Properties

Label 4.43.b.a.3.20
Level $4$
Weight $43$
Character 4.3
Analytic conductor $44.691$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4,43,Mod(3,4)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 43, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4.3");
 
S:= CuspForms(chi, 43);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 43 \)
Character orbit: \([\chi]\) \(=\) 4.b (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: \(44.6910828688\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 10 x^{19} + \cdots + 58\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.20
Root \(0.500000 - 5.70227e8i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.43.b.a.3.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.06680e6 + 355528. i) q^{2} +9.12363e9i q^{3} +(4.14525e12 + 1.46961e12i) q^{4} -1.85810e14 q^{5} +(-3.24370e15 + 1.88567e16i) q^{6} +7.39963e17i q^{7} +(8.04489e18 + 4.51113e18i) q^{8} +2.61784e19 q^{9} +O(q^{10})\) \(q+(2.06680e6 + 355528. i) q^{2} +9.12363e9i q^{3} +(4.14525e12 + 1.46961e12i) q^{4} -1.85810e14 q^{5} +(-3.24370e15 + 1.88567e16i) q^{6} +7.39963e17i q^{7} +(8.04489e18 + 4.51113e18i) q^{8} +2.61784e19 q^{9} +(-3.84032e20 - 6.60607e19i) q^{10} -7.81812e20i q^{11} +(-1.34081e22 + 3.78197e22i) q^{12} -1.76158e23 q^{13} +(-2.63078e23 + 1.52935e24i) q^{14} -1.69526e24i q^{15} +(1.50233e25 + 1.21838e25i) q^{16} +1.77660e25 q^{17} +(5.41055e25 + 9.30716e24i) q^{18} +8.99300e26i q^{19} +(-7.70229e26 - 2.73068e26i) q^{20} -6.75115e27 q^{21} +(2.77956e26 - 1.61585e27i) q^{22} -2.55743e28i q^{23} +(-4.11579e28 + 7.33986e28i) q^{24} -1.92848e29 q^{25} +(-3.64083e29 - 6.26291e28i) q^{26} +1.23714e30i q^{27} +(-1.08746e30 + 3.06733e30i) q^{28} -1.56307e30 q^{29} +(6.02713e29 - 3.50376e30i) q^{30} -3.90687e31i q^{31} +(2.67185e31 + 3.05226e31i) q^{32} +7.13296e30 q^{33} +(3.67187e31 + 6.31630e30i) q^{34} -1.37493e32i q^{35} +(1.08516e32 + 3.84720e31i) q^{36} +2.18801e32 q^{37} +(-3.19726e32 + 1.85867e33i) q^{38} -1.60720e33i q^{39} +(-1.49482e33 - 8.38214e32i) q^{40} -1.09206e34 q^{41} +(-1.39532e34 - 2.40022e33i) q^{42} +3.18319e34i q^{43} +(1.14896e33 - 3.24080e33i) q^{44} -4.86422e33 q^{45} +(9.09238e33 - 5.28569e34i) q^{46} +2.91371e34i q^{47} +(-1.11160e35 + 1.37067e35i) q^{48} -2.35572e35 q^{49} +(-3.98578e35 - 6.85629e34i) q^{50} +1.62090e35i q^{51} +(-7.30218e35 - 2.58883e35i) q^{52} -2.53747e36 q^{53} +(-4.39838e35 + 2.55692e36i) q^{54} +1.45269e35i q^{55} +(-3.33807e36 + 5.95292e36i) q^{56} -8.20487e36 q^{57} +(-3.23055e36 - 5.55715e35i) q^{58} -2.40962e36i q^{59} +(2.49137e36 - 7.02728e36i) q^{60} +4.12023e37 q^{61} +(1.38900e37 - 8.07469e37i) q^{62} +1.93711e37i q^{63} +(4.43700e37 + 7.25831e37i) q^{64} +3.27320e37 q^{65} +(1.47424e37 + 2.53597e36i) q^{66} +3.27491e37i q^{67} +(7.36444e37 + 2.61090e37i) q^{68} +2.33331e38 q^{69} +(4.88825e37 - 2.84169e38i) q^{70} -5.97202e38i q^{71} +(2.10603e38 + 1.18094e38i) q^{72} +8.93872e38 q^{73} +(4.52217e38 + 7.77898e37i) q^{74} -1.75948e39i q^{75} +(-1.32162e39 + 3.72782e39i) q^{76} +5.78512e38 q^{77} +(5.71404e38 - 3.32175e39i) q^{78} +7.24871e39i q^{79} +(-2.79149e39 - 2.26387e39i) q^{80} -8.42279e39 q^{81} +(-2.25706e40 - 3.88256e39i) q^{82} +1.04180e40i q^{83} +(-2.79852e40 - 9.92154e39i) q^{84} -3.30110e39 q^{85} +(-1.13171e40 + 6.57901e40i) q^{86} -1.42609e40i q^{87} +(3.52685e39 - 6.28959e39i) q^{88} +1.28853e41 q^{89} +(-1.00534e40 - 1.72937e39i) q^{90} -1.30350e41i q^{91} +(3.75842e40 - 1.06012e41i) q^{92} +3.56448e41 q^{93} +(-1.03591e40 + 6.02204e40i) q^{94} -1.67099e41i q^{95} +(-2.78477e41 + 2.43769e41i) q^{96} +5.53744e41 q^{97} +(-4.86879e41 - 8.37524e40i) q^{98} -2.04666e40i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots - 73\!\cdots\!76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots + 18\!\cdots\!96 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.06680e6 + 355528.i 0.985525 + 0.169529i
\(3\) 9.12363e9i 0.872210i 0.899896 + 0.436105i \(0.143642\pi\)
−0.899896 + 0.436105i \(0.856358\pi\)
\(4\) 4.14525e12 + 1.46961e12i 0.942520 + 0.334150i
\(5\) −1.85810e14 −0.389672 −0.194836 0.980836i \(-0.562418\pi\)
−0.194836 + 0.980836i \(0.562418\pi\)
\(6\) −3.24370e15 + 1.88567e16i −0.147865 + 0.859585i
\(7\) 7.39963e17i 1.32480i 0.749149 + 0.662401i \(0.230463\pi\)
−0.749149 + 0.662401i \(0.769537\pi\)
\(8\) 8.04489e18 + 4.51113e18i 0.872229 + 0.489098i
\(9\) 2.61784e19 0.239249
\(10\) −3.84032e20 6.60607e19i −0.384032 0.0660607i
\(11\) 7.81812e20i 0.105647i −0.998604 0.0528233i \(-0.983178\pi\)
0.998604 0.0528233i \(-0.0168220\pi\)
\(12\) −1.34081e22 + 3.78197e22i −0.291449 + 0.822075i
\(13\) −1.76158e23 −0.713004 −0.356502 0.934295i \(-0.616031\pi\)
−0.356502 + 0.934295i \(0.616031\pi\)
\(14\) −2.63078e23 + 1.52935e24i −0.224592 + 1.30563i
\(15\) 1.69526e24i 0.339876i
\(16\) 1.50233e25 + 1.21838e25i 0.776688 + 0.629886i
\(17\) 1.77660e25 0.257135 0.128568 0.991701i \(-0.458962\pi\)
0.128568 + 0.991701i \(0.458962\pi\)
\(18\) 5.41055e25 + 9.30716e24i 0.235786 + 0.0405597i
\(19\) 8.99300e26i 1.25915i 0.776938 + 0.629577i \(0.216772\pi\)
−0.776938 + 0.629577i \(0.783228\pi\)
\(20\) −7.70229e26 2.73068e26i −0.367274 0.130209i
\(21\) −6.75115e27 −1.15551
\(22\) 2.77956e26 1.61585e27i 0.0179102 0.104117i
\(23\) 2.55743e28i 0.647917i −0.946071 0.323959i \(-0.894986\pi\)
0.946071 0.323959i \(-0.105014\pi\)
\(24\) −4.11579e28 + 7.33986e28i −0.426596 + 0.760767i
\(25\) −1.92848e29 −0.848156
\(26\) −3.64083e29 6.26291e28i −0.702683 0.120875i
\(27\) 1.23714e30i 1.08089i
\(28\) −1.08746e30 + 3.06733e30i −0.442683 + 1.24865i
\(29\) −1.56307e30 −0.304523 −0.152262 0.988340i \(-0.548656\pi\)
−0.152262 + 0.988340i \(0.548656\pi\)
\(30\) 6.02713e29 3.50376e30i 0.0576188 0.334956i
\(31\) 3.90687e31i 1.87600i −0.346635 0.938000i \(-0.612676\pi\)
0.346635 0.938000i \(-0.387324\pi\)
\(32\) 2.67185e31 + 3.05226e31i 0.658661 + 0.752440i
\(33\) 7.13296e30 0.0921461
\(34\) 3.67187e31 + 6.31630e30i 0.253414 + 0.0435919i
\(35\) 1.37493e32i 0.516239i
\(36\) 1.08516e32 + 3.84720e31i 0.225497 + 0.0799452i
\(37\) 2.18801e32 0.255748 0.127874 0.991790i \(-0.459185\pi\)
0.127874 + 0.991790i \(0.459185\pi\)
\(38\) −3.19726e32 + 1.85867e33i −0.213463 + 1.24093i
\(39\) 1.60720e33i 0.621889i
\(40\) −1.49482e33 8.38214e32i −0.339883 0.190588i
\(41\) −1.09206e34 −1.47837 −0.739186 0.673501i \(-0.764790\pi\)
−0.739186 + 0.673501i \(0.764790\pi\)
\(42\) −1.39532e34 2.40022e33i −1.13878 0.195892i
\(43\) 3.18319e34i 1.58499i 0.609881 + 0.792493i \(0.291217\pi\)
−0.609881 + 0.792493i \(0.708783\pi\)
\(44\) 1.14896e33 3.24080e33i 0.0353018 0.0995741i
\(45\) −4.86422e33 −0.0932289
\(46\) 9.09238e33 5.28569e34i 0.109841 0.638539i
\(47\) 2.91371e34i 0.224074i 0.993704 + 0.112037i \(0.0357375\pi\)
−0.993704 + 0.112037i \(0.964262\pi\)
\(48\) −1.11160e35 + 1.37067e35i −0.549393 + 0.677435i
\(49\) −2.35572e35 −0.755103
\(50\) −3.98578e35 6.85629e34i −0.835879 0.143787i
\(51\) 1.62090e35i 0.224276i
\(52\) −7.30218e35 2.58883e35i −0.672020 0.238250i
\(53\) −2.53747e36 −1.56534 −0.782669 0.622439i \(-0.786142\pi\)
−0.782669 + 0.622439i \(0.786142\pi\)
\(54\) −4.39838e35 + 2.55692e36i −0.183241 + 1.06524i
\(55\) 1.45269e35i 0.0411676i
\(56\) −3.33807e36 + 5.95292e36i −0.647958 + 1.15553i
\(57\) −8.20487e36 −1.09825
\(58\) −3.23055e36 5.55715e35i −0.300115 0.0516255i
\(59\) 2.40962e36i 0.156335i −0.996940 0.0781675i \(-0.975093\pi\)
0.996940 0.0781675i \(-0.0249069\pi\)
\(60\) 2.49137e36 7.02728e36i 0.113570 0.320340i
\(61\) 4.12023e37 1.32738 0.663690 0.748008i \(-0.268989\pi\)
0.663690 + 0.748008i \(0.268989\pi\)
\(62\) 1.38900e37 8.07469e37i 0.318036 1.84885i
\(63\) 1.93711e37i 0.316958i
\(64\) 4.43700e37 + 7.25831e37i 0.521567 + 0.853210i
\(65\) 3.27320e37 0.277838
\(66\) 1.47424e37 + 2.53597e36i 0.0908123 + 0.0156214i
\(67\) 3.27491e37i 0.147106i 0.997291 + 0.0735528i \(0.0234337\pi\)
−0.997291 + 0.0735528i \(0.976566\pi\)
\(68\) 7.36444e37 + 2.61090e37i 0.242355 + 0.0859218i
\(69\) 2.33331e38 0.565120
\(70\) 4.88825e37 2.84169e38i 0.0875174 0.508766i
\(71\) 5.97202e38i 0.793772i −0.917868 0.396886i \(-0.870091\pi\)
0.917868 0.396886i \(-0.129909\pi\)
\(72\) 2.10603e38 + 1.18094e38i 0.208680 + 0.117016i
\(73\) 8.93872e38 0.662972 0.331486 0.943460i \(-0.392450\pi\)
0.331486 + 0.943460i \(0.392450\pi\)
\(74\) 4.52217e38 + 7.77898e37i 0.252047 + 0.0433567i
\(75\) 1.75948e39i 0.739770i
\(76\) −1.32162e39 + 3.72782e39i −0.420746 + 1.18678i
\(77\) 5.78512e38 0.139961
\(78\) 5.71404e38 3.32175e39i 0.105428 0.612888i
\(79\) 7.24871e39i 1.02351i 0.859132 + 0.511754i \(0.171004\pi\)
−0.859132 + 0.511754i \(0.828996\pi\)
\(80\) −2.79149e39 2.26387e39i −0.302654 0.245449i
\(81\) −8.42279e39 −0.703510
\(82\) −2.25706e40 3.88256e39i −1.45697 0.250627i
\(83\) 1.04180e40i 0.521367i 0.965424 + 0.260684i \(0.0839479\pi\)
−0.965424 + 0.260684i \(0.916052\pi\)
\(84\) −2.79852e40 9.92154e39i −1.08909 0.386113i
\(85\) −3.30110e39 −0.100199
\(86\) −1.13171e40 + 6.57901e40i −0.268701 + 1.56204i
\(87\) 1.42609e40i 0.265608i
\(88\) 3.52685e39 6.28959e39i 0.0516715 0.0921481i
\(89\) 1.28853e41 1.48903 0.744514 0.667607i \(-0.232681\pi\)
0.744514 + 0.667607i \(0.232681\pi\)
\(90\) −1.00534e40 1.72937e39i −0.0918794 0.0158050i
\(91\) 1.30350e41i 0.944590i
\(92\) 3.75842e40 1.06012e41i 0.216502 0.610675i
\(93\) 3.56448e41 1.63627
\(94\) −1.03591e40 + 6.02204e40i −0.0379870 + 0.220830i
\(95\) 1.67099e41i 0.490657i
\(96\) −2.78477e41 + 2.43769e41i −0.656285 + 0.574491i
\(97\) 5.53744e41 1.04979 0.524895 0.851167i \(-0.324105\pi\)
0.524895 + 0.851167i \(0.324105\pi\)
\(98\) −4.86879e41 8.37524e40i −0.744173 0.128012i
\(99\) 2.04666e40i 0.0252759i
\(100\) −7.99403e41 2.83411e41i −0.799403 0.283411i
\(101\) 2.23693e42 1.81511 0.907555 0.419933i \(-0.137947\pi\)
0.907555 + 0.419933i \(0.137947\pi\)
\(102\) −5.76276e40 + 3.35007e41i −0.0380213 + 0.221030i
\(103\) 2.35307e42i 1.26489i 0.774604 + 0.632447i \(0.217949\pi\)
−0.774604 + 0.632447i \(0.782051\pi\)
\(104\) −1.41717e42 7.94672e41i −0.621903 0.348729i
\(105\) 1.25443e42 0.450269
\(106\) −5.24444e42 9.02142e41i −1.54268 0.265370i
\(107\) 7.40104e42i 1.78745i −0.448618 0.893724i \(-0.648084\pi\)
0.448618 0.893724i \(-0.351916\pi\)
\(108\) −1.81811e42 + 5.12825e42i −0.361178 + 1.01876i
\(109\) 2.23024e42 0.365087 0.182543 0.983198i \(-0.441567\pi\)
0.182543 + 0.983198i \(0.441567\pi\)
\(110\) −5.16470e40 + 3.00241e41i −0.00697909 + 0.0405717i
\(111\) 1.99626e42i 0.223066i
\(112\) −9.01554e42 + 1.11167e43i −0.834475 + 1.02896i
\(113\) 9.60366e42 0.737547 0.368773 0.929519i \(-0.379778\pi\)
0.368773 + 0.929519i \(0.379778\pi\)
\(114\) −1.69578e43 2.91706e42i −1.08235 0.186185i
\(115\) 4.75197e42i 0.252475i
\(116\) −6.47931e42 2.29710e42i −0.287019 0.101756i
\(117\) −4.61154e42 −0.170586
\(118\) 8.56687e41 4.98019e42i 0.0265033 0.154072i
\(119\) 1.31462e43i 0.340654i
\(120\) 7.64755e42 1.36382e43i 0.166233 0.296450i
\(121\) 5.41525e43 0.988839
\(122\) 8.51568e43 + 1.46486e43i 1.30817 + 0.225029i
\(123\) 9.96351e43i 1.28945i
\(124\) 5.74156e43 1.61949e44i 0.626866 1.76817i
\(125\) 7.80815e43 0.720175
\(126\) −6.88696e42 + 4.00361e43i −0.0537336 + 0.312370i
\(127\) 2.35239e44i 1.55464i 0.629103 + 0.777322i \(0.283422\pi\)
−0.629103 + 0.777322i \(0.716578\pi\)
\(128\) 6.58985e43 + 1.65789e44i 0.369374 + 0.929281i
\(129\) −2.90423e44 −1.38244
\(130\) 6.76503e43 + 1.16371e43i 0.273816 + 0.0471015i
\(131\) 2.53620e44i 0.873950i −0.899474 0.436975i \(-0.856050\pi\)
0.899474 0.436975i \(-0.143950\pi\)
\(132\) 2.95679e43 + 1.04826e43i 0.0868495 + 0.0307906i
\(133\) −6.65449e44 −1.66813
\(134\) −1.16432e43 + 6.76858e43i −0.0249386 + 0.144976i
\(135\) 2.29873e44i 0.421191i
\(136\) 1.42925e44 + 8.01447e43i 0.224281 + 0.125764i
\(137\) −1.20317e45 −1.61881 −0.809404 0.587252i \(-0.800210\pi\)
−0.809404 + 0.587252i \(0.800210\pi\)
\(138\) 4.82247e44 + 8.29555e43i 0.556940 + 0.0958042i
\(139\) 1.76849e45i 1.75506i 0.479525 + 0.877528i \(0.340809\pi\)
−0.479525 + 0.877528i \(0.659191\pi\)
\(140\) 2.02060e44 5.69941e44i 0.172501 0.486565i
\(141\) −2.65836e44 −0.195440
\(142\) 2.12322e44 1.23429e45i 0.134567 0.782282i
\(143\) 1.37722e44i 0.0753265i
\(144\) 3.93287e44 + 3.18952e44i 0.185822 + 0.150700i
\(145\) 2.90434e44 0.118664
\(146\) 1.84745e45 + 3.17797e44i 0.653376 + 0.112393i
\(147\) 2.14927e45i 0.658608i
\(148\) 9.06984e44 + 3.21551e44i 0.241048 + 0.0854583i
\(149\) 6.29694e44 0.145284 0.0726420 0.997358i \(-0.476857\pi\)
0.0726420 + 0.997358i \(0.476857\pi\)
\(150\) 6.25543e44 3.63648e45i 0.125412 0.729062i
\(151\) 2.84562e45i 0.496204i −0.968734 0.248102i \(-0.920193\pi\)
0.968734 0.248102i \(-0.0798069\pi\)
\(152\) −4.05686e45 + 7.23477e45i −0.615849 + 1.09827i
\(153\) 4.65086e44 0.0615195
\(154\) 1.19567e45 + 2.05677e44i 0.137935 + 0.0237274i
\(155\) 7.25936e45i 0.731025i
\(156\) 2.36195e45 6.66224e45i 0.207804 0.586143i
\(157\) 1.97018e46 1.51570 0.757849 0.652430i \(-0.226250\pi\)
0.757849 + 0.652430i \(0.226250\pi\)
\(158\) −2.57712e45 + 1.49816e46i −0.173514 + 1.00869i
\(159\) 2.31509e46i 1.36530i
\(160\) −4.96457e45 5.67141e45i −0.256662 0.293205i
\(161\) 1.89241e46 0.858362
\(162\) −1.74082e46 2.99454e45i −0.693327 0.119265i
\(163\) 8.93294e45i 0.312647i 0.987706 + 0.156324i \(0.0499643\pi\)
−0.987706 + 0.156324i \(0.950036\pi\)
\(164\) −4.52684e46 1.60489e46i −1.39340 0.493998i
\(165\) −1.32538e45 −0.0359068
\(166\) −3.70388e45 + 2.15318e46i −0.0883868 + 0.513820i
\(167\) 4.98129e46i 1.04784i 0.851767 + 0.523921i \(0.175531\pi\)
−0.851767 + 0.523921i \(0.824469\pi\)
\(168\) −5.43123e46 3.04553e46i −1.00787 0.565155i
\(169\) −3.00092e46 −0.491625
\(170\) −6.82270e45 1.17363e45i −0.0987482 0.0169866i
\(171\) 2.35423e46i 0.301252i
\(172\) −4.67804e46 + 1.31951e47i −0.529623 + 1.49388i
\(173\) 7.00878e46 0.702545 0.351273 0.936273i \(-0.385749\pi\)
0.351273 + 0.936273i \(0.385749\pi\)
\(174\) 5.07014e45 2.94743e46i 0.0450283 0.261764i
\(175\) 1.42701e47i 1.12364i
\(176\) 9.52541e45 1.17454e46i 0.0665454 0.0820545i
\(177\) 2.19845e46 0.136357
\(178\) 2.66312e47 + 4.58107e46i 1.46747 + 0.252433i
\(179\) 2.19620e47i 1.07586i −0.842988 0.537932i \(-0.819206\pi\)
0.842988 0.537932i \(-0.180794\pi\)
\(180\) −2.01634e46 7.14849e45i −0.0878701 0.0311524i
\(181\) 1.12159e47 0.435096 0.217548 0.976050i \(-0.430194\pi\)
0.217548 + 0.976050i \(0.430194\pi\)
\(182\) 4.63432e46 2.69408e47i 0.160135 0.930917i
\(183\) 3.75915e47i 1.15775i
\(184\) 1.15369e47 2.05743e47i 0.316895 0.565132i
\(185\) −4.06554e46 −0.0996581
\(186\) 7.36705e47 + 1.26727e47i 1.61258 + 0.277394i
\(187\) 1.38897e46i 0.0271655i
\(188\) −4.28201e46 + 1.20780e47i −0.0748743 + 0.211194i
\(189\) −9.15438e47 −1.43196
\(190\) 5.94084e46 3.45360e47i 0.0831806 0.483555i
\(191\) 5.79692e47i 0.726937i 0.931606 + 0.363469i \(0.118408\pi\)
−0.931606 + 0.363469i \(0.881592\pi\)
\(192\) −6.62221e47 + 4.04815e47i −0.744179 + 0.454916i
\(193\) −1.31768e48 −1.32772 −0.663859 0.747858i \(-0.731082\pi\)
−0.663859 + 0.747858i \(0.731082\pi\)
\(194\) 1.14448e48 + 1.96871e47i 1.03459 + 0.177970i
\(195\) 2.98634e47i 0.242333i
\(196\) −9.76504e47 3.46198e47i −0.711699 0.252318i
\(197\) −9.14500e47 −0.598953 −0.299477 0.954104i \(-0.596812\pi\)
−0.299477 + 0.954104i \(0.596812\pi\)
\(198\) 7.27645e45 4.23003e46i 0.00428500 0.0249100i
\(199\) 7.99017e47i 0.423293i −0.977346 0.211647i \(-0.932117\pi\)
0.977346 0.211647i \(-0.0678826\pi\)
\(200\) −1.55144e48 8.69963e47i −0.739786 0.414831i
\(201\) −2.98791e47 −0.128307
\(202\) 4.62327e48 + 7.95290e47i 1.78884 + 0.307714i
\(203\) 1.15661e48i 0.403433i
\(204\) −2.38209e47 + 6.71904e47i −0.0749419 + 0.211385i
\(205\) 2.02915e48 0.576081
\(206\) −8.36584e47 + 4.86333e48i −0.214436 + 1.24658i
\(207\) 6.69495e47i 0.155014i
\(208\) −2.64648e48 2.14627e48i −0.553781 0.449111i
\(209\) 7.03083e47 0.133025
\(210\) 2.59266e48 + 4.45986e47i 0.443751 + 0.0763336i
\(211\) 5.02337e48i 0.778151i 0.921206 + 0.389076i \(0.127206\pi\)
−0.921206 + 0.389076i \(0.872794\pi\)
\(212\) −1.05184e49 3.72909e48i −1.47536 0.523057i
\(213\) 5.44865e48 0.692336
\(214\) 2.63128e48 1.52964e49i 0.303024 1.76157i
\(215\) 5.91470e48i 0.617625i
\(216\) −5.58090e48 + 9.95266e48i −0.528659 + 0.942780i
\(217\) 2.89094e49 2.48533
\(218\) 4.60946e48 + 7.92914e47i 0.359802 + 0.0618927i
\(219\) 8.15536e48i 0.578251i
\(220\) −2.13488e47 + 6.02174e47i −0.0137561 + 0.0388013i
\(221\) −3.12962e48 −0.183339
\(222\) −7.09725e47 + 4.12586e48i −0.0378162 + 0.219838i
\(223\) 2.97108e49i 1.44050i −0.693716 0.720249i \(-0.744028\pi\)
0.693716 0.720249i \(-0.255972\pi\)
\(224\) −2.25856e49 + 1.97707e49i −0.996834 + 0.872596i
\(225\) −5.04846e48 −0.202921
\(226\) 1.98488e49 + 3.41437e48i 0.726871 + 0.125035i
\(227\) 1.58388e49i 0.528664i 0.964432 + 0.264332i \(0.0851515\pi\)
−0.964432 + 0.264332i \(0.914848\pi\)
\(228\) −3.40112e49 1.20579e49i −1.03512 0.366979i
\(229\) 1.60852e48 0.0446562 0.0223281 0.999751i \(-0.492892\pi\)
0.0223281 + 0.999751i \(0.492892\pi\)
\(230\) −1.68946e48 + 9.82135e48i −0.0428019 + 0.248821i
\(231\) 5.27813e48i 0.122075i
\(232\) −1.25747e49 7.05121e48i −0.265614 0.148942i
\(233\) −5.90372e49 −1.13933 −0.569667 0.821876i \(-0.692928\pi\)
−0.569667 + 0.821876i \(0.692928\pi\)
\(234\) −9.53111e48 1.63953e48i −0.168117 0.0289192i
\(235\) 5.41397e48i 0.0873154i
\(236\) 3.54120e48 9.98847e48i 0.0522394 0.147349i
\(237\) −6.61345e49 −0.892715
\(238\) −4.67383e48 + 2.71705e49i −0.0577507 + 0.335723i
\(239\) 7.38705e49i 0.835825i 0.908487 + 0.417912i \(0.137238\pi\)
−0.908487 + 0.417912i \(0.862762\pi\)
\(240\) 2.06547e49 2.54685e49i 0.214083 0.263978i
\(241\) 2.17016e49 0.206127 0.103063 0.994675i \(-0.467136\pi\)
0.103063 + 0.994675i \(0.467136\pi\)
\(242\) 1.11922e50 + 1.92527e49i 0.974526 + 0.167637i
\(243\) 5.85203e49i 0.467277i
\(244\) 1.70794e50 + 6.05512e49i 1.25108 + 0.443544i
\(245\) 4.37717e49 0.294243
\(246\) 3.54230e49 2.05925e50i 0.218599 1.27079i
\(247\) 1.58419e50i 0.897782i
\(248\) 1.76244e50 3.14303e50i 0.917547 1.63630i
\(249\) −9.50498e49 −0.454742
\(250\) 1.61379e50 + 2.77602e49i 0.709751 + 0.122090i
\(251\) 7.60536e49i 0.307590i −0.988103 0.153795i \(-0.950850\pi\)
0.988103 0.153795i \(-0.0491495\pi\)
\(252\) −2.84679e49 + 8.02979e49i −0.105912 + 0.298740i
\(253\) −1.99943e49 −0.0684503
\(254\) −8.36340e49 + 4.86191e50i −0.263557 + 1.53214i
\(255\) 3.01180e49i 0.0873942i
\(256\) 7.72560e49 + 3.66081e50i 0.206487 + 0.978449i
\(257\) −3.66538e50 −0.902659 −0.451329 0.892357i \(-0.649050\pi\)
−0.451329 + 0.892357i \(0.649050\pi\)
\(258\) −6.00244e50 1.03253e50i −1.36243 0.234364i
\(259\) 1.61905e50i 0.338816i
\(260\) 1.35682e50 + 4.81031e49i 0.261868 + 0.0928395i
\(261\) −4.09187e49 −0.0728571
\(262\) 9.01690e49 5.24181e50i 0.148160 0.861300i
\(263\) 9.90397e48i 0.0150224i −0.999972 0.00751119i \(-0.997609\pi\)
0.999972 0.00751119i \(-0.00239091\pi\)
\(264\) 5.73839e49 + 3.21777e49i 0.0803725 + 0.0450684i
\(265\) 4.71488e50 0.609968
\(266\) −1.37535e51 2.36586e50i −1.64398 0.282796i
\(267\) 1.17560e51i 1.29875i
\(268\) −4.81284e49 + 1.35753e50i −0.0491553 + 0.138650i
\(269\) 1.35233e50 0.127727 0.0638637 0.997959i \(-0.479658\pi\)
0.0638637 + 0.997959i \(0.479658\pi\)
\(270\) 8.17264e49 4.75101e50i 0.0714041 0.415095i
\(271\) 1.61523e51i 1.30580i −0.757442 0.652902i \(-0.773551\pi\)
0.757442 0.652902i \(-0.226449\pi\)
\(272\) 2.66904e50 + 2.16457e50i 0.199714 + 0.161966i
\(273\) 1.18927e51 0.823881
\(274\) −2.48671e51 4.27761e50i −1.59538 0.274435i
\(275\) 1.50771e50i 0.0896048i
\(276\) 9.67212e50 + 3.42904e50i 0.532637 + 0.188835i
\(277\) 1.90483e51 0.972258 0.486129 0.873887i \(-0.338408\pi\)
0.486129 + 0.873887i \(0.338408\pi\)
\(278\) −6.28746e50 + 3.65510e51i −0.297533 + 1.72965i
\(279\) 1.02276e51i 0.448832i
\(280\) 6.20247e50 1.10611e51i 0.252491 0.450279i
\(281\) 1.31260e51 0.495792 0.247896 0.968787i \(-0.420261\pi\)
0.247896 + 0.968787i \(0.420261\pi\)
\(282\) −5.49429e50 9.45121e49i −0.192611 0.0331326i
\(283\) 2.85209e51i 0.928214i 0.885779 + 0.464107i \(0.153625\pi\)
−0.885779 + 0.464107i \(0.846375\pi\)
\(284\) 8.77652e50 2.47555e51i 0.265239 0.748146i
\(285\) 1.52455e51 0.427956
\(286\) −4.89642e49 + 2.84644e50i −0.0127700 + 0.0742362i
\(287\) 8.08081e51i 1.95855i
\(288\) 6.99448e50 + 7.99033e50i 0.157584 + 0.180021i
\(289\) −4.45807e51 −0.933881
\(290\) 6.00269e50 + 1.03258e50i 0.116947 + 0.0201170i
\(291\) 5.05215e51i 0.915638i
\(292\) 3.70532e51 + 1.31364e51i 0.624865 + 0.221532i
\(293\) 1.08229e51 0.169872 0.0849361 0.996386i \(-0.472931\pi\)
0.0849361 + 0.996386i \(0.472931\pi\)
\(294\) 7.64126e50 4.44210e51i 0.111653 0.649075i
\(295\) 4.47732e50i 0.0609194i
\(296\) 1.76023e51 + 9.87039e50i 0.223071 + 0.125086i
\(297\) 9.67211e50 0.114192
\(298\) 1.30145e51 + 2.23874e50i 0.143181 + 0.0246299i
\(299\) 4.50512e51i 0.461968i
\(300\) 2.58574e51 7.29346e51i 0.247194 0.697248i
\(301\) −2.35545e52 −2.09979
\(302\) 1.01170e51 5.88131e51i 0.0841210 0.489022i
\(303\) 2.04089e52i 1.58316i
\(304\) −1.09569e52 + 1.35105e52i −0.793124 + 0.977969i
\(305\) −7.65581e51 −0.517243
\(306\) 9.61237e50 + 1.65351e50i 0.0606290 + 0.0104293i
\(307\) 1.27509e52i 0.750990i −0.926824 0.375495i \(-0.877473\pi\)
0.926824 0.375495i \(-0.122527\pi\)
\(308\) 2.39807e51 + 8.50185e50i 0.131916 + 0.0467680i
\(309\) −2.14686e52 −1.10325
\(310\) −2.58090e51 + 1.50036e52i −0.123930 + 0.720444i
\(311\) 2.22773e52i 0.999755i −0.866096 0.499878i \(-0.833378\pi\)
0.866096 0.499878i \(-0.166622\pi\)
\(312\) 7.25029e51 1.29298e52i 0.304165 0.542430i
\(313\) −1.24552e52 −0.488562 −0.244281 0.969704i \(-0.578552\pi\)
−0.244281 + 0.969704i \(0.578552\pi\)
\(314\) 4.07196e52 + 7.00453e51i 1.49376 + 0.256955i
\(315\) 3.59934e51i 0.123510i
\(316\) −1.06528e52 + 3.00477e52i −0.342005 + 0.964677i
\(317\) 5.30020e52 1.59239 0.796193 0.605043i \(-0.206844\pi\)
0.796193 + 0.605043i \(0.206844\pi\)
\(318\) 8.23080e51 4.78483e52i 0.231458 1.34554i
\(319\) 1.22203e51i 0.0321719i
\(320\) −8.24440e51 1.34867e52i −0.203240 0.332472i
\(321\) 6.75243e52 1.55903
\(322\) 3.91122e52 + 6.72803e51i 0.845938 + 0.145517i
\(323\) 1.59769e52i 0.323773i
\(324\) −3.49145e52 1.23782e52i −0.663072 0.235078i
\(325\) 3.39718e52 0.604738
\(326\) −3.17591e51 + 1.84626e52i −0.0530028 + 0.308122i
\(327\) 2.03479e52i 0.318432i
\(328\) −8.78547e52 4.92640e52i −1.28948 0.723068i
\(329\) −2.15604e52 −0.296854
\(330\) −2.73928e51 4.71208e50i −0.0353870 0.00608724i
\(331\) 5.66239e52i 0.686455i −0.939252 0.343227i \(-0.888480\pi\)
0.939252 0.343227i \(-0.111520\pi\)
\(332\) −1.53103e52 + 4.31851e52i −0.174215 + 0.491399i
\(333\) 5.72787e51 0.0611877
\(334\) −1.77099e52 + 1.02953e53i −0.177640 + 1.03268i
\(335\) 6.08512e51i 0.0573229i
\(336\) −1.01425e53 8.22544e52i −0.897467 0.727837i
\(337\) 4.43746e52 0.368898 0.184449 0.982842i \(-0.440950\pi\)
0.184449 + 0.982842i \(0.440950\pi\)
\(338\) −6.20230e52 1.06691e52i −0.484509 0.0833447i
\(339\) 8.76202e52i 0.643296i
\(340\) −1.36839e52 4.85132e51i −0.0944391 0.0334814i
\(341\) −3.05443e52 −0.198193
\(342\) −8.36993e51 + 4.86570e52i −0.0510709 + 0.296891i
\(343\) 5.65343e52i 0.324441i
\(344\) −1.43598e53 + 2.56085e53i −0.775213 + 1.38247i
\(345\) −4.33552e52 −0.220212
\(346\) 1.44857e53 + 2.49182e52i 0.692376 + 0.119102i
\(347\) 2.18997e53i 0.985189i −0.870259 0.492594i \(-0.836049\pi\)
0.870259 0.492594i \(-0.163951\pi\)
\(348\) 2.09579e52 5.91148e52i 0.0887531 0.250341i
\(349\) 9.12545e52 0.363848 0.181924 0.983313i \(-0.441767\pi\)
0.181924 + 0.983313i \(0.441767\pi\)
\(350\) 5.07340e52 2.94933e53i 0.190489 1.10737i
\(351\) 2.17932e53i 0.770676i
\(352\) 2.38629e52 2.08888e52i 0.0794927 0.0695854i
\(353\) −1.04883e53 −0.329183 −0.164591 0.986362i \(-0.552631\pi\)
−0.164591 + 0.986362i \(0.552631\pi\)
\(354\) 4.54374e52 + 7.81609e51i 0.134383 + 0.0231165i
\(355\) 1.10966e53i 0.309311i
\(356\) 5.34125e53 + 1.89363e53i 1.40344 + 0.497559i
\(357\) −1.19941e53 −0.297122
\(358\) 7.80809e52 4.53909e53i 0.182390 1.06029i
\(359\) 5.78396e53i 1.27421i 0.770776 + 0.637106i \(0.219869\pi\)
−0.770776 + 0.637106i \(0.780131\pi\)
\(360\) −3.91321e52 2.19431e52i −0.0813169 0.0455980i
\(361\) −2.98645e53 −0.585469
\(362\) 2.31810e53 + 3.98757e52i 0.428798 + 0.0737613i
\(363\) 4.94067e53i 0.862475i
\(364\) 1.91564e53 5.40335e53i 0.315635 0.890295i
\(365\) −1.66091e53 −0.258342
\(366\) −1.33648e53 + 7.76939e53i −0.196273 + 1.14100i
\(367\) 6.95425e52i 0.0964412i −0.998837 0.0482206i \(-0.984645\pi\)
0.998837 0.0482206i \(-0.0153551\pi\)
\(368\) 3.11592e53 3.84211e53i 0.408114 0.503229i
\(369\) −2.85883e53 −0.353700
\(370\) −8.40265e52 1.44541e52i −0.0982155 0.0168949i
\(371\) 1.87764e54i 2.07376i
\(372\) 1.47756e54 + 5.23838e53i 1.54221 + 0.546758i
\(373\) 2.05688e53 0.202919 0.101460 0.994840i \(-0.467649\pi\)
0.101460 + 0.994840i \(0.467649\pi\)
\(374\) 4.93816e51 2.87071e52i 0.00460534 0.0267723i
\(375\) 7.12387e53i 0.628144i
\(376\) −1.31441e53 + 2.34405e53i −0.109594 + 0.195444i
\(377\) 2.75347e53 0.217126
\(378\) −1.89202e54 3.25464e53i −1.41123 0.242759i
\(379\) 1.30408e54i 0.920195i −0.887868 0.460097i \(-0.847814\pi\)
0.887868 0.460097i \(-0.152186\pi\)
\(380\) 2.45570e53 6.92667e53i 0.163953 0.462454i
\(381\) −2.14623e54 −1.35598
\(382\) −2.06097e53 + 1.19811e54i −0.123237 + 0.716415i
\(383\) 3.01942e54i 1.70903i 0.519429 + 0.854514i \(0.326145\pi\)
−0.519429 + 0.854514i \(0.673855\pi\)
\(384\) −1.51260e54 + 6.01233e53i −0.810528 + 0.322171i
\(385\) −1.07493e53 −0.0545389
\(386\) −2.72337e54 4.68471e53i −1.30850 0.225086i
\(387\) 8.33310e53i 0.379207i
\(388\) 2.29540e54 + 8.13786e53i 0.989448 + 0.350787i
\(389\) 2.49607e54 1.01933 0.509666 0.860372i \(-0.329769\pi\)
0.509666 + 0.860372i \(0.329769\pi\)
\(390\) −1.06173e53 + 6.17216e53i −0.0410824 + 0.238825i
\(391\) 4.54353e53i 0.166602i
\(392\) −1.89515e54 1.06270e54i −0.658622 0.369319i
\(393\) 2.31394e54 0.762268
\(394\) −1.89008e54 3.25130e53i −0.590283 0.101540i
\(395\) 1.34688e54i 0.398833i
\(396\) 3.00779e52 8.48391e52i 0.00844594 0.0238230i
\(397\) 2.13047e54 0.567380 0.283690 0.958916i \(-0.408441\pi\)
0.283690 + 0.958916i \(0.408441\pi\)
\(398\) 2.84073e53 1.65140e54i 0.0717604 0.417166i
\(399\) 6.07130e54i 1.45496i
\(400\) −2.89722e54 2.34962e54i −0.658752 0.534241i
\(401\) 7.18819e54 1.55091 0.775457 0.631401i \(-0.217520\pi\)
0.775457 + 0.631401i \(0.217520\pi\)
\(402\) −6.17540e53 1.06228e53i −0.126450 0.0217517i
\(403\) 6.88226e54i 1.33760i
\(404\) 9.27261e54 + 3.28740e54i 1.71078 + 0.606519i
\(405\) 1.56504e54 0.274138
\(406\) 4.11209e53 2.39049e54i 0.0683936 0.397594i
\(407\) 1.71061e53i 0.0270190i
\(408\) −7.31210e53 + 1.30400e54i −0.109693 + 0.195620i
\(409\) −2.09361e54 −0.298337 −0.149168 0.988812i \(-0.547660\pi\)
−0.149168 + 0.988812i \(0.547660\pi\)
\(410\) 4.19384e54 + 7.21420e53i 0.567742 + 0.0976623i
\(411\) 1.09773e55i 1.41194i
\(412\) −3.45810e54 + 9.75407e54i −0.422664 + 1.19219i
\(413\) 1.78303e54 0.207113
\(414\) 2.38024e53 1.38371e54i 0.0262793 0.152770i
\(415\) 1.93577e54i 0.203162i
\(416\) −4.70667e54 5.37680e54i −0.469628 0.536492i
\(417\) −1.61350e55 −1.53078
\(418\) 1.45313e54 + 2.49966e53i 0.131100 + 0.0225517i
\(419\) 1.55694e55i 1.33591i 0.744200 + 0.667957i \(0.232831\pi\)
−0.744200 + 0.667957i \(0.767169\pi\)
\(420\) 5.19993e54 + 1.84352e54i 0.424387 + 0.150457i
\(421\) −2.08192e55 −1.61636 −0.808182 0.588933i \(-0.799548\pi\)
−0.808182 + 0.588933i \(0.799548\pi\)
\(422\) −1.78595e54 + 1.03823e55i −0.131919 + 0.766888i
\(423\) 7.62764e53i 0.0536096i
\(424\) −2.04137e55 1.14469e55i −1.36533 0.765603i
\(425\) −3.42614e54 −0.218091
\(426\) 1.12612e55 + 1.93715e54i 0.682315 + 0.117371i
\(427\) 3.04882e55i 1.75852i
\(428\) 1.08766e55 3.06791e55i 0.597276 1.68470i
\(429\) −1.25653e54 −0.0657005
\(430\) 2.10284e54 1.22245e55i 0.104705 0.608685i
\(431\) 2.86805e55i 1.36008i −0.733176 0.680039i \(-0.761963\pi\)
0.733176 0.680039i \(-0.238037\pi\)
\(432\) −1.50730e55 + 1.85860e55i −0.680835 + 0.839511i
\(433\) −1.45804e55 −0.627370 −0.313685 0.949527i \(-0.601564\pi\)
−0.313685 + 0.949527i \(0.601564\pi\)
\(434\) 5.97498e55 + 1.02781e55i 2.44936 + 0.421335i
\(435\) 2.64982e54i 0.103500i
\(436\) 9.24491e54 + 3.27758e54i 0.344101 + 0.121994i
\(437\) 2.29990e55 0.815827
\(438\) −2.89946e54 + 1.68555e55i −0.0980303 + 0.569881i
\(439\) 1.17124e55i 0.377477i 0.982027 + 0.188738i \(0.0604398\pi\)
−0.982027 + 0.188738i \(0.939560\pi\)
\(440\) −6.55325e53 + 1.16867e54i −0.0201350 + 0.0359076i
\(441\) −6.16690e54 −0.180658
\(442\) −6.46829e54 1.11267e54i −0.180685 0.0310812i
\(443\) 5.65522e55i 1.50651i −0.657730 0.753254i \(-0.728483\pi\)
0.657730 0.753254i \(-0.271517\pi\)
\(444\) −2.93372e54 + 8.27498e54i −0.0745376 + 0.210244i
\(445\) −2.39421e55 −0.580233
\(446\) 1.05630e55 6.14062e55i 0.244206 1.41965i
\(447\) 5.74509e54i 0.126718i
\(448\) −5.37088e55 + 3.28322e55i −1.13034 + 0.690973i
\(449\) 7.97841e55 1.60230 0.801148 0.598466i \(-0.204223\pi\)
0.801148 + 0.598466i \(0.204223\pi\)
\(450\) −1.04341e55 1.79487e54i −0.199984 0.0344009i
\(451\) 8.53782e54i 0.156185i
\(452\) 3.98095e55 + 1.41136e55i 0.695152 + 0.246451i
\(453\) 2.59623e55 0.432794
\(454\) −5.63115e54 + 3.27356e55i −0.0896239 + 0.521012i
\(455\) 2.42204e55i 0.368080i
\(456\) −6.60073e55 3.70133e55i −0.957923 0.537150i
\(457\) 1.70643e55 0.236509 0.118254 0.992983i \(-0.462270\pi\)
0.118254 + 0.992983i \(0.462270\pi\)
\(458\) 3.32448e54 + 5.71874e53i 0.0440098 + 0.00757051i
\(459\) 2.19790e55i 0.277934i
\(460\) −6.98353e54 + 1.96981e55i −0.0843646 + 0.237963i
\(461\) 1.02450e56 1.18247 0.591236 0.806499i \(-0.298640\pi\)
0.591236 + 0.806499i \(0.298640\pi\)
\(462\) −1.87652e54 + 1.09088e55i −0.0206953 + 0.120308i
\(463\) 1.09737e56i 1.15652i −0.815854 0.578258i \(-0.803733\pi\)
0.815854 0.578258i \(-0.196267\pi\)
\(464\) −2.34825e55 1.90441e55i −0.236520 0.191815i
\(465\) −6.62316e55 −0.637608
\(466\) −1.22018e56 2.09894e55i −1.12284 0.193150i
\(467\) 9.47914e55i 0.833900i 0.908929 + 0.416950i \(0.136901\pi\)
−0.908929 + 0.416950i \(0.863099\pi\)
\(468\) −1.91160e55 6.77715e54i −0.160781 0.0570012i
\(469\) −2.42332e55 −0.194886
\(470\) 1.92482e54 1.11896e55i 0.0148025 0.0860515i
\(471\) 1.79752e56i 1.32201i
\(472\) 1.08701e55 1.93851e55i 0.0764631 0.136360i
\(473\) 2.48866e55 0.167449
\(474\) −1.36687e56 2.35127e55i −0.879793 0.151341i
\(475\) 1.73428e56i 1.06796i
\(476\) −1.93197e55 + 5.44941e55i −0.113829 + 0.321073i
\(477\) −6.64270e55 −0.374506
\(478\) −2.62630e55 + 1.52675e56i −0.141696 + 0.823727i
\(479\) 2.36040e56i 1.21882i −0.792854 0.609411i \(-0.791406\pi\)
0.792854 0.609411i \(-0.208594\pi\)
\(480\) 5.17438e55 4.52948e55i 0.255736 0.223863i
\(481\) −3.85435e55 −0.182350
\(482\) 4.48528e55 + 7.71553e54i 0.203143 + 0.0349444i
\(483\) 1.72656e56i 0.748672i
\(484\) 2.24475e56 + 7.95829e55i 0.932000 + 0.330420i
\(485\) −1.02891e56 −0.409074
\(486\) −2.08056e55 + 1.20949e56i −0.0792170 + 0.460513i
\(487\) 1.06895e56i 0.389807i 0.980822 + 0.194904i \(0.0624394\pi\)
−0.980822 + 0.194904i \(0.937561\pi\)
\(488\) 3.31468e56 + 1.85869e56i 1.15778 + 0.649218i
\(489\) −8.15008e55 −0.272694
\(490\) 9.04671e55 + 1.55621e55i 0.289983 + 0.0498826i
\(491\) 1.68700e56i 0.518088i −0.965865 0.259044i \(-0.916592\pi\)
0.965865 0.259044i \(-0.0834075\pi\)
\(492\) 1.46424e56 4.13012e56i 0.430870 1.21533i
\(493\) −2.77695e55 −0.0783038
\(494\) 5.63223e55 3.27419e56i 0.152200 0.884787i
\(495\) 3.80290e54i 0.00984932i
\(496\) 4.76003e56 5.86941e56i 1.18167 1.45707i
\(497\) 4.41907e56 1.05159
\(498\) −1.96449e56 3.37928e55i −0.448159 0.0770919i
\(499\) 2.28193e56i 0.499105i 0.968361 + 0.249552i \(0.0802835\pi\)
−0.968361 + 0.249552i \(0.919717\pi\)
\(500\) 3.23667e56 + 1.14749e56i 0.678779 + 0.240646i
\(501\) −4.54475e56 −0.913939
\(502\) 2.70392e55 1.57187e56i 0.0521454 0.303137i
\(503\) 1.52058e56i 0.281243i 0.990063 + 0.140622i \(0.0449101\pi\)
−0.990063 + 0.140622i \(0.955090\pi\)
\(504\) −8.73854e55 + 1.55838e56i −0.155024 + 0.276460i
\(505\) −4.15644e56 −0.707298
\(506\) −4.13241e55 7.10853e54i −0.0674595 0.0116043i
\(507\) 2.73793e56i 0.428801i
\(508\) −3.45709e56 + 9.75123e56i −0.519484 + 1.46528i
\(509\) 6.45110e55 0.0930165 0.0465083 0.998918i \(-0.485191\pi\)
0.0465083 + 0.998918i \(0.485191\pi\)
\(510\) 1.07078e55 6.22478e55i 0.0148158 0.0861292i
\(511\) 6.61433e56i 0.878308i
\(512\) 2.95202e55 + 7.84082e56i 0.0376228 + 0.999292i
\(513\) −1.11256e57 −1.36100
\(514\) −7.57559e56 1.30314e56i −0.889593 0.153027i
\(515\) 4.37225e56i 0.492894i
\(516\) −1.20387e57 4.26807e56i −1.30298 0.461943i
\(517\) 2.27797e55 0.0236727
\(518\) −5.75616e55 + 3.34624e56i −0.0574391 + 0.333912i
\(519\) 6.39455e56i 0.612767i
\(520\) 2.63325e56 + 1.47658e56i 0.242338 + 0.135890i
\(521\) 7.31241e56 0.646351 0.323176 0.946339i \(-0.395250\pi\)
0.323176 + 0.946339i \(0.395250\pi\)
\(522\) −8.45707e55 1.45478e55i −0.0718025 0.0123514i
\(523\) 1.53270e57i 1.25004i −0.780610 0.625018i \(-0.785092\pi\)
0.780610 0.625018i \(-0.214908\pi\)
\(524\) 3.72722e56 1.05132e57i 0.292030 0.823715i
\(525\) 1.30195e57 0.980049
\(526\) 3.52114e54 2.04695e55i 0.00254673 0.0148049i
\(527\) 6.94093e56i 0.482386i
\(528\) 1.07161e56 + 8.69063e55i 0.0715687 + 0.0580415i
\(529\) 9.03960e56 0.580203
\(530\) 9.74470e56 + 1.67627e56i 0.601139 + 0.103407i
\(531\) 6.30801e55i 0.0374031i
\(532\) −2.75845e57 9.77948e56i −1.57225 0.557406i
\(533\) 1.92374e57 1.05409
\(534\) −4.17959e56 + 2.42973e57i −0.220175 + 1.27995i
\(535\) 1.37519e57i 0.696519i
\(536\) −1.47736e56 + 2.63463e56i −0.0719490 + 0.128310i
\(537\) 2.00373e57 0.938380
\(538\) 2.79499e56 + 4.80790e55i 0.125879 + 0.0216535i
\(539\) 1.84173e56i 0.0797741i
\(540\) 3.37823e56 9.52881e56i 0.140741 0.396981i
\(541\) 7.70270e55 0.0308674 0.0154337 0.999881i \(-0.495087\pi\)
0.0154337 + 0.999881i \(0.495087\pi\)
\(542\) 5.74258e56 3.33834e57i 0.221372 1.28690i
\(543\) 1.02330e57i 0.379495i
\(544\) 4.74680e56 + 5.42264e56i 0.169365 + 0.193479i
\(545\) −4.14402e56 −0.142264
\(546\) 2.45798e57 + 4.22818e56i 0.811955 + 0.139672i
\(547\) 3.11561e56i 0.0990396i −0.998773 0.0495198i \(-0.984231\pi\)
0.998773 0.0495198i \(-0.0157691\pi\)
\(548\) −4.98744e57 1.76819e57i −1.52576 0.540925i
\(549\) 1.07861e57 0.317575
\(550\) −5.36033e55 + 3.11613e56i −0.0151906 + 0.0883078i
\(551\) 1.40567e57i 0.383442i
\(552\) 1.87712e57 + 1.05258e57i 0.492914 + 0.276399i
\(553\) −5.36378e57 −1.35595
\(554\) 3.93690e57 + 6.77221e56i 0.958185 + 0.164826i
\(555\) 3.70925e56i 0.0869228i
\(556\) −2.59898e57 + 7.33081e57i −0.586452 + 1.65418i
\(557\) −5.75909e57 −1.25139 −0.625697 0.780066i \(-0.715186\pi\)
−0.625697 + 0.780066i \(0.715186\pi\)
\(558\) 3.63618e56 2.11383e57i 0.0760900 0.442335i
\(559\) 5.60745e57i 1.13010i
\(560\) 1.67518e57 2.06560e57i 0.325172 0.400956i
\(561\) 1.26724e56 0.0236940
\(562\) 2.71287e57 + 4.66665e56i 0.488615 + 0.0840510i
\(563\) 7.98057e57i 1.38471i 0.721559 + 0.692353i \(0.243426\pi\)
−0.721559 + 0.692353i \(0.756574\pi\)
\(564\) −1.10196e57 3.90675e56i −0.184206 0.0653061i
\(565\) −1.78446e57 −0.287401
\(566\) −1.01400e57 + 5.89469e57i −0.157359 + 0.914778i
\(567\) 6.23255e57i 0.932012i
\(568\) 2.69406e57 4.80443e57i 0.388232 0.692351i
\(569\) −1.97666e57 −0.274521 −0.137260 0.990535i \(-0.543830\pi\)
−0.137260 + 0.990535i \(0.543830\pi\)
\(570\) 3.15093e57 + 5.42020e56i 0.421762 + 0.0725510i
\(571\) 1.39663e58i 1.80186i 0.433961 + 0.900932i \(0.357116\pi\)
−0.433961 + 0.900932i \(0.642884\pi\)
\(572\) −2.02398e56 + 5.70893e56i −0.0251704 + 0.0709967i
\(573\) −5.28890e57 −0.634042
\(574\) 2.87295e57 1.67014e58i 0.332031 1.93020i
\(575\) 4.93196e57i 0.549535i
\(576\) 1.16154e57 + 1.90011e57i 0.124785 + 0.204130i
\(577\) −4.09717e57 −0.424416 −0.212208 0.977225i \(-0.568065\pi\)
−0.212208 + 0.977225i \(0.568065\pi\)
\(578\) −9.21391e57 1.58497e57i −0.920364 0.158320i
\(579\) 1.20220e58i 1.15805i
\(580\) 1.20392e57 + 4.26825e56i 0.111843 + 0.0396517i
\(581\) −7.70892e57 −0.690709
\(582\) −1.79618e57 + 1.04418e58i −0.155227 + 0.902384i
\(583\) 1.98382e57i 0.165373i
\(584\) 7.19111e57 + 4.03237e57i 0.578264 + 0.324258i
\(585\) 8.56871e56 0.0664726
\(586\) 2.23687e57 + 3.84783e56i 0.167413 + 0.0287983i
\(587\) 2.25118e57i 0.162559i 0.996691 + 0.0812794i \(0.0259006\pi\)
−0.996691 + 0.0812794i \(0.974099\pi\)
\(588\) 3.15858e57 8.90926e57i 0.220074 0.620751i
\(589\) 3.51344e58 2.36217
\(590\) −1.59181e56 + 9.25371e56i −0.0103276 + 0.0600376i
\(591\) 8.34355e57i 0.522413i
\(592\) 3.28712e57 + 2.66582e57i 0.198637 + 0.161092i
\(593\) 1.62838e58 0.949743 0.474872 0.880055i \(-0.342494\pi\)
0.474872 + 0.880055i \(0.342494\pi\)
\(594\) 1.99903e57 + 3.43870e56i 0.112539 + 0.0193588i
\(595\) 2.44269e57i 0.132743i
\(596\) 2.61024e57 + 9.25403e56i 0.136933 + 0.0485467i
\(597\) 7.28993e57 0.369201
\(598\) −1.60170e57 + 9.31117e57i −0.0783168 + 0.455281i
\(599\) 1.87184e58i 0.883702i −0.897088 0.441851i \(-0.854322\pi\)
0.897088 0.441851i \(-0.145678\pi\)
\(600\) 7.93722e57 1.41548e58i 0.361820 0.645249i
\(601\) 6.65480e57 0.292935 0.146467 0.989215i \(-0.453210\pi\)
0.146467 + 0.989215i \(0.453210\pi\)
\(602\) −4.86823e58 8.37427e57i −2.06940 0.355976i
\(603\) 8.57321e56i 0.0351949i
\(604\) 4.18194e57 1.17958e58i 0.165807 0.467682i
\(605\) −1.00621e58 −0.385323
\(606\) −7.25593e57 + 4.21810e58i −0.268391 + 1.56024i
\(607\) 9.04232e57i 0.323085i 0.986866 + 0.161543i \(0.0516470\pi\)
−0.986866 + 0.161543i \(0.948353\pi\)
\(608\) −2.74489e58 + 2.40279e58i −0.947437 + 0.829356i
\(609\) 1.05525e58 0.351879
\(610\) −1.58230e58 2.72186e57i −0.509756 0.0876877i
\(611\) 5.13273e57i 0.159766i
\(612\) 1.92789e57 + 6.83493e56i 0.0579834 + 0.0205567i
\(613\) −1.40615e58 −0.408659 −0.204329 0.978902i \(-0.565501\pi\)
−0.204329 + 0.978902i \(0.565501\pi\)
\(614\) 4.53329e57 2.63535e58i 0.127314 0.740119i
\(615\) 1.85132e58i 0.502463i
\(616\) 4.65407e57 + 2.60974e57i 0.122078 + 0.0684546i
\(617\) −5.58230e58 −1.41522 −0.707612 0.706602i \(-0.750227\pi\)
−0.707612 + 0.706602i \(0.750227\pi\)
\(618\) −4.43712e58 7.63268e57i −1.08728 0.187033i
\(619\) 3.89176e57i 0.0921812i −0.998937 0.0460906i \(-0.985324\pi\)
0.998937 0.0460906i \(-0.0146763\pi\)
\(620\) −1.06684e58 + 3.00918e58i −0.244272 + 0.689006i
\(621\) 3.16390e58 0.700325
\(622\) 7.92019e57 4.60426e58i 0.169487 0.985284i
\(623\) 9.53461e58i 1.97267i
\(624\) 1.95818e58 2.41455e58i 0.391719 0.483014i
\(625\) 2.93403e58 0.567523
\(626\) −2.57424e58 4.42817e57i −0.481490 0.0828254i
\(627\) 6.41467e57i 0.116026i
\(628\) 8.16687e58 + 2.89539e58i 1.42858 + 0.506471i
\(629\) 3.88721e57 0.0657620
\(630\) 1.27967e57 7.43911e57i 0.0209385 0.121722i
\(631\) 1.14571e59i 1.81326i −0.421930 0.906628i \(-0.638647\pi\)
0.421930 0.906628i \(-0.361353\pi\)
\(632\) −3.26999e58 + 5.83151e58i −0.500596 + 0.892734i
\(633\) −4.58314e58 −0.678711
\(634\) 1.09544e59 + 1.88437e58i 1.56934 + 0.269955i
\(635\) 4.37098e58i 0.605802i
\(636\) 3.40228e58 9.59663e58i 0.456216 1.28683i
\(637\) 4.14979e58 0.538391
\(638\) −4.34465e56 + 2.52568e57i −0.00545406 + 0.0317062i
\(639\) 1.56338e58i 0.189910i
\(640\) −1.22446e58 3.08053e58i −0.143935 0.362115i
\(641\) −1.31593e59 −1.49697 −0.748484 0.663152i \(-0.769218\pi\)
−0.748484 + 0.663152i \(0.769218\pi\)
\(642\) 1.39559e59 + 2.40068e58i 1.53646 + 0.264301i
\(643\) 8.14606e58i 0.867995i −0.900914 0.433997i \(-0.857103\pi\)
0.900914 0.433997i \(-0.142897\pi\)
\(644\) 7.84449e58 + 2.78109e58i 0.809024 + 0.286822i
\(645\) 5.39635e58 0.538699
\(646\) −5.68025e57 + 3.30211e58i −0.0548889 + 0.319087i
\(647\) 5.88617e58i 0.550609i 0.961357 + 0.275304i \(0.0887786\pi\)
−0.961357 + 0.275304i \(0.911221\pi\)
\(648\) −6.77604e58 3.79963e58i −0.613622 0.344085i
\(649\) −1.88387e57 −0.0165163
\(650\) 7.02127e58 + 1.20779e58i 0.595985 + 0.102521i
\(651\) 2.63758e59i 2.16773i
\(652\) −1.31279e58 + 3.70292e58i −0.104471 + 0.294676i
\(653\) −1.57717e59 −1.21535 −0.607675 0.794186i \(-0.707898\pi\)
−0.607675 + 0.794186i \(0.707898\pi\)
\(654\) −7.23425e57 + 4.20550e58i −0.0539835 + 0.313823i
\(655\) 4.71252e58i 0.340554i
\(656\) −1.64063e59 1.33054e59i −1.14823 0.931206i
\(657\) 2.34002e58 0.158616
\(658\) −4.45609e58 7.66532e57i −0.292557 0.0503253i
\(659\) 1.50895e59i 0.959579i −0.877384 0.479789i \(-0.840713\pi\)
0.877384 0.479789i \(-0.159287\pi\)
\(660\) −5.49401e57 1.94778e57i −0.0338429 0.0119983i
\(661\) −1.26109e59 −0.752517 −0.376259 0.926515i \(-0.622790\pi\)
−0.376259 + 0.926515i \(0.622790\pi\)
\(662\) 2.01314e58 1.17030e59i 0.116374 0.676518i
\(663\) 2.85535e58i 0.159910i
\(664\) −4.69969e58 + 8.38115e58i −0.254999 + 0.454752i
\(665\) 1.23647e59 0.650024
\(666\) 1.18383e58 + 2.03642e57i 0.0603020 + 0.0103731i
\(667\) 3.99745e58i 0.197306i
\(668\) −7.32054e58 + 2.06487e59i −0.350137 + 0.987613i
\(669\) 2.71070e59 1.25642
\(670\) 2.16343e57 1.25767e58i 0.00971789 0.0564932i
\(671\) 3.22125e58i 0.140233i
\(672\) −1.80380e59 2.06062e59i −0.761087 0.869449i
\(673\) −2.35126e59 −0.961577 −0.480789 0.876837i \(-0.659650\pi\)
−0.480789 + 0.876837i \(0.659650\pi\)
\(674\) 9.17132e58 + 1.57764e58i 0.363558 + 0.0625389i
\(675\) 2.38580e59i 0.916759i
\(676\) −1.24396e59 4.41018e58i −0.463367 0.164277i
\(677\) 3.55696e59 1.28445 0.642225 0.766516i \(-0.278012\pi\)
0.642225 + 0.766516i \(0.278012\pi\)
\(678\) −3.11514e58 + 1.81093e59i −0.109057 + 0.633984i
\(679\) 4.09750e59i 1.39076i
\(680\) −2.65570e58 1.48917e58i −0.0873961 0.0490069i
\(681\) −1.44508e59 −0.461106
\(682\) −6.31289e58 1.08594e58i −0.195324 0.0335995i
\(683\) 2.95984e59i 0.888042i −0.896016 0.444021i \(-0.853552\pi\)
0.896016 0.444021i \(-0.146448\pi\)
\(684\) −3.45979e58 + 9.75885e58i −0.100663 + 0.283936i
\(685\) 2.23561e59 0.630805
\(686\) −2.00995e58 + 1.16845e59i −0.0550021 + 0.319745i
\(687\) 1.46755e58i 0.0389496i
\(688\) −3.87833e59 + 4.78221e59i −0.998361 + 1.23104i
\(689\) 4.46996e59 1.11609
\(690\) −8.96063e58 1.54140e58i −0.217024 0.0373322i
\(691\) 2.15531e58i 0.0506372i −0.999679 0.0253186i \(-0.991940\pi\)
0.999679 0.0253186i \(-0.00806003\pi\)
\(692\) 2.90531e59 + 1.03002e59i 0.662163 + 0.234756i
\(693\) 1.51445e58 0.0334856
\(694\) 7.78596e58 4.52622e59i 0.167018 0.970928i
\(695\) 3.28603e59i 0.683897i
\(696\) 6.43326e58 1.14727e59i 0.129908 0.231671i
\(697\) −1.94014e59 −0.380142
\(698\) 1.88604e59 + 3.24435e58i 0.358582 + 0.0616828i
\(699\) 5.38633e59i 0.993739i
\(700\) 2.09714e59 5.91529e59i 0.375464 1.05905i
\(701\) 7.18112e59 1.24771 0.623855 0.781540i \(-0.285565\pi\)
0.623855 + 0.781540i \(0.285565\pi\)
\(702\) 7.74810e58 4.50421e59i 0.130652 0.759521i
\(703\) 1.96768e59i 0.322027i
\(704\) 5.67463e58 3.46890e58i 0.0901388 0.0551018i
\(705\) 4.93950e58 0.0761574
\(706\) −2.16772e59 3.72889e58i −0.324418 0.0558060i
\(707\) 1.65524e60i 2.40466i
\(708\) 9.11311e58 + 3.23085e58i 0.128519 + 0.0455637i
\(709\) −4.70042e59 −0.643525 −0.321762 0.946820i \(-0.604275\pi\)
−0.321762 + 0.946820i \(0.604275\pi\)
\(710\) −3.94516e58 + 2.29345e59i −0.0524372 + 0.304834i
\(711\) 1.89760e59i 0.244874i
\(712\) 1.03660e60 + 5.81270e59i 1.29877 + 0.728280i
\(713\) −9.99154e59 −1.21549
\(714\) −2.47893e59 4.26423e58i −0.292821 0.0503707i
\(715\) 2.55902e58i 0.0293526i
\(716\) 3.22755e59 9.10377e59i 0.359500 1.01402i
\(717\) −6.73967e59 −0.729015
\(718\) −2.05636e59 + 1.19543e60i −0.216016 + 1.25577i
\(719\) 1.41173e60i 1.44027i −0.693834 0.720135i \(-0.744080\pi\)
0.693834 0.720135i \(-0.255920\pi\)
\(720\) −7.30767e58 5.92645e58i −0.0724097 0.0587236i
\(721\) −1.74119e60 −1.67573
\(722\) −6.17238e59 1.06177e59i −0.576994 0.0992539i
\(723\) 1.97998e59i 0.179786i
\(724\) 4.64927e59 + 1.64830e59i 0.410086 + 0.145387i
\(725\) 3.01435e59 0.258283
\(726\) −1.75655e59 + 1.02114e60i −0.146214 + 0.849991i
\(727\) 3.94107e59i 0.318707i −0.987222 0.159353i \(-0.949059\pi\)
0.987222 0.159353i \(-0.0509409\pi\)
\(728\) 5.88028e59 1.04866e60i 0.461997 0.823899i
\(729\) −1.45553e60 −1.11107
\(730\) −3.43275e59 5.90498e58i −0.254602 0.0437964i
\(731\) 5.65526e59i 0.407556i
\(732\) −5.52447e59 + 1.55826e60i −0.386864 + 1.09121i
\(733\) 3.63598e59 0.247422 0.123711 0.992318i \(-0.460520\pi\)
0.123711 + 0.992318i \(0.460520\pi\)
\(734\) 2.47243e58 1.43730e59i 0.0163496 0.0950453i
\(735\) 3.99356e59i 0.256641i
\(736\) 7.80594e59 6.83307e59i 0.487519 0.426758i
\(737\) 2.56037e58 0.0155412
\(738\) −5.90862e59 1.01639e59i −0.348580 0.0599623i
\(739\) 7.19815e59i 0.412750i 0.978473 + 0.206375i \(0.0661668\pi\)
−0.978473 + 0.206375i \(0.933833\pi\)
\(740\) −1.68527e59 5.97475e58i −0.0939297 0.0333007i
\(741\) 1.44535e60 0.783054
\(742\) 6.67552e59 3.88069e60i 0.351563 2.04375i
\(743\) 1.83146e59i 0.0937631i −0.998900 0.0468816i \(-0.985072\pi\)
0.998900 0.0468816i \(-0.0149283\pi\)
\(744\) 2.86758e60 + 1.60798e60i 1.42720 + 0.800294i
\(745\) −1.17004e59 −0.0566132
\(746\) 4.25115e59 + 7.31278e58i 0.199982 + 0.0344007i
\(747\) 2.72726e59i 0.124737i
\(748\) 2.04123e58 5.75761e58i 0.00907735 0.0256040i
\(749\) 5.47649e60 2.36802
\(750\) −2.53273e59 + 1.47236e60i −0.106489 + 0.619052i
\(751\) 2.98766e60i 1.22150i −0.791824 0.610749i \(-0.790868\pi\)
0.791824 0.610749i \(-0.209132\pi\)
\(752\) −3.55000e59 + 4.37736e59i −0.141141 + 0.174035i
\(753\) 6.93885e59 0.268283
\(754\) 5.69087e59 + 9.78937e58i 0.213984 + 0.0368092i
\(755\) 5.28745e59i 0.193357i
\(756\) −3.79472e60 1.34533e60i −1.34965 0.478490i
\(757\) 1.80666e60 0.624976 0.312488 0.949922i \(-0.398838\pi\)
0.312488 + 0.949922i \(0.398838\pi\)
\(758\) 4.63636e59 2.69526e60i 0.156000 0.906875i
\(759\) 1.82421e59i 0.0597030i
\(760\) 7.53806e59 1.34429e60i 0.239979 0.427966i
\(761\) −9.77729e59 −0.302790 −0.151395 0.988473i \(-0.548376\pi\)
−0.151395 + 0.988473i \(0.548376\pi\)
\(762\) −4.43582e60 7.63045e59i −1.33635 0.229877i
\(763\) 1.65030e60i 0.483668i
\(764\) −8.51920e59 + 2.40297e60i −0.242906 + 0.685153i
\(765\) −8.64177e58 −0.0239724
\(766\) −1.07349e60 + 6.24052e60i −0.289730 + 1.68429i
\(767\) 4.24474e59i 0.111468i
\(768\) −3.33999e60 + 7.04855e59i −0.853413 + 0.180100i
\(769\) −4.50113e60 −1.11910 −0.559549 0.828797i \(-0.689026\pi\)
−0.559549 + 0.828797i \(0.689026\pi\)
\(770\) −2.22167e59 3.82169e58i −0.0537495 0.00924592i
\(771\) 3.34416e60i 0.787308i
\(772\) −5.46210e60 1.93647e60i −1.25140 0.443657i
\(773\) 5.68528e60 1.26760 0.633801 0.773497i \(-0.281494\pi\)
0.633801 + 0.773497i \(0.281494\pi\)
\(774\) −2.96265e59 + 1.72228e60i −0.0642866 + 0.373718i
\(775\) 7.53432e60i 1.59114i
\(776\) 4.45481e60 + 2.49801e60i 0.915657 + 0.513450i
\(777\) −1.47716e60 −0.295519
\(778\) 5.15887e60 + 8.87423e59i 1.00458 + 0.172806i
\(779\) 9.82085e60i 1.86150i
\(780\) −4.38875e59 + 1.23791e60i −0.0809756 + 0.228404i
\(781\) −4.66899e59 −0.0838594
\(782\) 1.61535e59 9.39055e59i 0.0282439 0.164191i
\(783\) 1.93374e60i 0.329155i
\(784\) −3.53907e60 2.87015e60i −0.586479 0.475629i
\(785\) −3.66079e60 −0.590625
\(786\) 4.78243e60 + 8.22668e59i 0.751234 + 0.129226i
\(787\) 2.10897e60i 0.322553i 0.986909 + 0.161276i \(0.0515610\pi\)
−0.986909 + 0.161276i \(0.948439\pi\)
\(788\) −3.79083e60 1.34396e60i −0.564525 0.200140i
\(789\) 9.03601e58 0.0131027
\(790\) 4.78855e59 2.78373e60i 0.0676137 0.393060i
\(791\) 7.10635e60i 0.977104i
\(792\) 9.23275e58 1.64652e59i 0.0123624 0.0220464i
\(793\) −7.25812e60 −0.946427
\(794\) 4.40324e60 + 7.57441e59i 0.559168 + 0.0961874i
\(795\) 4.30168e60i 0.532021i
\(796\) 1.17424e60 3.31212e60i 0.141443 0.398962i
\(797\) 3.04020e60 0.356679 0.178339 0.983969i \(-0.442928\pi\)
0.178339 + 0.983969i \(0.442928\pi\)
\(798\) 2.15852e60 1.25481e61i 0.246658 1.43390i
\(799\) 5.17649e59i 0.0576173i
\(800\) −5.15261e60 5.88623e60i −0.558647 0.638186i
\(801\) 3.37316e60 0.356249
\(802\) 1.48565e61 + 2.55560e60i 1.52846 + 0.262925i
\(803\) 6.98840e59i 0.0700408i
\(804\) −1.23856e60 4.39105e59i −0.120932 0.0428738i
\(805\) −3.51628e60 −0.334480
\(806\) −2.44683e60 + 1.42242e61i −0.226761 + 1.31823i
\(807\) 1.23381e60i 0.111405i
\(808\) 1.79958e61 + 1.00911e61i 1.58319 + 0.887766i
\(809\) −1.23032e61 −1.05463 −0.527315 0.849670i \(-0.676801\pi\)
−0.527315 + 0.849670i \(0.676801\pi\)
\(810\) 3.23462e60 + 5.56415e59i 0.270170 + 0.0464744i
\(811\) 6.49185e60i 0.528361i −0.964473 0.264180i \(-0.914899\pi\)
0.964473 0.264180i \(-0.0851015\pi\)
\(812\) 1.69977e60 4.79445e60i 0.134807 0.380244i
\(813\) 1.47367e61 1.13894
\(814\) 6.08170e58 3.53549e59i 0.00458050 0.0266279i
\(815\) 1.65983e60i 0.121830i
\(816\) −1.97487e60 + 2.43513e60i −0.141268 + 0.174193i
\(817\) −2.86264e61 −1.99574
\(818\) −4.32707e60 7.44338e59i −0.294019 0.0505767i
\(819\) 3.41237e60i 0.225993i
\(820\) 8.41133e60 + 2.98205e60i 0.542967 + 0.192497i
\(821\) 1.89733e61 1.19382 0.596908 0.802309i \(-0.296396\pi\)
0.596908 + 0.802309i \(0.296396\pi\)
\(822\) 3.90273e60 2.26878e61i 0.239365 1.39150i
\(823\) 1.75773e61i 1.05089i −0.850829 0.525443i \(-0.823900\pi\)
0.850829 0.525443i \(-0.176100\pi\)
\(824\) −1.06150e61 + 1.89302e61i −0.618656 + 1.10328i
\(825\) −1.37558e60 −0.0781542
\(826\) 3.68516e60 + 6.33917e59i 0.204115 + 0.0351117i
\(827\) 1.42009e61i 0.766831i 0.923576 + 0.383416i \(0.125252\pi\)
−0.923576 + 0.383416i \(0.874748\pi\)
\(828\) 9.83895e59 2.77522e60i 0.0517979 0.146104i
\(829\) −5.95082e60 −0.305444 −0.152722 0.988269i \(-0.548804\pi\)
−0.152722 + 0.988269i \(0.548804\pi\)
\(830\) 6.88219e59 4.00084e60i 0.0344419 0.200222i
\(831\) 1.73790e61i 0.848014i
\(832\) −7.81613e60 1.27861e61i −0.371879 0.608342i
\(833\) −4.18517e60 −0.194164
\(834\) −3.33478e61 5.73645e60i −1.50862 0.259511i
\(835\) 9.25575e60i 0.408315i
\(836\) 2.91445e60 + 1.03326e60i 0.125379 + 0.0444504i
\(837\) 4.83334e61 2.02774
\(838\) −5.53537e60 + 3.21789e61i −0.226476 + 1.31658i
\(839\) 1.32492e61i 0.528675i −0.964430 0.264338i \(-0.914847\pi\)
0.964430 0.264338i \(-0.0851533\pi\)
\(840\) 1.00918e61 + 5.65891e60i 0.392738 + 0.220225i
\(841\) −2.39029e61 −0.907265
\(842\) −4.30290e61 7.40179e60i −1.59297 0.274020i
\(843\) 1.19757e61i 0.432434i
\(844\) −7.38239e60 + 2.08231e61i −0.260019 + 0.733423i
\(845\) 5.57602e60 0.191573
\(846\) −2.71184e59 + 1.57648e60i −0.00908837 + 0.0528336i
\(847\) 4.00708e61i 1.31002i
\(848\) −3.81212e61 3.09160e61i −1.21578 0.985984i
\(849\) −2.60214e61 −0.809597
\(850\) −7.08113e60 1.21809e60i −0.214934 0.0369727i
\(851\) 5.59568e60i 0.165704i
\(852\) 2.25860e61 + 8.00737e60i 0.652541 + 0.231344i
\(853\) 2.31643e61 0.652964 0.326482 0.945203i \(-0.394137\pi\)
0.326482 + 0.945203i \(0.394137\pi\)
\(854\) −1.08394e61 + 6.30129e61i −0.298119 + 1.73306i
\(855\) 4.37439e60i 0.117389i
\(856\) 3.33870e61 5.95406e61i 0.874236 1.55906i
\(857\) 3.00133e61 0.766860 0.383430 0.923570i \(-0.374743\pi\)
0.383430 + 0.923570i \(0.374743\pi\)
\(858\) −2.59699e60 4.46731e59i −0.0647495 0.0111381i
\(859\) 1.33009e60i 0.0323611i −0.999869 0.0161806i \(-0.994849\pi\)
0.999869 0.0161806i \(-0.00515065\pi\)
\(860\) 8.69228e60 2.45179e61i 0.206379 0.582124i
\(861\) 7.37263e61 1.70827
\(862\) 1.01967e61 5.92767e61i 0.230573 1.34039i
\(863\) 7.89149e61i 1.74153i −0.491695 0.870767i \(-0.663623\pi\)
0.491695 0.870767i \(-0.336377\pi\)
\(864\) −3.77607e61 + 3.30545e61i −0.813301 + 0.711938i
\(865\) −1.30230e61 −0.273762
\(866\) −3.01347e61 5.18374e60i −0.618289 0.106357i
\(867\) 4.06737e61i 0.814541i
\(868\) 1.19836e62 + 4.24854e61i 2.34247 + 0.830473i
\(869\) 5.66712e60 0.108130
\(870\) −9.42083e59 + 5.47663e60i −0.0175463 + 0.102002i
\(871\) 5.76902e60i 0.104887i
\(872\) 1.79421e61 + 1.00609e61i 0.318439 + 0.178563i
\(873\) 1.44961e61 0.251162
\(874\) 4.75342e61 + 8.17678e60i 0.804019 + 0.138306i
\(875\) 5.77774e61i 0.954090i
\(876\) −1.19852e61 + 3.38060e61i −0.193223 + 0.545013i
\(877\) 1.97462e61 0.310808 0.155404 0.987851i \(-0.450332\pi\)
0.155404 + 0.987851i \(0.450332\pi\)
\(878\) −4.16408e60 + 2.42071e61i −0.0639932 + 0.372013i
\(879\) 9.87438e60i 0.148164i
\(880\) −1.76992e60 + 2.18242e60i −0.0259309 + 0.0319743i
\(881\) −1.24161e62 −1.77619 −0.888095 0.459659i \(-0.847972\pi\)
−0.888095 + 0.459659i \(0.847972\pi\)
\(882\) −1.27457e61 2.19251e60i −0.178043 0.0306267i
\(883\) 2.67978e61i 0.365531i −0.983157 0.182765i \(-0.941495\pi\)
0.983157 0.182765i \(-0.0585049\pi\)
\(884\) −1.29730e61 4.59931e60i −0.172800 0.0612626i
\(885\) −4.08494e60 −0.0531346
\(886\) 2.01059e61 1.16882e62i 0.255397 1.48470i
\(887\) 1.30509e62i 1.61899i 0.587124 + 0.809497i \(0.300260\pi\)
−0.587124 + 0.809497i \(0.699740\pi\)
\(888\) −9.00538e60 + 1.60597e61i −0.109101 + 0.194565i
\(889\) −1.74068e62 −2.05960
\(890\) −4.94835e61 8.51209e60i −0.571834 0.0983662i
\(891\) 6.58503e60i 0.0743235i
\(892\) 4.36632e61 1.23159e62i 0.481342 1.35770i
\(893\) −2.62030e61 −0.282144
\(894\) −2.04254e60 + 1.18739e61i −0.0214824 + 0.124884i
\(895\) 4.08076e61i 0.419234i
\(896\) −1.22678e62 + 4.87624e61i −1.23111 + 0.489347i
\(897\) −4.11030e61 −0.402933
\(898\) 1.64897e62 + 2.83655e61i 1.57910 + 0.271636i
\(899\) 6.10671e61i 0.571286i
\(900\) −2.09271e61 7.41926e60i −0.191257 0.0678060i
\(901\) −4.50807e61 −0.402504
\(902\) −3.03543e60 + 1.76459e61i −0.0264779 + 0.153924i
\(903\) 2.14902e62i 1.83146i
\(904\) 7.72604e61 + 4.33234e61i 0.643310 + 0.360732i
\(905\) −2.08403e61 −0.169545
\(906\) 5.36589e61 + 9.23034e60i 0.426530 + 0.0733712i
\(907\) 1.86719e62i 1.45022i 0.688631 + 0.725112i \(0.258212\pi\)
−0.688631 + 0.725112i \(0.741788\pi\)
\(908\) −2.32769e61 + 6.56559e61i −0.176653 + 0.498277i
\(909\) 5.85592e61 0.434264
\(910\) −8.61104e60 + 5.00587e61i −0.0624003 + 0.362753i
\(911\) 1.33909e62i 0.948253i −0.880457 0.474126i \(-0.842764\pi\)
0.880457 0.474126i \(-0.157236\pi\)
\(912\) −1.23264e62 9.99663e61i −0.852995 0.691770i
\(913\) 8.14490e60 0.0550807
\(914\) 3.52684e61 + 6.06682e60i 0.233085 + 0.0400951i
\(915\) 6.98488e61i 0.451145i
\(916\) 6.66771e60 + 2.36389e60i 0.0420893 + 0.0149219i
\(917\) 1.87670e62 1.15781
\(918\) −7.81415e60 + 4.54261e61i −0.0471179 + 0.273911i
\(919\) 9.20724e61i 0.542630i −0.962491 0.271315i \(-0.912542\pi\)
0.962491 0.271315i \(-0.0874585\pi\)
\(920\) −2.14367e61 + 3.82291e61i −0.123485 + 0.220216i
\(921\) 1.16334e62 0.655021
\(922\) 2.11742e62 + 3.64237e61i 1.16536 + 0.200463i
\(923\) 1.05202e62i 0.565963i
\(924\) −7.75677e60 + 2.18791e61i −0.0407915 + 0.115059i
\(925\) −4.21954e61 −0.216914
\(926\) 3.90145e61 2.26803e62i 0.196063 1.13977i
\(927\) 6.15998e61i 0.302625i
\(928\) −4.17629e61 4.77089e61i −0.200578 0.229135i
\(929\) 2.24606e62 1.05461 0.527304 0.849677i \(-0.323203\pi\)
0.527304 + 0.849677i \(0.323203\pi\)
\(930\) −1.36887e62 2.35472e61i −0.628378 0.108093i
\(931\) 2.11850e62i 0.950790i
\(932\) −2.44724e62 8.67614e61i −1.07384 0.380708i
\(933\) 2.03249e62 0.871997
\(934\) −3.37010e61 + 1.95914e62i −0.141370 + 0.821830i
\(935\) 2.58084e60i 0.0105856i
\(936\) −3.70993e61 2.08033e61i −0.148790 0.0834331i
\(937\) −4.19898e62 −1.64669 −0.823345 0.567541i \(-0.807895\pi\)
−0.823345 + 0.567541i \(0.807895\pi\)
\(938\) −5.00850e61 8.61556e60i −0.192065 0.0330388i
\(939\) 1.13637e62i 0.426129i
\(940\) 7.95641e60 2.24422e61i 0.0291764 0.0822965i
\(941\) 4.11281e62 1.47488 0.737439 0.675414i \(-0.236035\pi\)
0.737439 + 0.675414i \(0.236035\pi\)
\(942\) −6.39067e61 + 3.71510e62i −0.224118 + 1.30287i
\(943\) 2.79286e62i 0.957863i
\(944\) 2.93583e61 3.62005e61i 0.0984733 0.121424i
\(945\) 1.70098e62 0.557995
\(946\) 5.14355e61 + 8.84787e60i 0.165025 + 0.0283874i
\(947\) 1.14975e62i 0.360789i 0.983594 + 0.180395i \(0.0577375\pi\)
−0.983594 + 0.180395i \(0.942262\pi\)
\(948\) −2.74144e62 9.71917e61i −0.841401 0.298301i
\(949\) −1.57463e62 −0.472702
\(950\) 6.16586e61 3.58441e62i 0.181050 1.05250i
\(951\) 4.83571e62i 1.38889i
\(952\) −5.93041e61 + 1.05760e62i −0.166613 + 0.297128i
\(953\) 5.01879e62 1.37927 0.689633 0.724159i \(-0.257772\pi\)
0.689633 + 0.724159i \(0.257772\pi\)
\(954\) −1.37291e62 2.36167e61i −0.369085 0.0634896i
\(955\) 1.07713e62i 0.283267i
\(956\) −1.08561e62 + 3.06212e62i −0.279291 + 0.787782i
\(957\) −1.11493e61 −0.0280606
\(958\) 8.39189e61 4.87847e62i 0.206626 1.20118i
\(959\) 8.90302e62i 2.14460i
\(960\) 1.23047e62 7.52188e61i 0.289986 0.177268i
\(961\) −1.09266e63 −2.51938
\(962\) −7.96616e61 1.37033e61i −0.179710 0.0309135i
\(963\) 1.93748e62i 0.427646i
\(964\) 8.99586e61 + 3.18929e61i 0.194279 + 0.0688773i
\(965\) 2.44838e62 0.517375
\(966\) −6.13840e61 + 3.56845e62i −0.126922 + 0.737836i
\(967\) 7.61171e62i 1.54002i 0.638032 + 0.770010i \(0.279749\pi\)
−0.638032 + 0.770010i \(0.720251\pi\)
\(968\) 4.35651e62 + 2.44289e62i 0.862494 + 0.483639i
\(969\) −1.45768e62 −0.282398
\(970\) −2.12655e62 3.65807e61i −0.403153 0.0693499i
\(971\) 5.06333e62i 0.939360i −0.882837 0.469680i \(-0.844369\pi\)
0.882837 0.469680i \(-0.155631\pi\)
\(972\) −8.60018e61 + 2.42581e62i −0.156141 + 0.440418i
\(973\) −1.30862e63 −2.32510
\(974\) −3.80042e61 + 2.20931e62i −0.0660836 + 0.384165i
\(975\) 3.09946e62i 0.527459i
\(976\) 6.18996e62 + 5.02000e62i 1.03096 + 0.836098i
\(977\) 5.75301e61 0.0937797 0.0468899 0.998900i \(-0.485069\pi\)
0.0468899 + 0.998900i \(0.485069\pi\)
\(978\) −1.68446e62 2.89758e61i −0.268747 0.0462296i
\(979\) 1.00738e62i 0.157311i
\(980\) 1.81444e62 + 6.43272e61i 0.277329 + 0.0983211i
\(981\) 5.83843e61 0.0873468
\(982\) 5.99776e61 3.48669e62i 0.0878310 0.510589i
\(983\) 5.65404e62i 0.810466i 0.914213 + 0.405233i \(0.132810\pi\)
−0.914213 + 0.405233i \(0.867190\pi\)
\(984\) 4.49467e62 8.01553e62i 0.630668 1.12470i
\(985\) 1.69923e62 0.233395
\(986\) −5.73939e61 9.87283e60i −0.0771703 0.0132748i
\(987\) 1.96709e62i 0.258919i
\(988\) 2.32813e62 6.56685e62i 0.299994 0.846177i
\(989\) 8.14080e62 1.02694
\(990\) −1.35204e60 + 7.85983e60i −0.00166974 + 0.00970675i
\(991\) 1.77300e62i 0.214369i 0.994239 + 0.107184i \(0.0341835\pi\)
−0.994239 + 0.107184i \(0.965816\pi\)
\(992\) 1.19248e63 1.04385e63i 1.41158 1.23565i
\(993\) 5.16615e62 0.598733
\(994\) 9.13333e62 + 1.57110e62i 1.03637 + 0.178275i
\(995\) 1.48465e62i 0.164946i
\(996\) −3.94005e62 1.39686e62i −0.428603 0.151952i
\(997\) −6.85556e62 −0.730205 −0.365102 0.930967i \(-0.618966\pi\)
−0.365102 + 0.930967i \(0.618966\pi\)
\(998\) −8.11291e61 + 4.71629e62i −0.0846127 + 0.491880i
\(999\) 2.70687e62i 0.276435i
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 4.43.b.a.3.20 yes 20
4.3 odd 2 inner 4.43.b.a.3.19 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4.43.b.a.3.19 20 4.3 odd 2 inner
4.43.b.a.3.20 yes 20 1.1 even 1 trivial