Properties

Label 14.16.c.a.9.5
Level $14$
Weight $16$
Character 14.9
Analytic conductor $19.977$
Analytic rank $0$
Dimension $10$
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] = [14,16,Mod(9,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 16, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.9");
 
S:= CuspForms(chi, 16);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.9770907140\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2 x^{9} + 11041039 x^{8} + 10251836788 x^{7} + 100086056086567 x^{6} + \cdots + 12\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{3}\cdot 5^{2}\cdot 7^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.5
Root \(1594.44 - 2761.64i\) of defining polynomial
Character \(\chi\) \(=\) 14.9
Dual form 14.16.c.a.11.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-64.0000 + 110.851i) q^{2} +(3386.37 + 5865.37i) q^{3} +(-8192.00 - 14189.0i) q^{4} +(127571. - 220960. i) q^{5} -866911. q^{6} +(-273416. + 2.16167e6i) q^{7} +2.09715e6 q^{8} +(-1.57606e7 + 2.72981e7i) q^{9} +O(q^{10})\) \(q+(-64.0000 + 110.851i) q^{2} +(3386.37 + 5865.37i) q^{3} +(-8192.00 - 14189.0i) q^{4} +(127571. - 220960. i) q^{5} -866911. q^{6} +(-273416. + 2.16167e6i) q^{7} +2.09715e6 q^{8} +(-1.57606e7 + 2.72981e7i) q^{9} +(1.63291e7 + 2.82829e7i) q^{10} +(2.83184e7 + 4.90489e7i) q^{11} +(5.54823e7 - 9.60982e7i) q^{12} -3.32442e8 q^{13} +(-2.22125e8 - 1.68655e8i) q^{14} +1.72801e9 q^{15} +(-1.34218e8 + 2.32472e8i) q^{16} +(4.48427e8 + 7.76699e8i) q^{17} +(-2.01735e9 - 3.49416e9i) q^{18} +(-2.15919e9 + 3.73982e9i) q^{19} -4.18025e9 q^{20} +(-1.36049e10 + 5.71652e9i) q^{21} -7.24952e9 q^{22} +(1.81000e9 - 3.13501e9i) q^{23} +(7.10174e9 + 1.23006e10i) q^{24} +(-1.72901e10 - 2.99473e10i) q^{25} +(2.12763e10 - 3.68517e10i) q^{26} -1.16303e11 q^{27} +(3.29116e10 - 1.38289e10i) q^{28} +4.50225e10 q^{29} +(-1.10593e11 + 1.91553e11i) q^{30} +(-8.76950e10 - 1.51892e11i) q^{31} +(-1.71799e10 - 2.97564e10i) q^{32} +(-1.91793e11 + 3.32196e11i) q^{33} -1.14797e11 q^{34} +(4.42762e11 + 3.36181e11i) q^{35} +5.16443e11 q^{36} +(-3.61683e11 + 6.26453e11i) q^{37} +(-2.76376e11 - 4.78697e11i) q^{38} +(-1.12577e12 - 1.94990e12i) q^{39} +(2.67536e11 - 4.63386e11i) q^{40} +2.11168e12 q^{41} +(2.37028e11 - 1.87397e12i) q^{42} +4.29894e11 q^{43} +(4.63969e11 - 8.03618e11i) q^{44} +(4.02119e12 + 6.96491e12i) q^{45} +(2.31680e11 + 4.01281e11i) q^{46} +(5.51759e11 - 9.55675e11i) q^{47} -1.81804e12 q^{48} +(-4.59805e12 - 1.18207e12i) q^{49} +4.42625e12 q^{50} +(-3.03708e12 + 5.26038e12i) q^{51} +(2.72337e12 + 4.71701e12i) q^{52} +(-1.61255e12 - 2.79302e12i) q^{53} +(7.44341e12 - 1.28924e13i) q^{54} +1.44505e13 q^{55} +(-5.73395e11 + 4.53334e12i) q^{56} -2.92472e13 q^{57} +(-2.88144e12 + 4.99081e12i) q^{58} +(1.38584e12 + 2.40035e12i) q^{59} +(-1.41559e13 - 2.45187e13i) q^{60} +(-3.44977e12 + 5.97517e12i) q^{61} +2.24499e13 q^{62} +(-5.47003e13 - 4.15329e13i) q^{63} +4.39805e12 q^{64} +(-4.24101e13 + 7.34564e13i) q^{65} +(-2.45496e13 - 4.25211e13i) q^{66} +(2.57287e13 + 4.45635e13i) q^{67} +(7.34703e12 - 1.27254e13i) q^{68} +2.45173e13 q^{69} +(-6.56028e13 + 2.75651e13i) q^{70} +4.86187e13 q^{71} +(-3.30523e13 + 5.72483e13i) q^{72} +(8.55296e13 + 1.48142e14i) q^{73} +(-4.62954e13 - 8.01859e13i) q^{74} +(1.17101e14 - 2.02825e14i) q^{75} +7.07522e13 q^{76} +(-1.13770e14 + 4.78042e13i) q^{77} +2.88198e14 q^{78} +(1.25430e14 - 2.17252e14i) q^{79} +(3.42446e13 + 5.93135e13i) q^{80} +(-1.67699e14 - 2.90464e14i) q^{81} +(-1.35148e14 + 2.34083e14i) q^{82} -5.88072e13 q^{83} +(1.92563e14 + 1.46209e14i) q^{84} +2.28826e14 q^{85} +(-2.75132e13 + 4.76543e13i) q^{86} +(1.52463e14 + 2.64074e14i) q^{87} +(5.93880e13 + 1.02863e14i) q^{88} +(-2.63516e14 + 4.56423e14i) q^{89} -1.02943e15 q^{90} +(9.08951e13 - 7.18630e14i) q^{91} -5.93100e13 q^{92} +(5.93936e14 - 1.02873e15i) q^{93} +(7.06252e13 + 1.22326e14i) q^{94} +(5.50900e14 + 9.54187e14i) q^{95} +(1.16355e14 - 2.01533e14i) q^{96} +1.86034e14 q^{97} +(4.25309e14 - 4.34047e14i) q^{98} -1.78526e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 640 q^{2} + 1979 q^{3} - 81920 q^{4} + 300953 q^{5} - 506624 q^{6} + 4054316 q^{7} + 20971520 q^{8} - 17367046 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 640 q^{2} + 1979 q^{3} - 81920 q^{4} + 300953 q^{5} - 506624 q^{6} + 4054316 q^{7} + 20971520 q^{8} - 17367046 q^{9} + 38521984 q^{10} + 14189887 q^{11} + 32423936 q^{12} - 772602348 q^{13} - 815024000 q^{14} + 1426775646 q^{15} - 1342177280 q^{16} - 145564295 q^{17} - 2222981888 q^{18} + 3550131629 q^{19} - 9861627904 q^{20} - 9326509885 q^{21} - 3632611072 q^{22} + 9869524537 q^{23} + 4150263808 q^{24} - 51839554204 q^{25} + 49446550272 q^{26} - 342946209778 q^{27} + 37897158656 q^{28} - 165255956188 q^{29} - 91313641344 q^{30} - 106825666677 q^{31} - 171798691840 q^{32} - 139826141649 q^{33} + 37264459520 q^{34} + 1475862848131 q^{35} + 569083363328 q^{36} - 596799401515 q^{37} + 454416848512 q^{38} - 2827795559666 q^{39} + 631144185856 q^{40} + 1756981189740 q^{41} + 3047643214336 q^{42} - 5305116572344 q^{43} + 232487108608 q^{44} + 10836341974062 q^{45} + 1263299140736 q^{46} + 4284391851525 q^{47} - 1062467534848 q^{48} + 1588100454346 q^{49} + 13270925876224 q^{50} - 8298359375823 q^{51} + 6329158434816 q^{52} - 4037801378823 q^{53} + 21948557425792 q^{54} - 47232884322970 q^{55} + 8502516908032 q^{56} - 75972269020058 q^{57} + 10576381196032 q^{58} + 6081930248483 q^{59} - 11688146092032 q^{60} + 29484338931189 q^{61} + 27347370669312 q^{62} - 151569370755754 q^{63} + 43980465111040 q^{64} + 78038741223618 q^{65} - 17897746131072 q^{66} - 2851190345117 q^{67} - 2384925409280 q^{68} - 41705305747074 q^{69} - 190125208943488 q^{70} + 190169727933856 q^{71} - 36421335252992 q^{72} + 284202883487269 q^{73} - 76390323393920 q^{74} - 151851953188876 q^{75} - 116330713219072 q^{76} - 656655421831969 q^{77} + 723915663274496 q^{78} + 536529323488905 q^{79} + 80786455789568 q^{80} + 23023662902123 q^{81} - 112446796143360 q^{82} - 949641950127416 q^{83} - 237292793479168 q^{84} + 24\!\cdots\!86 q^{85}+ \cdots - 989855214604404 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −64.0000 + 110.851i −0.353553 + 0.612372i
\(3\) 3386.37 + 5865.37i 0.893975 + 1.54841i 0.835068 + 0.550146i \(0.185428\pi\)
0.0589066 + 0.998263i \(0.481239\pi\)
\(4\) −8192.00 14189.0i −0.250000 0.433013i
\(5\) 127571. 220960.i 0.730260 1.26485i −0.226511 0.974009i \(-0.572732\pi\)
0.956772 0.290840i \(-0.0939346\pi\)
\(6\) −866911. −1.26427
\(7\) −273416. + 2.16167e6i −0.125484 + 0.992096i
\(8\) 2.09715e6 0.353553
\(9\) −1.57606e7 + 2.72981e7i −1.09838 + 1.90245i
\(10\) 1.63291e7 + 2.82829e7i 0.516372 + 0.894383i
\(11\) 2.83184e7 + 4.90489e7i 0.438151 + 0.758900i 0.997547 0.0700007i \(-0.0223001\pi\)
−0.559396 + 0.828901i \(0.688967\pi\)
\(12\) 5.54823e7 9.60982e7i 0.446987 0.774205i
\(13\) −3.32442e8 −1.46940 −0.734702 0.678390i \(-0.762678\pi\)
−0.734702 + 0.678390i \(0.762678\pi\)
\(14\) −2.22125e8 1.68655e8i −0.563167 0.427602i
\(15\) 1.72801e9 2.61134
\(16\) −1.34218e8 + 2.32472e8i −0.125000 + 0.216506i
\(17\) 4.48427e8 + 7.76699e8i 0.265048 + 0.459077i 0.967576 0.252579i \(-0.0812787\pi\)
−0.702528 + 0.711656i \(0.747945\pi\)
\(18\) −2.01735e9 3.49416e9i −0.776673 1.34524i
\(19\) −2.15919e9 + 3.73982e9i −0.554164 + 0.959840i 0.443804 + 0.896124i \(0.353629\pi\)
−0.997968 + 0.0637163i \(0.979705\pi\)
\(20\) −4.18025e9 −0.730260
\(21\) −1.36049e10 + 5.71652e9i −1.64835 + 0.692608i
\(22\) −7.24952e9 −0.619639
\(23\) 1.81000e9 3.13501e9i 0.110846 0.191991i −0.805266 0.592914i \(-0.797977\pi\)
0.916112 + 0.400923i \(0.131311\pi\)
\(24\) 7.10174e9 + 1.23006e10i 0.316068 + 0.547446i
\(25\) −1.72901e10 2.99473e10i −0.566560 0.981312i
\(26\) 2.12763e10 3.68517e10i 0.519513 0.899823i
\(27\) −1.16303e11 −2.13975
\(28\) 3.29116e10 1.38289e10i 0.460961 0.193688i
\(29\) 4.50225e10 0.484669 0.242334 0.970193i \(-0.422087\pi\)
0.242334 + 0.970193i \(0.422087\pi\)
\(30\) −1.10593e11 + 1.91553e11i −0.923247 + 1.59911i
\(31\) −8.76950e10 1.51892e11i −0.572482 0.991568i −0.996310 0.0858255i \(-0.972647\pi\)
0.423828 0.905743i \(-0.360686\pi\)
\(32\) −1.71799e10 2.97564e10i −0.0883883 0.153093i
\(33\) −1.91793e11 + 3.32196e11i −0.783392 + 1.35688i
\(34\) −1.14797e11 −0.374835
\(35\) 4.42762e11 + 3.36181e11i 1.16321 + 0.883207i
\(36\) 5.16443e11 1.09838
\(37\) −3.61683e11 + 6.26453e11i −0.626346 + 1.08486i 0.361932 + 0.932204i \(0.382117\pi\)
−0.988279 + 0.152660i \(0.951216\pi\)
\(38\) −2.76376e11 4.78697e11i −0.391853 0.678709i
\(39\) −1.12577e12 1.94990e12i −1.31361 2.27524i
\(40\) 2.67536e11 4.63386e11i 0.258186 0.447191i
\(41\) 2.11168e12 1.69336 0.846681 0.532100i \(-0.178597\pi\)
0.846681 + 0.532100i \(0.178597\pi\)
\(42\) 2.37028e11 1.87397e12i 0.158646 1.25428i
\(43\) 4.29894e11 0.241184 0.120592 0.992702i \(-0.461521\pi\)
0.120592 + 0.992702i \(0.461521\pi\)
\(44\) 4.63969e11 8.03618e11i 0.219076 0.379450i
\(45\) 4.02119e12 + 6.96491e12i 1.60421 + 2.77857i
\(46\) 2.31680e11 + 4.01281e11i 0.0783799 + 0.135758i
\(47\) 5.51759e11 9.55675e11i 0.158860 0.275154i −0.775598 0.631228i \(-0.782551\pi\)
0.934458 + 0.356073i \(0.115885\pi\)
\(48\) −1.81804e12 −0.446987
\(49\) −4.59805e12 1.18207e12i −0.968507 0.248985i
\(50\) 4.42625e12 0.801238
\(51\) −3.03708e12 + 5.26038e12i −0.473893 + 0.820807i
\(52\) 2.72337e12 + 4.71701e12i 0.367351 + 0.636271i
\(53\) −1.61255e12 2.79302e12i −0.188558 0.326591i 0.756212 0.654327i \(-0.227048\pi\)
−0.944770 + 0.327735i \(0.893715\pi\)
\(54\) 7.44341e12 1.28924e13i 0.756517 1.31033i
\(55\) 1.44505e13 1.27986
\(56\) −5.73395e11 + 4.53334e12i −0.0443654 + 0.350759i
\(57\) −2.92472e13 −1.98163
\(58\) −2.88144e12 + 4.99081e12i −0.171356 + 0.296798i
\(59\) 1.38584e12 + 2.40035e12i 0.0724976 + 0.125569i 0.899995 0.435900i \(-0.143570\pi\)
−0.827498 + 0.561469i \(0.810236\pi\)
\(60\) −1.41559e13 2.45187e13i −0.652834 1.13074i
\(61\) −3.44977e12 + 5.97517e12i −0.140545 + 0.243431i −0.927702 0.373321i \(-0.878219\pi\)
0.787157 + 0.616753i \(0.211552\pi\)
\(62\) 2.24499e13 0.809612
\(63\) −5.47003e13 4.15329e13i −1.74959 1.32843i
\(64\) 4.39805e12 0.125000
\(65\) −4.24101e13 + 7.34564e13i −1.07305 + 1.85857i
\(66\) −2.45496e13 4.25211e13i −0.553942 0.959456i
\(67\) 2.57287e13 + 4.45635e13i 0.518630 + 0.898293i 0.999766 + 0.0216468i \(0.00689094\pi\)
−0.481136 + 0.876646i \(0.659776\pi\)
\(68\) 7.34703e12 1.27254e13i 0.132524 0.229539i
\(69\) 2.45173e13 0.396374
\(70\) −6.56028e13 + 2.75651e13i −0.952110 + 0.400060i
\(71\) 4.86187e13 0.634404 0.317202 0.948358i \(-0.397257\pi\)
0.317202 + 0.948358i \(0.397257\pi\)
\(72\) −3.30523e13 + 5.72483e13i −0.388337 + 0.672619i
\(73\) 8.55296e13 + 1.48142e14i 0.906139 + 1.56948i 0.819380 + 0.573250i \(0.194318\pi\)
0.0867591 + 0.996229i \(0.472349\pi\)
\(74\) −4.62954e13 8.01859e13i −0.442894 0.767115i
\(75\) 1.17101e14 2.02825e14i 1.01298 1.75454i
\(76\) 7.07522e13 0.554164
\(77\) −1.13770e14 + 4.78042e13i −0.807882 + 0.339458i
\(78\) 2.88198e14 1.85773
\(79\) 1.25430e14 2.17252e14i 0.734852 1.27280i −0.219937 0.975514i \(-0.570585\pi\)
0.954788 0.297286i \(-0.0960816\pi\)
\(80\) 3.42446e13 + 5.93135e13i 0.182565 + 0.316212i
\(81\) −1.67699e14 2.90464e14i −0.814504 1.41076i
\(82\) −1.35148e14 + 2.34083e14i −0.598694 + 1.03697i
\(83\) −5.88072e13 −0.237873 −0.118936 0.992902i \(-0.537948\pi\)
−0.118936 + 0.992902i \(0.537948\pi\)
\(84\) 1.92563e14 + 1.46209e14i 0.711995 + 0.540605i
\(85\) 2.28826e14 0.774217
\(86\) −2.75132e13 + 4.76543e13i −0.0852713 + 0.147694i
\(87\) 1.52463e14 + 2.64074e14i 0.433282 + 0.750466i
\(88\) 5.93880e13 + 1.02863e14i 0.154910 + 0.268312i
\(89\) −2.63516e14 + 4.56423e14i −0.631513 + 1.09381i 0.355730 + 0.934589i \(0.384232\pi\)
−0.987243 + 0.159223i \(0.949101\pi\)
\(90\) −1.02943e15 −2.26870
\(91\) 9.08951e13 7.18630e14i 0.184387 1.45779i
\(92\) −5.93100e13 −0.110846
\(93\) 5.93936e14 1.02873e15i 1.02357 1.77287i
\(94\) 7.06252e13 + 1.22326e14i 0.112331 + 0.194563i
\(95\) 5.50900e14 + 9.54187e14i 0.809368 + 1.40187i
\(96\) 1.16355e14 2.01533e14i 0.158034 0.273723i
\(97\) 1.86034e14 0.233779 0.116889 0.993145i \(-0.462708\pi\)
0.116889 + 0.993145i \(0.462708\pi\)
\(98\) 4.25309e14 4.34047e14i 0.494890 0.505058i
\(99\) −1.78526e15 −1.92503
\(100\) −2.83280e14 + 4.90656e14i −0.283280 + 0.490656i
\(101\) −4.89317e14 8.47523e14i −0.454130 0.786577i 0.544507 0.838756i \(-0.316717\pi\)
−0.998638 + 0.0521793i \(0.983383\pi\)
\(102\) −3.88747e14 6.73329e14i −0.335093 0.580398i
\(103\) 1.51081e14 2.61681e14i 0.121041 0.209649i −0.799138 0.601148i \(-0.794710\pi\)
0.920178 + 0.391499i \(0.128043\pi\)
\(104\) −6.97182e14 −0.519513
\(105\) −4.72467e14 + 3.73539e15i −0.327682 + 2.59070i
\(106\) 4.12813e14 0.266661
\(107\) 7.97180e14 1.38076e15i 0.479930 0.831263i −0.519805 0.854285i \(-0.673995\pi\)
0.999735 + 0.0230218i \(0.00732872\pi\)
\(108\) 9.52757e14 + 1.65022e15i 0.534939 + 0.926541i
\(109\) 5.75242e14 + 9.96348e14i 0.301406 + 0.522050i 0.976455 0.215723i \(-0.0692108\pi\)
−0.675049 + 0.737773i \(0.735877\pi\)
\(110\) −9.24830e14 + 1.60185e15i −0.452498 + 0.783750i
\(111\) −4.89917e15 −2.23975
\(112\) −4.65830e14 3.53696e14i −0.199109 0.151180i
\(113\) 2.65586e14 0.106198 0.0530990 0.998589i \(-0.483090\pi\)
0.0530990 + 0.998589i \(0.483090\pi\)
\(114\) 1.87182e15 3.24209e15i 0.700614 1.21350i
\(115\) −4.61808e14 7.99874e14i −0.161893 0.280406i
\(116\) −3.68825e14 6.38823e14i −0.121167 0.209868i
\(117\) 5.23949e15 9.07505e15i 1.61397 2.79547i
\(118\) −3.54775e14 −0.102527
\(119\) −1.80157e15 + 7.56989e14i −0.488708 + 0.205346i
\(120\) 3.62391e15 0.923247
\(121\) 4.84758e14 8.39625e14i 0.116047 0.201000i
\(122\) −4.41570e14 7.64822e14i −0.0993805 0.172132i
\(123\) 7.15095e15 + 1.23858e16i 1.51382 + 2.62202i
\(124\) −1.43679e15 + 2.48860e15i −0.286241 + 0.495784i
\(125\) −1.03652e15 −0.194426
\(126\) 8.10479e15 3.40549e15i 1.43206 0.601728i
\(127\) 4.19039e15 0.697793 0.348896 0.937161i \(-0.386557\pi\)
0.348896 + 0.937161i \(0.386557\pi\)
\(128\) −2.81475e14 + 4.87529e14i −0.0441942 + 0.0765466i
\(129\) 1.45578e15 + 2.52149e15i 0.215612 + 0.373451i
\(130\) −5.42849e15 9.40242e15i −0.758759 1.31421i
\(131\) −2.03828e15 + 3.53040e15i −0.268985 + 0.465896i −0.968600 0.248624i \(-0.920022\pi\)
0.699615 + 0.714520i \(0.253355\pi\)
\(132\) 6.28469e15 0.783392
\(133\) −7.49389e15 5.68997e15i −0.882714 0.670228i
\(134\) −6.58655e15 −0.733453
\(135\) −1.48370e16 + 2.56984e16i −1.56258 + 2.70646i
\(136\) 9.40420e14 + 1.62886e15i 0.0937088 + 0.162308i
\(137\) −4.48804e14 7.77351e14i −0.0423304 0.0733183i 0.844084 0.536211i \(-0.180145\pi\)
−0.886414 + 0.462893i \(0.846812\pi\)
\(138\) −1.56911e15 + 2.71778e15i −0.140139 + 0.242728i
\(139\) 1.64387e16 1.39077 0.695386 0.718637i \(-0.255234\pi\)
0.695386 + 0.718637i \(0.255234\pi\)
\(140\) 1.14295e15 9.03632e15i 0.0916361 0.724488i
\(141\) 7.47385e15 0.568069
\(142\) −3.11160e15 + 5.38944e15i −0.224296 + 0.388491i
\(143\) −9.41424e15 1.63059e16i −0.643821 1.11513i
\(144\) −4.23070e15 7.32779e15i −0.274596 0.475613i
\(145\) 5.74358e15 9.94818e15i 0.353934 0.613032i
\(146\) −2.18956e16 −1.28147
\(147\) −8.63743e15 3.09722e16i −0.480291 1.72223i
\(148\) 1.18516e16 0.626346
\(149\) −2.08714e15 + 3.61504e15i −0.104871 + 0.181642i −0.913685 0.406422i \(-0.866776\pi\)
0.808815 + 0.588064i \(0.200110\pi\)
\(150\) 1.49889e16 + 2.59616e16i 0.716286 + 1.24064i
\(151\) −1.03481e16 1.79234e16i −0.470470 0.814877i 0.528960 0.848647i \(-0.322582\pi\)
−0.999430 + 0.0337696i \(0.989249\pi\)
\(152\) −4.52814e15 + 7.84297e15i −0.195927 + 0.339355i
\(153\) −2.82699e16 −1.16450
\(154\) 1.98214e15 1.56710e16i 0.0777549 0.614741i
\(155\) −4.47494e16 −1.67224
\(156\) −1.84447e16 + 3.19471e16i −0.656805 + 1.13762i
\(157\) 2.30082e16 + 3.98514e16i 0.780972 + 1.35268i 0.931376 + 0.364059i \(0.118609\pi\)
−0.150403 + 0.988625i \(0.548057\pi\)
\(158\) 1.60551e16 + 2.78082e16i 0.519619 + 0.900006i
\(159\) 1.09214e16 1.89164e16i 0.337131 0.583929i
\(160\) −8.76663e15 −0.258186
\(161\) 6.28196e15 + 4.76978e15i 0.176564 + 0.134061i
\(162\) 4.29310e16 1.15188
\(163\) 5.30901e15 9.19548e15i 0.136021 0.235596i −0.789966 0.613151i \(-0.789902\pi\)
0.925987 + 0.377555i \(0.123235\pi\)
\(164\) −1.72989e16 2.99626e16i −0.423341 0.733248i
\(165\) 4.89347e16 + 8.47573e16i 1.14416 + 1.98174i
\(166\) 3.76366e15 6.51885e15i 0.0841008 0.145667i
\(167\) 6.77764e16 1.44779 0.723894 0.689912i \(-0.242351\pi\)
0.723894 + 0.689912i \(0.242351\pi\)
\(168\) −2.85315e16 + 1.19884e16i −0.582780 + 0.244874i
\(169\) 5.93320e16 1.15915
\(170\) −1.46448e16 + 2.53656e16i −0.273727 + 0.474109i
\(171\) −6.80601e16 1.17884e17i −1.21737 2.10854i
\(172\) −3.52169e15 6.09975e15i −0.0602959 0.104436i
\(173\) 5.44024e16 9.42277e16i 0.891810 1.54466i 0.0541055 0.998535i \(-0.482769\pi\)
0.837704 0.546124i \(-0.183897\pi\)
\(174\) −3.90306e16 −0.612753
\(175\) 6.94634e16 2.91873e16i 1.04465 0.438943i
\(176\) −1.52033e16 −0.219076
\(177\) −9.38595e15 + 1.62569e16i −0.129622 + 0.224512i
\(178\) −3.37301e16 5.84222e16i −0.446547 0.773442i
\(179\) 6.75423e16 + 1.16987e17i 0.857390 + 1.48504i 0.874410 + 0.485188i \(0.161249\pi\)
−0.0170203 + 0.999855i \(0.505418\pi\)
\(180\) 6.58832e16 1.14113e17i 0.802105 1.38929i
\(181\) −1.67728e17 −1.95892 −0.979460 0.201640i \(-0.935373\pi\)
−0.979460 + 0.201640i \(0.935373\pi\)
\(182\) 7.38437e16 + 5.60681e16i 0.827519 + 0.628320i
\(183\) −4.67288e16 −0.502576
\(184\) 3.79584e15 6.57459e15i 0.0391899 0.0678789i
\(185\) 9.22806e16 + 1.59835e17i 0.914792 + 1.58447i
\(186\) 7.60238e16 + 1.31677e17i 0.723773 + 1.25361i
\(187\) −2.53975e16 + 4.39898e16i −0.232263 + 0.402290i
\(188\) −1.80800e16 −0.158860
\(189\) 3.17992e16 2.51409e17i 0.268505 2.12284i
\(190\) −1.41030e17 −1.14462
\(191\) −4.10647e16 + 7.11261e16i −0.320419 + 0.554982i −0.980575 0.196147i \(-0.937157\pi\)
0.660156 + 0.751129i \(0.270490\pi\)
\(192\) 1.48934e16 + 2.57962e16i 0.111747 + 0.193551i
\(193\) −2.13419e16 3.69652e16i −0.154011 0.266755i 0.778687 0.627412i \(-0.215886\pi\)
−0.932699 + 0.360657i \(0.882553\pi\)
\(194\) −1.19062e16 + 2.06221e16i −0.0826532 + 0.143160i
\(195\) −5.74465e17 −3.83711
\(196\) 2.08949e16 + 7.49250e16i 0.134313 + 0.481622i
\(197\) 1.82861e17 1.13142 0.565711 0.824603i \(-0.308602\pi\)
0.565711 + 0.824603i \(0.308602\pi\)
\(198\) 1.14257e17 1.97898e17i 0.680601 1.17883i
\(199\) 3.31199e16 + 5.73653e16i 0.189972 + 0.329042i 0.945241 0.326374i \(-0.105827\pi\)
−0.755268 + 0.655416i \(0.772493\pi\)
\(200\) −3.62599e16 6.28039e16i −0.200309 0.346946i
\(201\) −1.74254e17 + 3.01817e17i −0.927284 + 1.60610i
\(202\) 1.25265e17 0.642237
\(203\) −1.23099e16 + 9.73238e16i −0.0608183 + 0.480838i
\(204\) 9.95192e16 0.473893
\(205\) 2.69390e17 4.66597e17i 1.23660 2.14185i
\(206\) 1.93384e16 + 3.34951e16i 0.0855888 + 0.148244i
\(207\) 5.70533e16 + 9.88191e16i 0.243502 + 0.421758i
\(208\) 4.46197e16 7.72835e16i 0.183676 0.318135i
\(209\) −2.44579e17 −0.971230
\(210\) −3.83835e17 2.91439e17i −1.47062 1.11661i
\(211\) 7.29432e16 0.269691 0.134846 0.990867i \(-0.456946\pi\)
0.134846 + 0.990867i \(0.456946\pi\)
\(212\) −2.64200e16 + 4.57608e16i −0.0942788 + 0.163296i
\(213\) 1.64641e17 + 2.85167e17i 0.567141 + 0.982317i
\(214\) 1.02039e17 + 1.76737e17i 0.339362 + 0.587792i
\(215\) 5.48421e16 9.49893e16i 0.176127 0.305061i
\(216\) −2.43906e17 −0.756517
\(217\) 3.52317e17 1.48038e17i 1.05557 0.443531i
\(218\) −1.47262e17 −0.426252
\(219\) −5.79270e17 + 1.00333e18i −1.62013 + 2.80615i
\(220\) −1.18378e17 2.05037e17i −0.319964 0.554195i
\(221\) −1.49076e17 2.58208e17i −0.389463 0.674570i
\(222\) 3.13547e17 5.43079e17i 0.791872 1.37156i
\(223\) −9.19576e16 −0.224544 −0.112272 0.993678i \(-0.535813\pi\)
−0.112272 + 0.993678i \(0.535813\pi\)
\(224\) 6.90207e16 2.90013e16i 0.162974 0.0684789i
\(225\) 1.09001e18 2.48920
\(226\) −1.69975e16 + 2.94405e16i −0.0375467 + 0.0650327i
\(227\) −1.25879e17 2.18029e17i −0.269005 0.465930i 0.699600 0.714534i \(-0.253361\pi\)
−0.968605 + 0.248604i \(0.920028\pi\)
\(228\) 2.39593e17 + 4.14988e17i 0.495409 + 0.858073i
\(229\) 2.22352e17 3.85126e17i 0.444914 0.770613i −0.553133 0.833093i \(-0.686568\pi\)
0.998046 + 0.0624803i \(0.0199011\pi\)
\(230\) 1.18223e17 0.228951
\(231\) −6.65658e17 5.05421e17i −1.24785 0.947466i
\(232\) 9.44191e16 0.171356
\(233\) −1.98864e17 + 3.44443e17i −0.349452 + 0.605269i −0.986152 0.165843i \(-0.946966\pi\)
0.636700 + 0.771111i \(0.280299\pi\)
\(234\) 6.70654e17 + 1.16161e18i 1.14125 + 1.97670i
\(235\) −1.40777e17 2.43833e17i −0.232019 0.401869i
\(236\) 2.27056e16 3.93273e16i 0.0362488 0.0627847i
\(237\) 1.69902e18 2.62776
\(238\) 3.13875e16 2.48154e17i 0.0470359 0.371872i
\(239\) 3.24811e17 0.471680 0.235840 0.971792i \(-0.424216\pi\)
0.235840 + 0.971792i \(0.424216\pi\)
\(240\) −2.31930e17 + 4.01715e17i −0.326417 + 0.565371i
\(241\) −3.18834e17 5.52236e17i −0.434947 0.753350i 0.562344 0.826903i \(-0.309900\pi\)
−0.997291 + 0.0735529i \(0.976566\pi\)
\(242\) 6.20490e16 + 1.07472e17i 0.0820577 + 0.142128i
\(243\) 3.01371e17 5.21990e17i 0.386416 0.669292i
\(244\) 1.13042e17 0.140545
\(245\) −8.47769e17 + 8.65186e17i −1.02219 + 1.04319i
\(246\) −1.83064e18 −2.14087
\(247\) 7.17805e17 1.24328e18i 0.814291 1.41039i
\(248\) −1.83910e17 3.18541e17i −0.202403 0.350572i
\(249\) −1.99143e17 3.44926e17i −0.212652 0.368325i
\(250\) 6.63375e16 1.14900e17i 0.0687399 0.119061i
\(251\) −1.50514e18 −1.51365 −0.756823 0.653620i \(-0.773250\pi\)
−0.756823 + 0.653620i \(0.773250\pi\)
\(252\) −1.41204e17 + 1.11638e18i −0.137830 + 1.08970i
\(253\) 2.05025e17 0.194269
\(254\) −2.68185e17 + 4.64510e17i −0.246707 + 0.427309i
\(255\) 7.74889e17 + 1.34215e18i 0.692131 + 1.19881i
\(256\) −3.60288e16 6.24037e16i −0.0312500 0.0541266i
\(257\) −2.22116e17 + 3.84715e17i −0.187103 + 0.324072i −0.944283 0.329134i \(-0.893243\pi\)
0.757180 + 0.653206i \(0.226576\pi\)
\(258\) −3.72680e17 −0.304922
\(259\) −1.25529e18 9.53120e17i −0.997692 0.757529i
\(260\) 1.38969e18 1.07305
\(261\) −7.09581e17 + 1.22903e18i −0.532351 + 0.922060i
\(262\) −2.60899e17 4.51891e17i −0.190201 0.329438i
\(263\) 5.98835e17 + 1.03721e18i 0.424267 + 0.734851i 0.996352 0.0853429i \(-0.0271986\pi\)
−0.572085 + 0.820194i \(0.693865\pi\)
\(264\) −4.02220e17 + 6.96666e17i −0.276971 + 0.479728i
\(265\) −8.22859e17 −0.550784
\(266\) 1.11035e18 4.66549e17i 0.722516 0.303588i
\(267\) −3.56945e18 −2.25823
\(268\) 4.21539e17 7.30128e17i 0.259315 0.449146i
\(269\) −7.98712e17 1.38341e18i −0.477802 0.827578i 0.521874 0.853023i \(-0.325233\pi\)
−0.999676 + 0.0254447i \(0.991900\pi\)
\(270\) −1.89913e18 3.28939e18i −1.10491 1.91376i
\(271\) 3.26988e17 5.66360e17i 0.185039 0.320496i −0.758551 0.651614i \(-0.774092\pi\)
0.943590 + 0.331117i \(0.107426\pi\)
\(272\) −2.40748e17 −0.132524
\(273\) 4.52283e18 1.90041e18i 2.42209 1.01772i
\(274\) 1.14894e17 0.0598642
\(275\) 9.79254e17 1.69612e18i 0.496478 0.859926i
\(276\) −2.00846e17 3.47875e17i −0.0990934 0.171635i
\(277\) 1.09837e18 + 1.90244e18i 0.527415 + 0.913509i 0.999489 + 0.0319507i \(0.0101720\pi\)
−0.472075 + 0.881559i \(0.656495\pi\)
\(278\) −1.05207e18 + 1.82225e18i −0.491712 + 0.851670i
\(279\) 5.52849e18 2.51522
\(280\) 9.28538e17 + 7.05022e17i 0.411258 + 0.312261i
\(281\) −7.38264e17 −0.318357 −0.159178 0.987250i \(-0.550885\pi\)
−0.159178 + 0.987250i \(0.550885\pi\)
\(282\) −4.78326e17 + 8.28486e17i −0.200843 + 0.347870i
\(283\) −5.73433e17 9.93216e17i −0.234469 0.406111i 0.724650 0.689118i \(-0.242002\pi\)
−0.959118 + 0.283006i \(0.908668\pi\)
\(284\) −3.98284e17 6.89849e17i −0.158601 0.274705i
\(285\) −3.73111e18 + 6.46247e18i −1.44711 + 2.50647i
\(286\) 2.41005e18 0.910500
\(287\) −5.77369e17 + 4.56476e18i −0.212490 + 1.67998i
\(288\) 1.08306e18 0.388337
\(289\) 1.02904e18 1.78234e18i 0.359499 0.622670i
\(290\) 7.35178e17 + 1.27337e18i 0.250269 + 0.433479i
\(291\) 6.29981e17 + 1.09116e18i 0.208992 + 0.361985i
\(292\) 1.40132e18 2.42715e18i 0.453070 0.784740i
\(293\) −2.89255e18 −0.911537 −0.455768 0.890098i \(-0.650635\pi\)
−0.455768 + 0.890098i \(0.650635\pi\)
\(294\) 3.98610e18 + 1.02475e18i 1.22446 + 0.314784i
\(295\) 7.07174e17 0.211768
\(296\) −7.58503e17 + 1.31377e18i −0.221447 + 0.383557i
\(297\) −3.29353e18 5.70456e18i −0.937536 1.62386i
\(298\) −2.67154e17 4.62725e17i −0.0741550 0.128440i
\(299\) −6.01720e17 + 1.04221e18i −0.162877 + 0.282112i
\(300\) −3.83717e18 −1.01298
\(301\) −1.17540e17 + 9.29288e17i −0.0302647 + 0.239277i
\(302\) 2.64910e18 0.665344
\(303\) 3.31402e18 5.74006e18i 0.811962 1.40636i
\(304\) −5.79602e17 1.00390e18i −0.138541 0.239960i
\(305\) 8.80182e17 + 1.52452e18i 0.205269 + 0.355537i
\(306\) 1.80927e18 3.13375e18i 0.411712 0.713106i
\(307\) 6.96752e18 1.54718 0.773589 0.633687i \(-0.218459\pi\)
0.773589 + 0.633687i \(0.218459\pi\)
\(308\) 1.61030e18 + 1.22267e18i 0.348960 + 0.264959i
\(309\) 2.04647e18 0.432830
\(310\) 2.86396e18 4.96053e18i 0.591228 1.02404i
\(311\) −3.71126e18 6.42810e18i −0.747857 1.29533i −0.948848 0.315734i \(-0.897749\pi\)
0.200990 0.979593i \(-0.435584\pi\)
\(312\) −2.36092e18 4.08923e18i −0.464431 0.804419i
\(313\) −1.08696e18 + 1.88268e18i −0.208753 + 0.361570i −0.951322 0.308199i \(-0.900274\pi\)
0.742569 + 0.669769i \(0.233607\pi\)
\(314\) −5.89011e18 −1.10446
\(315\) −1.61553e19 + 6.78816e18i −2.95791 + 1.24286i
\(316\) −4.11010e18 −0.734852
\(317\) −3.19571e17 + 5.53514e17i −0.0557986 + 0.0966460i −0.892575 0.450898i \(-0.851104\pi\)
0.836777 + 0.547544i \(0.184437\pi\)
\(318\) 1.39794e18 + 2.42130e18i 0.238388 + 0.412900i
\(319\) 1.27497e18 + 2.20831e18i 0.212358 + 0.367815i
\(320\) 5.61064e17 9.71792e17i 0.0912825 0.158106i
\(321\) 1.07982e19 1.71618
\(322\) −9.30781e17 + 3.91098e17i −0.144520 + 0.0607248i
\(323\) −3.87295e18 −0.587521
\(324\) −2.74758e18 + 4.75896e18i −0.407252 + 0.705381i
\(325\) 5.74795e18 + 9.95574e18i 0.832506 + 1.44194i
\(326\) 6.79553e17 + 1.17702e18i 0.0961815 + 0.166591i
\(327\) −3.89597e18 + 6.74801e18i −0.538899 + 0.933400i
\(328\) 4.42852e18 0.598694
\(329\) 1.91499e18 + 1.45402e18i 0.253045 + 0.192132i
\(330\) −1.25273e19 −1.61809
\(331\) −2.80383e18 + 4.85638e18i −0.354031 + 0.613200i −0.986952 0.161017i \(-0.948523\pi\)
0.632920 + 0.774217i \(0.281856\pi\)
\(332\) 4.81749e17 + 8.34413e17i 0.0594682 + 0.103002i
\(333\) −1.14007e19 1.97465e19i −1.37594 2.38319i
\(334\) −4.33769e18 + 7.51309e18i −0.511870 + 0.886585i
\(335\) 1.31290e19 1.51494
\(336\) 4.97083e17 3.93001e18i 0.0560898 0.443454i
\(337\) −1.36093e19 −1.50180 −0.750901 0.660415i \(-0.770380\pi\)
−0.750901 + 0.660415i \(0.770380\pi\)
\(338\) −3.79725e18 + 6.57703e18i −0.409821 + 0.709830i
\(339\) 8.99372e17 + 1.55776e18i 0.0949383 + 0.164438i
\(340\) −1.87454e18 3.24680e18i −0.193554 0.335246i
\(341\) 4.96677e18 8.60269e18i 0.501667 0.868913i
\(342\) 1.74234e19 1.72162
\(343\) 3.81242e18 9.61625e18i 0.368549 0.929608i
\(344\) 9.01553e17 0.0852713
\(345\) 3.12770e18 5.41734e18i 0.289456 0.501352i
\(346\) 6.96351e18 + 1.20611e19i 0.630605 + 1.09224i
\(347\) −1.41536e18 2.45147e18i −0.125428 0.217248i 0.796472 0.604675i \(-0.206697\pi\)
−0.921900 + 0.387427i \(0.873364\pi\)
\(348\) 2.49796e18 4.32659e18i 0.216641 0.375233i
\(349\) −2.05252e19 −1.74220 −0.871098 0.491110i \(-0.836591\pi\)
−0.871098 + 0.491110i \(0.836591\pi\)
\(350\) −1.21021e18 + 9.56809e18i −0.100543 + 0.794904i
\(351\) 3.86642e19 3.14416
\(352\) 9.73014e17 1.68531e18i 0.0774549 0.134156i
\(353\) −9.21441e18 1.59598e19i −0.718054 1.24371i −0.961770 0.273860i \(-0.911700\pi\)
0.243715 0.969847i \(-0.421634\pi\)
\(354\) −1.20140e18 2.08089e18i −0.0916566 0.158754i
\(355\) 6.20235e18 1.07428e19i 0.463280 0.802424i
\(356\) 8.63489e18 0.631513
\(357\) −1.05408e19 8.00344e18i −0.754853 0.573146i
\(358\) −1.72908e19 −1.21253
\(359\) −7.27400e18 + 1.25989e19i −0.499534 + 0.865218i −1.00000 0.000538108i \(-0.999829\pi\)
0.500466 + 0.865756i \(0.333162\pi\)
\(360\) 8.43306e18 + 1.46065e19i 0.567174 + 0.982374i
\(361\) −1.73361e18 3.00271e18i −0.114195 0.197792i
\(362\) 1.07346e19 1.85929e19i 0.692583 1.19959i
\(363\) 6.56628e18 0.414973
\(364\) −1.09412e19 + 4.59731e18i −0.677338 + 0.284605i
\(365\) 4.36445e19 2.64687
\(366\) 2.99064e18 5.17994e18i 0.177687 0.307763i
\(367\) 8.75092e18 + 1.51570e19i 0.509399 + 0.882306i 0.999941 + 0.0108878i \(0.00346576\pi\)
−0.490541 + 0.871418i \(0.663201\pi\)
\(368\) 4.85868e17 + 8.41548e17i 0.0277115 + 0.0479977i
\(369\) −3.32814e19 + 5.76450e19i −1.85996 + 3.22154i
\(370\) −2.36238e19 −1.29371
\(371\) 6.47847e18 2.72214e18i 0.347671 0.146085i
\(372\) −1.94621e19 −1.02357
\(373\) 1.67998e19 2.90981e19i 0.865941 1.49985i −0.000169634 1.00000i \(-0.500054\pi\)
0.866110 0.499853i \(-0.166613\pi\)
\(374\) −3.25088e18 5.63069e18i −0.164234 0.284462i
\(375\) −3.51006e18 6.07959e18i −0.173812 0.301051i
\(376\) 1.15712e18 2.00420e18i 0.0561656 0.0972817i
\(377\) −1.49674e19 −0.712174
\(378\) 2.58339e19 + 1.96152e19i 1.20504 + 0.914963i
\(379\) 6.94803e18 0.317737 0.158868 0.987300i \(-0.449215\pi\)
0.158868 + 0.987300i \(0.449215\pi\)
\(380\) 9.02595e18 1.56334e19i 0.404684 0.700933i
\(381\) 1.41902e19 + 2.45782e19i 0.623809 + 1.08047i
\(382\) −5.25628e18 9.10414e18i −0.226570 0.392432i
\(383\) 5.06565e18 8.77396e18i 0.214113 0.370855i −0.738884 0.673832i \(-0.764647\pi\)
0.952998 + 0.302977i \(0.0979804\pi\)
\(384\) −3.81272e18 −0.158034
\(385\) −3.95099e18 + 3.12371e19i −0.160602 + 1.26974i
\(386\) 5.46352e18 0.217805
\(387\) −6.77538e18 + 1.17353e19i −0.264912 + 0.458841i
\(388\) −1.52399e18 2.63963e18i −0.0584446 0.101229i
\(389\) −2.73787e18 4.74213e18i −0.102989 0.178382i 0.809926 0.586532i \(-0.199507\pi\)
−0.912915 + 0.408150i \(0.866174\pi\)
\(390\) 3.67658e19 6.36802e19i 1.35662 2.34974i
\(391\) 3.24661e18 0.117518
\(392\) −9.64281e18 2.47898e18i −0.342419 0.0880293i
\(393\) −2.76095e19 −0.961864
\(394\) −1.17031e19 + 2.02704e19i −0.400018 + 0.692852i
\(395\) −3.20026e19 5.54302e19i −1.07327 1.85895i
\(396\) 1.46248e19 + 2.53310e19i 0.481257 + 0.833562i
\(397\) −2.90981e19 + 5.03993e19i −0.939584 + 1.62741i −0.173335 + 0.984863i \(0.555454\pi\)
−0.766249 + 0.642544i \(0.777879\pi\)
\(398\) −8.47869e18 −0.268662
\(399\) 7.99667e18 6.32228e19i 0.248664 1.96597i
\(400\) 9.28253e18 0.283280
\(401\) 4.10953e18 7.11791e18i 0.123086 0.213192i −0.797897 0.602794i \(-0.794054\pi\)
0.920983 + 0.389602i \(0.127388\pi\)
\(402\) −2.23045e19 3.86326e19i −0.655688 1.13569i
\(403\) 2.91535e19 + 5.04954e19i 0.841208 + 1.45701i
\(404\) −8.01698e18 + 1.38858e19i −0.227065 + 0.393288i
\(405\) −8.55744e19 −2.37920
\(406\) −1.00006e19 7.59329e18i −0.272949 0.207245i
\(407\) −4.09691e19 −1.09774
\(408\) −6.36923e18 + 1.10318e19i −0.167547 + 0.290199i
\(409\) −2.19395e19 3.80003e19i −0.566632 0.981436i −0.996896 0.0787326i \(-0.974913\pi\)
0.430263 0.902703i \(-0.358421\pi\)
\(410\) 3.44819e19 + 5.97245e19i 0.874405 + 1.51451i
\(411\) 3.03963e18 5.26480e18i 0.0756846 0.131090i
\(412\) −4.95063e18 −0.121041
\(413\) −5.56766e18 + 2.33943e18i −0.133674 + 0.0561675i
\(414\) −1.46056e19 −0.344364
\(415\) −7.50211e18 + 1.29940e19i −0.173709 + 0.300873i
\(416\) 5.71132e18 + 9.89229e18i 0.129878 + 0.224956i
\(417\) 5.56675e19 + 9.64189e19i 1.24331 + 2.15348i
\(418\) 1.56531e19 2.71119e19i 0.343382 0.594755i
\(419\) 5.20972e19 1.12256 0.561279 0.827626i \(-0.310309\pi\)
0.561279 + 0.827626i \(0.310309\pi\)
\(420\) 5.68718e19 2.38965e19i 1.20372 0.505784i
\(421\) −5.70346e18 −0.118583 −0.0592915 0.998241i \(-0.518884\pi\)
−0.0592915 + 0.998241i \(0.518884\pi\)
\(422\) −4.66837e18 + 8.08585e18i −0.0953502 + 0.165151i
\(423\) 1.73921e19 + 3.01240e19i 0.348979 + 0.604449i
\(424\) −3.38176e18 5.85738e18i −0.0666652 0.115467i
\(425\) 1.55067e19 2.68583e19i 0.300332 0.520190i
\(426\) −4.21481e19 −0.802058
\(427\) −1.19731e19 9.09096e18i −0.223871 0.169981i
\(428\) −2.61220e19 −0.479930
\(429\) 6.37603e19 1.10436e20i 1.15112 1.99380i
\(430\) 7.01979e18 + 1.21586e19i 0.124541 + 0.215711i
\(431\) −1.76694e19 3.06044e19i −0.308066 0.533585i 0.669874 0.742475i \(-0.266348\pi\)
−0.977939 + 0.208890i \(0.933015\pi\)
\(432\) 1.56100e19 2.70373e19i 0.267469 0.463270i
\(433\) −9.85742e18 −0.165998 −0.0829992 0.996550i \(-0.526450\pi\)
−0.0829992 + 0.996550i \(0.526450\pi\)
\(434\) −6.13817e18 + 4.85292e19i −0.101593 + 0.803213i
\(435\) 7.77996e19 1.26563
\(436\) 9.42476e18 1.63242e19i 0.150703 0.261025i
\(437\) 7.81625e18 + 1.35381e19i 0.122854 + 0.212789i
\(438\) −7.41466e19 1.28426e20i −1.14561 1.98425i
\(439\) −3.78985e19 + 6.56421e19i −0.575622 + 0.997007i 0.420351 + 0.907361i \(0.361907\pi\)
−0.995974 + 0.0896457i \(0.971427\pi\)
\(440\) 3.03048e19 0.452498
\(441\) 1.04736e20 1.06888e20i 1.53747 1.56906i
\(442\) 3.81635e19 0.550784
\(443\) −4.19577e19 + 7.26728e19i −0.595365 + 1.03120i 0.398130 + 0.917329i \(0.369659\pi\)
−0.993495 + 0.113874i \(0.963674\pi\)
\(444\) 4.01340e19 + 6.95141e19i 0.559938 + 0.969841i
\(445\) 6.72341e19 + 1.16453e20i 0.922337 + 1.59754i
\(446\) 5.88528e18 1.01936e19i 0.0793882 0.137504i
\(447\) −2.82714e19 −0.375008
\(448\) −1.20250e18 + 9.50711e18i −0.0156855 + 0.124012i
\(449\) 1.01408e20 1.30084 0.650422 0.759573i \(-0.274592\pi\)
0.650422 + 0.759573i \(0.274592\pi\)
\(450\) −6.97603e19 + 1.20828e20i −0.880065 + 1.52432i
\(451\) 5.97996e19 + 1.03576e20i 0.741949 + 1.28509i
\(452\) −2.17568e18 3.76838e18i −0.0265495 0.0459851i
\(453\) 7.00847e19 1.21390e20i 0.841176 1.45696i
\(454\) 3.22251e19 0.380430
\(455\) −1.47193e20 1.11761e20i −1.70923 1.29779i
\(456\) −6.13359e19 −0.700614
\(457\) −7.11523e19 + 1.23239e20i −0.799498 + 1.38477i 0.120445 + 0.992720i \(0.461568\pi\)
−0.919943 + 0.392052i \(0.871765\pi\)
\(458\) 2.84611e19 + 4.92961e19i 0.314601 + 0.544906i
\(459\) −5.21536e19 9.03327e19i −0.567138 0.982313i
\(460\) −7.56625e18 + 1.31051e19i −0.0809463 + 0.140203i
\(461\) −6.23798e19 −0.656579 −0.328290 0.944577i \(-0.606472\pi\)
−0.328290 + 0.944577i \(0.606472\pi\)
\(462\) 9.86287e19 4.14420e19i 1.02138 0.429167i
\(463\) 1.20990e19 0.123280 0.0616398 0.998098i \(-0.480367\pi\)
0.0616398 + 0.998098i \(0.480367\pi\)
\(464\) −6.04282e18 + 1.04665e19i −0.0605836 + 0.104934i
\(465\) −1.51538e20 2.62472e20i −1.49494 2.58932i
\(466\) −2.54546e19 4.40887e19i −0.247100 0.427990i
\(467\) 9.17533e19 1.58921e20i 0.876486 1.51812i 0.0213143 0.999773i \(-0.493215\pi\)
0.855172 0.518345i \(-0.173452\pi\)
\(468\) −1.71687e20 −1.61397
\(469\) −1.03366e20 + 4.34326e19i −0.956272 + 0.401809i
\(470\) 3.60390e19 0.328124
\(471\) −1.55829e20 + 2.69903e20i −1.39634 + 2.41853i
\(472\) 2.90632e18 + 5.03389e18i 0.0256318 + 0.0443955i
\(473\) 1.21739e19 + 2.10858e19i 0.105675 + 0.183034i
\(474\) −1.08737e20 + 1.88338e20i −0.929052 + 1.60917i
\(475\) 1.49330e20 1.25587
\(476\) 2.54994e19 + 1.93612e19i 0.211095 + 0.160280i
\(477\) 1.01659e20 0.828433
\(478\) −2.07879e19 + 3.60058e19i −0.166764 + 0.288844i
\(479\) −3.04944e19 5.28179e19i −0.240826 0.417124i 0.720123 0.693846i \(-0.244085\pi\)
−0.960950 + 0.276722i \(0.910752\pi\)
\(480\) −2.96871e19 5.14195e19i −0.230812 0.399778i
\(481\) 1.20239e20 2.08259e20i 0.920356 1.59410i
\(482\) 8.16214e19 0.615108
\(483\) −6.70343e18 + 5.29983e19i −0.0497386 + 0.393241i
\(484\) −1.58845e19 −0.116047
\(485\) 2.37326e19 4.11061e19i 0.170719 0.295694i
\(486\) 3.85755e19 + 6.68148e19i 0.273237 + 0.473261i
\(487\) −7.10973e19 1.23144e20i −0.495891 0.858908i 0.504098 0.863646i \(-0.331825\pi\)
−0.999989 + 0.00473860i \(0.998492\pi\)
\(488\) −7.23469e18 + 1.25308e19i −0.0496902 + 0.0860660i
\(489\) 7.19132e19 0.486398
\(490\) −4.16498e19 1.49348e20i −0.277423 0.994785i
\(491\) −2.46867e20 −1.61939 −0.809696 0.586850i \(-0.800368\pi\)
−0.809696 + 0.586850i \(0.800368\pi\)
\(492\) 1.17161e20 2.02929e20i 0.756912 1.31101i
\(493\) 2.01893e19 + 3.49690e19i 0.128461 + 0.222500i
\(494\) 9.18791e19 + 1.59139e20i 0.575791 + 0.997298i
\(495\) −2.27748e20 + 3.94471e20i −1.40577 + 2.43487i
\(496\) 4.70809e19 0.286241
\(497\) −1.32931e19 + 1.05097e20i −0.0796076 + 0.629389i
\(498\) 5.09806e19 0.300736
\(499\) 1.37266e20 2.37751e20i 0.797642 1.38156i −0.123506 0.992344i \(-0.539414\pi\)
0.921148 0.389212i \(-0.127253\pi\)
\(500\) 8.49120e18 + 1.47072e19i 0.0486065 + 0.0841889i
\(501\) 2.29516e20 + 3.97533e20i 1.29429 + 2.24177i
\(502\) 9.63290e19 1.66847e20i 0.535155 0.926915i
\(503\) −2.14622e20 −1.17466 −0.587332 0.809346i \(-0.699822\pi\)
−0.587332 + 0.809346i \(0.699822\pi\)
\(504\) −1.14715e20 8.71008e19i −0.618572 0.469670i
\(505\) −2.49691e20 −1.32653
\(506\) −1.31216e19 + 2.27273e19i −0.0686844 + 0.118965i
\(507\) 2.00920e20 + 3.48004e20i 1.03625 + 1.79484i
\(508\) −3.43277e19 5.94573e19i −0.174448 0.302153i
\(509\) −1.83134e19 + 3.17198e19i −0.0917035 + 0.158835i −0.908228 0.418476i \(-0.862565\pi\)
0.816525 + 0.577311i \(0.195898\pi\)
\(510\) −1.98372e20 −0.978821
\(511\) −3.43618e20 + 1.44382e20i −1.67078 + 0.702032i
\(512\) 9.22337e18 0.0441942
\(513\) 2.51121e20 4.34954e20i 1.18577 2.05382i
\(514\) −2.84308e19 4.92436e19i −0.132302 0.229153i
\(515\) −3.85473e19 6.67658e19i −0.176783 0.306196i
\(516\) 2.38515e19 4.13120e19i 0.107806 0.186726i
\(517\) 6.24998e19 0.278419
\(518\) 1.85993e20 7.81510e19i 0.816627 0.343132i
\(519\) 7.36907e20 3.18902
\(520\) −8.89404e19 + 1.54049e20i −0.379380 + 0.657105i
\(521\) 5.32319e19 + 9.22003e19i 0.223815 + 0.387659i 0.955963 0.293486i \(-0.0948156\pi\)
−0.732148 + 0.681145i \(0.761482\pi\)
\(522\) −9.08264e19 1.57316e20i −0.376429 0.651995i
\(523\) 2.28542e20 3.95847e20i 0.933692 1.61720i 0.156743 0.987639i \(-0.449901\pi\)
0.776949 0.629563i \(-0.216766\pi\)
\(524\) 6.67903e19 0.268985
\(525\) 4.06423e20 + 3.08589e20i 1.61355 + 1.22514i
\(526\) −1.53302e20 −0.600004
\(527\) 7.86496e19 1.36225e20i 0.303471 0.525627i
\(528\) −5.14842e19 8.91732e19i −0.195848 0.339219i
\(529\) 1.26765e20 + 2.19564e20i 0.475426 + 0.823463i
\(530\) 5.26630e19 9.12150e19i 0.194732 0.337285i
\(531\) −8.73667e19 −0.318520
\(532\) −1.93448e19 + 1.52943e20i −0.0695388 + 0.549784i
\(533\) −7.02013e20 −2.48823
\(534\) 2.28445e20 3.95678e20i 0.798403 1.38288i
\(535\) −2.03394e20 3.52289e20i −0.700948 1.21408i
\(536\) 5.39570e19 + 9.34564e19i 0.183363 + 0.317594i
\(537\) −4.57447e20 + 7.92321e20i −1.53297 + 2.65518i
\(538\) 2.04470e20 0.675715
\(539\) −7.22302e19 2.59004e20i −0.235398 0.844093i
\(540\) 4.86177e20 1.56258
\(541\) 2.10670e20 3.64891e20i 0.667765 1.15660i −0.310763 0.950487i \(-0.600585\pi\)
0.978528 0.206115i \(-0.0660822\pi\)
\(542\) 4.18545e19 + 7.24941e19i 0.130842 + 0.226625i
\(543\) −5.67990e20 9.83787e20i −1.75122 3.03321i
\(544\) 1.54078e19 2.66872e19i 0.0468544 0.0811542i
\(545\) 2.93537e20 0.880419
\(546\) −7.87980e19 + 6.22988e20i −0.233115 + 1.84304i
\(547\) 1.01935e20 0.297454 0.148727 0.988878i \(-0.452482\pi\)
0.148727 + 0.988878i \(0.452482\pi\)
\(548\) −7.35320e18 + 1.27361e19i −0.0211652 + 0.0366592i
\(549\) −1.08741e20 1.88344e20i −0.308745 0.534761i
\(550\) 1.25345e20 + 2.17103e20i 0.351063 + 0.608059i
\(551\) −9.72121e19 + 1.68376e20i −0.268586 + 0.465205i
\(552\) 5.14165e19 0.140139
\(553\) 4.35331e20 + 3.30539e20i 1.17053 + 0.888759i
\(554\) −2.81184e20 −0.745877
\(555\) −6.24993e20 + 1.08252e21i −1.63560 + 2.83295i
\(556\) −1.34666e20 2.33248e20i −0.347693 0.602222i
\(557\) 1.59733e20 + 2.76665e20i 0.406892 + 0.704758i 0.994540 0.104359i \(-0.0332791\pi\)
−0.587647 + 0.809117i \(0.699946\pi\)
\(558\) −3.53824e20 + 6.12841e20i −0.889263 + 1.54025i
\(559\) −1.42915e20 −0.354396
\(560\) −1.37579e20 + 5.78083e19i −0.336622 + 0.141442i
\(561\) −3.44022e20 −0.830547
\(562\) 4.72489e19 8.18375e19i 0.112556 0.194953i
\(563\) 2.28946e20 + 3.96545e20i 0.538170 + 0.932138i 0.999003 + 0.0446506i \(0.0142175\pi\)
−0.460833 + 0.887487i \(0.652449\pi\)
\(564\) −6.12258e19 1.06046e20i −0.142017 0.245981i
\(565\) 3.38811e19 5.86838e19i 0.0775522 0.134324i
\(566\) 1.46799e20 0.331589
\(567\) 6.73737e20 2.83092e20i 1.50182 0.631038i
\(568\) 1.01961e20 0.224296
\(569\) 1.91029e20 3.30873e20i 0.414723 0.718321i −0.580676 0.814134i \(-0.697212\pi\)
0.995399 + 0.0958132i \(0.0305452\pi\)
\(570\) −4.77582e20 8.27196e20i −1.02326 1.77234i
\(571\) −6.79080e19 1.17620e20i −0.143599 0.248720i 0.785251 0.619178i \(-0.212534\pi\)
−0.928849 + 0.370458i \(0.879201\pi\)
\(572\) −1.54243e20 + 2.67157e20i −0.321911 + 0.557565i
\(573\) −5.56241e20 −1.14579
\(574\) −4.69058e20 3.56147e20i −0.953645 0.724085i
\(575\) −1.25180e20 −0.251204
\(576\) −6.93158e19 + 1.20058e20i −0.137298 + 0.237807i
\(577\) 5.85177e18 + 1.01356e19i 0.0114411 + 0.0198166i 0.871689 0.490059i \(-0.163025\pi\)
−0.860248 + 0.509876i \(0.829691\pi\)
\(578\) 1.31717e20 + 2.28140e20i 0.254204 + 0.440294i
\(579\) 1.44543e20 2.50356e20i 0.275364 0.476945i
\(580\) −1.88206e20 −0.353934
\(581\) 1.60788e19 1.27122e20i 0.0298493 0.235993i
\(582\) −1.61275e20 −0.295560
\(583\) 9.13297e19 1.58188e20i 0.165233 0.286193i
\(584\) 1.79369e20 + 3.10676e20i 0.320369 + 0.554895i
\(585\) −1.33682e21 2.31543e21i −2.35723 4.08285i
\(586\) 1.85123e20 3.20643e20i 0.322277 0.558200i
\(587\) 8.61204e20 1.48020 0.740100 0.672497i \(-0.234778\pi\)
0.740100 + 0.672497i \(0.234778\pi\)
\(588\) −3.68705e20 + 3.76280e20i −0.625676 + 0.638530i
\(589\) 7.57399e20 1.26900
\(590\) −4.52591e19 + 7.83911e19i −0.0748714 + 0.129681i
\(591\) 6.19236e20 + 1.07255e21i 1.01146 + 1.75191i
\(592\) −9.70884e19 1.68162e20i −0.156587 0.271216i
\(593\) 4.53264e20 7.85077e20i 0.721840 1.25026i −0.238421 0.971162i \(-0.576630\pi\)
0.960261 0.279102i \(-0.0900368\pi\)
\(594\) 8.43143e20 1.32588
\(595\) −6.25647e19 + 4.94645e20i −0.0971520 + 0.768098i
\(596\) 6.83915e19 0.104871
\(597\) −2.24312e20 + 3.88521e20i −0.339661 + 0.588310i
\(598\) −7.70202e19 1.33403e20i −0.115172 0.199483i
\(599\) 4.45997e20 + 7.72490e20i 0.658614 + 1.14075i 0.980975 + 0.194136i \(0.0621902\pi\)
−0.322361 + 0.946617i \(0.604476\pi\)
\(600\) 2.45579e20 4.25355e20i 0.358143 0.620322i
\(601\) 3.78078e20 0.544532 0.272266 0.962222i \(-0.412227\pi\)
0.272266 + 0.962222i \(0.412227\pi\)
\(602\) −9.54901e19 7.25039e19i −0.135827 0.103131i
\(603\) −1.62200e21 −2.27861
\(604\) −1.69542e20 + 2.93656e20i −0.235235 + 0.407439i
\(605\) −1.23682e20 2.14224e20i −0.169489 0.293564i
\(606\) 4.24195e20 + 7.34727e20i 0.574144 + 0.994446i
\(607\) −3.81158e20 + 6.60185e20i −0.509553 + 0.882573i 0.490385 + 0.871506i \(0.336856\pi\)
−0.999939 + 0.0110668i \(0.996477\pi\)
\(608\) 1.48378e20 0.195927
\(609\) −6.12526e20 + 2.57372e20i −0.798904 + 0.335685i
\(610\) −2.25327e20 −0.290294
\(611\) −1.83428e20 + 3.17707e20i −0.233430 + 0.404313i
\(612\) 2.31587e20 + 4.01121e20i 0.291124 + 0.504242i
\(613\) 3.55867e20 + 6.16380e20i 0.441911 + 0.765412i 0.997831 0.0658237i \(-0.0209675\pi\)
−0.555921 + 0.831235i \(0.687634\pi\)
\(614\) −4.45921e20 + 7.72358e20i −0.547010 + 0.947450i
\(615\) 3.64902e21 4.42194
\(616\) −2.38593e20 + 1.00253e20i −0.285630 + 0.120016i
\(617\) 2.29885e20 0.271877 0.135938 0.990717i \(-0.456595\pi\)
0.135938 + 0.990717i \(0.456595\pi\)
\(618\) −1.30974e20 + 2.26854e20i −0.153028 + 0.265053i
\(619\) −6.61618e20 1.14596e21i −0.763708 1.32278i −0.940927 0.338609i \(-0.890044\pi\)
0.177219 0.984171i \(-0.443290\pi\)
\(620\) 3.66587e20 + 6.34948e20i 0.418061 + 0.724103i
\(621\) −2.10509e20 + 3.64612e20i −0.237183 + 0.410813i
\(622\) 9.50083e20 1.05763
\(623\) −9.14586e20 6.94428e20i −1.00592 0.763777i
\(624\) 6.04395e20 0.656805
\(625\) 3.95420e20 6.84887e20i 0.424579 0.735392i
\(626\) −1.39131e20 2.40982e20i −0.147611 0.255669i
\(627\) −8.28236e20 1.43455e21i −0.868255 1.50386i
\(628\) 3.76967e20 6.52926e20i 0.390486 0.676342i
\(629\) −6.48753e20 −0.664049
\(630\) 2.81462e20 2.22528e21i 0.284685 2.25076i
\(631\) −6.08942e19 −0.0608634 −0.0304317 0.999537i \(-0.509688\pi\)
−0.0304317 + 0.999537i \(0.509688\pi\)
\(632\) 2.63047e20 4.55610e20i 0.259809 0.450003i
\(633\) 2.47013e20 + 4.27839e20i 0.241097 + 0.417592i
\(634\) −4.09051e19 7.08497e19i −0.0394556 0.0683390i
\(635\) 5.34573e20 9.25908e20i 0.509570 0.882602i
\(636\) −3.57872e20 −0.337131
\(637\) 1.52859e21 + 3.92970e20i 1.42313 + 0.365859i
\(638\) −3.26392e20 −0.300320
\(639\) −7.66259e20 + 1.32720e21i −0.696817 + 1.20692i
\(640\) 7.18162e19 + 1.24389e20i 0.0645465 + 0.111798i
\(641\) 7.82962e20 + 1.35613e21i 0.695513 + 1.20466i 0.970007 + 0.243075i \(0.0781561\pi\)
−0.274495 + 0.961589i \(0.588511\pi\)
\(642\) −6.91084e20 + 1.19699e21i −0.606762 + 1.05094i
\(643\) −1.21443e21 −1.05388 −0.526939 0.849903i \(-0.676660\pi\)
−0.526939 + 0.849903i \(0.676660\pi\)
\(644\) 1.62163e19 1.28209e20i 0.0139094 0.109970i
\(645\) 7.42863e20 0.629812
\(646\) 2.47869e20 4.29322e20i 0.207720 0.359782i
\(647\) −7.99390e20 1.38458e21i −0.662181 1.14693i −0.980041 0.198793i \(-0.936298\pi\)
0.317861 0.948137i \(-0.397036\pi\)
\(648\) −3.51691e20 6.09146e20i −0.287971 0.498780i
\(649\) −7.84897e19 + 1.35948e20i −0.0635298 + 0.110037i
\(650\) −1.47147e21 −1.17734
\(651\) 2.06137e21 + 1.56516e21i 1.63042 + 1.23795i
\(652\) −1.73966e20 −0.136021
\(653\) −1.06833e21 + 1.85039e21i −0.825761 + 1.43026i 0.0755745 + 0.997140i \(0.475921\pi\)
−0.901336 + 0.433121i \(0.857412\pi\)
\(654\) −4.98684e20 8.63745e20i −0.381059 0.660013i
\(655\) 5.20051e20 + 9.00755e20i 0.392859 + 0.680451i
\(656\) −2.83425e20 + 4.90907e20i −0.211670 + 0.366624i
\(657\) −5.39199e21 −3.98115
\(658\) −2.83739e20 + 1.19222e20i −0.207121 + 0.0870287i
\(659\) −8.65907e20 −0.624929 −0.312464 0.949929i \(-0.601154\pi\)
−0.312464 + 0.949929i \(0.601154\pi\)
\(660\) 8.01745e20 1.38866e21i 0.572080 0.990872i
\(661\) 7.94210e19 + 1.37561e20i 0.0560305 + 0.0970476i 0.892680 0.450691i \(-0.148822\pi\)
−0.836650 + 0.547738i \(0.815489\pi\)
\(662\) −3.58890e20 6.21616e20i −0.250338 0.433598i
\(663\) 1.00966e21 1.74877e21i 0.696341 1.20610i
\(664\) −1.23328e20 −0.0841008
\(665\) −2.21326e21 + 9.29973e20i −1.49235 + 0.627058i
\(666\) 2.91857e21 1.94587
\(667\) 8.14907e19 1.41146e20i 0.0537235 0.0930519i
\(668\) −5.55224e20 9.61676e20i −0.361947 0.626910i
\(669\) −3.11403e20 5.39365e20i −0.200736 0.347686i
\(670\) −8.40255e20 + 1.45536e21i −0.535612 + 0.927707i
\(671\) −3.90768e20 −0.246320
\(672\) 4.03833e20 + 3.06623e20i 0.251728 + 0.191133i
\(673\) −1.69054e21 −1.04211 −0.521053 0.853524i \(-0.674461\pi\)
−0.521053 + 0.853524i \(0.674461\pi\)
\(674\) 8.70997e20 1.50861e21i 0.530967 0.919662i
\(675\) 2.01089e21 + 3.48296e21i 1.21230 + 2.09977i
\(676\) −4.86048e20 8.41860e20i −0.289787 0.501926i
\(677\) 1.63394e20 2.83008e20i 0.0963435 0.166872i −0.813825 0.581110i \(-0.802619\pi\)
0.910169 + 0.414238i \(0.135952\pi\)
\(678\) −2.30239e20 −0.134263
\(679\) −5.08647e19 + 4.02144e20i −0.0293355 + 0.231931i
\(680\) 4.79882e20 0.273727
\(681\) 8.52548e20 1.47666e21i 0.480967 0.833059i
\(682\) 6.35746e20 + 1.10114e21i 0.354732 + 0.614415i
\(683\) 3.53311e20 + 6.11952e20i 0.194985 + 0.337724i 0.946896 0.321541i \(-0.104201\pi\)
−0.751910 + 0.659265i \(0.770867\pi\)
\(684\) −1.11510e21 + 1.93140e21i −0.608684 + 1.05427i
\(685\) −2.29018e20 −0.123649
\(686\) 8.21979e20 + 1.03805e21i 0.438965 + 0.554355i
\(687\) 3.01187e21 1.59097
\(688\) −5.76994e19 + 9.99383e19i −0.0301480 + 0.0522178i
\(689\) 5.36080e20 + 9.28517e20i 0.277067 + 0.479894i
\(690\) 4.00346e20 + 6.93420e20i 0.204676 + 0.354510i
\(691\) 1.24192e21 2.15107e21i 0.628072 1.08785i −0.359867 0.933004i \(-0.617178\pi\)
0.987938 0.154848i \(-0.0494889\pi\)
\(692\) −1.78266e21 −0.891810
\(693\) 4.88119e20 3.85914e21i 0.241561 1.90981i
\(694\) 3.62332e20 0.177382
\(695\) 2.09710e21 3.63229e21i 1.01563 1.75911i
\(696\) 3.19738e20 + 5.53803e20i 0.153188 + 0.265330i
\(697\) 9.46937e20 + 1.64014e21i 0.448823 + 0.777384i
\(698\) 1.31361e21 2.27524e21i 0.615959 1.06687i
\(699\) −2.69372e21 −1.24961
\(700\) −9.83181e20 7.46511e20i −0.451230 0.342611i
\(701\) −6.99108e20 −0.317438 −0.158719 0.987324i \(-0.550736\pi\)
−0.158719 + 0.987324i \(0.550736\pi\)
\(702\) −2.47451e21 + 4.28597e21i −1.11163 + 1.92540i
\(703\) −1.56188e21 2.70526e21i −0.694197 1.20238i
\(704\) 1.24546e20 + 2.15720e20i 0.0547689 + 0.0948625i
\(705\) 9.53448e20 1.65142e21i 0.414838 0.718521i
\(706\) 2.35889e21 1.01548
\(707\) 1.96585e21 8.26015e20i 0.837345 0.351838i
\(708\) 3.07559e20 0.129622
\(709\) −5.20032e20 + 9.00722e20i −0.216862 + 0.375616i −0.953847 0.300293i \(-0.902915\pi\)
0.736985 + 0.675909i \(0.236249\pi\)
\(710\) 7.93900e20 + 1.37508e21i 0.327588 + 0.567400i
\(711\) 3.95371e21 + 6.84803e21i 1.61430 + 2.79604i
\(712\) −5.52633e20 + 9.57189e20i −0.223273 + 0.386721i
\(713\) −6.34911e20 −0.253829
\(714\) 1.56180e21 6.56242e20i 0.617860 0.259614i
\(715\) −4.80395e21 −1.88063
\(716\) 1.10661e21 1.91671e21i 0.428695 0.742521i
\(717\) 1.09993e21 + 1.90514e21i 0.421670 + 0.730353i
\(718\) −9.31072e20 1.61266e21i −0.353224 0.611802i
\(719\) 1.03055e21 1.78496e21i 0.386902 0.670134i −0.605129 0.796127i \(-0.706879\pi\)
0.992031 + 0.125994i \(0.0402119\pi\)
\(720\) −2.15886e21 −0.802105
\(721\) 5.24358e20 + 3.98135e20i 0.192803 + 0.146392i
\(722\) 4.43805e20 0.161497
\(723\) 2.15938e21 3.74015e21i 0.777663 1.34695i
\(724\) 1.37403e21 + 2.37989e21i 0.489730 + 0.848237i
\(725\) −7.78442e20 1.34830e21i −0.274594 0.475611i
\(726\) −4.20242e20 + 7.27881e20i −0.146715 + 0.254118i
\(727\) 1.15396e21 0.398734 0.199367 0.979925i \(-0.436111\pi\)
0.199367 + 0.979925i \(0.436111\pi\)
\(728\) 1.90621e20 1.50708e21i 0.0651906 0.515406i
\(729\) −7.30380e20 −0.247225
\(730\) −2.79325e21 + 4.83804e21i −0.935810 + 1.62087i
\(731\) 1.92776e20 + 3.33898e20i 0.0639254 + 0.110722i
\(732\) 3.82802e20 + 6.63033e20i 0.125644 + 0.217622i
\(733\) −8.48642e20 + 1.46989e21i −0.275705 + 0.477535i −0.970313 0.241854i \(-0.922245\pi\)
0.694608 + 0.719389i \(0.255578\pi\)
\(734\) −2.24024e21 −0.720400
\(735\) −7.94550e21 2.04263e21i −2.52910 0.650183i
\(736\) −1.24382e20 −0.0391899
\(737\) −1.45719e21 + 2.52393e21i −0.454476 + 0.787176i
\(738\) −4.26002e21 7.37856e21i −1.31519 2.27798i
\(739\) 2.83513e20 + 4.91060e20i 0.0866444 + 0.150072i 0.906091 0.423083i \(-0.139052\pi\)
−0.819446 + 0.573156i \(0.805719\pi\)
\(740\) 1.51193e21 2.61873e21i 0.457396 0.792233i
\(741\) 9.72302e21 2.91182
\(742\) −1.12870e20 + 8.92363e20i −0.0334617 + 0.264553i
\(743\) 5.34375e21 1.56830 0.784151 0.620570i \(-0.213099\pi\)
0.784151 + 0.620570i \(0.213099\pi\)
\(744\) 1.24557e21 2.15740e21i 0.361886 0.626806i
\(745\) 5.32519e20 + 9.22350e20i 0.153166 + 0.265292i
\(746\) 2.15038e21 + 3.72456e21i 0.612312 + 1.06056i
\(747\) 9.26836e20 1.60533e21i 0.261275 0.452542i
\(748\) 8.32226e20 0.232263
\(749\) 2.76677e21 + 2.10076e21i 0.764469 + 0.580447i
\(750\) 8.98574e20 0.245807
\(751\) −1.90653e21 + 3.30222e21i −0.516351 + 0.894347i 0.483469 + 0.875362i \(0.339377\pi\)
−0.999820 + 0.0189849i \(0.993957\pi\)
\(752\) 1.48112e20 + 2.56537e20i 0.0397151 + 0.0687886i
\(753\) −5.09697e21 8.82821e21i −1.35316 2.34374i
\(754\) 9.57914e20 1.65916e21i 0.251792 0.436116i
\(755\) −5.28046e21 −1.37426
\(756\) −3.82773e21 + 1.60835e21i −0.986343 + 0.414444i
\(757\) −1.23228e21 −0.314405 −0.157203 0.987566i \(-0.550248\pi\)
−0.157203 + 0.987566i \(0.550248\pi\)
\(758\) −4.44674e20 + 7.70198e20i −0.112337 + 0.194573i
\(759\) 6.94292e20 + 1.20255e21i 0.173672 + 0.300808i
\(760\) 1.15532e21 + 2.00108e21i 0.286155 + 0.495635i
\(761\) 2.30181e21 3.98684e21i 0.564526 0.977787i −0.432568 0.901601i \(-0.642392\pi\)
0.997094 0.0761859i \(-0.0242742\pi\)
\(762\) −3.63270e21 −0.882199
\(763\) −2.31105e21 + 9.71064e20i −0.555745 + 0.233514i
\(764\) 1.34561e21 0.320419
\(765\) −3.60643e21 + 6.24651e21i −0.850387 + 1.47291i
\(766\) 6.48403e20 + 1.12307e21i 0.151401 + 0.262234i
\(767\) −4.60712e20 7.97977e20i −0.106528 0.184512i
\(768\) 2.44014e20 4.22644e20i 0.0558734 0.0967756i
\(769\) −1.36597e21 −0.309738 −0.154869 0.987935i \(-0.549496\pi\)
−0.154869 + 0.987935i \(0.549496\pi\)
\(770\) −3.20981e21 2.43715e21i −0.720773 0.547269i
\(771\) −3.00866e21 −0.669061
\(772\) −3.49665e20 + 6.05638e20i −0.0770056 + 0.133378i
\(773\) 1.57140e21 + 2.72174e21i 0.342721 + 0.593609i 0.984937 0.172914i \(-0.0553183\pi\)
−0.642216 + 0.766523i \(0.721985\pi\)
\(774\) −8.67249e20 1.50212e21i −0.187321 0.324449i
\(775\) −3.03250e21 + 5.25245e21i −0.648692 + 1.12357i
\(776\) 3.90142e20 0.0826532
\(777\) 1.33951e21 1.05904e22i 0.281053 2.22205i
\(778\) 7.00895e20 0.145648
\(779\) −4.55952e21 + 7.89732e21i −0.938401 + 1.62536i
\(780\) 4.70602e21 + 8.15107e21i 0.959278 + 1.66152i
\(781\) 1.37680e21 + 2.38470e21i 0.277965 + 0.481449i
\(782\) −2.07783e20 + 3.59891e20i −0.0415489 + 0.0719648i
\(783\) −5.23627e21 −1.03707
\(784\) 8.91938e20 9.10263e20i 0.174970 0.178565i
\(785\) 1.17408e22 2.28125
\(786\) 1.76701e21 3.06054e21i 0.340070 0.589019i
\(787\) −9.01278e20 1.56106e21i −0.171810 0.297583i 0.767243 0.641357i \(-0.221628\pi\)
−0.939053 + 0.343773i \(0.888295\pi\)
\(788\) −1.49800e21 2.59461e21i −0.282856 0.489921i
\(789\) −4.05576e21 + 7.02477e21i −0.758568 + 1.31388i
\(790\) 8.19267e21 1.51783
\(791\) −7.26154e19 + 5.74108e20i −0.0133262 + 0.105359i
\(792\) −3.74396e21 −0.680601
\(793\) 1.14685e21 1.98640e21i 0.206518 0.357699i
\(794\) −3.72455e21 6.45112e21i −0.664386 1.15075i
\(795\) −2.78651e21 4.82637e21i −0.492387 0.852840i
\(796\) 5.42636e20 9.39873e20i 0.0949862 0.164521i
\(797\) 5.88541e21 1.02056 0.510281 0.860008i \(-0.329541\pi\)
0.510281 + 0.860008i \(0.329541\pi\)
\(798\) 6.49654e21 + 4.93270e21i 1.11599 + 0.847351i
\(799\) 9.89696e20 0.168423
\(800\) −5.94082e20 + 1.02898e21i −0.100155 + 0.173473i
\(801\) −8.30633e21 1.43870e22i −1.38728 2.40285i
\(802\) 5.26020e20 + 9.11093e20i 0.0870351 + 0.150749i
\(803\) −4.84413e21 + 8.39027e21i −0.794052 + 1.37534i
\(804\) 5.70996e21 0.927284
\(805\) 1.85533e21 7.79576e20i 0.298505 0.125426i
\(806\) −7.46330e21 −1.18965
\(807\) 5.40948e21 9.36949e21i 0.854287 1.47967i
\(808\) −1.02617e21 1.77738e21i −0.160559 0.278097i
\(809\) −3.83234e20 6.63781e20i −0.0594087 0.102899i 0.834791 0.550566i \(-0.185588\pi\)
−0.894200 + 0.447667i \(0.852255\pi\)
\(810\) 5.47676e21 9.48603e21i 0.841175 1.45696i
\(811\) −3.09727e21 −0.471327 −0.235663 0.971835i \(-0.575726\pi\)
−0.235663 + 0.971835i \(0.575726\pi\)
\(812\) 1.48177e21 6.22612e20i 0.223413 0.0938744i
\(813\) 4.42922e21 0.661680
\(814\) 2.62202e21 4.54148e21i 0.388109 0.672224i
\(815\) −1.35455e21 2.34616e21i −0.198662 0.344092i
\(816\) −8.15261e20 1.41207e21i −0.118473 0.205202i
\(817\) −9.28222e20 + 1.60773e21i −0.133655 + 0.231498i
\(818\) 5.61650e21 0.801339
\(819\) 1.81847e22 + 1.38073e22i 2.57085 + 1.95200i
\(820\) −8.82738e21 −1.23660
\(821\) −5.82584e21 + 1.00907e22i −0.808696 + 1.40070i 0.105072 + 0.994465i \(0.466493\pi\)
−0.913768 + 0.406237i \(0.866841\pi\)
\(822\) 3.89073e20 + 6.73894e20i 0.0535171 + 0.0926943i
\(823\) −1.54081e20 2.66876e20i −0.0210015 0.0363757i 0.855334 0.518078i \(-0.173352\pi\)
−0.876335 + 0.481702i \(0.840019\pi\)
\(824\) 3.16841e20 5.48784e20i 0.0427944 0.0741220i
\(825\) 1.32645e22 1.77536
\(826\) 9.70013e19 7.66906e20i 0.0128655 0.101717i
\(827\) 8.65216e21 1.13719 0.568595 0.822617i \(-0.307487\pi\)
0.568595 + 0.822617i \(0.307487\pi\)
\(828\) 9.34761e20 1.61905e21i 0.121751 0.210879i
\(829\) 5.19930e21 + 9.00546e21i 0.671099 + 1.16238i 0.977593 + 0.210504i \(0.0675106\pi\)
−0.306494 + 0.951872i \(0.599156\pi\)
\(830\) −9.60270e20 1.66324e21i −0.122831 0.212749i
\(831\) −7.43901e21 + 1.28847e22i −0.942991 + 1.63331i
\(832\) −1.46210e21 −0.183676
\(833\) −1.14378e21 4.10137e21i −0.142398 0.510613i
\(834\) −1.42509e22 −1.75831
\(835\) 8.64631e21 1.49759e22i 1.05726 1.83123i
\(836\) 2.00359e21 + 3.47032e21i 0.242808 + 0.420555i
\(837\) 1.01992e22 + 1.76656e22i 1.22497 + 2.12171i
\(838\) −3.33422e21 + 5.77504e21i −0.396884 + 0.687424i
\(839\) −1.09289e22 −1.28932 −0.644661 0.764469i \(-0.723001\pi\)
−0.644661 + 0.764469i \(0.723001\pi\)
\(840\) −9.90836e20 + 7.83369e21i −0.115853 + 0.915950i
\(841\) −6.60216e21 −0.765096
\(842\) 3.65021e20 6.32235e20i 0.0419254 0.0726170i
\(843\) −2.50004e21 4.33019e21i −0.284603 0.492947i
\(844\) −5.97551e20 1.03499e21i −0.0674228 0.116780i
\(845\) 7.56906e21 1.31100e22i 0.846480 1.46615i
\(846\) −4.45238e21 −0.493531
\(847\) 1.68245e21 + 1.27745e21i 0.184849 + 0.140352i
\(848\) 8.65731e20 0.0942788
\(849\) 3.88372e21 6.72680e21i 0.419218 0.726107i
\(850\) 1.98485e21 + 3.43787e21i 0.212367 + 0.367830i
\(851\) 1.30929e21 + 2.26776e21i 0.138856 + 0.240505i
\(852\) 2.69748e21 4.67217e21i 0.283570 0.491158i
\(853\) −8.33417e21 −0.868449 −0.434225 0.900805i \(-0.642978\pi\)
−0.434225 + 0.900805i \(0.642978\pi\)
\(854\) 1.77402e21 7.45413e20i 0.183242 0.0769951i
\(855\) −3.47300e22 −3.55598
\(856\) 1.67181e21 2.89565e21i 0.169681 0.293896i
\(857\) 4.14721e20 + 7.18318e20i 0.0417253 + 0.0722704i 0.886134 0.463429i \(-0.153381\pi\)
−0.844409 + 0.535700i \(0.820048\pi\)
\(858\) 8.16131e21 + 1.41358e22i 0.813964 + 1.40983i
\(859\) 1.21163e20 2.09861e20i 0.0119791 0.0207483i −0.859974 0.510338i \(-0.829520\pi\)
0.871953 + 0.489590i \(0.162854\pi\)
\(860\) −1.79707e21 −0.176127
\(861\) −2.87292e22 + 1.20715e22i −2.79126 + 1.17284i
\(862\) 4.52338e21 0.435671
\(863\) 6.85170e21 1.18675e22i 0.654211 1.13313i −0.327881 0.944719i \(-0.606334\pi\)
0.982091 0.188407i \(-0.0603323\pi\)
\(864\) 1.99808e21 + 3.46077e21i 0.189129 + 0.327582i
\(865\) −1.38804e22 2.40415e22i −1.30251 2.25601i
\(866\) 6.30875e20 1.09271e21i 0.0586893 0.101653i
\(867\) 1.39388e22 1.28553
\(868\) −4.98668e21 3.78629e21i −0.455947 0.346192i
\(869\) 1.42080e22 1.28790
\(870\) −4.97918e21 + 8.62419e21i −0.447469 + 0.775039i
\(871\) −8.55332e21 1.48148e22i −0.762076 1.31995i
\(872\) 1.20637e21 + 2.08949e21i 0.106563 + 0.184573i
\(873\) −2.93201e21 + 5.07838e21i −0.256778 + 0.444753i
\(874\) −2.00096e21 −0.173741
\(875\) 2.83402e20 2.24062e21i 0.0243974 0.192889i
\(876\) 1.89815e22 1.62013
\(877\) 5.12170e21 8.87104e21i 0.433428 0.750720i −0.563738 0.825954i \(-0.690637\pi\)
0.997166 + 0.0752343i \(0.0239705\pi\)
\(878\) −4.85100e21 8.40218e21i −0.407026 0.704990i
\(879\) −9.79526e21 1.69659e22i −0.814891 1.41143i
\(880\) −1.93951e21 + 3.35933e21i −0.159982 + 0.277097i
\(881\) −2.42640e21 −0.198446 −0.0992232 0.995065i \(-0.531636\pi\)
−0.0992232 + 0.995065i \(0.531636\pi\)
\(882\) 5.14555e21 + 1.84510e22i 0.417271 + 1.49625i
\(883\) 2.06931e22 1.66387 0.831936 0.554872i \(-0.187233\pi\)
0.831936 + 0.554872i \(0.187233\pi\)
\(884\) −2.44247e21 + 4.23047e21i −0.194732 + 0.337285i
\(885\) 2.39475e21 + 4.14784e21i 0.189316 + 0.327904i
\(886\) −5.37058e21 9.30212e21i −0.420987 0.729171i
\(887\) −1.07767e22 + 1.86657e22i −0.837640 + 1.45083i 0.0542229 + 0.998529i \(0.482732\pi\)
−0.891863 + 0.452306i \(0.850602\pi\)
\(888\) −1.02743e22 −0.791872
\(889\) −1.14572e21 + 9.05823e21i −0.0875619 + 0.692277i
\(890\) −1.72119e22 −1.30438
\(891\) 9.49796e21 1.64509e22i 0.713752 1.23625i
\(892\) 7.53316e20 + 1.30478e21i 0.0561359 + 0.0972303i
\(893\) 2.38270e21 + 4.12696e21i 0.176069 + 0.304961i
\(894\) 1.80937e21 3.13392e21i 0.132585 0.229645i
\(895\) 3.44658e22 2.50447
\(896\) −9.76916e20 7.41754e20i −0.0703958 0.0534502i
\(897\) −8.15059e21 −0.582433
\(898\) −6.49012e21 + 1.12412e22i −0.459918 + 0.796601i
\(899\) −3.94825e21 6.83857e21i −0.277464 0.480582i
\(900\) −8.92932e21 1.54660e22i −0.622300 1.07786i
\(901\) 1.44622e21 2.50493e21i 0.0999538 0.173125i
\(902\) −1.53087e22 −1.04927
\(903\) −5.84865e21 + 2.45750e21i −0.397555 + 0.167046i
\(904\) 5.56973e20 0.0375467
\(905\) −2.13973e22 + 3.70612e22i −1.43052 + 2.47774i
\(906\) 8.97084e21 + 1.55380e22i 0.594801 + 1.03023i
\(907\) −3.02074e21 5.23208e21i −0.198637 0.344049i 0.749450 0.662061i \(-0.230318\pi\)
−0.948087 + 0.318012i \(0.896985\pi\)
\(908\) −2.06240e21 + 3.57219e21i −0.134502 + 0.232965i
\(909\) 3.08477e22 1.99523
\(910\) 2.18091e22 9.16382e21i 1.39903 0.587849i
\(911\) 2.46256e21 0.156675 0.0783374 0.996927i \(-0.475039\pi\)
0.0783374 + 0.996927i \(0.475039\pi\)
\(912\) 3.92550e21 6.79916e21i 0.247704 0.429036i
\(913\) −1.66533e21 2.88443e21i −0.104224 0.180522i
\(914\) −9.10750e21 1.57746e22i −0.565331 0.979182i
\(915\) −5.96125e21 + 1.03252e22i −0.367011 + 0.635682i
\(916\) −7.28604e21 −0.444914
\(917\) −7.07425e21 5.37134e21i −0.428460 0.325322i
\(918\) 1.33513e22 0.802055
\(919\) −1.09081e22 + 1.88934e22i −0.649956 + 1.12576i 0.333177 + 0.942864i \(0.391879\pi\)
−0.983133 + 0.182892i \(0.941454\pi\)
\(920\) −9.68481e20 1.67746e21i −0.0572377 0.0991386i
\(921\) 2.35946e22 + 4.08671e22i 1.38314 + 2.39567i
\(922\) 3.99231e21 6.91488e21i 0.232136 0.402071i
\(923\) −1.61629e22 −0.932195
\(924\) −1.71834e21 + 1.35854e22i −0.0983033 + 0.777200i
\(925\) 2.50140e22 1.41945
\(926\) −7.74335e20 + 1.34119e21i −0.0435859 + 0.0754931i
\(927\) 4.76226e21 + 8.24848e21i 0.265898 + 0.460549i
\(928\) −7.73481e20 1.33971e21i −0.0428391 0.0741994i
\(929\) 6.74778e21 1.16875e22i 0.370717 0.642101i −0.618959 0.785424i \(-0.712445\pi\)
0.989676 + 0.143322i \(0.0457785\pi\)
\(930\) 3.87938e22 2.11417
\(931\) 1.43488e22 1.46436e22i 0.775697 0.791634i
\(932\) 6.51639e21 0.349452
\(933\) 2.51354e22 4.35359e22i 1.33713 2.31598i
\(934\) 1.17444e22 + 2.03419e22i 0.619769 + 1.07347i
\(935\) 6.47998e21 + 1.12237e22i 0.339224 + 0.587554i
\(936\) 1.09880e22 1.90318e22i 0.570624 0.988349i
\(937\) 2.87255e20 0.0147986 0.00739930 0.999973i \(-0.497645\pi\)
0.00739930 + 0.999973i \(0.497645\pi\)
\(938\) 1.80087e21 1.42379e22i 0.0920367 0.727655i
\(939\) −1.47234e22 −0.746479
\(940\) −2.30649e21 + 3.99497e21i −0.116009 + 0.200934i
\(941\) 1.68121e22 + 2.91195e22i 0.838882 + 1.45299i 0.890831 + 0.454336i \(0.150123\pi\)
−0.0519491 + 0.998650i \(0.516543\pi\)
\(942\) −1.99461e22 3.45476e22i −0.987361 1.71016i
\(943\) 3.82214e21 6.62015e21i 0.187702 0.325110i
\(944\) −7.44018e20 −0.0362488
\(945\) −5.14947e22 3.90989e22i −2.48899 1.88984i
\(946\) −3.11652e21 −0.149447
\(947\) 7.81293e21 1.35324e22i 0.371697 0.643798i −0.618130 0.786076i \(-0.712109\pi\)
0.989827 + 0.142278i \(0.0454426\pi\)
\(948\) −1.39183e22 2.41073e22i −0.656939 1.13785i
\(949\) −2.84337e22 4.92486e22i −1.33148 2.30620i
\(950\) −9.55711e21 + 1.65534e22i −0.444017 + 0.769060i
\(951\) −4.32875e21 −0.199530
\(952\) −3.77817e21 + 1.58752e21i −0.172784 + 0.0726009i
\(953\) −2.55462e22 −1.15913 −0.579563 0.814928i \(-0.696777\pi\)
−0.579563 + 0.814928i \(0.696777\pi\)
\(954\) −6.50617e21 + 1.12690e22i −0.292895 + 0.507309i
\(955\) 1.04773e22 + 1.81473e22i 0.467979 + 0.810563i
\(956\) −2.66086e21 4.60874e21i −0.117920 0.204243i
\(957\) −8.63503e21 + 1.49563e22i −0.379686 + 0.657635i
\(958\) 7.80658e21 0.340580
\(959\) 1.80308e21 7.57624e20i 0.0780506 0.0327955i
\(960\) 7.59989e21 0.326417
\(961\) −3.64818e21 + 6.31884e21i −0.155472 + 0.269285i
\(962\) 1.53905e22 + 2.66572e22i 0.650790 + 1.12720i
\(963\) 2.51280e22 + 4.35230e22i 1.05429 + 1.82609i
\(964\) −5.22377e21 + 9.04784e21i −0.217474 + 0.376675i
\(965\) −1.08904e22 −0.449873
\(966\) −5.44591e21 4.13497e21i −0.223224 0.169490i
\(967\) 2.39258e22 0.973122 0.486561 0.873647i \(-0.338251\pi\)
0.486561 + 0.873647i \(0.338251\pi\)
\(968\) 1.01661e21 1.76082e21i 0.0410289 0.0710641i
\(969\) −1.31153e22 2.27163e22i −0.525229 0.909723i
\(970\) 3.03777e21 + 5.26158e21i 0.120717 + 0.209087i
\(971\) −5.37942e20 + 9.31743e20i −0.0212125 + 0.0367411i −0.876437 0.481517i \(-0.840086\pi\)
0.855224 + 0.518258i \(0.173419\pi\)
\(972\) −9.87533e21 −0.386416
\(973\) −4.49460e21 + 3.55349e22i −0.174520 + 1.37978i
\(974\) 1.82009e22 0.701295
\(975\) −3.89294e22 + 6.74277e22i −1.48848 + 2.57812i
\(976\) −9.26040e20 1.60395e21i −0.0351363 0.0608579i
\(977\) −5.31494e21 9.20574e21i −0.200119 0.346617i 0.748447 0.663194i \(-0.230800\pi\)
−0.948567 + 0.316577i \(0.897466\pi\)
\(978\) −4.60244e21 + 7.97166e21i −0.171968 + 0.297857i
\(979\) −2.98494e22 −1.10679
\(980\) 1.92210e22 + 4.94135e21i 0.707263 + 0.181824i
\(981\) −3.62646e22 −1.32424
\(982\) 1.57995e22 2.73655e22i 0.572541 0.991670i
\(983\) 6.66552e21 + 1.15450e22i 0.239708 + 0.415187i 0.960630 0.277829i \(-0.0896149\pi\)
−0.720922 + 0.693016i \(0.756282\pi\)
\(984\) 1.49966e22 + 2.59749e22i 0.535218 + 0.927024i
\(985\) 2.33278e22 4.04050e22i 0.826233 1.43108i
\(986\) −5.16847e21 −0.181671
\(987\) −2.04347e21 + 1.61560e22i −0.0712837 + 0.563579i
\(988\) −2.35210e22 −0.814291
\(989\) 7.78107e20 1.34772e21i 0.0267342 0.0463050i
\(990\) −2.91517e22 5.04922e22i −0.994031 1.72171i
\(991\) −4.50301e21 7.79944e21i −0.152388 0.263944i 0.779717 0.626132i \(-0.215363\pi\)
−0.932105 + 0.362189i \(0.882030\pi\)
\(992\) −3.01318e21 + 5.21897e21i −0.101202 + 0.175286i
\(993\) −3.79793e22 −1.26598
\(994\) −1.07994e22 8.19980e21i −0.357275 0.271272i
\(995\) 1.69006e22 0.554917
\(996\) −3.26276e21 + 5.65127e21i −0.106326 + 0.184162i
\(997\) −4.55495e21 7.88941e21i −0.147323 0.255171i 0.782914 0.622130i \(-0.213732\pi\)
−0.930237 + 0.366959i \(0.880399\pi\)
\(998\) 1.75700e22 + 3.04321e22i 0.564018 + 0.976908i
\(999\) 4.20649e22 7.28585e22i 1.34023 2.32134i
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 14.16.c.a.9.5 10
3.2 odd 2 126.16.g.e.37.2 10
7.2 even 3 98.16.a.j.1.1 5
7.3 odd 6 98.16.c.m.67.1 10
7.4 even 3 inner 14.16.c.a.11.5 yes 10
7.5 odd 6 98.16.a.k.1.5 5
7.6 odd 2 98.16.c.m.79.1 10
21.11 odd 6 126.16.g.e.109.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.16.c.a.9.5 10 1.1 even 1 trivial
14.16.c.a.11.5 yes 10 7.4 even 3 inner
98.16.a.j.1.1 5 7.2 even 3
98.16.a.k.1.5 5 7.5 odd 6
98.16.c.m.67.1 10 7.3 odd 6
98.16.c.m.79.1 10 7.6 odd 2
126.16.g.e.37.2 10 3.2 odd 2
126.16.g.e.109.2 10 21.11 odd 6