e21i −2.07945 1.48241i
\(223\) 2.13650e20i 0.156660i −0.996927 0.0783301i \(-0.975041\pi\)
0.996927 0.0783301i \(-0.0249588\pi\)
\(224\) −3.28146e20 + 1.47706e19i −0.231119 + 0.0104032i
\(225\) 5.48863e19 0.0371382
\(226\) 1.45218e20 2.03704e20i 0.0944155 0.132441i
\(227\) −2.19788e21 −1.37332 −0.686660 0.726978i \(-0.740924\pi\)
−0.686660 + 0.726978i \(0.740924\pi\)
\(228\) 1.23954e21 + 3.59359e21i 0.744470 + 2.15832i
\(229\) 5.72813e20i 0.330745i −0.986231 0.165373i \(-0.947117\pi\)
0.986231 0.165373i \(-0.0528827\pi\)
\(230\) −1.47935e21 + 2.07516e21i −0.821337 + 1.15213i
\(231\) 7.12337e20i 0.380345i
\(232\) −7.27995e20 + 2.46499e21i −0.373884 + 1.26597i
\(233\) −5.62737e20 −0.278037 −0.139018 0.990290i \(-0.544395\pi\)
−0.139018 + 0.990290i \(0.544395\pi\)
\(234\) −9.11288e20 6.49644e20i −0.433224 0.308840i
\(235\) 4.20588e20 0.192418
\(236\) −2.27695e20 6.60117e20i −0.100264 0.290679i
\(237\) 1.69493e21i 0.718482i
\(238\) −5.48032e19 3.90685e19i −0.0223673 0.0159453i
\(239\) 2.59086e21i 1.01827i −0.860687 0.509135i \(-0.829965\pi\)
0.860687 0.509135i \(-0.170035\pi\)
\(240\) 2.09036e21 + 2.66959e21i 0.791260 + 1.01052i
\(241\) 3.96324e21 1.44510 0.722549 0.691320i \(-0.242970\pi\)
0.722549 + 0.691320i \(0.242970\pi\)
\(242\) 9.21834e20 1.29310e21i 0.323828 0.454250i
\(243\) 3.61786e21 1.22460
\(244\) −5.02676e21 + 1.73389e21i −1.63976 + 0.565604i
\(245\) 2.93322e21i 0.922251i
\(246\) −6.12235e20 + 8.58812e20i −0.185568 + 0.260305i
\(247\) 4.29405e21i 1.25486i
\(248\) 1.35783e21 4.59762e21i 0.382631 1.29559i
\(249\) −2.82756e21 −0.768453
\(250\) 3.17965e21 + 2.26673e21i 0.833527 + 0.594210i
\(251\) −6.40834e21 −1.62062 −0.810312 0.585999i \(-0.800702\pi\)
−0.810312 + 0.585999i \(0.800702\pi\)
\(252\) 6.58725e20 2.27215e20i 0.160731 0.0554411i
\(253\) 7.69734e21i 1.81241i
\(254\) −1.69266e21 1.20667e21i −0.384651 0.274212i
\(255\) 6.94719e20i 0.152387i
\(256\) 1.13255e21 4.58455e21i 0.239827 0.970816i
\(257\) 4.82903e21 0.987329 0.493665 0.869652i \(-0.335657\pi\)
0.493665 + 0.869652i \(0.335657\pi\)
\(258\) 2.79695e21 3.92342e21i 0.552214 0.774618i
\(259\) −2.35241e21 −0.448555
\(260\) −1.24891e21 3.62074e21i −0.230022 0.666863i
\(261\) 5.45234e21i 0.970104i
\(262\) 1.43693e21 2.01565e21i 0.247015 0.346500i
\(263\) 9.58434e21i 1.59206i 0.605255 + 0.796032i \(0.293071\pi\)
−0.605255 + 0.796032i \(0.706929\pi\)
\(264\) 9.82153e21 + 2.90063e21i 1.57668 + 0.465647i
\(265\) −2.32616e21 −0.360933
\(266\) 2.17704e21 + 1.55198e21i 0.326536 + 0.232783i
\(267\) 8.15357e21 1.18235
\(268\) −3.39888e21 9.85379e21i −0.476565 1.38162i
\(269\) 1.09608e21i 0.148618i 0.997235 + 0.0743091i \(0.0236751\pi\)
−0.997235 + 0.0743091i \(0.976325\pi\)
\(270\) 2.11257e21 + 1.50603e21i 0.277037 + 0.197496i
\(271\) 4.44119e21i 0.563346i 0.959510 + 0.281673i \(0.0908894\pi\)
−0.959510 + 0.281673i \(0.909111\pi\)
\(272\) 7.61825e20 5.96528e20i 0.0934835 0.0731999i
\(273\) −1.85817e21 −0.220608
\(274\) −6.02159e21 + 8.44677e21i −0.691761 + 0.970367i
\(275\) 5.67341e20 0.0630740
\(276\) −1.68036e22 + 5.79608e21i −1.80809 + 0.623666i
\(277\) 2.22727e21i 0.231982i −0.993250 0.115991i \(-0.962996\pi\)
0.993250 0.115991i \(-0.0370044\pi\)
\(278\) 3.83325e20 5.37708e20i 0.0386513 0.0542180i
\(279\) 1.01695e22i 0.992800i
\(280\) 2.28706e21 + 6.75445e20i 0.216200 + 0.0638510i
\(281\) −1.87209e22 −1.71384 −0.856919 0.515451i \(-0.827624\pi\)
−0.856919 + 0.515451i \(0.827624\pi\)
\(282\) 2.38867e21 + 1.70285e21i 0.211794 + 0.150985i
\(283\) −1.49875e21 −0.128721 −0.0643607 0.997927i \(-0.520501\pi\)
−0.0643607 + 0.997927i \(0.520501\pi\)
\(284\) −3.10635e21 + 1.07148e21i −0.258455 + 0.0891491i
\(285\) 2.75974e22i 2.22467i
\(286\) −9.41968e21 6.71516e21i −0.735769 0.524520i
\(287\) 7.41798e20i 0.0561499i
\(288\) 4.50464e20 + 1.00076e22i 0.0330467 + 0.734169i
\(289\) −1.38648e22 −0.985903
\(290\) 1.08316e22 1.51941e22i 0.746642 1.04735i
\(291\) 1.43806e22 0.961039
\(292\) −5.38391e20 1.56087e21i −0.0348861 0.101139i
\(293\) 9.73171e21i 0.611478i 0.952115 + 0.305739i \(0.0989035\pi\)
−0.952115 + 0.305739i \(0.901097\pi\)
\(294\) −1.18758e22 + 1.66588e22i −0.723666 + 1.01512i
\(295\) 5.06946e21i 0.299615i
\(296\) 9.57900e21 3.24345e22i 0.549155 1.85944i
\(297\) 7.83612e21 0.435806
\(298\) 2.55519e22 + 1.82156e22i 1.37872 + 0.982871i
\(299\) 2.00789e22 1.05123
\(300\) 4.27206e20 + 1.23853e21i 0.0217043 + 0.0629237i
\(301\) 3.38885e21i 0.167091i
\(302\) 1.21936e22 + 8.69261e21i 0.583536 + 0.415995i
\(303\) 9.69380e21i 0.450309i
\(304\) −3.02632e22 + 2.36968e22i −1.36475 + 1.06863i
\(305\) 3.86037e22 1.69017
\(306\) −1.19148e21 + 1.67135e21i −0.0506517 + 0.0710516i
\(307\) −2.45469e22 −1.01333 −0.506665 0.862143i \(-0.669122\pi\)
−0.506665 + 0.862143i \(0.669122\pi\)
\(308\) 6.80902e21 2.34864e21i 0.272978 0.0941587i
\(309\) 2.79205e22i 1.08717i
\(310\) −2.02028e22 + 2.83394e22i −0.764110 + 1.07185i
\(311\) 1.32062e22i 0.485216i −0.970124 0.242608i \(-0.921997\pi\)
0.970124 0.242608i \(-0.0780030\pi\)
\(312\) 7.56644e21 2.56200e22i 0.270085 0.914508i
\(313\) 2.13013e22 0.738766 0.369383 0.929277i \(-0.379569\pi\)
0.369383 + 0.929277i \(0.379569\pi\)
\(314\) 1.11689e22 + 7.96217e21i 0.376396 + 0.268327i
\(315\) −5.05876e21 −0.165672
\(316\) 1.62013e22 5.58834e21i 0.515664 0.177868i
\(317\) 2.97371e22i 0.919952i 0.887931 + 0.459976i \(0.152142\pi\)
−0.887931 + 0.459976i \(0.847858\pi\)
\(318\) −1.32111e22 9.41803e21i −0.397279 0.283215i
\(319\) 5.63590e22i 1.64758i
\(320\) −1.86258e22 + 2.87830e22i −0.529376 + 0.818063i
\(321\) −3.22667e22 −0.891681
\(322\) −7.25703e21 + 1.01798e22i −0.195010 + 0.273550i
\(323\) −7.87551e21 −0.205805
\(324\) 1.53295e22 + 4.44422e22i 0.389604 + 1.12951i
\(325\) 1.47994e21i 0.0365842i
\(326\) 3.24632e22 4.55377e22i 0.780608 1.09500i
\(327\) 4.95591e21i 0.115929i
\(328\) −1.02277e22 3.02059e21i −0.232764 0.0687429i
\(329\) 2.06321e21 0.0456857
\(330\) −6.05393e22 4.31576e22i −1.30440 0.929891i
\(331\) −2.58777e22 −0.542593 −0.271297 0.962496i \(-0.587452\pi\)
−0.271297 + 0.962496i \(0.587452\pi\)
\(332\) −9.32273e21 2.70278e22i −0.190239 0.551528i
\(333\) 7.17422e22i 1.42487i
\(334\) −2.69792e22 1.92331e22i −0.521568 0.371819i
\(335\) 7.56735e22i 1.42410i
\(336\) 1.02543e22 + 1.30958e22i 0.187869 + 0.239927i
\(337\) −7.84080e22 −1.39859 −0.699297 0.714832i \(-0.746503\pi\)
−0.699297 + 0.714832i \(0.746503\pi\)
\(338\) 1.59057e22 2.23118e22i 0.276251 0.387510i
\(339\) −1.26675e22 −0.214236
\(340\) −6.64062e21 + 2.29056e21i −0.109370 + 0.0377251i
\(341\) 1.05119e23i 1.68613i
\(342\) 4.73311e22 6.63937e22i 0.739455 1.03727i
\(343\) 2.95918e22i 0.450322i
\(344\) 4.67247e22 + 1.37994e22i 0.692660 + 0.204566i
\(345\) 1.29045e23 1.86367
\(346\) −7.25909e22 5.17490e22i −1.02140 0.728144i
\(347\) −9.46254e21 −0.129731 −0.0648653 0.997894i \(-0.520662\pi\)
−0.0648653 + 0.997894i \(0.520662\pi\)
\(348\) 1.23034e23 4.24382e22i 1.64366 0.566949i
\(349\) 9.78658e22i 1.27410i −0.770824 0.637048i \(-0.780155\pi\)
0.770824 0.637048i \(-0.219845\pi\)
\(350\) 7.50313e20 + 5.34888e20i 0.00951985 + 0.00678657i
\(351\) 2.04409e22i 0.252777i
\(352\) 4.65629e21 + 1.03445e23i 0.0561250 + 1.24688i
\(353\) −9.40912e22 −1.10555 −0.552773 0.833332i \(-0.686430\pi\)
−0.552773 + 0.833332i \(0.686430\pi\)
\(354\) −2.05249e22 + 2.87913e22i −0.235100 + 0.329786i
\(355\) 2.38556e22 0.266401
\(356\) 2.68831e22 + 7.79376e22i 0.292705 + 0.848588i
\(357\) 3.40798e21i 0.0361812i
\(358\) 3.34335e22 4.68988e22i 0.346126 0.485528i
\(359\) 1.20975e23i 1.22136i −0.791877 0.610681i \(-0.790896\pi\)
0.791877 0.610681i \(-0.209104\pi\)
\(360\) 2.05992e22 6.97491e22i 0.202828 0.686777i
\(361\) 2.08724e23 2.00451
\(362\) −1.03511e23 7.37916e22i −0.969638 0.691242i
\(363\) −8.04124e22 −0.734791
\(364\) −6.12656e21 1.77617e22i −0.0546140 0.158333i
\(365\) 1.19869e22i 0.104249i
\(366\) 2.19244e23 + 1.56296e23i 1.86037 + 1.32623i
\(367\) 4.06630e22i 0.336670i −0.985730 0.168335i \(-0.946161\pi\)
0.985730 0.168335i \(-0.0538390\pi\)
\(368\) −1.10806e23 1.41510e23i −0.895226 1.14329i
\(369\) 2.26228e22 0.178365
\(370\) −1.42523e23 + 1.99924e23i −1.09666 + 1.53833i
\(371\) −1.14111e22 −0.0856963
\(372\) −2.29478e23 + 7.91541e22i −1.68211 + 0.580213i
\(373\) 3.49817e21i 0.0250300i −0.999922 0.0125150i \(-0.996016\pi\)
0.999922 0.0125150i \(-0.00398376\pi\)
\(374\) −1.23159e22 + 1.72762e22i −0.0860247 + 0.120671i
\(375\) 1.97729e23i 1.34831i
\(376\) −8.40137e21 + 2.84471e22i −0.0559319 + 0.189386i
\(377\) −1.47016e23 −0.955633
\(378\) 1.03633e22 + 7.38787e21i 0.0657769 + 0.0468914i
\(379\) 2.17964e23 1.35092 0.675462 0.737395i \(-0.263944\pi\)
0.675462 + 0.737395i \(0.263944\pi\)
\(380\) 2.63796e23 9.09915e22i 1.59667 0.550742i
\(381\) 1.05259e23i 0.622208i
\(382\) 1.40182e23 + 9.99338e22i 0.809323 + 0.576955i
\(383\) 3.16907e23i 1.78707i 0.448989 + 0.893537i \(0.351784\pi\)
−0.448989 + 0.893537i \(0.648216\pi\)
\(384\) −2.22318e23 + 8.80585e22i −1.22460 + 0.485054i
\(385\) −5.22908e22 −0.281370
\(386\) 1.55070e23 2.17525e23i 0.815160 1.14347i
\(387\) −1.03351e23 −0.530780
\(388\) 4.74143e22 + 1.37460e23i 0.237916 + 0.689750i
\(389\) 1.96504e23i 0.963441i −0.876325 0.481721i \(-0.840012\pi\)
0.876325 0.481721i \(-0.159988\pi\)
\(390\) −1.12579e23 + 1.57920e23i −0.539357 + 0.756582i
\(391\) 3.68258e22i 0.172409i
\(392\) −1.98392e23 5.85919e22i −0.907717 0.268079i
\(393\) −1.25345e23 −0.560496
\(394\) 2.16477e23 + 1.54323e23i 0.946117 + 0.674474i
\(395\) −1.24420e23 −0.531517
\(396\) −7.16272e22 2.07656e23i −0.299103 0.867139i
\(397\) 3.12937e23i 1.27745i −0.769437 0.638723i \(-0.779463\pi\)
0.769437 0.638723i \(-0.220537\pi\)
\(398\) −3.54082e23 2.52420e23i −1.41304 1.00734i
\(399\) 1.35381e23i 0.528202i
\(400\) −1.04302e22 + 8.16708e21i −0.0397879 + 0.0311549i
\(401\) −1.05642e23 −0.394037 −0.197018 0.980400i \(-0.563126\pi\)
−0.197018 + 0.980400i \(0.563126\pi\)
\(402\) −3.06382e23 + 4.29777e23i −1.11745 + 1.56751i
\(403\) 2.74208e23 0.977990
\(404\) 9.26602e22 3.19614e22i 0.323192 0.111479i
\(405\) 3.41300e23i 1.16424i
\(406\) 5.31351e22 7.45352e22i 0.177275 0.248672i
\(407\) 7.41575e23i 2.41994i
\(408\) −4.69884e22 1.38772e22i −0.149985 0.0442957i
\(409\) 4.40895e22 0.137666 0.0688328 0.997628i \(-0.478073\pi\)
0.0688328 + 0.997628i \(0.478073\pi\)
\(410\) 6.30432e22 + 4.49426e22i 0.192568 + 0.137279i
\(411\) 5.25269e23 1.56966
\(412\) 2.66884e23 9.20566e22i 0.780275 0.269141i
\(413\) 2.48685e22i 0.0711375i
\(414\) 3.10456e23 + 2.21320e23i 0.868954 + 0.619465i
\(415\) 2.07564e23i 0.568484i
\(416\) 2.69841e23 1.21462e22i 0.723217 0.0325537i
\(417\) −3.34378e22 −0.0877027
\(418\) 4.89246e23 6.86289e23i 1.25586 1.76165i
\(419\) −1.70150e23 −0.427470 −0.213735 0.976892i \(-0.568563\pi\)
−0.213735 + 0.976892i \(0.568563\pi\)
\(420\) −3.93748e22 1.14153e23i −0.0968222 0.280700i
\(421\) 6.33068e22i 0.152374i −0.997094 0.0761871i \(-0.975725\pi\)
0.997094 0.0761871i \(-0.0242746\pi\)
\(422\) 1.21990e23 1.71122e23i 0.287417 0.403174i
\(423\) 6.29223e22i 0.145125i
\(424\) 4.64658e22 1.57333e23i 0.104916 0.355245i
\(425\) −2.71429e21 −0.00600005
\(426\) 1.35485e23 + 9.65851e22i 0.293227 + 0.209037i
\(427\) 1.89372e23 0.401296
\(428\) −1.06386e23 3.08428e23i −0.220746 0.639970i
\(429\) 5.85769e23i 1.19017i
\(430\) −2.88008e23 2.05317e23i −0.573045 0.408516i
\(431\) 2.34828e23i 0.457567i 0.973477 + 0.228783i \(0.0734747\pi\)
−0.973477 + 0.228783i \(0.926525\pi\)
\(432\) −1.44062e23 + 1.12804e23i −0.274913 + 0.215263i
\(433\) −5.71351e23 −1.06785 −0.533927 0.845531i \(-0.679284\pi\)
−0.533927 + 0.845531i \(0.679284\pi\)
\(434\) −9.91057e22 + 1.39020e23i −0.181422 + 0.254490i
\(435\) −9.44854e23 −1.69419
\(436\) −4.73721e22 + 1.63401e22i −0.0832039 + 0.0286996i
\(437\) 1.46289e24i 2.51697i
\(438\) −4.85318e22 + 6.80778e22i −0.0818011 + 0.114746i
\(439\) 1.88369e23i 0.311050i −0.987832 0.155525i \(-0.950293\pi\)
0.987832 0.155525i \(-0.0497068\pi\)
\(440\) 2.12927e23 7.20973e23i 0.344475 1.16639i
\(441\) 4.38826e23 0.695576
\(442\) 4.50658e22 + 3.21268e22i 0.0699917 + 0.0498961i
\(443\) −4.33548e23 −0.659787 −0.329893 0.944018i \(-0.607013\pi\)
−0.329893 + 0.944018i \(0.607013\pi\)
\(444\) −1.61888e24 + 5.58404e23i −2.41418 + 0.832725i
\(445\) 5.98532e23i 0.874676i
\(446\) −8.90721e22 6.34983e22i −0.127564 0.0909386i
\(447\) 1.58896e24i 2.23021i
\(448\) −9.13695e22 + 1.41196e23i −0.125690 + 0.194232i
\(449\) 6.38051e23 0.860277 0.430139 0.902763i \(-0.358465\pi\)
0.430139 + 0.902763i \(0.358465\pi\)
\(450\) 1.63126e22 2.28825e22i 0.0215581 0.0302406i
\(451\) 2.33844e23 0.302927
\(452\) −4.17659e22 1.21085e23i −0.0530366 0.153760i
\(453\) 7.58264e23i 0.943924i
\(454\) −6.53227e23 + 9.16314e23i −0.797190 + 1.11826i
\(455\) 1.36403e23i 0.163201i
\(456\) 1.86659e24 + 5.51268e23i 2.18961 + 0.646665i
\(457\) −2.32448e23 −0.267350 −0.133675 0.991025i \(-0.542678\pi\)
−0.133675 + 0.991025i \(0.542678\pi\)
\(458\) −2.38810e23 1.70244e23i −0.269317 0.191992i
\(459\) −3.74897e22 −0.0414570
\(460\) 4.25475e23 + 1.23351e24i 0.461374 + 1.33758i
\(461\) 1.95601e22i 0.0208000i −0.999946 0.0104000i \(-0.996690\pi\)
0.999946 0.0104000i \(-0.00331048\pi\)
\(462\) −2.96978e23 2.11712e23i −0.309704 0.220784i
\(463\) 3.50452e23i 0.358426i −0.983810 0.179213i \(-0.942645\pi\)
0.983810 0.179213i \(-0.0573551\pi\)
\(464\) 8.11309e23 + 1.03612e24i 0.813812 + 1.03932i
\(465\) 1.76231e24 1.73382
\(466\) −1.67250e23 + 2.34609e23i −0.161396 + 0.226397i
\(467\) −2.45856e23 −0.232717 −0.116359 0.993207i \(-0.537122\pi\)
−0.116359 + 0.993207i \(0.537122\pi\)
\(468\) −5.41683e23 + 1.86843e23i −0.502959 + 0.173486i
\(469\) 3.71220e23i 0.338123i
\(470\) 1.25002e23 1.75346e23i 0.111695 0.156681i
\(471\) 6.94547e23i 0.608855i
\(472\) −3.42880e23 1.01264e23i −0.294893 0.0870918i
\(473\) −1.06830e24 −0.901453
\(474\) −7.06628e23 5.03745e23i −0.585040 0.417067i
\(475\) 1.07824e23 0.0875937
\(476\) −3.25758e22 + 1.12364e22i −0.0259677 + 0.00895706i
\(477\) 3.48007e23i 0.272222i
\(478\) −1.08015e24 7.70023e23i −0.829149 0.591089i
\(479\) 4.93215e23i 0.371549i −0.982592 0.185775i \(-0.940521\pi\)
0.982592 0.185775i \(-0.0594794\pi\)
\(480\) 1.73424e24 7.80624e22i 1.28215 0.0577126i
\(481\) 1.93444e24 1.40362
\(482\) 1.17791e24 1.65231e24i 0.838855 1.17670i
\(483\) 6.33037e23 0.442492
\(484\) −2.65128e23 7.68639e23i −0.181906 0.527369i
\(485\) 1.05564e24i 0.710955i
\(486\) 1.07525e24 1.50831e24i 0.710861 0.997159i
\(487\) 6.02753e23i 0.391182i 0.980686 + 0.195591i \(0.0626625\pi\)
−0.980686 + 0.195591i \(0.937338\pi\)
\(488\) −7.71121e23 + 2.61102e24i −0.491297 + 1.66353i
\(489\) −2.83179e24 −1.77126
\(490\) 1.22288e24 + 8.71774e23i 0.750963 + 0.535351i
\(491\) 2.08982e24 1.26001 0.630006 0.776590i \(-0.283052\pi\)
0.630006 + 0.776590i \(0.283052\pi\)
\(492\) 1.76084e23 + 5.10491e23i 0.104240 + 0.302205i
\(493\) 2.69634e23i 0.156730i
\(494\) −1.79022e24 1.27622e24i −1.02180 0.728424i
\(495\) 1.59473e24i 0.893797i
\(496\) −1.51322e24 1.93253e24i −0.832852 1.06363i
\(497\) 1.17025e23 0.0632514
\(498\) −8.40371e23 + 1.17883e24i −0.446074 + 0.625730i
\(499\) −2.80590e24 −1.46274 −0.731371 0.681980i \(-0.761119\pi\)
−0.731371 + 0.681980i \(0.761119\pi\)
\(500\) 1.89003e24 6.51931e23i 0.967697 0.333789i
\(501\) 1.67772e24i 0.843685i
\(502\) −1.90461e24 + 2.67169e24i −0.940745 + 1.31963i
\(503\) 1.74591e24i 0.847050i −0.905884 0.423525i \(-0.860793\pi\)
0.905884 0.423525i \(-0.139207\pi\)
\(504\) 1.01050e23 3.42157e23i 0.0481574 0.163061i
\(505\) −7.11596e23 −0.333128
\(506\) 3.20908e24 + 2.28771e24i 1.47579 + 1.05207i
\(507\) −1.38747e24 −0.626834
\(508\) −1.00614e24 + 3.47050e23i −0.446567 + 0.154035i
\(509\) 1.30535e24i 0.569204i 0.958646 + 0.284602i \(0.0918615\pi\)
−0.958646 + 0.284602i \(0.908139\pi\)
\(510\) 2.89633e23 + 2.06476e23i 0.124084 + 0.0884580i
\(511\) 5.88022e22i 0.0247517i
\(512\) −1.57473e24 1.83473e24i −0.651292 0.758827i
\(513\) 1.48927e24 0.605223
\(514\) 1.43522e24 2.01326e24i 0.573128 0.803955i
\(515\) −2.04957e24 −0.804263
\(516\) −8.04428e23 2.33214e24i −0.310198 0.899305i
\(517\) 6.50407e23i 0.246474i
\(518\) −6.99155e23 + 9.80738e23i −0.260379 + 0.365246i
\(519\) 4.51411e24i 1.65221i
\(520\) −1.88070e24 5.55432e23i −0.676532 0.199803i
\(521\) 1.37668e24 0.486735 0.243368 0.969934i \(-0.421748\pi\)
0.243368 + 0.969934i \(0.421748\pi\)
\(522\) −2.27312e24 1.62048e24i −0.789929 0.563129i
\(523\) 2.71686e24 0.928009 0.464005 0.885833i \(-0.346412\pi\)
0.464005 + 0.885833i \(0.346412\pi\)
\(524\) −4.13273e23 1.19813e24i −0.138757 0.402275i
\(525\) 4.66587e22i 0.0153992i
\(526\) 3.99578e24 + 2.84854e24i 1.29637 + 0.924166i
\(527\) 5.02911e23i 0.160397i
\(528\) 4.12832e24 3.23258e24i 1.29440 1.01355i
\(529\) −3.59630e24 −1.10855
\(530\) −6.91353e23 + 9.69794e23i −0.209516 + 0.293898i
\(531\) 7.58420e23 0.225974
\(532\) 1.29406e24 4.46363e23i 0.379097 0.130762i
\(533\) 6.09996e23i 0.175704i
\(534\) 2.42330e24 3.39928e24i 0.686335 0.962756i
\(535\) 2.36861e24i 0.659645i
\(536\) −5.11829e24 1.51160e24i −1.40166 0.413956i
\(537\) −2.91643e24 −0.785386
\(538\) 4.56964e23 + 3.25763e23i 0.121016 + 0.0862703i
\(539\) 4.53600e24 1.18134
\(540\) 1.25575e24 4.33146e23i 0.321631 0.110941i
\(541\) 4.31846e24i 1.08781i −0.839146 0.543906i \(-0.816945\pi\)
0.839146 0.543906i \(-0.183055\pi\)
\(542\) 1.85156e24 + 1.31995e24i 0.458717 + 0.327013i
\(543\) 6.43691e24i 1.56848i
\(544\) −2.22767e22 4.94903e23i −0.00533902 0.118612i
\(545\) 3.63800e23 0.0857619
\(546\) −5.52262e23 + 7.74684e23i −0.128059 + 0.179635i
\(547\) −2.16653e24 −0.494172 −0.247086 0.968994i \(-0.579473\pi\)
−0.247086 + 0.968994i \(0.579473\pi\)
\(548\) 1.73186e24 + 5.02089e24i 0.388587 + 1.12656i
\(549\) 5.77533e24i 1.27475i
\(550\) 1.68618e23 2.36529e23i 0.0366134 0.0513594i
\(551\) 1.07111e25i 2.28807i
\(552\) −2.57772e24 + 8.72817e24i −0.541731 + 1.83430i
\(553\) −6.10349e23 −0.126198
\(554\) −9.28565e23 6.61961e23i −0.188897 0.134662i
\(555\) 1.24324e25 2.48840
\(556\) −1.10248e23 3.19622e23i −0.0217118 0.0629453i
\(557\) 1.39730e24i 0.270765i −0.990793 0.135382i \(-0.956774\pi\)
0.990793 0.135382i \(-0.0432263\pi\)
\(558\) 4.23974e24 + 3.02245e24i 0.808410 + 0.576304i
\(559\) 2.78672e24i 0.522862i
\(560\) 9.61329e23 7.52744e23i 0.177492 0.138981i
\(561\) 1.07433e24 0.195197
\(562\) −5.56399e24 + 7.80488e24i −0.994854 + 1.39553i
\(563\) −2.45279e24 −0.431604 −0.215802 0.976437i \(-0.569237\pi\)
−0.215802 + 0.976437i \(0.569237\pi\)
\(564\) 1.41986e24 4.89755e23i 0.245886 0.0848138i
\(565\) 9.29885e23i 0.158487i
\(566\) −4.45439e23 + 6.24839e23i −0.0747206 + 0.104814i
\(567\) 1.67426e24i 0.276424i
\(568\) −4.76523e23 + 1.61351e24i −0.0774371 + 0.262202i
\(569\) 5.44844e24 0.871488 0.435744 0.900071i \(-0.356485\pi\)
0.435744 + 0.900071i \(0.356485\pi\)
\(570\) −1.15056e25 8.20217e24i −1.81149 1.29138i
\(571\) −2.77886e24 −0.430667 −0.215333 0.976541i \(-0.569084\pi\)
−0.215333 + 0.976541i \(0.569084\pi\)
\(572\) −5.59920e24 + 1.93134e24i −0.854204 + 0.294641i
\(573\) 8.71731e24i 1.30915i
\(574\) 3.09261e23 + 2.20468e23i 0.0457213 + 0.0325941i
\(575\) 5.04183e23i 0.0733800i
\(576\) 4.30611e24 + 2.78652e24i 0.616996 + 0.399264i
\(577\) −1.00961e25 −1.42421 −0.712104 0.702074i \(-0.752257\pi\)
−0.712104 + 0.702074i \(0.752257\pi\)
\(578\) −4.12073e24 + 5.78035e24i −0.572300 + 0.802793i
\(579\) −1.35269e25 −1.84966
\(580\) −3.11528e24 9.03159e24i −0.419416 1.21594i
\(581\) 1.01821e24i 0.134975i
\(582\) 4.27403e24 5.99539e24i 0.557867 0.782547i
\(583\) 3.59723e24i 0.462330i
\(584\) −8.10750e23 2.39442e23i −0.102606 0.0303029i
\(585\) 4.15993e24 0.518421
\(586\) 4.05722e24 + 2.89234e24i 0.497909 + 0.354953i
\(587\) −8.87476e24 −1.07254 −0.536270 0.844046i \(-0.680167\pi\)
−0.536270 + 0.844046i \(0.680167\pi\)
\(588\) 3.41559e24 + 9.90224e24i 0.406509 + 1.17852i
\(589\) 1.99780e25i 2.34160i
\(590\) 2.11349e24 + 1.50668e24i 0.243968 + 0.173921i
\(591\) 1.34617e25i 1.53043i
\(592\) −1.06752e25 1.36333e25i −1.19531 1.52654i
\(593\) 5.60679e24 0.618333 0.309166 0.951008i \(-0.399950\pi\)
0.309166 + 0.951008i \(0.399950\pi\)
\(594\) 2.32895e24 3.26694e24i 0.252978 0.354865i
\(595\) 2.50171e23 0.0267660
\(596\) 1.51884e25 5.23896e24i 1.60065 0.552114i
\(597\) 2.20188e25i 2.28573i
\(598\) 5.96761e24 8.37105e24i 0.610224 0.855991i
\(599\) 3.41193e24i 0.343684i −0.985125 0.171842i \(-0.945028\pi\)
0.985125 0.171842i \(-0.0549718\pi\)
\(600\) 6.43320e23 + 1.89994e23i 0.0638360 + 0.0188529i
\(601\) 1.55289e25 1.51799 0.758996 0.651096i \(-0.225690\pi\)
0.758996 + 0.651096i \(0.225690\pi\)
\(602\) −1.41284e24 1.00719e24i −0.136058 0.0969937i
\(603\) 1.13212e25 1.07408
\(604\) 7.24803e24 2.50007e24i 0.677466 0.233679i
\(605\) 5.90287e24i 0.543581i
\(606\) −4.04142e24 2.88107e24i −0.366674 0.261397i
\(607\) 1.87918e23i 0.0167985i −0.999965 0.00839926i \(-0.997326\pi\)
0.999965 0.00839926i \(-0.00267360\pi\)
\(608\) 8.84935e23 + 1.96598e25i 0.0779434 + 1.73160i
\(609\) −4.63503e24 −0.402250
\(610\) 1.14733e25 1.60942e25i 0.981115 1.37626i
\(611\) −1.69662e24 −0.142960
\(612\) 3.42680e23 + 9.93474e23i 0.0284529 + 0.0824886i
\(613\) 1.63477e25i 1.33756i −0.743461 0.668779i \(-0.766817\pi\)
0.743461 0.668779i \(-0.233183\pi\)
\(614\) −7.29552e24 + 1.02338e25i −0.588221 + 0.825127i
\(615\) 3.92038e24i 0.311496i
\(616\) 1.04452e24 3.53676e24i 0.0817885 0.276936i
\(617\) 6.58005e24 0.507765 0.253882 0.967235i \(-0.418292\pi\)
0.253882 + 0.967235i \(0.418292\pi\)
\(618\) −1.16403e25 8.29819e24i −0.885252 0.631084i
\(619\) 1.49523e25 1.12070 0.560352 0.828254i \(-0.310666\pi\)
0.560352 + 0.828254i \(0.310666\pi\)
\(620\) 5.81050e24 + 1.68454e25i 0.429228 + 1.24439i
\(621\) 6.96378e24i 0.507015i
\(622\) −5.50578e24 3.92499e24i −0.395098 0.281660i
\(623\) 2.93613e24i 0.207674i
\(624\) −8.43236e24 1.07690e25i −0.587879 0.750779i
\(625\) −1.37794e25 −0.946912
\(626\) 6.33090e24 8.88067e24i 0.428841 0.601557i
\(627\) −4.26774e25 −2.84964
\(628\) 6.63897e24 2.28999e24i 0.436983 0.150729i
\(629\) 3.54786e24i 0.230203i
\(630\) −1.50350e24 + 2.10904e24i −0.0961699 + 0.134902i
\(631\) 2.04517e25i 1.28963i 0.764340 + 0.644814i \(0.223065\pi\)
−0.764340 + 0.644814i \(0.776935\pi\)
\(632\) 2.48533e24 8.41534e24i 0.154501 0.523140i
\(633\) −1.06413e25 −0.652172
\(634\) 1.23976e25 + 8.83809e24i 0.749091 + 0.534017i
\(635\) 7.72681e24 0.460295
\(636\) −7.85289e24 + 2.70871e24i −0.461228 + 0.159092i
\(637\) 1.18324e25i 0.685200i
\(638\) −2.34965e25 1.67503e25i −1.34158 0.956395i
\(639\) 3.56893e24i 0.200923i
\(640\) 6.46414e24 + 1.63197e25i 0.358832 + 0.905928i
\(641\) 4.66244e24 0.255206 0.127603 0.991825i \(-0.459272\pi\)
0.127603 + 0.991825i \(0.459272\pi\)
\(642\) −9.58990e24 + 1.34522e25i −0.517606 + 0.726071i
\(643\) 2.00719e25 1.06829 0.534146 0.845392i \(-0.320633\pi\)
0.534146 + 0.845392i \(0.320633\pi\)
\(644\) 2.08719e24 + 6.05102e24i 0.109544 + 0.317582i
\(645\) 1.79100e25i 0.926953i
\(646\) −2.34066e24 + 3.28336e24i −0.119466 + 0.167581i
\(647\) 1.11315e25i 0.560291i 0.959958 + 0.280146i \(0.0903827\pi\)
−0.959958 + 0.280146i \(0.909617\pi\)
\(648\) 2.30843e25 + 6.81757e24i 1.14589 + 0.338419i
\(649\) 7.83953e24 0.383785
\(650\) −6.16998e23 4.39849e23i −0.0297895 0.0212365i
\(651\) 8.64508e24 0.411661
\(652\) −9.33669e24 2.70683e25i −0.438495 1.27125i
\(653\) 3.18524e25i 1.47545i −0.675102 0.737724i \(-0.735900\pi\)
0.675102 0.737724i \(-0.264100\pi\)
\(654\) 2.06615e24 + 1.47293e24i 0.0943980 + 0.0672950i
\(655\) 9.20121e24i 0.414642i
\(656\) −4.29907e24 + 3.36628e24i −0.191091 + 0.149629i
\(657\) 1.79330e24 0.0786259
\(658\) 6.13202e23 8.60168e23i 0.0265198 0.0372006i
\(659\) −3.67144e25 −1.56628 −0.783138 0.621848i \(-0.786382\pi\)
−0.783138 + 0.621848i \(0.786382\pi\)
\(660\) −3.59855e25 + 1.24125e25i −1.51437 + 0.522353i
\(661\) 6.25876e24i 0.259821i −0.991526 0.129911i \(-0.958531\pi\)
0.991526 0.129911i \(-0.0414691\pi\)
\(662\) −7.69105e24 + 1.07886e25i −0.314966 + 0.441818i
\(663\) 2.80245e24i 0.113218i
\(664\) −1.40389e25 4.14615e24i −0.559525 0.165246i
\(665\) −9.93793e24 −0.390752
\(666\) 2.99098e25 + 2.13223e25i 1.16024 + 0.827116i
\(667\) 5.00850e25 1.91679
\(668\) −1.60368e25 + 5.53161e24i −0.605523 + 0.208864i
\(669\) 5.53901e24i 0.206347i
\(670\) 3.15488e25 + 2.24907e25i 1.15960 + 0.826666i
\(671\) 5.96977e25i 2.16498i
\(672\) 8.50741e24 3.82939e23i 0.304420 0.0137027i
\(673\) −4.46463e25 −1.57634 −0.788170 0.615457i \(-0.788971\pi\)
−0.788170 + 0.615457i \(0.788971\pi\)
\(674\) −2.33035e25 + 3.26889e25i −0.811860 + 1.13884i
\(675\) 5.13273e23 0.0176447
\(676\) −4.57463e24 1.32624e25i −0.155180 0.449887i
\(677\) 2.43011e25i 0.813444i −0.913552 0.406722i \(-0.866672\pi\)
0.913552 0.406722i \(-0.133328\pi\)
\(678\) −3.76486e24 + 5.28116e24i −0.124360 + 0.174446i
\(679\) 5.17851e24i 0.168802i
\(680\) −1.01869e24 + 3.44929e24i −0.0327689 + 0.110956i
\(681\) 5.69816e25 1.80888
\(682\) 4.38248e25 + 3.12421e25i 1.37297 + 0.978770i
\(683\) 4.85583e25 1.50133 0.750666 0.660682i \(-0.229733\pi\)
0.750666 + 0.660682i \(0.229733\pi\)
\(684\) −1.36128e25 3.94654e25i −0.415378 1.20424i
\(685\) 3.85586e25i 1.16120i
\(686\) 1.23370e25 + 8.79489e24i 0.366685 + 0.261405i
\(687\) 1.48506e25i 0.435645i
\(688\) 1.96400e25 1.53786e25i 0.568650 0.445267i
\(689\) 9.38358e24 0.268161
\(690\) 3.83532e25 5.37999e25i 1.08183 1.51754i
\(691\) −5.60552e25 −1.56068 −0.780339 0.625356i \(-0.784954\pi\)
−0.780339 + 0.625356i \(0.784954\pi\)
\(692\) −4.31491e25 + 1.48835e25i −1.18582 + 0.409025i
\(693\) 7.82300e24i 0.212214i
\(694\) −2.81234e24 + 3.94500e24i −0.0753065 + 0.105636i
\(695\) 2.45458e24i 0.0648804i
\(696\) 1.88738e25 6.39066e25i 0.492465 1.66749i
\(697\) −1.11876e24 −0.0288166
\(698\) −4.08010e25 2.90865e25i −1.03746 0.739592i
\(699\) 1.45893e25 0.366219
\(700\) 4.45997e23 1.53838e23i 0.0110522 0.00381226i
\(701\) 7.35112e25i 1.79842i 0.437516 + 0.899211i \(0.355858\pi\)
−0.437516 + 0.899211i \(0.644142\pi\)
\(702\) −8.52198e24 6.07520e24i −0.205829 0.146733i
\(703\) 1.40937e26i 3.36069i
\(704\) 4.45108e25 + 2.88033e25i 1.04788 + 0.678092i
\(705\) −1.09040e25 −0.253445
\(706\) −2.79646e25 + 3.92273e25i −0.641751 + 0.900215i
\(707\) −3.49077e24 −0.0790945
\(708\) 5.90315e24 + 1.71140e25i 0.132064 + 0.382870i
\(709\) 6.76581e25i 1.49453i −0.664528 0.747263i \(-0.731367\pi\)
0.664528 0.747263i \(-0.268633\pi\)
\(710\) 7.09006e24 9.94557e24i 0.154641 0.216923i
\(711\) 1.86140e25i 0.400878i
\(712\) 4.04826e25 + 1.19559e25i 0.860892 + 0.254250i
\(713\) −9.34166e25 −1.96164
\(714\) 1.42081e24 + 1.01288e24i 0.0294613 + 0.0210026i
\(715\) 4.29998e25 0.880464
\(716\) −9.61576e24 2.78773e25i −0.194431 0.563682i
\(717\) 6.71698e25i 1.34123i
\(718\) −5.04352e25 3.59546e25i −0.994521 0.708980i
\(719\) 1.48792e24i 0.0289747i −0.999895 0.0144873i \(-0.995388\pi\)
0.999895 0.0144873i \(-0.00461162\pi\)
\(720\) −2.29566e25 2.93179e25i −0.441485 0.563820i
\(721\) −1.00543e25 −0.190956
\(722\) 6.20344e25 8.70187e25i 1.16358 1.63222i
\(723\) −1.02750e26 −1.90343
\(724\) −6.15286e25 + 2.12231e25i −1.12572 + 0.388295i
\(725\) 3.69157e24i 0.0667066i
\(726\) −2.38992e25 + 3.35245e25i −0.426534 + 0.598320i
\(727\) 5.98201e24i 0.105448i −0.998609 0.0527239i \(-0.983210\pi\)
0.998609 0.0527239i \(-0.0167903\pi\)
\(728\) −9.22584e24 2.72470e24i −0.160629 0.0474391i
\(729\) −2.43171e25 −0.418180
\(730\) 4.99742e24 + 3.56259e24i 0.0848867 + 0.0605146i
\(731\) 5.11099e24 0.0857528
\(732\) 1.30322e26 4.49522e25i 2.15983 0.744991i
\(733\) 1.02391e26i 1.67620i −0.545520 0.838098i \(-0.683668\pi\)
0.545520 0.838098i \(-0.316332\pi\)
\(734\) −1.69527e25 1.20853e25i −0.274141 0.195431i
\(735\) 7.60456e25i 1.21475i
\(736\) −9.19290e25 + 4.13794e24i −1.45062 + 0.0652956i
\(737\) 1.17023e26 1.82417
\(738\) 6.72367e24 9.43162e24i 0.103538 0.145238i
\(739\) 5.22864e25 0.795405 0.397703 0.917514i \(-0.369808\pi\)
0.397703 + 0.917514i \(0.369808\pi\)
\(740\) 4.09910e25 + 1.18838e26i 0.616031 + 1.78595i
\(741\) 1.11326e26i 1.65285i
\(742\) −3.39146e24 + 4.75737e24i −0.0497453 + 0.0697801i
\(743\) 9.56206e23i 0.0138564i 0.999976 + 0.00692822i \(0.00220534\pi\)
−0.999976 + 0.00692822i \(0.997795\pi\)
\(744\) −3.52026e25 + 1.19196e26i −0.503986 + 1.70650i
\(745\) −1.16641e26 −1.64986
\(746\) −1.45841e24 1.03968e24i −0.0203813 0.0145295i
\(747\) 3.10527e25 0.428760
\(748\) 3.54217e24 + 1.02692e25i 0.0483231 + 0.140095i
\(749\) 1.16193e25i 0.156619i
\(750\) −8.24346e25 5.87665e25i −1.09789 0.782669i
\(751\) 2.03300e25i 0.267534i −0.991013 0.133767i \(-0.957293\pi\)
0.991013 0.133767i \(-0.0427074\pi\)
\(752\) 9.36285e24 + 1.19573e25i 0.121744 + 0.155479i
\(753\) 1.66141e26 2.13462
\(754\) −4.36941e25 + 6.12919e25i −0.554729 + 0.778145i
\(755\) −5.56622e25 −0.698293
\(756\) 6.16012e24 2.12482e24i 0.0763647 0.0263406i
\(757\) 7.07010e25i 0.866089i 0.901372 + 0.433045i \(0.142561\pi\)
−0.901372 + 0.433045i \(0.857439\pi\)
\(758\) 6.47804e25 9.08706e25i 0.784189 1.10002i
\(759\) 1.99559e26i 2.38723i
\(760\) 4.04671e25 1.37022e26i 0.478388 1.61982i
\(761\) 5.11578e25 0.597654 0.298827 0.954307i \(-0.403405\pi\)
0.298827 + 0.954307i \(0.403405\pi\)
\(762\) 4.38834e25 + 3.12838e25i 0.506647 + 0.361181i
\(763\) 1.78464e24 0.0203624
\(764\) 8.33262e25 2.87418e25i 0.939597 0.324096i
\(765\) 7.62952e24i 0.0850245i
\(766\) 1.32121e26 + 9.41871e25i 1.45516 + 1.03737i
\(767\) 2.04498e25i 0.222603i
\(768\) −2.93622e25 + 1.18857e26i −0.315891 + 1.27872i
\(769\) 1.08358e26 1.15219 0.576094 0.817383i \(-0.304576\pi\)
0.576094 + 0.817383i \(0.304576\pi\)
\(770\) −1.55412e25 + 2.18004e25i −0.163331 + 0.229112i
\(771\) −1.25196e26 −1.30047
\(772\) −4.45996e25 1.29300e26i −0.457905 1.32752i
\(773\) 1.02495e26i 1.04013i 0.854127 + 0.520064i \(0.174092\pi\)
−0.854127 + 0.520064i \(0.825908\pi\)
\(774\) −3.07166e25 + 4.30876e25i −0.308109 + 0.432199i
\(775\) 6.88538e24i 0.0682673i
\(776\) 7.14001e25 + 2.10868e25i 0.699750 + 0.206660i
\(777\) 6.09879e25 0.590819
\(778\) −8.19240e25 5.84025e25i −0.784503 0.559262i
\(779\) 4.44425e25 0.420689
\(780\) 3.23787e25 + 9.38701e25i 0.302976 + 0.878366i
\(781\) 3.68909e25i 0.341240i
\(782\) −1.53529e25 1.09449e25i −0.140388 0.100081i
\(783\) 5.09880e25i 0.460906i
\(784\) −8.33911e25 + 6.52973e25i −0.745204 + 0.583513i
\(785\) −5.09849e25 −0.450417
\(786\) −3.72533e25 + 5.22571e25i −0.325358 + 0.456396i
\(787\) −1.21477e26 −1.04887 −0.524436 0.851450i \(-0.675724\pi\)
−0.524436 + 0.851450i \(0.675724\pi\)
\(788\) 1.28677e26 4.43847e25i 1.09841 0.378876i
\(789\) 2.48480e26i 2.09700i
\(790\) −3.69786e25 + 5.18717e25i −0.308537 + 0.432799i
\(791\) 4.56159e24i 0.0376295i
\(792\) −1.07862e26 3.18551e25i −0.879712 0.259808i
\(793\) −1.55725e26 −1.25574
\(794\) −1.30466e26 9.30073e25i −1.04019 0.741536i
\(795\) 6.03073e25 0.475407
\(796\) −2.10471e26 + 7.25981e25i −1.64050 + 0.565859i
\(797\) 1.99141e26i 1.53474i 0.641204 + 0.767370i \(0.278435\pi\)
−0.641204 + 0.767370i \(0.721565\pi\)
\(798\) −5.64411e25 4.02361e25i −0.430100 0.306613i
\(799\) 3.11169e24i 0.0234464i
\(800\) 3.04992e23 + 6.77573e24i 0.00227237 + 0.0504831i
\(801\) −8.95438e25 −0.659695
\(802\) −3.13976e25 + 4.40429e25i −0.228732 + 0.320853i
\(803\) 1.85368e25 0.133535
\(804\) 8.81182e25 + 2.55466e26i 0.627713 + 1.81982i
\(805\) 4.64696e25i 0.327345i
\(806\) 8.14966e25 1.14319e26i 0.567707 0.796350i
\(807\) 2.84166e25i 0.195754i
\(808\) 1.42144e25 4.81299e25i 0.0968334 0.327878i
\(809\) 1.20488e26 0.811724 0.405862 0.913934i \(-0.366971\pi\)
0.405862 + 0.913934i \(0.366971\pi\)
\(810\) −1.42290e26 1.01437e26i −0.948005 0.675819i
\(811\) 2.18180e26 1.43756 0.718781 0.695237i \(-0.244701\pi\)
0.718781 + 0.695237i \(0.244701\pi\)
\(812\) −1.52821e25 4.43049e25i −0.0995817 0.288700i
\(813\) 1.15141e26i 0.742018i
\(814\) 3.09168e26 + 2.20402e26i 1.97049 + 1.40474i
\(815\) 2.07874e26i 1.31034i
\(816\) −1.97508e25 + 1.54654e25i −0.123133 + 0.0964160i
\(817\) −2.03032e26 −1.25189
\(818\) 1.31037e25 1.83812e25i 0.0799125 0.112097i
\(819\) 2.04067e25 0.123089
\(820\) 3.74738e25 1.29259e25i 0.223565 0.0771144i
\(821\) 9.20761e25i 0.543324i 0.962393 + 0.271662i \(0.0875732\pi\)
−0.962393 + 0.271662i \(0.912427\pi\)
\(822\) 1.56114e26 2.18988e26i 0.911160 1.27813i
\(823\) 3.23025e26i 1.86482i 0.361400 + 0.932411i \(0.382299\pi\)
−0.361400 + 0.932411i \(0.617701\pi\)
\(824\) 4.09408e25 1.38626e26i 0.233782 0.791588i
\(825\) −1.47087e25 −0.0830785
\(826\) 1.03678e25 + 7.39109e24i 0.0579252 + 0.0412941i
\(827\) −1.80676e26 −0.998509 −0.499254 0.866455i \(-0.666393\pi\)
−0.499254 + 0.866455i \(0.666393\pi\)
\(828\) 1.84540e26 6.36534e25i 1.00883 0.347976i
\(829\) 1.13783e26i 0.615301i −0.951499 0.307651i \(-0.900457\pi\)
0.951499 0.307651i \(-0.0995428\pi\)
\(830\) 8.65348e25 + 6.16894e25i 0.462901 + 0.329995i
\(831\) 5.77434e25i 0.305558i
\(832\) 7.51350e25 1.16109e26i 0.393308 0.607792i
\(833\) −2.17012e25 −0.112377
\(834\) −9.93796e24 + 1.39405e25i −0.0509099 + 0.0714138i
\(835\) 1.23157e26 0.624139
\(836\) −1.40711e26 4.07940e26i −0.705461 2.04522i
\(837\) 9.51009e25i 0.471689i
\(838\) −5.05698e25 + 7.09367e25i −0.248139 + 0.348077i
\(839\) 3.30245e25i 0.160317i 0.996782 + 0.0801583i \(0.0255426\pi\)
−0.996782 + 0.0801583i \(0.974457\pi\)
\(840\) −5.92935e25 1.75114e25i −0.284770 0.0841020i
\(841\) −1.56259e26 −0.742474
\(842\) −2.63931e25 1.88152e25i −0.124074 0.0884506i
\(843\) 4.85352e26 2.25740
\(844\) −3.50855e25 1.01717e26i −0.161453 0.468072i
\(845\) 1.01851e26i 0.463717i
\(846\) −2.62328e25 1.87010e25i −0.118171 0.0842425i
\(847\) 2.89568e25i 0.129062i
\(848\) −5.17835e25 6.61326e25i −0.228365 0.291644i
\(849\) 3.88560e25 0.169547
\(850\) −8.06706e23 + 1.13161e24i −0.00348293 + 0.00488568i
\(851\) −6.59021e26 −2.81535
\(852\) 8.05341e25 2.77787e25i 0.340427 0.117424i
\(853\) 3.34899e26i 1.40079i −0.713755 0.700395i \(-0.753007\pi\)
0.713755 0.700395i \(-0.246993\pi\)
\(854\) 5.62828e25 7.89506e25i 0.232946 0.326764i
\(855\) 3.03080e26i 1.24126i
\(856\) −1.60205e26 4.73138e25i −0.649249 0.191745i
\(857\) 2.21197e26 0.887059 0.443530 0.896260i \(-0.353726\pi\)
0.443530 + 0.896260i \(0.353726\pi\)
\(858\) 2.44211e26 + 1.74095e26i 0.969126 + 0.690877i
\(859\) −1.39462e25 −0.0547668 −0.0273834 0.999625i \(-0.508718\pi\)
−0.0273834 + 0.999625i \(0.508718\pi\)
\(860\) −1.71196e26 + 5.90509e25i −0.665286 + 0.229478i
\(861\) 1.92316e25i 0.0739584i
\(862\) 9.79015e25 + 6.97926e25i 0.372584 + 0.265610i
\(863\) 4.01195e26i 1.51098i −0.655160 0.755490i \(-0.727399\pi\)
0.655160 0.755490i \(-0.272601\pi\)
\(864\) 4.21255e24 + 9.35865e25i 0.0157008 + 0.348810i
\(865\) 3.31369e26 1.22227
\(866\) −1.69810e26 + 2.38200e26i −0.619871 + 0.869523i
\(867\) 3.59455e26 1.29859
\(868\) 2.85037e25 + 8.26358e25i 0.101911 + 0.295454i
\(869\) 1.92406e26i 0.680834i
\(870\) −2.80818e26 + 3.93917e26i −0.983448 + 1.37953i
\(871\) 3.05261e26i 1.05806i
\(872\) −7.26702e24 + 2.46062e25i −0.0249292 + 0.0844103i
\(873\) −1.57930e26 −0.536213
\(874\) 6.09889e26 + 4.34782e26i 2.04950 + 1.46106i
\(875\) −7.12028e25 −0.236823
\(876\) 1.39582e25 + 4.04665e25i 0.0459506 + 0.133217i
\(877\) 1.63704e26i 0.533411i −0.963778 0.266705i \(-0.914065\pi\)
0.963778 0.266705i \(-0.0859351\pi\)
\(878\) −7.85326e25 5.59848e25i −0.253279 0.180559i
\(879\) 2.52301e26i 0.805414i
\(880\) −2.37295e26 3.03049e26i −0.749799 0.957568i
\(881\) −4.63397e26 −1.44934 −0.724670 0.689096i \(-0.758008\pi\)
−0.724670 + 0.689096i \(0.758008\pi\)
\(882\) 1.30422e26 1.82950e26i 0.403771 0.566388i
\(883\) 1.38157e26 0.423375 0.211688 0.977337i \(-0.432104\pi\)
0.211688 + 0.977337i \(0.432104\pi\)
\(884\) 2.67878e25 9.23994e24i 0.0812581 0.0280284i
\(885\) 1.31429e26i 0.394641i
\(886\) −1.28854e26 + 1.80749e26i −0.382995 + 0.537246i
\(887\) 2.16587e26i 0.637266i 0.947878 + 0.318633i \(0.103224\pi\)
−0.947878 + 0.318633i \(0.896776\pi\)
\(888\) −2.48342e26 + 8.40887e26i −0.723325 + 2.44918i
\(889\) 3.79042e25 0.109288
\(890\) −2.49532e26 1.77888e26i −0.712225 0.507735i
\(891\) −5.27794e26 −1.49130
\(892\) −5.29458e25 + 1.82627e25i −0.148098 + 0.0510835i
\(893\) 1.23611e26i 0.342289i
\(894\) −6.62450e26 4.72251e26i −1.81600 1.29460i
\(895\) 2.14088e26i 0.581011i
\(896\) 3.17101e25 + 8.00572e25i 0.0851974 + 0.215094i
\(897\) −5.20560e26 −1.38465
\(898\) 1.89634e26 2.66008e26i 0.499377 0.700500i
\(899\) 6.83986e26 1.78324
\(900\) −4.69165e24 1.36017e25i −0.0121100 0.0351084i
\(901\) 1.72100e25i 0.0439802i
\(902\) 6.95003e25 9.74915e25i 0.175844 0.246665i
\(903\) 8.78582e25i 0.220086i
\(904\) −6.28942e25 1.85748e25i −0.155989 0.0460688i
\(905\) 4.72517e26 1.16033
\(906\) −3.16126e26 2.25362e26i −0.768611 0.547932i
\(907\) 2.92584e26 0.704344 0.352172 0.935935i \(-0.385443\pi\)
0.352172 + 0.935935i \(0.385443\pi\)
\(908\) 1.87874e26 + 5.44671e26i 0.447810 + 1.29826i
\(909\) 1.06459e26i 0.251250i
\(910\) 5.68675e25 + 4.05401e25i 0.132890 + 0.0947353i
\(911\) 2.29099e26i 0.530101i −0.964235 0.265050i \(-0.914611\pi\)
0.964235 0.265050i \(-0.0853886\pi\)
\(912\) 7.84593e26 6.14356e26i 1.79759 1.40756i
\(913\) 3.20981e26 0.728187
\(914\) −6.90854e25 + 9.69095e25i −0.155192 + 0.217696i
\(915\) −1.00083e27 −2.22622
\(916\) −1.41952e26 + 4.89638e25i −0.312668 + 0.107849i
\(917\) 4.51370e25i 0.0984483i
\(918\) −1.11422e25 + 1.56297e25i −0.0240651 + 0.0337573i
\(919\) 5.13378e26i 1.09799i −0.835827 0.548994i \(-0.815011\pi\)
0.835827 0.548994i \(-0.184989\pi\)
\(920\) 6.40712e26 + 1.89224e26i 1.35698 + 0.400761i
\(921\) 6.36394e26 1.33472
\(922\) −8.15476e24 5.81341e24i −0.0169369 0.0120741i
\(923\) −9.62318e25 −0.197926
\(924\) −1.76528e26 + 6.08901e25i −0.359556 + 0.124022i
\(925\) 4.85739e25i 0.0979777i
\(926\) −1.46106e26 1.04157e26i −0.291856 0.208060i
\(927\) 3.06628e26i 0.606588i
\(928\) 6.73094e26 3.02975e25i 1.31869 0.0593575i
\(929\) −2.51419e26 −0.487817 −0.243909 0.969798i \(-0.578430\pi\)
−0.243909 + 0.969798i \(0.578430\pi\)
\(930\) 5.23771e26 7.34719e26i 1.00646 1.41180i
\(931\) 8.62072e26 1.64058
\(932\) 4.81024e25 + 1.39455e26i 0.0906617 + 0.262840i
\(933\) 3.42381e26i 0.639108i
\(934\) −7.30702e25 + 1.02499e26i −0.135089 + 0.189495i
\(935\) 7.88638e25i 0.144402i
\(936\) −8.30959e25 + 2.81363e26i −0.150694 + 0.510251i
\(937\) 3.73439e26 0.670754 0.335377 0.942084i \(-0.391136\pi\)
0.335377 + 0.942084i \(0.391136\pi\)
\(938\) 1.54764e26 + 1.10329e26i 0.275324 + 0.196275i
\(939\) −5.52250e26 −0.973074
\(940\) −3.59516e25 1.04228e26i −0.0627433 0.181901i
\(941\) 1.37271e26i 0.237285i 0.992937 + 0.118643i \(0.0378543\pi\)
−0.992937 + 0.118643i \(0.962146\pi\)
\(942\) −2.89562e26 2.06425e26i −0.495773 0.353430i
\(943\) 2.07812e26i 0.352424i
\(944\) −1.44124e26 + 1.12853e26i −0.242097 + 0.189568i
\(945\) −4.73074e25 −0.0787124
\(946\) −3.17507e26 + 4.45382e26i −0.523279 + 0.734028i
\(947\) −3.55248e26 −0.579938 −0.289969 0.957036i \(-0.593645\pi\)
−0.289969 + 0.957036i \(0.593645\pi\)
\(948\) −4.20030e26 + 1.44881e26i −0.679212 + 0.234281i
\(949\) 4.83542e25i 0.0774530i
\(950\) 3.20461e25 4.49526e25i 0.0508467 0.0713251i
\(951\) 7.70954e26i 1.21172i
\(952\) −4.99724e24 + 1.69207e25i −0.00778032 + 0.0263442i
\(953\) 1.26477e26 0.195063 0.0975315 0.995232i \(-0.468905\pi\)
0.0975315 + 0.995232i \(0.468905\pi\)
\(954\) 1.45087e26 + 1.03430e26i 0.221663 + 0.158020i
\(955\) −6.39915e26 −0.968483
\(956\) −6.42057e26 + 2.21465e26i −0.962614 + 0.332036i
\(957\) 1.46115e27i 2.17013i
\(958\) −2.05625e26 1.46587e26i −0.302542 0.215678i
\(959\) 1.89151e26i 0.275703i
\(960\) 4.82885e26 7.46219e26i 0.697273 1.07752i
\(961\) −5.76691e26 −0.824959
\(962\) 5.74929e26 8.06481e26i 0.814777 1.14293i
\(963\) 3.54358e26 0.497515
\(964\) −3.38776e26 9.82155e26i −0.471215 1.36611i
\(965\) 9.92976e26i 1.36834i
\(966\) 1.88143e26 2.63918e26i 0.256859 0.360309i
\(967\) 3.93340e26i 0.532022i 0.963970 + 0.266011i \(0.0857058\pi\)
−0.963970 + 0.266011i \(0.914294\pi\)
\(968\) −3.99249e26 1.17912e26i −0.535015 0.158008i
\(969\) 2.04178e26 0.271078
\(970\) −4.40106e26 3.13745e26i −0.578911 0.412697i
\(971\) −3.37169e26 −0.439414 −0.219707 0.975566i \(-0.570510\pi\)
−0.219707 + 0.975566i \(0.570510\pi\)
\(972\) −3.09252e26 8.96562e26i −0.399316 1.15767i
\(973\) 1.20410e25i 0.0154045i
\(974\) 2.51292e26 + 1.79143e26i 0.318528 + 0.227075i
\(975\) 3.83684e25i 0.0481873i
\(976\) 8.59370e26 + 1.09750e27i 1.06938 + 1.36570i
\(977\) −1.57789e26 −0.194547 −0.0972737 0.995258i \(-0.531012\pi\)
−0.0972737 + 0.995258i \(0.531012\pi\)
\(978\) −8.41630e26 + 1.18060e27i −1.02819 + 1.44229i
\(979\) −9.25585e26 −1.12040
\(980\) 7.26898e26 2.50730e26i 0.871844 0.300726i
\(981\) 5.44266e25i 0.0646830i
\(982\) 6.21109e26 8.71260e26i 0.731416 1.02599i
\(983\) 9.44218e26i 1.10177i −0.834582 0.550884i \(-0.814291\pi\)
0.834582 0.550884i \(-0.185709\pi\)
\(984\) 2.65161e26 + 7.83109e25i 0.306587 + 0.0905454i
\(985\) −9.88192e26 −1.13218
\(986\) 1.12412e26 + 8.01372e25i 0.127621 + 0.0909792i
\(987\) −5.34902e25 −0.0601755
\(988\) −1.06413e27 + 3.67053e26i −1.18627 + 0.409182i
\(989\) 9.49375e26i 1.04875i
\(990\) 6.64853e26 + 4.73964e26i 0.727794 + 0.518834i
\(991\) 1.51912e27i 1.64790i 0.566665 + 0.823948i \(0.308233\pi\)
−0.566665 + 0.823948i \(0.691767\pi\)
\(992\) −1.25543e27 + 5.65098e25i −1.34954 + 0.0607462i
\(993\) 6.70897e26 0.714682
\(994\) 3.47806e25 4.87885e25i 0.0367164 0.0515038i
\(995\) 1.61634e27 1.69093
\(996\) 2.41698e26 + 7.00714e26i 0.250576 + 0.726451i
\(997\) 7.65044e26i 0.786013i −0.919536 0.393007i \(-0.871435\pi\)
0.919536 0.393007i \(-0.128565\pi\)
\(998\) −8.33935e26 + 1.16980e27i −0.849097 + 1.19107i
\(999\) 6.70903e26i 0.676971i
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 8.19.d.b.3.11 16
3.2 odd 2 72.19.b.b.19.6 16
4.3 odd 2 32.19.d.b.15.14 16
8.3 odd 2 inner 8.19.d.b.3.12 yes 16
8.5 even 2 32.19.d.b.15.13 16
24.11 even 2 72.19.b.b.19.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.19.d.b.3.11 16 1.1 even 1 trivial
8.19.d.b.3.12 yes 16 8.3 odd 2 inner
32.19.d.b.15.13 16 8.5 even 2
32.19.d.b.15.14 16 4.3 odd 2
72.19.b.b.19.5 16 24.11 even 2
72.19.b.b.19.6 16 3.2 odd 2