Properties

Label 21.30.e.b.4.7
Level $21$
Weight $30$
Character 21.4
Analytic conductor $111.884$
Analytic rank $0$
Dimension $40$
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] = [21,30,Mod(4,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 30, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.4");
 
S:= CuspForms(chi, 30);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.e (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: \(111.883889004\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.7
Character \(\chi\) \(=\) 21.4
Dual form 21.30.e.b.16.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-9025.62 - 15632.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(1.05512e8 - 1.82752e8i) q^{4} +(-6.88316e9 - 1.19220e10i) q^{5} +8.63385e10 q^{6} +(-1.50044e12 - 9.84161e11i) q^{7} -1.35004e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\) \(q+(-9025.62 - 15632.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(1.05512e8 - 1.82752e8i) q^{4} +(-6.88316e9 - 1.19220e10i) q^{5} +8.63385e10 q^{6} +(-1.50044e12 - 9.84161e11i) q^{7} -1.35004e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-1.24249e14 + 2.15206e14i) q^{10} +(-3.33533e14 + 5.77697e14i) q^{11} +(5.04660e14 + 8.74098e14i) q^{12} -1.84474e16 q^{13} +(-1.84278e15 + 3.23388e16i) q^{14} +6.58439e16 q^{15} +(6.52033e16 + 1.12935e17i) q^{16} +(-2.58314e17 + 4.47413e17i) q^{17} +(-2.06477e17 + 3.57629e17i) q^{18} +(2.79792e18 + 4.84614e18i) q^{19} -2.90502e18 q^{20} +(7.66485e18 - 3.86149e18i) q^{21} +1.20414e19 q^{22} +(-1.01019e19 - 1.74969e19i) q^{23} +(3.22861e19 - 5.59211e19i) q^{24} +(-1.62349e18 + 2.81196e18i) q^{25} +(1.66499e20 + 2.88385e20i) q^{26} +1.09419e20 q^{27} +(-3.38172e20 + 1.70369e20i) q^{28} +2.56826e21 q^{29} +(-5.94281e20 - 1.02933e21i) q^{30} +(-1.84738e21 + 3.19976e21i) q^{31} +(-2.44699e21 + 4.23831e21i) q^{32} +(-1.59528e21 - 2.76310e21i) q^{33} +9.32577e21 q^{34} +(-1.40535e21 + 2.46624e22i) q^{35} -4.82755e21 q^{36} +(-3.72400e22 - 6.45015e22i) q^{37} +(5.05059e22 - 8.74788e22i) q^{38} +(4.41166e22 - 7.64122e22i) q^{39} +(9.29256e22 + 1.60952e23i) q^{40} -4.72810e23 q^{41} +(-1.29546e23 - 8.49710e22i) q^{42} -1.19955e23 q^{43} +(7.03835e22 + 1.21908e23i) q^{44} +(-1.57465e23 + 2.72737e23i) q^{45} +(-1.82351e23 + 3.15841e23i) q^{46} +(4.26144e23 + 7.38103e23i) q^{47} -6.23731e23 q^{48} +(1.28276e24 + 2.95336e24i) q^{49} +5.86118e22 q^{50} +(-1.23551e24 - 2.13996e24i) q^{51} +(-1.94642e24 + 3.37130e24i) q^{52} +(-8.73619e23 + 1.51315e24i) q^{53} +(-9.87574e23 - 1.71053e24i) q^{54} +9.18305e24 q^{55} +(2.02566e25 + 1.32866e25i) q^{56} -2.67647e25 q^{57} +(-2.31802e25 - 4.01492e25i) q^{58} +(2.18537e25 - 3.78517e25i) q^{59} +(6.94732e24 - 1.20331e25i) q^{60} +(6.32579e25 + 1.09566e26i) q^{61} +6.66951e25 q^{62} +(-2.33540e24 + 4.09838e25i) q^{63} +1.58354e26 q^{64} +(1.26976e26 + 2.19929e26i) q^{65} +(-2.87968e25 + 4.98774e25i) q^{66} +(-9.73747e25 + 1.68658e26i) q^{67} +(5.45104e25 + 9.44148e25i) q^{68} +9.66337e25 q^{69} +(3.98227e26 - 2.00624e26i) q^{70} -4.09404e26 q^{71} +(1.54423e26 + 2.67469e26i) q^{72} +(4.48142e25 - 7.76205e25i) q^{73} +(-6.72227e26 + 1.16433e27i) q^{74} +(-7.76508e24 - 1.34495e25i) q^{75} +1.18086e27 q^{76} +(1.06899e27 - 5.38551e26i) q^{77} -1.59272e27 q^{78} +(-2.20780e27 - 3.82403e27i) q^{79} +(8.97610e26 - 1.55471e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(4.26741e27 + 7.39136e27i) q^{82} -1.03646e28 q^{83} +(1.03038e26 - 1.80820e27i) q^{84} +7.11206e27 q^{85} +(1.08267e27 + 1.87524e27i) q^{86} +(-6.14196e27 + 1.06382e28i) q^{87} +(4.50284e27 - 7.79915e27i) q^{88} +(-1.40869e28 - 2.43992e28i) q^{89} +5.68486e27 q^{90} +(2.76793e28 + 1.81552e28i) q^{91} -4.26347e27 q^{92} +(-8.83597e27 - 1.53044e28i) q^{93} +(7.69243e27 - 1.33237e28i) q^{94} +(3.85170e28 - 6.67135e28i) q^{95} +(-1.17039e28 - 2.02717e28i) q^{96} -8.32280e28 q^{97} +(3.45916e28 - 4.67090e28i) q^{98} +1.52603e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9} - 167879133295903 q^{10} - 31\!\cdots\!14 q^{11}+ \cdots + 14\!\cdots\!08 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9025.62 15632.8i −0.389531 0.674687i 0.602856 0.797850i \(-0.294030\pi\)
−0.992386 + 0.123163i \(0.960696\pi\)
\(3\) −2.39148e6 + 4.14217e6i −0.288675 + 0.500000i
\(4\) 1.05512e8 1.82752e8i 0.196531 0.340402i
\(5\) −6.88316e9 1.19220e10i −0.504339 0.873541i −0.999987 0.00501772i \(-0.998403\pi\)
0.495648 0.868523i \(-0.334931\pi\)
\(6\) 8.63385e10 0.449792
\(7\) −1.50044e12 9.84161e11i −0.836177 0.548459i
\(8\) −1.35004e13 −1.08528
\(9\) −1.14384e13 1.98119e13i −0.166667 0.288675i
\(10\) −1.24249e14 + 2.15206e14i −0.392911 + 0.680543i
\(11\) −3.33533e14 + 5.77697e14i −0.264817 + 0.458676i −0.967516 0.252811i \(-0.918645\pi\)
0.702699 + 0.711487i \(0.251978\pi\)
\(12\) 5.04660e14 + 8.74098e14i 0.113467 + 0.196531i
\(13\) −1.84474e16 −1.29944 −0.649720 0.760174i \(-0.725114\pi\)
−0.649720 + 0.760174i \(0.725114\pi\)
\(14\) −1.84278e15 + 3.23388e16i −0.0443218 + 0.777800i
\(15\) 6.58439e16 0.582361
\(16\) 6.52033e16 + 1.12935e17i 0.226220 + 0.391824i
\(17\) −2.58314e17 + 4.47413e17i −0.372082 + 0.644465i −0.989886 0.141868i \(-0.954689\pi\)
0.617804 + 0.786332i \(0.288023\pi\)
\(18\) −2.06477e17 + 3.57629e17i −0.129844 + 0.224896i
\(19\) 2.79792e18 + 4.84614e18i 0.803356 + 1.39145i 0.917396 + 0.397977i \(0.130288\pi\)
−0.114040 + 0.993476i \(0.536379\pi\)
\(20\) −2.90502e18 −0.396474
\(21\) 7.66485e18 3.86149e18i 0.515613 0.259762i
\(22\) 1.20414e19 0.412617
\(23\) −1.01019e19 1.74969e19i −0.181697 0.314708i 0.760762 0.649031i \(-0.224826\pi\)
−0.942458 + 0.334323i \(0.891492\pi\)
\(24\) 3.22861e19 5.59211e19i 0.313294 0.542641i
\(25\) −1.62349e18 + 2.81196e18i −0.00871602 + 0.0150966i
\(26\) 1.66499e20 + 2.88385e20i 0.506172 + 0.876715i
\(27\) 1.09419e20 0.192450
\(28\) −3.38172e20 + 1.70369e20i −0.351032 + 0.176847i
\(29\) 2.56826e21 1.60276 0.801380 0.598155i \(-0.204099\pi\)
0.801380 + 0.598155i \(0.204099\pi\)
\(30\) −5.94281e20 1.02933e21i −0.226848 0.392911i
\(31\) −1.84738e21 + 3.19976e21i −0.438341 + 0.759229i −0.997562 0.0697897i \(-0.977767\pi\)
0.559221 + 0.829019i \(0.311101\pi\)
\(32\) −2.44699e21 + 4.23831e21i −0.366402 + 0.634627i
\(33\) −1.59528e21 2.76310e21i −0.152892 0.264817i
\(34\) 9.32577e21 0.579749
\(35\) −1.40535e21 + 2.46624e22i −0.0573850 + 1.00704i
\(36\) −4.82755e21 −0.131021
\(37\) −3.72400e22 6.45015e22i −0.679335 1.17664i −0.975181 0.221408i \(-0.928935\pi\)
0.295846 0.955236i \(-0.404398\pi\)
\(38\) 5.05059e22 8.74788e22i 0.625864 1.08403i
\(39\) 4.41166e22 7.64122e22i 0.375116 0.649720i
\(40\) 9.29256e22 + 1.60952e23i 0.547350 + 0.948038i
\(41\) −4.72810e23 −1.94680 −0.973400 0.229114i \(-0.926417\pi\)
−0.973400 + 0.229114i \(0.926417\pi\)
\(42\) −1.29546e23 8.49710e22i −0.376105 0.246692i
\(43\) −1.19955e23 −0.247586 −0.123793 0.992308i \(-0.539506\pi\)
−0.123793 + 0.992308i \(0.539506\pi\)
\(44\) 7.03835e22 + 1.21908e23i 0.104090 + 0.180288i
\(45\) −1.57465e23 + 2.72737e23i −0.168113 + 0.291180i
\(46\) −1.82351e23 + 3.15841e23i −0.141553 + 0.245177i
\(47\) 4.26144e23 + 7.38103e23i 0.242180 + 0.419467i 0.961335 0.275382i \(-0.0888043\pi\)
−0.719155 + 0.694849i \(0.755471\pi\)
\(48\) −6.23731e23 −0.261216
\(49\) 1.28276e24 + 2.95336e24i 0.398384 + 0.917219i
\(50\) 5.86118e22 0.0135806
\(51\) −1.23551e24 2.13996e24i −0.214822 0.372082i
\(52\) −1.94642e24 + 3.37130e24i −0.255381 + 0.442332i
\(53\) −8.73619e23 + 1.51315e24i −0.0869605 + 0.150620i −0.906225 0.422796i \(-0.861049\pi\)
0.819264 + 0.573416i \(0.194382\pi\)
\(54\) −9.87574e23 1.71053e24i −0.0749653 0.129844i
\(55\) 9.18305e24 0.534230
\(56\) 2.02566e25 + 1.32866e25i 0.907488 + 0.595233i
\(57\) −2.67647e25 −0.927635
\(58\) −2.31802e25 4.01492e25i −0.624325 1.08136i
\(59\) 2.18537e25 3.78517e25i 0.459379 0.795667i −0.539550 0.841954i \(-0.681405\pi\)
0.998928 + 0.0462867i \(0.0147388\pi\)
\(60\) 6.94732e24 1.20331e25i 0.114452 0.198237i
\(61\) 6.32579e25 + 1.09566e26i 0.820034 + 1.42034i 0.905656 + 0.424014i \(0.139379\pi\)
−0.0856213 + 0.996328i \(0.527288\pi\)
\(62\) 6.66951e25 0.682990
\(63\) −2.33540e24 + 4.09838e25i −0.0189637 + 0.332793i
\(64\) 1.58354e26 1.02334
\(65\) 1.26976e26 + 2.19929e26i 0.655358 + 1.13511i
\(66\) −2.87968e25 + 4.98774e25i −0.119112 + 0.206309i
\(67\) −9.73747e25 + 1.68658e26i −0.323863 + 0.560947i −0.981282 0.192578i \(-0.938315\pi\)
0.657418 + 0.753526i \(0.271648\pi\)
\(68\) 5.45104e25 + 9.44148e25i 0.146251 + 0.253315i
\(69\) 9.66337e25 0.209805
\(70\) 3.98227e26 2.00624e26i 0.701794 0.353558i
\(71\) −4.09404e26 −0.587362 −0.293681 0.955903i \(-0.594880\pi\)
−0.293681 + 0.955903i \(0.594880\pi\)
\(72\) 1.54423e26 + 2.67469e26i 0.180880 + 0.313294i
\(73\) 4.48142e25 7.76205e25i 0.0429768 0.0744381i −0.843737 0.536757i \(-0.819649\pi\)
0.886714 + 0.462319i \(0.152982\pi\)
\(74\) −6.72227e26 + 1.16433e27i −0.529244 + 0.916678i
\(75\) −7.76508e24 1.34495e25i −0.00503220 0.00871602i
\(76\) 1.18086e27 0.631538
\(77\) 1.06899e27 5.38551e26i 0.472999 0.238293i
\(78\) −1.59272e27 −0.584477
\(79\) −2.20780e27 3.82403e27i −0.673547 1.16662i −0.976891 0.213736i \(-0.931437\pi\)
0.303344 0.952881i \(-0.401897\pi\)
\(80\) 8.97610e26 1.55471e27i 0.228183 0.395224i
\(81\) −2.61674e26 + 4.53232e26i −0.0555556 + 0.0962250i
\(82\) 4.26741e27 + 7.39136e27i 0.758338 + 1.31348i
\(83\) −1.03646e28 −1.54498 −0.772488 0.635029i \(-0.780988\pi\)
−0.772488 + 0.635029i \(0.780988\pi\)
\(84\) 1.03038e26 1.80820e27i 0.0129106 0.226567i
\(85\) 7.11206e27 0.750622
\(86\) 1.08267e27 + 1.87524e27i 0.0964425 + 0.167043i
\(87\) −6.14196e27 + 1.06382e28i −0.462677 + 0.801380i
\(88\) 4.50284e27 7.79915e27i 0.287401 0.497793i
\(89\) −1.40869e28 2.43992e28i −0.763238 1.32197i −0.941173 0.337925i \(-0.890275\pi\)
0.177935 0.984042i \(-0.443058\pi\)
\(90\) 5.68486e27 0.261941
\(91\) 2.76793e28 + 1.81552e28i 1.08656 + 0.712690i
\(92\) −4.26347e27 −0.142837
\(93\) −8.83597e27 1.53044e28i −0.253076 0.438341i
\(94\) 7.69243e27 1.33237e28i 0.188673 0.326791i
\(95\) 3.85170e28 6.67135e28i 0.810328 1.40353i
\(96\) −1.17039e28 2.02717e28i −0.211542 0.366402i
\(97\) −8.32280e28 −1.29443 −0.647216 0.762307i \(-0.724067\pi\)
−0.647216 + 0.762307i \(0.724067\pi\)
\(98\) 3.45916e28 4.67090e28i 0.463653 0.626070i
\(99\) 1.52603e28 0.176544
\(100\) 3.42594e26 + 5.93391e26i 0.00342594 + 0.00593391i
\(101\) −7.60341e28 + 1.31695e29i −0.658186 + 1.14001i 0.322899 + 0.946434i \(0.395343\pi\)
−0.981085 + 0.193578i \(0.937991\pi\)
\(102\) −2.23024e28 + 3.86289e28i −0.167359 + 0.289875i
\(103\) −1.27941e29 2.21600e29i −0.833432 1.44355i −0.895301 0.445462i \(-0.853039\pi\)
0.0618688 0.998084i \(-0.480294\pi\)
\(104\) 2.49047e29 1.41026
\(105\) −9.87951e28 6.48010e28i −0.486957 0.319401i
\(106\) 3.15398e28 0.135495
\(107\) −4.44681e28 7.70210e28i −0.166719 0.288765i 0.770546 0.637385i \(-0.219984\pi\)
−0.937264 + 0.348620i \(0.886650\pi\)
\(108\) 1.15450e28 1.99965e28i 0.0378225 0.0655104i
\(109\) 9.52228e28 1.64931e29i 0.272933 0.472735i −0.696678 0.717384i \(-0.745339\pi\)
0.969612 + 0.244649i \(0.0786728\pi\)
\(110\) −8.28827e28 1.43557e29i −0.208099 0.360438i
\(111\) 3.56235e29 0.784429
\(112\) 1.33127e28 2.33624e29i 0.0257398 0.451706i
\(113\) 3.40220e29 0.578259 0.289130 0.957290i \(-0.406634\pi\)
0.289130 + 0.957290i \(0.406634\pi\)
\(114\) 2.41568e29 + 4.18408e29i 0.361343 + 0.625864i
\(115\) −1.39065e29 + 2.40868e29i −0.183274 + 0.317439i
\(116\) 2.70983e29 4.69356e29i 0.314993 0.545583i
\(117\) 2.11008e29 + 3.65477e29i 0.216573 + 0.375116i
\(118\) −7.88972e29 −0.715769
\(119\) 8.27912e29 4.17096e29i 0.664589 0.334815i
\(120\) −8.88920e29 −0.632026
\(121\) 5.70666e29 + 9.88422e29i 0.359744 + 0.623095i
\(122\) 1.14188e30 1.97780e30i 0.638858 1.10653i
\(123\) 1.13072e30 1.95846e30i 0.561993 0.973400i
\(124\) 3.89842e29 + 6.75226e29i 0.172296 + 0.298425i
\(125\) −2.51948e30 −0.991095
\(126\) 6.61772e29 3.33396e29i 0.231918 0.116839i
\(127\) 2.71889e30 0.849645 0.424823 0.905277i \(-0.360336\pi\)
0.424823 + 0.905277i \(0.360336\pi\)
\(128\) −1.15524e29 2.00093e29i −0.0322201 0.0558068i
\(129\) 2.86871e29 4.96875e29i 0.0714720 0.123793i
\(130\) 2.29208e30 3.96999e30i 0.510565 0.884324i
\(131\) −1.78449e30 3.09083e30i −0.355697 0.616086i 0.631540 0.775343i \(-0.282423\pi\)
−0.987237 + 0.159258i \(0.949090\pi\)
\(132\) −6.73284e29 −0.120192
\(133\) 5.71258e29 1.00250e31i 0.0914078 1.60411i
\(134\) 3.51547e30 0.504619
\(135\) −7.53148e29 1.30449e30i −0.0970601 0.168113i
\(136\) 3.48735e30 6.04026e30i 0.403814 0.699426i
\(137\) 1.66915e29 2.89105e29i 0.0173799 0.0301029i −0.857205 0.514976i \(-0.827801\pi\)
0.874585 + 0.484873i \(0.161134\pi\)
\(138\) −8.72179e29 1.51066e30i −0.0817257 0.141553i
\(139\) 1.71061e31 1.44356 0.721781 0.692122i \(-0.243324\pi\)
0.721781 + 0.692122i \(0.243324\pi\)
\(140\) 4.35882e30 + 2.85901e30i 0.331522 + 0.217450i
\(141\) −4.07647e30 −0.279645
\(142\) 3.69512e30 + 6.40014e30i 0.228796 + 0.396286i
\(143\) 6.15281e30 1.06570e31i 0.344113 0.596021i
\(144\) 1.49164e30 2.58360e30i 0.0754065 0.130608i
\(145\) −1.76778e31 3.06188e31i −0.808335 1.40008i
\(146\) −1.61790e30 −0.0669632
\(147\) −1.53010e31 1.74949e30i −0.573613 0.0655860i
\(148\) −1.57170e31 −0.534043
\(149\) −1.27971e31 2.21652e31i −0.394376 0.683079i 0.598646 0.801014i \(-0.295706\pi\)
−0.993021 + 0.117935i \(0.962372\pi\)
\(150\) −1.40169e29 + 2.42780e29i −0.00392039 + 0.00679032i
\(151\) 2.38204e31 4.12582e31i 0.605040 1.04796i −0.387005 0.922078i \(-0.626490\pi\)
0.992045 0.125883i \(-0.0401763\pi\)
\(152\) −3.77731e31 6.54249e31i −0.871867 1.51012i
\(153\) 1.18188e31 0.248055
\(154\) −1.80674e31 1.18506e31i −0.345021 0.226304i
\(155\) 5.08633e31 0.884291
\(156\) −9.30966e30 1.61248e31i −0.147444 0.255381i
\(157\) 9.54560e30 1.65335e31i 0.137803 0.238681i −0.788862 0.614571i \(-0.789329\pi\)
0.926665 + 0.375889i \(0.122663\pi\)
\(158\) −3.98536e31 + 6.90285e31i −0.524735 + 0.908867i
\(159\) −4.17849e30 7.23736e30i −0.0502067 0.0869605i
\(160\) 6.73721e31 0.739163
\(161\) −2.06252e30 + 3.61950e31i −0.0206739 + 0.362805i
\(162\) 9.44707e30 0.0865624
\(163\) 2.71893e31 + 4.70932e31i 0.227865 + 0.394673i 0.957175 0.289510i \(-0.0934922\pi\)
−0.729310 + 0.684183i \(0.760159\pi\)
\(164\) −4.98872e31 + 8.64071e31i −0.382607 + 0.662695i
\(165\) −2.19611e31 + 3.80378e31i −0.154219 + 0.267115i
\(166\) 9.35473e31 + 1.62029e32i 0.601816 + 1.04238i
\(167\) 2.29146e32 1.35121 0.675605 0.737264i \(-0.263882\pi\)
0.675605 + 0.737264i \(0.263882\pi\)
\(168\) −1.03479e32 + 5.21318e31i −0.559586 + 0.281915i
\(169\) 1.38768e32 0.688542
\(170\) −6.41907e31 1.11182e32i −0.292390 0.506435i
\(171\) 6.40074e31 1.10864e32i 0.267785 0.463818i
\(172\) −1.26567e31 + 2.19221e31i −0.0486585 + 0.0842790i
\(173\) −7.00551e31 1.21339e32i −0.247612 0.428876i 0.715251 0.698868i \(-0.246312\pi\)
−0.962863 + 0.269991i \(0.912979\pi\)
\(174\) 2.21740e32 0.720908
\(175\) 5.20337e30 2.62142e30i 0.0155680 0.00784304i
\(176\) −8.69899e31 −0.239627
\(177\) 1.04526e32 + 1.81044e32i 0.265222 + 0.459379i
\(178\) −2.54286e32 + 4.40436e32i −0.594610 + 1.02989i
\(179\) −3.02655e32 + 5.24213e32i −0.652497 + 1.13016i 0.330018 + 0.943975i \(0.392945\pi\)
−0.982515 + 0.186183i \(0.940388\pi\)
\(180\) 3.32288e31 + 5.75540e31i 0.0660790 + 0.114452i
\(181\) 2.32387e32 0.426454 0.213227 0.977003i \(-0.431603\pi\)
0.213227 + 0.977003i \(0.431603\pi\)
\(182\) 3.39945e31 5.96567e32i 0.0575935 1.01070i
\(183\) −6.05121e32 −0.946894
\(184\) 1.36379e32 + 2.36216e32i 0.197192 + 0.341547i
\(185\) −5.12657e32 + 8.87948e32i −0.685231 + 1.18685i
\(186\) −1.59500e32 + 2.76262e32i −0.197162 + 0.341495i
\(187\) −1.72313e32 2.98454e32i −0.197067 0.341330i
\(188\) 1.79853e32 0.190384
\(189\) −1.64177e32 1.07686e32i −0.160922 0.105551i
\(190\) −1.39056e33 −1.26259
\(191\) 1.47630e32 + 2.55703e32i 0.124220 + 0.215155i 0.921428 0.388550i \(-0.127024\pi\)
−0.797208 + 0.603705i \(0.793690\pi\)
\(192\) −3.78701e32 + 6.55930e32i −0.295412 + 0.511669i
\(193\) −4.88351e32 + 8.45849e32i −0.353306 + 0.611944i −0.986827 0.161782i \(-0.948276\pi\)
0.633520 + 0.773726i \(0.281609\pi\)
\(194\) 7.51184e32 + 1.30109e33i 0.504221 + 0.873336i
\(195\) −1.21465e33 −0.756742
\(196\) 6.75079e32 + 7.71874e31i 0.390518 + 0.0446512i
\(197\) −6.78060e32 −0.364341 −0.182170 0.983267i \(-0.558312\pi\)
−0.182170 + 0.983267i \(0.558312\pi\)
\(198\) −1.37734e32 2.38562e32i −0.0687695 0.119112i
\(199\) 1.49566e33 2.59056e33i 0.694165 1.20233i −0.276296 0.961073i \(-0.589107\pi\)
0.970461 0.241257i \(-0.0775596\pi\)
\(200\) 2.19177e31 3.79626e31i 0.00945934 0.0163841i
\(201\) −4.65740e32 8.06686e32i −0.186982 0.323863i
\(202\) 2.74502e33 1.02554
\(203\) −3.85354e33 2.52759e33i −1.34019 0.879049i
\(204\) −5.21443e32 −0.168877
\(205\) 3.25443e33 + 5.63684e33i 0.981847 + 1.70061i
\(206\) −2.30949e33 + 4.00016e33i −0.649295 + 1.12461i
\(207\) −2.31098e32 + 4.00273e32i −0.0605656 + 0.104903i
\(208\) −1.20283e33 2.08336e33i −0.293959 0.509151i
\(209\) −3.73280e33 −0.850968
\(210\) −1.21336e32 + 2.12931e33i −0.0258113 + 0.452960i
\(211\) 5.69004e33 1.12985 0.564924 0.825143i \(-0.308905\pi\)
0.564924 + 0.825143i \(0.308905\pi\)
\(212\) 1.84354e32 + 3.19311e32i 0.0341809 + 0.0592031i
\(213\) 9.79084e32 1.69582e33i 0.169557 0.293681i
\(214\) −8.02704e32 + 1.39032e33i −0.129884 + 0.224966i
\(215\) 8.25671e32 + 1.43010e33i 0.124868 + 0.216277i
\(216\) −1.47720e33 −0.208863
\(217\) 5.92097e33 2.98294e33i 0.782937 0.394438i
\(218\) −3.43778e33 −0.425264
\(219\) 2.14345e32 + 3.71257e32i 0.0248127 + 0.0429768i
\(220\) 9.68922e32 1.67822e33i 0.104993 0.181853i
\(221\) 4.76521e33 8.25359e33i 0.483498 0.837443i
\(222\) −3.21524e33 5.56896e33i −0.305559 0.529244i
\(223\) 1.18863e34 1.05834 0.529169 0.848516i \(-0.322504\pi\)
0.529169 + 0.848516i \(0.322504\pi\)
\(224\) 7.84276e33 3.95112e33i 0.654444 0.329704i
\(225\) 7.42803e31 0.00581068
\(226\) −3.07070e33 5.31860e33i −0.225250 0.390144i
\(227\) −8.92577e33 + 1.54599e34i −0.614145 + 1.06373i 0.376389 + 0.926462i \(0.377166\pi\)
−0.990534 + 0.137268i \(0.956168\pi\)
\(228\) −2.82400e33 + 4.89131e33i −0.182309 + 0.315769i
\(229\) 7.83028e33 + 1.35624e34i 0.474420 + 0.821719i 0.999571 0.0292898i \(-0.00932458\pi\)
−0.525151 + 0.851009i \(0.675991\pi\)
\(230\) 5.02060e33 0.285563
\(231\) −3.25712e32 + 5.71590e33i −0.0173964 + 0.305289i
\(232\) −3.46727e34 −1.73945
\(233\) −1.90916e33 3.30677e33i −0.0899875 0.155863i 0.817518 0.575903i \(-0.195349\pi\)
−0.907506 + 0.420040i \(0.862016\pi\)
\(234\) 3.80896e33 6.59732e33i 0.168724 0.292238i
\(235\) 5.86644e33 1.01610e34i 0.244281 0.423108i
\(236\) −4.61165e33 7.98762e33i −0.180565 0.312747i
\(237\) 2.11197e34 0.777745
\(238\) −1.39928e34 9.17806e33i −0.484773 0.317969i
\(239\) 2.34496e34 0.764481 0.382240 0.924063i \(-0.375153\pi\)
0.382240 + 0.924063i \(0.375153\pi\)
\(240\) 4.29324e33 + 7.43611e33i 0.131741 + 0.228183i
\(241\) 1.80219e34 3.12148e34i 0.520658 0.901806i −0.479054 0.877786i \(-0.659020\pi\)
0.999711 0.0240203i \(-0.00764664\pi\)
\(242\) 1.03012e34 1.78422e34i 0.280263 0.485430i
\(243\) −1.25158e33 2.16780e33i −0.0320750 0.0555556i
\(244\) 2.66979e34 0.644650
\(245\) 2.63804e34 3.56215e34i 0.600307 0.810594i
\(246\) −4.08217e34 −0.875654
\(247\) −5.16143e34 8.93985e34i −1.04391 1.80811i
\(248\) 2.49404e34 4.31981e34i 0.475724 0.823978i
\(249\) 2.47869e34 4.29321e34i 0.445996 0.772488i
\(250\) 2.27398e34 + 3.93866e34i 0.386062 + 0.668679i
\(251\) −6.32721e34 −1.01378 −0.506889 0.862011i \(-0.669205\pi\)
−0.506889 + 0.862011i \(0.669205\pi\)
\(252\) 7.24347e33 + 4.75109e33i 0.109557 + 0.0718596i
\(253\) 1.34772e34 0.192465
\(254\) −2.45397e34 4.25039e34i −0.330963 0.573245i
\(255\) −1.70084e34 + 2.94594e34i −0.216686 + 0.375311i
\(256\) 4.04225e34 7.00138e34i 0.486568 0.842760i
\(257\) 2.01462e34 + 3.48943e34i 0.229173 + 0.396939i 0.957563 0.288223i \(-0.0930645\pi\)
−0.728390 + 0.685162i \(0.759731\pi\)
\(258\) −1.03568e34 −0.111362
\(259\) −7.60337e33 + 1.33431e35i −0.0772965 + 1.35647i
\(260\) 5.35900e34 0.515194
\(261\) −2.93768e34 5.08822e34i −0.267127 0.462677i
\(262\) −3.22123e34 + 5.57933e34i −0.277110 + 0.479969i
\(263\) 4.93918e34 8.55492e34i 0.402066 0.696398i −0.591910 0.806004i \(-0.701626\pi\)
0.993975 + 0.109606i \(0.0349591\pi\)
\(264\) 2.15369e34 + 3.73031e34i 0.165931 + 0.287401i
\(265\) 2.40530e34 0.175430
\(266\) −1.61874e35 + 8.15511e34i −1.11788 + 0.563178i
\(267\) 1.34754e35 0.881311
\(268\) 2.05484e34 + 3.55909e34i 0.127299 + 0.220488i
\(269\) −2.42039e34 + 4.19224e34i −0.142062 + 0.246058i −0.928273 0.371900i \(-0.878707\pi\)
0.786211 + 0.617958i \(0.212040\pi\)
\(270\) −1.35953e34 + 2.35477e34i −0.0756158 + 0.130970i
\(271\) 6.00897e33 + 1.04078e34i 0.0316771 + 0.0548663i 0.881429 0.472316i \(-0.156582\pi\)
−0.849752 + 0.527182i \(0.823249\pi\)
\(272\) −6.73717e34 −0.336689
\(273\) −1.41396e35 + 7.12344e34i −0.670008 + 0.337545i
\(274\) −6.02604e33 −0.0270800
\(275\) −1.08297e33 1.87576e33i −0.00461629 0.00799566i
\(276\) 1.01960e34 1.76600e34i 0.0412334 0.0714183i
\(277\) −1.50659e35 + 2.60950e35i −0.578149 + 1.00138i 0.417543 + 0.908657i \(0.362891\pi\)
−0.995692 + 0.0927256i \(0.970442\pi\)
\(278\) −1.54393e35 2.67416e35i −0.562312 0.973953i
\(279\) 8.45244e34 0.292227
\(280\) 1.89728e34 3.32953e35i 0.0622789 1.09293i
\(281\) 2.81861e34 0.0878604 0.0439302 0.999035i \(-0.486012\pi\)
0.0439302 + 0.999035i \(0.486012\pi\)
\(282\) 3.67926e34 + 6.37267e34i 0.108930 + 0.188673i
\(283\) −2.26878e35 + 3.92965e35i −0.638101 + 1.10522i 0.347748 + 0.937588i \(0.386946\pi\)
−0.985849 + 0.167635i \(0.946387\pi\)
\(284\) −4.31970e34 + 7.48194e34i −0.115435 + 0.199939i
\(285\) 1.84226e35 + 3.19088e35i 0.467843 + 0.810328i
\(286\) −2.22132e35 −0.536171
\(287\) 7.09426e35 + 4.65322e35i 1.62787 + 1.06774i
\(288\) 1.11959e35 0.244268
\(289\) 1.07532e35 + 1.86251e35i 0.223110 + 0.386438i
\(290\) −3.19106e35 + 5.52707e35i −0.629743 + 1.09075i
\(291\) 1.99038e35 3.44745e35i 0.373670 0.647216i
\(292\) −9.45687e33 1.63798e34i −0.0168926 0.0292588i
\(293\) −2.21795e35 −0.377026 −0.188513 0.982071i \(-0.560367\pi\)
−0.188513 + 0.982071i \(0.560367\pi\)
\(294\) 1.10752e35 + 2.54988e35i 0.179190 + 0.412557i
\(295\) −6.01690e35 −0.926731
\(296\) 5.02755e35 + 8.70798e35i 0.737270 + 1.27699i
\(297\) −3.64949e34 + 6.32110e34i −0.0509640 + 0.0882722i
\(298\) −2.31003e35 + 4.00109e35i −0.307243 + 0.532161i
\(299\) 1.86353e35 + 3.22772e35i 0.236104 + 0.408944i
\(300\) −3.27723e33 −0.00395594
\(301\) 1.79986e35 + 1.18055e35i 0.207026 + 0.135791i
\(302\) −8.59977e35 −0.942727
\(303\) −3.63669e35 6.29893e35i −0.380004 0.658186i
\(304\) −3.64867e35 + 6.31969e35i −0.363470 + 0.629548i
\(305\) 8.70828e35 1.50832e36i 0.827151 1.43267i
\(306\) −1.06672e35 1.84761e35i −0.0966249 0.167359i
\(307\) −7.24376e34 −0.0625831 −0.0312916 0.999510i \(-0.509962\pi\)
−0.0312916 + 0.999510i \(0.509962\pi\)
\(308\) 1.43704e34 2.52185e35i 0.0118436 0.207842i
\(309\) 1.22388e36 0.962364
\(310\) −4.59073e35 7.95137e35i −0.344459 0.596620i
\(311\) 3.92832e35 6.80404e35i 0.281307 0.487238i −0.690400 0.723428i \(-0.742565\pi\)
0.971707 + 0.236190i \(0.0758987\pi\)
\(312\) −5.95593e35 + 1.03160e36i −0.407106 + 0.705129i
\(313\) −5.08479e34 8.80711e34i −0.0331803 0.0574699i 0.848958 0.528460i \(-0.177230\pi\)
−0.882139 + 0.470990i \(0.843897\pi\)
\(314\) −3.44620e35 −0.214714
\(315\) 5.04684e35 2.54256e35i 0.300273 0.151275i
\(316\) −9.31799e35 −0.529492
\(317\) −1.42951e36 2.47598e36i −0.775938 1.34396i −0.934266 0.356577i \(-0.883944\pi\)
0.158328 0.987387i \(-0.449390\pi\)
\(318\) −7.54269e34 + 1.30643e35i −0.0391141 + 0.0677476i
\(319\) −8.56602e35 + 1.48368e36i −0.424438 + 0.735148i
\(320\) −1.08998e36 1.88789e36i −0.516110 0.893928i
\(321\) 4.25379e35 0.192510
\(322\) 5.84446e35 2.94439e35i 0.252833 0.127375i
\(323\) −2.89097e36 −1.19566
\(324\) 5.52194e34 + 9.56429e34i 0.0218368 + 0.0378225i
\(325\) 2.99490e34 5.18733e34i 0.0113259 0.0196171i
\(326\) 4.90800e35 8.50090e35i 0.177521 0.307475i
\(327\) 4.55448e35 + 7.88859e35i 0.157578 + 0.272933i
\(328\) 6.38314e36 2.11283
\(329\) 8.70069e34 1.52688e36i 0.0275558 0.483575i
\(330\) 7.92851e35 0.240292
\(331\) 6.85761e35 + 1.18777e36i 0.198915 + 0.344531i 0.948177 0.317743i \(-0.102925\pi\)
−0.749262 + 0.662274i \(0.769592\pi\)
\(332\) −1.09359e36 + 1.89416e36i −0.303636 + 0.525914i
\(333\) −8.51931e35 + 1.47559e36i −0.226445 + 0.392214i
\(334\) −2.06818e36 3.58220e36i −0.526338 0.911644i
\(335\) 2.68098e36 0.653348
\(336\) 9.35874e35 + 6.13852e35i 0.218423 + 0.143266i
\(337\) 6.29368e36 1.40693 0.703463 0.710732i \(-0.251636\pi\)
0.703463 + 0.710732i \(0.251636\pi\)
\(338\) −1.25246e36 2.16933e36i −0.268209 0.464551i
\(339\) −8.13631e35 + 1.40925e36i −0.166929 + 0.289130i
\(340\) 7.50408e35 1.29974e36i 0.147521 0.255513i
\(341\) −1.23233e36 2.13445e36i −0.232160 0.402113i
\(342\) −2.31083e36 −0.417243
\(343\) 9.81868e35 5.69379e36i 0.169937 0.985455i
\(344\) 1.61945e36 0.268701
\(345\) −6.65145e35 1.15207e36i −0.105813 0.183274i
\(346\) −1.26458e36 + 2.19032e36i −0.192905 + 0.334121i
\(347\) −5.32739e35 + 9.22731e35i −0.0779358 + 0.134989i −0.902359 0.430985i \(-0.858166\pi\)
0.824423 + 0.565974i \(0.191500\pi\)
\(348\) 1.29610e36 + 2.24491e36i 0.181861 + 0.314993i
\(349\) 9.17906e36 1.23546 0.617731 0.786389i \(-0.288052\pi\)
0.617731 + 0.786389i \(0.288052\pi\)
\(350\) −8.79438e34 5.76835e34i −0.0113558 0.00744843i
\(351\) −2.01849e36 −0.250077
\(352\) −1.63231e36 2.82724e36i −0.194059 0.336119i
\(353\) 5.36805e36 9.29773e36i 0.612468 1.06083i −0.378355 0.925660i \(-0.623510\pi\)
0.990823 0.135165i \(-0.0431564\pi\)
\(354\) 1.88682e36 3.26806e36i 0.206625 0.357884i
\(355\) 2.81799e36 + 4.88091e36i 0.296230 + 0.513085i
\(356\) −5.94534e36 −0.600001
\(357\) −2.52256e35 + 4.42683e36i −0.0244429 + 0.428947i
\(358\) 1.09266e37 1.01667
\(359\) −9.88729e36 1.71253e37i −0.883503 1.53027i −0.847420 0.530923i \(-0.821845\pi\)
−0.0360826 0.999349i \(-0.511488\pi\)
\(360\) 2.12584e36 3.68206e36i 0.182450 0.316013i
\(361\) −9.59179e36 + 1.66135e37i −0.790761 + 1.36964i
\(362\) −2.09743e36 3.63286e36i −0.166117 0.287723i
\(363\) −5.45895e36 −0.415397
\(364\) 6.23839e36 3.14285e36i 0.456145 0.229802i
\(365\) −1.23385e36 −0.0866996
\(366\) 5.46159e36 + 9.45975e36i 0.368845 + 0.638858i
\(367\) −2.88220e36 + 4.99212e36i −0.187097 + 0.324061i −0.944281 0.329140i \(-0.893241\pi\)
0.757184 + 0.653201i \(0.226574\pi\)
\(368\) 1.31735e36 2.28172e36i 0.0822068 0.142386i
\(369\) 5.40819e36 + 9.36727e36i 0.324467 + 0.561993i
\(370\) 1.85082e37 1.06767
\(371\) 2.80000e36 1.41062e36i 0.155323 0.0782507i
\(372\) −3.72920e36 −0.198950
\(373\) 1.13789e37 + 1.97089e37i 0.583880 + 1.01131i 0.995014 + 0.0997352i \(0.0317996\pi\)
−0.411134 + 0.911575i \(0.634867\pi\)
\(374\) −3.11045e36 + 5.38746e36i −0.153527 + 0.265917i
\(375\) 6.02529e36 1.04361e37i 0.286104 0.495548i
\(376\) −5.75313e36 9.96471e36i −0.262833 0.455240i
\(377\) −4.73777e37 −2.08269
\(378\) −2.01635e35 + 3.53848e36i −0.00852973 + 0.149688i
\(379\) −2.74214e37 −1.11640 −0.558201 0.829706i \(-0.688508\pi\)
−0.558201 + 0.829706i \(0.688508\pi\)
\(380\) −8.12802e36 1.40781e37i −0.318510 0.551675i
\(381\) −6.50218e36 + 1.12621e37i −0.245272 + 0.424823i
\(382\) 2.66491e36 4.61576e36i 0.0967751 0.167619i
\(383\) −8.58577e36 1.48710e37i −0.300191 0.519945i 0.675988 0.736912i \(-0.263717\pi\)
−0.976179 + 0.216967i \(0.930384\pi\)
\(384\) 1.10509e36 0.0372045
\(385\) −1.37787e37 9.03760e36i −0.446711 0.293003i
\(386\) 1.76307e37 0.550495
\(387\) 1.37210e36 + 2.37654e36i 0.0412644 + 0.0714720i
\(388\) −8.78154e36 + 1.52101e37i −0.254396 + 0.440627i
\(389\) −1.98376e37 + 3.43598e37i −0.553632 + 0.958918i 0.444377 + 0.895840i \(0.353425\pi\)
−0.998009 + 0.0630782i \(0.979908\pi\)
\(390\) 1.09629e37 + 1.89884e37i 0.294775 + 0.510565i
\(391\) 1.04378e37 0.270424
\(392\) −1.73178e37 3.98716e37i −0.432359 0.995441i
\(393\) 1.70703e37 0.410724
\(394\) 6.11991e36 + 1.06000e37i 0.141922 + 0.245816i
\(395\) −3.03933e37 + 5.26428e37i −0.679392 + 1.17674i
\(396\) 1.61015e36 2.78886e36i 0.0346965 0.0600961i
\(397\) 2.40028e37 + 4.15741e37i 0.498655 + 0.863696i 0.999999 0.00155232i \(-0.000494118\pi\)
−0.501344 + 0.865248i \(0.667161\pi\)
\(398\) −5.39970e37 −1.08160
\(399\) 4.01590e37 + 2.63408e37i 0.775667 + 0.508770i
\(400\) −4.23427e35 −0.00788694
\(401\) −3.69759e37 6.40442e37i −0.664241 1.15050i −0.979490 0.201490i \(-0.935422\pi\)
0.315249 0.949009i \(-0.397912\pi\)
\(402\) −8.40719e36 + 1.45617e37i −0.145671 + 0.252309i
\(403\) 3.40794e37 5.90272e37i 0.569598 0.986572i
\(404\) 1.60450e37 + 2.77908e37i 0.258708 + 0.448096i
\(405\) 7.20457e36 0.112075
\(406\) −4.73275e36 + 8.30547e37i −0.0710372 + 1.24663i
\(407\) 4.96831e37 0.719597
\(408\) 1.66799e37 + 2.88904e37i 0.233142 + 0.403814i
\(409\) −5.82837e37 + 1.00950e38i −0.786247 + 1.36182i 0.142004 + 0.989866i \(0.454646\pi\)
−0.928251 + 0.371954i \(0.878688\pi\)
\(410\) 5.87465e37 1.01752e38i 0.764920 1.32488i
\(411\) 7.98349e35 + 1.38278e36i 0.0100343 + 0.0173799i
\(412\) −5.39972e37 −0.655182
\(413\) −7.00424e37 + 3.52868e37i −0.820513 + 0.413368i
\(414\) 8.34321e36 0.0943687
\(415\) 7.13415e37 + 1.23567e38i 0.779192 + 1.34960i
\(416\) 4.51406e37 7.81858e37i 0.476117 0.824659i
\(417\) −4.09089e37 + 7.08563e37i −0.416720 + 0.721781i
\(418\) 3.36908e37 + 5.83542e37i 0.331478 + 0.574137i
\(419\) 6.07527e37 0.577380 0.288690 0.957423i \(-0.406780\pi\)
0.288690 + 0.957423i \(0.406780\pi\)
\(420\) −2.22666e37 + 1.12177e37i −0.204427 + 0.102989i
\(421\) 1.84374e38 1.63535 0.817674 0.575682i \(-0.195263\pi\)
0.817674 + 0.575682i \(0.195263\pi\)
\(422\) −5.13561e37 8.89515e37i −0.440111 0.762294i
\(423\) 9.74881e36 1.68854e37i 0.0807265 0.139822i
\(424\) 1.17942e37 2.04282e37i 0.0943766 0.163465i
\(425\) −8.38738e35 1.45274e36i −0.00648614 0.0112343i
\(426\) −3.53473e37 −0.264191
\(427\) 1.29155e37 2.26653e38i 0.0933056 1.63741i
\(428\) −1.87677e37 −0.131062
\(429\) 2.94287e37 + 5.09720e37i 0.198674 + 0.344113i
\(430\) 1.49044e37 2.58151e37i 0.0972795 0.168493i
\(431\) −5.11713e36 + 8.86312e36i −0.0322928 + 0.0559328i −0.881720 0.471773i \(-0.843614\pi\)
0.849427 + 0.527706i \(0.176948\pi\)
\(432\) 7.13448e36 + 1.23573e37i 0.0435360 + 0.0754065i
\(433\) −2.21088e38 −1.30464 −0.652320 0.757943i \(-0.726204\pi\)
−0.652320 + 0.757943i \(0.726204\pi\)
\(434\) −1.00072e38 6.56387e37i −0.571100 0.374592i
\(435\) 1.69104e38 0.933385
\(436\) −2.00943e37 3.48043e37i −0.107280 0.185814i
\(437\) 5.65283e37 9.79099e37i 0.291934 0.505645i
\(438\) 3.86919e36 6.70164e36i 0.0193306 0.0334816i
\(439\) 7.97066e37 + 1.38056e38i 0.385264 + 0.667297i 0.991806 0.127755i \(-0.0407770\pi\)
−0.606542 + 0.795052i \(0.707444\pi\)
\(440\) −1.23975e38 −0.579790
\(441\) 4.38388e37 5.91956e37i 0.198381 0.267873i
\(442\) −1.72036e38 −0.753349
\(443\) −2.10638e38 3.64835e38i −0.892651 1.54612i −0.836685 0.547685i \(-0.815509\pi\)
−0.0559664 0.998433i \(-0.517824\pi\)
\(444\) 3.75871e37 6.51027e37i 0.154165 0.267021i
\(445\) −1.93925e38 + 3.35887e38i −0.769862 + 1.33344i
\(446\) −1.07281e38 1.85816e38i −0.412255 0.714047i
\(447\) 1.22416e38 0.455386
\(448\) −2.37601e38 1.55846e38i −0.855692 0.561260i
\(449\) 1.00487e38 0.350381 0.175190 0.984535i \(-0.443946\pi\)
0.175190 + 0.984535i \(0.443946\pi\)
\(450\) −6.70425e35 1.16121e36i −0.00226344 0.00392039i
\(451\) 1.57698e38 2.73141e38i 0.515545 0.892950i
\(452\) 3.58973e37 6.21759e37i 0.113646 0.196841i
\(453\) 1.13932e38 + 1.97337e38i 0.349320 + 0.605040i
\(454\) 3.22242e38 0.956914
\(455\) 2.59250e37 4.54957e38i 0.0745683 1.30859i
\(456\) 3.61335e38 1.00675
\(457\) −2.69358e38 4.66542e38i −0.727018 1.25923i −0.958138 0.286306i \(-0.907572\pi\)
0.231120 0.972925i \(-0.425761\pi\)
\(458\) 1.41346e38 2.44819e38i 0.369602 0.640170i
\(459\) −2.82644e37 + 4.89555e37i −0.0716072 + 0.124027i
\(460\) 2.93461e37 + 5.08290e37i 0.0720381 + 0.124774i
\(461\) 1.84846e38 0.439691 0.219845 0.975535i \(-0.429445\pi\)
0.219845 + 0.975535i \(0.429445\pi\)
\(462\) 9.22954e37 4.64977e37i 0.212751 0.107182i
\(463\) 3.10253e38 0.693093 0.346547 0.938033i \(-0.387354\pi\)
0.346547 + 0.938033i \(0.387354\pi\)
\(464\) 1.67459e38 + 2.90048e38i 0.362576 + 0.628000i
\(465\) −1.21639e38 + 2.10685e38i −0.255273 + 0.442145i
\(466\) −3.44628e37 + 5.96912e37i −0.0701058 + 0.121427i
\(467\) 5.18638e36 + 8.98307e36i 0.0102275 + 0.0177145i 0.871094 0.491117i \(-0.163411\pi\)
−0.860866 + 0.508831i \(0.830078\pi\)
\(468\) 8.90556e37 0.170254
\(469\) 3.12092e38 1.57229e38i 0.578464 0.291426i
\(470\) −2.11793e38 −0.380621
\(471\) 4.56563e37 + 7.90790e37i 0.0795605 + 0.137803i
\(472\) −2.95034e38 + 5.11014e38i −0.498555 + 0.863523i
\(473\) 4.00091e37 6.92978e37i 0.0655650 0.113562i
\(474\) −1.90619e38 3.30161e38i −0.302956 0.524735i
\(475\) −1.81695e37 −0.0280083
\(476\) 1.11295e37 1.95311e38i 0.0166409 0.292029i
\(477\) 3.99712e37 0.0579737
\(478\) −2.11647e38 3.66584e38i −0.297789 0.515785i
\(479\) −3.74456e38 + 6.48577e38i −0.511135 + 0.885312i 0.488782 + 0.872406i \(0.337442\pi\)
−0.999917 + 0.0129059i \(0.995892\pi\)
\(480\) −1.61119e38 + 2.79067e38i −0.213378 + 0.369582i
\(481\) 6.86980e38 + 1.18988e39i 0.882755 + 1.52898i
\(482\) −6.50634e38 −0.811249
\(483\) −1.44993e38 9.51031e37i −0.175435 0.115070i
\(484\) 2.40848e38 0.282804
\(485\) 5.72871e38 + 9.92242e38i 0.652832 + 1.13074i
\(486\) −2.25925e37 + 3.91314e37i −0.0249884 + 0.0432812i
\(487\) 7.36102e38 1.27497e39i 0.790256 1.36876i −0.135552 0.990770i \(-0.543281\pi\)
0.925808 0.377994i \(-0.123386\pi\)
\(488\) −8.54008e38 1.47919e39i −0.889969 1.54147i
\(489\) −2.60091e38 −0.263116
\(490\) −7.94964e38 9.08949e37i −0.780736 0.0892681i
\(491\) 1.03963e39 0.991283 0.495641 0.868527i \(-0.334933\pi\)
0.495641 + 0.868527i \(0.334933\pi\)
\(492\) −2.38609e38 4.13282e38i −0.220898 0.382607i
\(493\) −6.63418e38 + 1.14907e39i −0.596358 + 1.03292i
\(494\) −9.31701e38 + 1.61375e39i −0.813272 + 1.40863i
\(495\) −1.05039e38 1.81934e38i −0.0890383 0.154219i
\(496\) −4.81822e38 −0.396645
\(497\) 6.14288e38 + 4.02919e38i 0.491139 + 0.322144i
\(498\) −8.94868e38 −0.694918
\(499\) 1.02026e39 + 1.76715e39i 0.769581 + 1.33295i 0.937790 + 0.347202i \(0.112868\pi\)
−0.168209 + 0.985751i \(0.553798\pi\)
\(500\) −2.65835e38 + 4.60440e38i −0.194781 + 0.337371i
\(501\) −5.47998e38 + 9.49161e38i −0.390061 + 0.675605i
\(502\) 5.71070e38 + 9.89122e38i 0.394898 + 0.683984i
\(503\) −2.37381e38 −0.159481 −0.0797406 0.996816i \(-0.525409\pi\)
−0.0797406 + 0.996816i \(0.525409\pi\)
\(504\) 3.15290e37 5.53299e38i 0.0205810 0.361175i
\(505\) 2.09342e39 1.32780
\(506\) −1.21640e38 2.10687e38i −0.0749712 0.129854i
\(507\) −3.31860e38 + 5.74799e38i −0.198765 + 0.344271i
\(508\) 2.86875e38 4.96883e38i 0.166982 0.289221i
\(509\) −1.16863e38 2.02413e38i −0.0661103 0.114506i 0.831076 0.556159i \(-0.187726\pi\)
−0.897186 + 0.441653i \(0.854392\pi\)
\(510\) 6.14045e38 0.337623
\(511\) −1.43632e38 + 7.23609e37i −0.0767625 + 0.0386724i
\(512\) −1.58339e39 −0.822573
\(513\) 3.06145e38 + 5.30259e38i 0.154606 + 0.267785i
\(514\) 3.63664e38 6.29885e38i 0.178540 0.309240i
\(515\) −1.76128e39 + 3.05062e39i −0.840665 + 1.45607i
\(516\) −6.05367e37 1.04853e38i −0.0280930 0.0486585i
\(517\) −5.68533e38 −0.256533
\(518\) 2.15453e39 1.08543e39i 0.945303 0.476236i
\(519\) 6.70143e38 0.285918
\(520\) −1.71423e39 2.96914e39i −0.711248 1.23192i
\(521\) −1.10712e39 + 1.91758e39i −0.446731 + 0.773762i −0.998171 0.0604532i \(-0.980745\pi\)
0.551440 + 0.834215i \(0.314079\pi\)
\(522\) −5.30288e38 + 9.18486e38i −0.208108 + 0.360454i
\(523\) 1.21899e39 + 2.11135e39i 0.465291 + 0.805908i 0.999215 0.0396246i \(-0.0126162\pi\)
−0.533923 + 0.845533i \(0.679283\pi\)
\(524\) −7.53140e38 −0.279623
\(525\) −1.58541e36 + 2.78223e37i −0.000572576 + 0.0100481i
\(526\) −1.78317e39 −0.626468
\(527\) −9.54409e38 1.65309e39i −0.326198 0.564991i
\(528\) 2.08035e38 3.60327e38i 0.0691743 0.119813i
\(529\) 1.34143e39 2.32343e39i 0.433972 0.751662i
\(530\) −2.17093e38 3.76017e38i −0.0683355 0.118361i
\(531\) −9.99885e38 −0.306252
\(532\) −1.77181e39 1.16215e39i −0.528078 0.346373i
\(533\) 8.72211e39 2.52975
\(534\) −1.21624e39 2.10659e39i −0.343298 0.594610i
\(535\) −6.12162e38 + 1.06030e39i −0.168165 + 0.291271i
\(536\) 1.31460e39 2.27695e39i 0.351483 0.608786i
\(537\) −1.44759e39 2.50730e39i −0.376719 0.652497i
\(538\) 8.73820e38 0.221350
\(539\) −2.13399e39 2.43997e38i −0.526205 0.0601654i
\(540\) −3.17865e38 −0.0763014
\(541\) −1.89667e39 3.28513e39i −0.443233 0.767701i 0.554695 0.832054i \(-0.312835\pi\)
−0.997927 + 0.0643526i \(0.979502\pi\)
\(542\) 1.08469e38 1.87874e38i 0.0246784 0.0427442i
\(543\) −5.55749e38 + 9.62586e38i −0.123107 + 0.213227i
\(544\) −1.26418e39 2.18963e39i −0.272663 0.472266i
\(545\) −2.62173e39 −0.550604
\(546\) 2.38979e39 + 1.56749e39i 0.488726 + 0.320562i
\(547\) −4.59814e39 −0.915726 −0.457863 0.889023i \(-0.651385\pi\)
−0.457863 + 0.889023i \(0.651385\pi\)
\(548\) −3.52231e37 6.10081e37i −0.00683139 0.0118323i
\(549\) 1.44714e39 2.50652e39i 0.273345 0.473447i
\(550\) −1.95490e37 + 3.38598e37i −0.00359638 + 0.00622911i
\(551\) 7.18579e39 + 1.24462e40i 1.28759 + 2.23017i
\(552\) −1.30460e39 −0.227698
\(553\) −4.50773e38 + 7.91058e39i −0.0766378 + 1.34491i
\(554\) 5.43917e39 0.900827
\(555\) −2.45202e39 4.24703e39i −0.395618 0.685231i
\(556\) 1.80489e39 3.12617e39i 0.283705 0.491392i
\(557\) 1.92959e39 3.34215e39i 0.295505 0.511830i −0.679597 0.733586i \(-0.737845\pi\)
0.975102 + 0.221756i \(0.0711787\pi\)
\(558\) −7.62885e38 1.32135e39i −0.113832 0.197162i
\(559\) 2.21286e39 0.321723
\(560\) −2.87689e39 + 1.44936e39i −0.407566 + 0.205328i
\(561\) 1.64833e39 0.227553
\(562\) −2.54397e38 4.40628e38i −0.0342243 0.0592783i
\(563\) −3.83175e39 + 6.63678e39i −0.502372 + 0.870133i 0.497625 + 0.867392i \(0.334206\pi\)
−0.999996 + 0.00274065i \(0.999128\pi\)
\(564\) −4.30116e38 + 7.44983e38i −0.0549590 + 0.0951918i
\(565\) −2.34179e39 4.05610e39i −0.291639 0.505133i
\(566\) 8.19086e39 0.994240
\(567\) 8.38681e38 4.22521e38i 0.0992298 0.0499912i
\(568\) 5.52713e39 0.637454
\(569\) −1.42318e39 2.46502e39i −0.160005 0.277136i 0.774866 0.632126i \(-0.217818\pi\)
−0.934870 + 0.354990i \(0.884484\pi\)
\(570\) 3.32550e39 5.75994e39i 0.364478 0.631295i
\(571\) 7.76677e39 1.34524e40i 0.829883 1.43740i −0.0682473 0.997668i \(-0.521741\pi\)
0.898130 0.439730i \(-0.144926\pi\)
\(572\) −1.29839e39 2.24888e39i −0.135258 0.234274i
\(573\) −1.41222e39 −0.143437
\(574\) 8.71287e38 1.52901e40i 0.0862856 1.51422i
\(575\) 6.56008e37 0.00633469
\(576\) −1.81132e39 3.13729e39i −0.170556 0.295412i
\(577\) −6.70616e39 + 1.16154e40i −0.615778 + 1.06656i 0.374469 + 0.927239i \(0.377825\pi\)
−0.990247 + 0.139320i \(0.955508\pi\)
\(578\) 1.94109e39 3.36206e39i 0.173817 0.301059i
\(579\) −2.33577e39 4.04567e39i −0.203981 0.353306i
\(580\) −7.46086e39 −0.635453
\(581\) 1.55516e40 + 1.02005e40i 1.29187 + 0.847357i
\(582\) −7.18578e39 −0.582224
\(583\) −5.82762e38 1.00937e39i −0.0460572 0.0797733i
\(584\) −6.05011e38 + 1.04791e39i −0.0466420 + 0.0807863i
\(585\) 2.90481e39 5.03128e39i 0.218453 0.378371i
\(586\) 2.00184e39 + 3.46729e39i 0.146863 + 0.254375i
\(587\) 2.56735e40 1.83752 0.918762 0.394812i \(-0.129190\pi\)
0.918762 + 0.394812i \(0.129190\pi\)
\(588\) −1.93416e39 + 2.61170e39i −0.135059 + 0.182369i
\(589\) −2.06753e40 −1.40858
\(590\) 5.43062e39 + 9.40611e39i 0.360990 + 0.625253i
\(591\) 1.62157e39 2.80864e39i 0.105176 0.182170i
\(592\) 4.85634e39 8.41143e39i 0.307358 0.532359i
\(593\) −1.50168e39 2.60099e39i −0.0927438 0.160637i 0.815921 0.578163i \(-0.196230\pi\)
−0.908665 + 0.417527i \(0.862897\pi\)
\(594\) 1.31755e39 0.0794082
\(595\) −1.06713e40 6.99941e39i −0.627653 0.411686i
\(596\) −5.40098e39 −0.310029
\(597\) 7.15369e39 + 1.23905e40i 0.400776 + 0.694165i
\(598\) 3.36390e39 5.82644e39i 0.183940 0.318593i
\(599\) −1.64881e40 + 2.85581e40i −0.879996 + 1.52420i −0.0286515 + 0.999589i \(0.509121\pi\)
−0.851344 + 0.524608i \(0.824212\pi\)
\(600\) 1.04832e38 + 1.81574e38i 0.00546135 + 0.00945934i
\(601\) 1.99492e40 1.01449 0.507243 0.861803i \(-0.330665\pi\)
0.507243 + 0.861803i \(0.330665\pi\)
\(602\) 2.21051e38 3.87921e39i 0.0109735 0.192573i
\(603\) 4.45524e39 0.215909
\(604\) −5.02668e39 8.70647e39i −0.237819 0.411914i
\(605\) 7.85597e39 1.36069e40i 0.362866 0.628503i
\(606\) −6.56467e39 + 1.13703e40i −0.296047 + 0.512768i
\(607\) 9.18335e39 + 1.59060e40i 0.404357 + 0.700367i 0.994246 0.107117i \(-0.0341620\pi\)
−0.589889 + 0.807484i \(0.700829\pi\)
\(608\) −2.73859e40 −1.17740
\(609\) 1.96854e40 9.91734e39i 0.826405 0.416336i
\(610\) −3.14390e40 −1.28880
\(611\) −7.86124e39 1.36161e40i −0.314698 0.545072i
\(612\) 1.24702e39 2.15991e39i 0.0487505 0.0844383i
\(613\) 2.95385e38 5.11623e38i 0.0112775 0.0195332i −0.860332 0.509735i \(-0.829744\pi\)
0.871609 + 0.490202i \(0.163077\pi\)
\(614\) 6.53794e38 + 1.13240e39i 0.0243781 + 0.0422241i
\(615\) −3.11317e40 −1.13374
\(616\) −1.44319e40 + 7.27067e39i −0.513337 + 0.258615i
\(617\) 1.59945e39 0.0555692 0.0277846 0.999614i \(-0.491155\pi\)
0.0277846 + 0.999614i \(0.491155\pi\)
\(618\) −1.10462e40 1.91326e40i −0.374871 0.649295i
\(619\) −8.29268e39 + 1.43633e40i −0.274904 + 0.476147i −0.970111 0.242662i \(-0.921979\pi\)
0.695207 + 0.718810i \(0.255313\pi\)
\(620\) 5.36669e39 9.29538e39i 0.173791 0.301015i
\(621\) −1.10533e39 1.91450e39i −0.0349676 0.0605656i
\(622\) −1.41822e40 −0.438311
\(623\) −2.87615e39 + 5.04734e40i −0.0868431 + 1.52400i
\(624\) 1.15062e40 0.339434
\(625\) 1.76444e40 + 3.05609e40i 0.508564 + 0.880859i
\(626\) −9.17867e38 + 1.58979e39i −0.0258495 + 0.0447726i
\(627\) 8.92692e39 1.54619e40i 0.245653 0.425484i
\(628\) −2.01435e39 3.48896e39i −0.0541651 0.0938168i
\(629\) 3.84784e40 1.01107
\(630\) −8.52982e39 5.59482e39i −0.219029 0.143664i
\(631\) −5.76460e40 −1.44658 −0.723292 0.690542i \(-0.757372\pi\)
−0.723292 + 0.690542i \(0.757372\pi\)
\(632\) 2.98063e40 + 5.16260e40i 0.730988 + 1.26611i
\(633\) −1.36077e40 + 2.35691e40i −0.326159 + 0.564924i
\(634\) −2.58044e40 + 4.46945e40i −0.604503 + 1.04703i
\(635\) −1.87146e40 3.24146e40i −0.428509 0.742200i
\(636\) −1.76352e39 −0.0394687
\(637\) −2.36636e40 5.44817e40i −0.517676 1.19187i
\(638\) 3.09254e40 0.661326
\(639\) 4.68293e39 + 8.11107e39i 0.0978937 + 0.169557i
\(640\) −1.59033e39 + 2.75454e39i −0.0324997 + 0.0562911i
\(641\) −3.15195e40 + 5.45935e40i −0.629707 + 1.09068i 0.357903 + 0.933759i \(0.383492\pi\)
−0.987610 + 0.156926i \(0.949842\pi\)
\(642\) −3.83931e39 6.64988e39i −0.0749886 0.129884i
\(643\) 7.08503e40 1.35295 0.676477 0.736464i \(-0.263506\pi\)
0.676477 + 0.736464i \(0.263506\pi\)
\(644\) 6.39709e39 + 4.19594e39i 0.119437 + 0.0783400i
\(645\) −7.89832e39 −0.144185
\(646\) 2.60927e40 + 4.51940e40i 0.465745 + 0.806694i
\(647\) 2.13363e40 3.69555e40i 0.372397 0.645010i −0.617537 0.786542i \(-0.711869\pi\)
0.989934 + 0.141532i \(0.0452027\pi\)
\(648\) 3.53271e39 6.11883e39i 0.0602934 0.104431i
\(649\) 1.45779e40 + 2.52496e40i 0.243302 + 0.421412i
\(650\) −1.08123e39 −0.0176472
\(651\) −1.80406e39 + 3.16594e40i −0.0287957 + 0.505333i
\(652\) 1.14752e40 0.179130
\(653\) 3.02259e40 + 5.23529e40i 0.461465 + 0.799281i 0.999034 0.0439388i \(-0.0139907\pi\)
−0.537569 + 0.843220i \(0.680657\pi\)
\(654\) 8.22139e39 1.42399e40i 0.122763 0.212632i
\(655\) −2.45659e40 + 4.25493e40i −0.358784 + 0.621432i
\(656\) −3.08288e40 5.33971e40i −0.440404 0.762802i
\(657\) −2.05041e39 −0.0286512
\(658\) −2.46547e40 + 1.24208e40i −0.336996 + 0.169776i
\(659\) −4.28596e38 −0.00573072 −0.00286536 0.999996i \(-0.500912\pi\)
−0.00286536 + 0.999996i \(0.500912\pi\)
\(660\) 4.63432e39 + 8.02688e39i 0.0606177 + 0.104993i
\(661\) 6.22844e40 1.07880e41i 0.796999 1.38044i −0.124562 0.992212i \(-0.539753\pi\)
0.921562 0.388232i \(-0.126914\pi\)
\(662\) 1.23788e40 2.14408e40i 0.154967 0.268411i
\(663\) 2.27919e40 + 3.94767e40i 0.279148 + 0.483498i
\(664\) 1.39927e41 1.67674
\(665\) −1.23449e41 + 6.21929e40i −1.44736 + 0.729167i
\(666\) 3.07568e40 0.352829
\(667\) −2.59442e40 4.49367e40i −0.291217 0.504402i
\(668\) 2.41776e40 4.18769e40i 0.265555 0.459955i
\(669\) −2.84258e40 + 4.92349e40i −0.305516 + 0.529169i
\(670\) −2.41975e40 4.19113e40i −0.254499 0.440805i
\(671\) −8.43945e40 −0.868635
\(672\) −2.38961e39 + 4.19351e40i −0.0240698 + 0.422399i
\(673\) 9.88507e40 0.974454 0.487227 0.873275i \(-0.338008\pi\)
0.487227 + 0.873275i \(0.338008\pi\)
\(674\) −5.68044e40 9.83881e40i −0.548041 0.949235i
\(675\) −1.77640e38 + 3.07682e38i −0.00167740 + 0.00290534i
\(676\) 1.46416e40 2.53601e40i 0.135320 0.234381i
\(677\) 1.74012e40 + 3.01398e40i 0.157414 + 0.272649i 0.933935 0.357442i \(-0.116351\pi\)
−0.776521 + 0.630091i \(0.783018\pi\)
\(678\) 2.93741e40 0.260096
\(679\) 1.24879e41 + 8.19097e40i 1.08237 + 0.709943i
\(680\) −9.60158e40 −0.814636
\(681\) −4.26917e40 7.39442e40i −0.354577 0.614145i
\(682\) −2.22450e40 + 3.85295e40i −0.180867 + 0.313271i
\(683\) 1.16367e41 2.01554e41i 0.926257 1.60432i 0.136730 0.990608i \(-0.456341\pi\)
0.789527 0.613716i \(-0.210326\pi\)
\(684\) −1.35071e40 2.33950e40i −0.105256 0.182309i
\(685\) −4.59561e39 −0.0350615
\(686\) −9.78720e40 + 3.60406e40i −0.731070 + 0.269211i
\(687\) −7.49040e40 −0.547813
\(688\) −7.82148e39 1.35472e40i −0.0560089 0.0970102i
\(689\) 1.61160e40 2.79137e40i 0.113000 0.195722i
\(690\) −1.20067e40 + 2.07962e40i −0.0824350 + 0.142782i
\(691\) −1.03685e40 1.79587e40i −0.0697081 0.120738i 0.829065 0.559153i \(-0.188873\pi\)
−0.898773 + 0.438415i \(0.855540\pi\)
\(692\) −2.95666e40 −0.194654
\(693\) −2.28973e40 1.50186e40i −0.147622 0.0968275i
\(694\) 1.92332e40 0.121434
\(695\) −1.17744e41 2.03938e41i −0.728045 1.26101i
\(696\) 8.29191e40 1.43620e41i 0.502135 0.869724i
\(697\) 1.22134e41 2.11541e41i 0.724369 1.25464i
\(698\) −8.28467e40 1.43495e41i −0.481251 0.833551i
\(699\) 1.82629e40 0.103909
\(700\) 6.99483e37 1.22752e39i 0.000389812 0.00684079i
\(701\) −1.62292e41 −0.885904 −0.442952 0.896545i \(-0.646069\pi\)
−0.442952 + 0.896545i \(0.646069\pi\)
\(702\) 1.82181e40 + 3.15548e40i 0.0974128 + 0.168724i
\(703\) 2.08389e41 3.60940e41i 1.09150 1.89053i
\(704\) −5.28163e40 + 9.14806e40i −0.270997 + 0.469381i
\(705\) 2.80590e40 + 4.85996e40i 0.141036 + 0.244281i
\(706\) −1.93800e41 −0.954300
\(707\) 2.43694e41 1.22771e41i 1.17561 0.592263i
\(708\) 4.41148e40 0.208498
\(709\) 4.46824e40 + 7.73922e40i 0.206903 + 0.358366i 0.950737 0.309998i \(-0.100328\pi\)
−0.743835 + 0.668364i \(0.766995\pi\)
\(710\) 5.08683e40 8.81064e40i 0.230781 0.399725i
\(711\) −5.05075e40 + 8.74815e40i −0.224516 + 0.388872i
\(712\) 1.90179e41 + 3.29400e41i 0.828328 + 1.43471i
\(713\) 7.46480e40 0.318581
\(714\) 7.14806e40 3.60114e40i 0.298926 0.150597i
\(715\) −1.69403e41 −0.694199
\(716\) 6.38674e40 + 1.10622e41i 0.256472 + 0.444223i
\(717\) −5.60794e40 + 9.71324e40i −0.220687 + 0.382240i
\(718\) −1.78478e41 + 3.09133e41i −0.688303 + 1.19218i
\(719\) −1.17389e41 2.03323e41i −0.443667 0.768453i 0.554292 0.832323i \(-0.312989\pi\)
−0.997958 + 0.0638694i \(0.979656\pi\)
\(720\) −4.10689e40 −0.152122
\(721\) −2.61220e40 + 4.58414e41i −0.0948300 + 1.66416i
\(722\) 3.46287e41 1.23210
\(723\) 8.61980e40 + 1.49299e41i 0.300602 + 0.520658i
\(724\) 2.45196e40 4.24692e40i 0.0838115 0.145166i
\(725\) −4.16954e39 + 7.22185e39i −0.0139697 + 0.0241962i
\(726\) 4.92704e40 + 8.53389e40i 0.161810 + 0.280263i
\(727\) −9.07994e40 −0.292303 −0.146152 0.989262i \(-0.546689\pi\)
−0.146152 + 0.989262i \(0.546689\pi\)
\(728\) −3.73682e41 2.45103e41i −1.17923 0.773469i
\(729\) 1.19725e40 0.0370370
\(730\) 1.11363e40 + 1.92886e40i 0.0337722 + 0.0584951i
\(731\) 3.09861e40 5.36695e40i 0.0921224 0.159561i
\(732\) −6.38475e40 + 1.10587e41i −0.186094 + 0.322325i
\(733\) −2.15240e41 3.72806e41i −0.615057 1.06531i −0.990375 0.138413i \(-0.955800\pi\)
0.375318 0.926896i \(-0.377533\pi\)
\(734\) 1.04055e41 0.291520
\(735\) 8.44619e40 + 1.94460e41i 0.232003 + 0.534152i
\(736\) 9.88766e40 0.266296
\(737\) −6.49554e40 1.12506e41i −0.171529 0.297096i
\(738\) 9.76246e40 1.69091e41i 0.252779 0.437827i
\(739\) 4.17264e40 7.22723e40i 0.105942 0.183496i −0.808181 0.588934i \(-0.799548\pi\)
0.914123 + 0.405438i \(0.132881\pi\)
\(740\) 1.08183e41 + 1.87378e41i 0.269339 + 0.466508i
\(741\) 4.93739e41 1.20541
\(742\) −4.73237e40 3.10402e40i −0.113298 0.0743136i
\(743\) −1.37770e41 −0.323458 −0.161729 0.986835i \(-0.551707\pi\)
−0.161729 + 0.986835i \(0.551707\pi\)
\(744\) 1.19289e41 + 2.06615e41i 0.274659 + 0.475724i
\(745\) −1.76169e41 + 3.05133e41i −0.397798 + 0.689007i
\(746\) 2.05404e41 3.55770e41i 0.454879 0.787873i
\(747\) 1.18555e41 + 2.05343e41i 0.257496 + 0.445996i
\(748\) −7.27241e40 −0.154919
\(749\) −9.07916e39 + 1.59330e41i −0.0189697 + 0.332897i
\(750\) −2.17528e41 −0.445786
\(751\) −2.26445e41 3.92214e41i −0.455180 0.788396i 0.543518 0.839397i \(-0.317092\pi\)
−0.998699 + 0.0510018i \(0.983759\pi\)
\(752\) −5.55720e40 + 9.62536e40i −0.109572 + 0.189783i
\(753\) 1.51314e41 2.62084e41i 0.292653 0.506889i
\(754\) 4.27613e41 + 7.40648e41i 0.811272 + 1.40516i
\(755\) −6.55840e41 −1.22058
\(756\) −3.70025e40 + 1.86416e40i −0.0675561 + 0.0340342i
\(757\) 4.71197e40 0.0843941 0.0421970 0.999109i \(-0.486564\pi\)
0.0421970 + 0.999109i \(0.486564\pi\)
\(758\) 2.47495e41 + 4.28673e41i 0.434873 + 0.753222i
\(759\) −3.22306e40 + 5.58250e40i −0.0555600 + 0.0962327i
\(760\) −5.19996e41 + 9.00660e41i −0.879434 + 1.52322i
\(761\) −1.22144e41 2.11560e41i −0.202673 0.351040i 0.746716 0.665143i \(-0.231630\pi\)
−0.949389 + 0.314103i \(0.898296\pi\)
\(762\) 2.34745e41 0.382163
\(763\) −3.05195e41 + 1.53755e41i −0.487496 + 0.245597i
\(764\) 6.23070e40 0.0976525
\(765\) −8.13506e40 1.40903e41i −0.125104 0.216686i
\(766\) −1.54984e41 + 2.68440e41i −0.233867 + 0.405070i
\(767\) −4.03143e41 + 6.98265e41i −0.596935 + 1.03392i
\(768\) 1.93339e41 + 3.34874e41i 0.280920 + 0.486568i
\(769\) 7.26557e40 0.103595 0.0517974 0.998658i \(-0.483505\pi\)
0.0517974 + 0.998658i \(0.483505\pi\)
\(770\) −1.69224e40 + 2.96969e41i −0.0236780 + 0.415524i
\(771\) −1.92717e41 −0.264626
\(772\) 1.03054e41 + 1.78494e41i 0.138871 + 0.240532i
\(773\) −6.74869e41 + 1.16891e42i −0.892517 + 1.54589i −0.0556697 + 0.998449i \(0.517729\pi\)
−0.836848 + 0.547436i \(0.815604\pi\)
\(774\) 2.47680e40 4.28995e40i 0.0321475 0.0556811i
\(775\) −5.99840e39 1.03895e40i −0.00764118 0.0132349i
\(776\) 1.12361e42 1.40482
\(777\) −5.34511e41 3.50593e41i −0.655921 0.430227i
\(778\) 7.16188e41 0.862627
\(779\) −1.32289e42 2.29130e42i −1.56397 2.70888i
\(780\) −1.28160e41 + 2.21979e41i −0.148724 + 0.257597i
\(781\) 1.36550e41 2.36511e41i 0.155543 0.269409i
\(782\) −9.42075e40 1.63172e41i −0.105339 0.182452i
\(783\) 2.81017e41 0.308451
\(784\) −2.49899e41 + 3.37438e41i −0.269266 + 0.363589i
\(785\) −2.62815e41 −0.277997
\(786\) −1.54070e41 2.66857e41i −0.159990 0.277110i
\(787\) −5.80733e40 + 1.00586e41i −0.0592029 + 0.102542i −0.894108 0.447852i \(-0.852189\pi\)
0.834905 + 0.550394i \(0.185523\pi\)
\(788\) −7.15434e40 + 1.23917e41i −0.0716043 + 0.124022i
\(789\) 2.36240e41 + 4.09179e41i 0.232133 + 0.402066i
\(790\) 1.09727e42 1.05858
\(791\) −5.10481e41 3.34831e41i −0.483527 0.317152i
\(792\) −2.06021e41 −0.191600
\(793\) −1.16694e42 2.02120e42i −1.06559 1.84565i
\(794\) 4.33281e41 7.50464e41i 0.388483 0.672872i
\(795\) −5.75225e40 + 9.96318e40i −0.0506424 + 0.0877152i
\(796\) −3.15620e41 5.46669e41i −0.272850 0.472591i
\(797\) 2.24694e42 1.90742 0.953710 0.300727i \(-0.0972292\pi\)
0.953710 + 0.300727i \(0.0972292\pi\)
\(798\) 4.93215e40 8.65540e41i 0.0411145 0.721515i
\(799\) −4.40316e41 −0.360443
\(800\) −7.94531e39 1.37617e40i −0.00638713 0.0110628i
\(801\) −3.22263e41 + 5.58176e41i −0.254413 + 0.440656i
\(802\) −6.67461e41 + 1.15608e42i −0.517485 + 0.896310i
\(803\) 2.98941e40 + 5.17781e40i 0.0227620 + 0.0394249i
\(804\) −1.96565e41 −0.146992
\(805\) 4.45713e41 2.24547e41i 0.327352 0.164917i
\(806\) −1.23035e42 −0.887504
\(807\) −1.15766e41 2.00513e41i −0.0820194 0.142062i
\(808\) 1.02649e42 1.77794e42i 0.714318 1.23723i
\(809\) −4.94185e41 + 8.55954e41i −0.337782 + 0.585055i −0.984015 0.178085i \(-0.943010\pi\)
0.646233 + 0.763140i \(0.276343\pi\)
\(810\) −6.50257e40 1.12628e41i −0.0436568 0.0756158i
\(811\) 8.97128e41 0.591633 0.295816 0.955245i \(-0.404408\pi\)
0.295816 + 0.955245i \(0.404408\pi\)
\(812\) −8.68516e41 + 4.37551e41i −0.562620 + 0.283444i
\(813\) −5.74814e40 −0.0365775
\(814\) −4.48420e41 7.76687e41i −0.280305 0.485503i
\(815\) 3.74296e41 6.48300e41i 0.229842 0.398099i
\(816\) 1.61118e41 2.79065e41i 0.0971936 0.168344i
\(817\) −3.35625e41 5.81320e41i −0.198900 0.344505i
\(818\) 2.10419e42 1.22507
\(819\) 4.30821e40 7.56044e41i 0.0246422 0.432445i
\(820\) 1.37352e42 0.771855
\(821\) 1.32147e42 + 2.28885e42i 0.729595 + 1.26370i 0.957055 + 0.289908i \(0.0936246\pi\)
−0.227460 + 0.973787i \(0.573042\pi\)
\(822\) 1.44112e40 2.49609e40i 0.00781733 0.0135400i
\(823\) −4.65315e41 + 8.05949e41i −0.247999 + 0.429546i −0.962970 0.269607i \(-0.913106\pi\)
0.714972 + 0.699153i \(0.246439\pi\)
\(824\) 1.72726e42 + 2.99170e42i 0.904509 + 1.56665i
\(825\) 1.03596e40 0.00533044
\(826\) 1.18381e42 + 7.76476e41i 0.598509 + 0.392570i
\(827\) 3.42231e42 1.70016 0.850079 0.526654i \(-0.176554\pi\)
0.850079 + 0.526654i \(0.176554\pi\)
\(828\) 4.87672e40 + 8.44673e40i 0.0238061 + 0.0412334i
\(829\) −7.87401e41 + 1.36382e42i −0.377707 + 0.654208i −0.990728 0.135859i \(-0.956621\pi\)
0.613021 + 0.790067i \(0.289954\pi\)
\(830\) 1.28780e42 2.23054e42i 0.607039 1.05142i
\(831\) −7.20599e41 1.24811e42i −0.333794 0.578149i
\(832\) −2.92122e42 −1.32977
\(833\) −1.65272e42 1.88970e41i −0.739346 0.0845356i
\(834\) 1.47691e42 0.649302
\(835\) −1.57725e42 2.73187e42i −0.681468 1.18034i
\(836\) −3.93855e41 + 6.82176e41i −0.167242 + 0.289671i
\(837\) −2.02139e41 + 3.50115e41i −0.0843588 + 0.146114i
\(838\) −5.48330e41 9.49736e41i −0.224907 0.389551i
\(839\) 7.48218e40 0.0301634 0.0150817 0.999886i \(-0.495199\pi\)
0.0150817 + 0.999886i \(0.495199\pi\)
\(840\) 1.33378e42 + 8.74840e41i 0.528485 + 0.346640i
\(841\) 4.02830e42 1.56884
\(842\) −1.66409e42 2.88229e42i −0.637018 1.10335i
\(843\) −6.74066e40 + 1.16752e41i −0.0253631 + 0.0439302i
\(844\) 6.00368e41 1.03987e42i 0.222051 0.384603i
\(845\) −9.55159e41 1.65438e42i −0.347259 0.601470i
\(846\) −3.51956e41 −0.125782
\(847\) 1.16514e41 2.04470e42i 0.0409326 0.718323i
\(848\) −2.27851e41 −0.0786886
\(849\) −1.08515e42 1.87954e42i −0.368408 0.638101i
\(850\) −1.51402e40 + 2.62237e40i −0.00505311 + 0.00875224i
\(851\) −7.52385e41 + 1.30317e42i −0.246866 + 0.427585i
\(852\) −2.06610e41 3.57859e41i −0.0666465 0.115435i
\(853\) 1.97177e42 0.625309 0.312655 0.949867i \(-0.398782\pi\)
0.312655 + 0.949867i \(0.398782\pi\)
\(854\) −3.65980e42 + 1.84378e42i −1.14109 + 0.574871i
\(855\) −1.76229e42 −0.540218
\(856\) 6.00338e41 + 1.03982e42i 0.180937 + 0.313391i
\(857\) −1.35950e41 + 2.35473e41i −0.0402864 + 0.0697781i −0.885466 0.464705i \(-0.846160\pi\)
0.845179 + 0.534483i \(0.179494\pi\)
\(858\) 5.31225e41 9.20108e41i 0.154779 0.268085i
\(859\) 1.36711e42 + 2.36791e42i 0.391655 + 0.678367i 0.992668 0.120872i \(-0.0385692\pi\)
−0.601013 + 0.799240i \(0.705236\pi\)
\(860\) 3.48473e41 0.0981615
\(861\) −3.62402e42 + 1.82575e42i −1.00380 + 0.505704i
\(862\) 1.84741e41 0.0503162
\(863\) −1.49408e42 2.58783e42i −0.400146 0.693073i 0.593597 0.804762i \(-0.297707\pi\)
−0.993743 + 0.111689i \(0.964374\pi\)
\(864\) −2.67747e41 + 4.63752e41i −0.0705141 + 0.122134i
\(865\) −9.64401e41 + 1.67039e42i −0.249761 + 0.432598i
\(866\) 1.99546e42 + 3.45623e42i 0.508198 + 0.880225i
\(867\) −1.02865e42 −0.257626
\(868\) 7.95950e40 1.39681e42i 0.0196042 0.344033i
\(869\) 2.94551e42 0.713466
\(870\) −1.52627e42 2.64358e42i −0.363582 0.629743i
\(871\) 1.79631e42 3.11130e42i 0.420841 0.728917i
\(872\) −1.28555e42 + 2.22663e42i −0.296210 + 0.513050i
\(873\) 9.51994e41 + 1.64890e42i 0.215739 + 0.373670i
\(874\) −2.04081e42 −0.454870
\(875\) 3.78034e42 + 2.47957e42i 0.828731 + 0.543575i
\(876\) 9.04639e40 0.0195059
\(877\) −1.74802e42 3.02766e42i −0.370725 0.642114i 0.618952 0.785429i \(-0.287557\pi\)
−0.989677 + 0.143314i \(0.954224\pi\)
\(878\) 1.43880e42 2.49208e42i 0.300145 0.519866i
\(879\) 5.30420e41 9.18714e41i 0.108838 0.188513i
\(880\) 5.98766e41 + 1.03709e42i 0.120853 + 0.209324i
\(881\) 1.24917e42 0.248011 0.124005 0.992282i \(-0.460426\pi\)
0.124005 + 0.992282i \(0.460426\pi\)
\(882\) −1.32107e42 1.51049e41i −0.258006 0.0295000i
\(883\) 1.46375e41 0.0281215 0.0140607 0.999901i \(-0.495524\pi\)
0.0140607 + 0.999901i \(0.495524\pi\)
\(884\) −1.00557e42 1.74171e42i −0.190045 0.329167i
\(885\) 1.43893e42 2.49230e42i 0.267524 0.463365i
\(886\) −3.80227e42 + 6.58572e42i −0.695430 + 1.20452i
\(887\) 5.34238e42 + 9.25328e42i 0.961263 + 1.66496i 0.719335 + 0.694663i \(0.244446\pi\)
0.241928 + 0.970294i \(0.422220\pi\)
\(888\) −4.80933e42 −0.851326
\(889\) −4.07954e42 2.67583e42i −0.710454 0.465996i
\(890\) 7.00115e42 1.19954
\(891\) −1.74554e41 3.02336e41i −0.0294241 0.0509640i
\(892\) 1.25414e42 2.17224e42i 0.207997 0.360261i
\(893\) −2.38463e42 + 4.13031e42i −0.389113 + 0.673963i
\(894\) −1.10488e42 1.91371e42i −0.177387 0.307243i
\(895\) 8.33288e42 1.31632
\(896\) −2.35867e40 + 4.13922e41i −0.00366608 + 0.0643357i
\(897\) −1.78264e42 −0.272629
\(898\) −9.06961e41 1.57090e42i −0.136484 0.236397i
\(899\) −4.74457e42 + 8.21783e42i −0.702556 + 1.21686i
\(900\) 7.83746e39 1.35749e40i 0.00114198 0.00197797i
\(901\) −4.51336e41 7.81737e41i −0.0647128 0.112086i
\(902\) −5.69329e42 −0.803283
\(903\) −9.19440e41 + 4.63207e41i −0.127659 + 0.0643135i
\(904\) −4.59312e42 −0.627574
\(905\) −1.59955e42 2.77051e42i −0.215077 0.372525i
\(906\) 2.05662e42 3.56217e42i 0.272142 0.471364i
\(907\) −2.81496e42 + 4.87565e42i −0.366578 + 0.634932i −0.989028 0.147728i \(-0.952804\pi\)
0.622450 + 0.782660i \(0.286137\pi\)
\(908\) 1.88355e42 + 3.26241e42i 0.241397 + 0.418113i
\(909\) 3.47883e42 0.438791
\(910\) −7.34625e42 + 3.70098e42i −0.911938 + 0.459427i
\(911\) −7.40934e41 −0.0905239 −0.0452619 0.998975i \(-0.514412\pi\)
−0.0452619 + 0.998975i \(0.514412\pi\)
\(912\) −1.74515e42 3.02269e42i −0.209849 0.363470i
\(913\) 3.45695e42 5.98762e42i 0.409136 0.708644i
\(914\) −4.86224e42 + 8.42165e42i −0.566392 + 0.981019i
\(915\) 4.16514e42 + 7.21424e42i 0.477556 + 0.827151i
\(916\) 3.30475e42 0.372953
\(917\) −3.64344e41 + 6.39384e42i −0.0404721 + 0.710242i
\(918\) 1.02042e42 0.111573
\(919\) −5.62526e42 9.74323e42i −0.605435 1.04864i −0.991983 0.126375i \(-0.959666\pi\)
0.386548 0.922269i \(-0.373667\pi\)
\(920\) 1.87744e42 3.25182e42i 0.198904 0.344511i
\(921\) 1.73233e41 3.00049e41i 0.0180662 0.0312916i
\(922\) −1.66835e42 2.88967e42i −0.171273 0.296654i
\(923\) 7.55243e42 0.763242
\(924\) 1.01023e42 + 6.62620e41i 0.100502 + 0.0659206i
\(925\) 2.41834e41 0.0236844
\(926\) −2.80022e42 4.85013e42i −0.269981 0.467621i
\(927\) −2.92688e42 + 5.06951e42i −0.277811 + 0.481182i
\(928\) −6.28452e42 + 1.08851e43i −0.587255 + 1.01716i
\(929\) 1.30911e42 + 2.26744e42i 0.120434 + 0.208597i 0.919939 0.392062i \(-0.128238\pi\)
−0.799505 + 0.600659i \(0.794905\pi\)
\(930\) 4.39146e42 0.397746
\(931\) −1.07233e43 + 1.44797e43i −0.956222 + 1.29119i
\(932\) −8.05758e41 −0.0707415
\(933\) 1.87890e42 + 3.25435e42i 0.162413 + 0.281307i
\(934\) 9.36205e40 1.62156e41i 0.00796785 0.0138007i
\(935\) −2.37211e42 + 4.10861e42i −0.198777 + 0.344292i
\(936\) −2.84870e42 4.93410e42i −0.235043 0.407106i
\(937\) 5.96823e42 0.484866 0.242433 0.970168i \(-0.422055\pi\)
0.242433 + 0.970168i \(0.422055\pi\)
\(938\) −5.27476e42 3.45979e42i −0.421951 0.276763i
\(939\) 4.86408e41 0.0383133
\(940\) −1.23796e42 2.14421e42i −0.0960179 0.166308i
\(941\) 3.61707e42 6.26495e42i 0.276253 0.478485i −0.694197 0.719785i \(-0.744240\pi\)
0.970451 + 0.241300i \(0.0775738\pi\)
\(942\) 8.24152e41 1.42747e42i 0.0619825 0.107357i
\(943\) 4.77626e42 + 8.27273e42i 0.353727 + 0.612674i
\(944\) 5.69974e42 0.415682
\(945\) −1.53772e41 + 2.69854e42i −0.0110437 + 0.193806i
\(946\) −1.44443e42 −0.102158
\(947\) −7.25553e41 1.25670e42i −0.0505353 0.0875297i 0.839651 0.543126i \(-0.182759\pi\)
−0.890187 + 0.455596i \(0.849426\pi\)
\(948\) 2.22838e42 3.85967e42i 0.152851 0.264746i
\(949\) −8.26705e41 + 1.43189e42i −0.0558458 + 0.0967277i
\(950\) 1.63991e41 + 2.84041e41i 0.0109101 + 0.0188968i
\(951\) 1.36746e43 0.895976
\(952\) −1.11772e43 + 5.63097e42i −0.721266 + 0.363368i
\(953\) 2.45702e43 1.56157 0.780785 0.624799i \(-0.214819\pi\)
0.780785 + 0.624799i \(0.214819\pi\)
\(954\) −3.60765e41 6.24863e41i −0.0225825 0.0391141i
\(955\) 2.03232e42 3.52009e42i 0.125298 0.217023i
\(956\) 2.47422e42 4.28547e42i 0.150244 0.260231i
\(957\) −4.09710e42 7.09638e42i −0.245049 0.424438i
\(958\) 1.35188e43 0.796412
\(959\) −5.34973e41 + 2.69515e41i −0.0310429 + 0.0156392i
\(960\) 1.04266e43 0.595952
\(961\) 2.05530e42 + 3.55988e42i 0.115714 + 0.200422i
\(962\) 1.24008e43 2.14789e43i 0.687721 1.19117i
\(963\) −1.01729e42 + 1.76199e42i −0.0555729 + 0.0962550i
\(964\) −3.80304e42 6.58706e42i −0.204651 0.354466i
\(965\) 1.34456e43 0.712744
\(966\) −1.78075e41 + 3.12502e42i −0.00929896 + 0.163187i
\(967\) 9.75838e42 0.501989 0.250994 0.967989i \(-0.419242\pi\)
0.250994 + 0.967989i \(0.419242\pi\)
\(968\) −7.70423e42 1.33441e43i −0.390424 0.676234i
\(969\) 6.91370e42 1.19749e43i 0.345156 0.597828i
\(970\) 1.03410e43 1.79112e43i 0.508597 0.880916i
\(971\) −1.30620e43 2.26241e43i −0.632894 1.09620i −0.986957 0.160983i \(-0.948534\pi\)
0.354063 0.935221i \(-0.384800\pi\)
\(972\) −5.28226e41 −0.0252150
\(973\) −2.56667e43 1.68351e43i −1.20707 0.791735i
\(974\) −2.65751e43 −1.23132
\(975\) 1.43245e41 + 2.48108e41i 0.00653903 + 0.0113259i
\(976\) −8.24925e42 + 1.42881e43i −0.371016 + 0.642618i
\(977\) −1.24448e43 + 2.15551e43i −0.551465 + 0.955165i 0.446704 + 0.894682i \(0.352598\pi\)
−0.998169 + 0.0604834i \(0.980736\pi\)
\(978\) 2.34748e42 + 4.06595e42i 0.102492 + 0.177521i
\(979\) 1.87938e43 0.808472
\(980\) −3.72645e42 8.57957e42i −0.157949 0.363653i
\(981\) −4.35678e42 −0.181956
\(982\) −9.38331e42 1.62524e43i −0.386135 0.668806i
\(983\) 1.90796e43 3.30468e43i 0.773647 1.34000i −0.161905 0.986806i \(-0.551764\pi\)
0.935552 0.353189i \(-0.114903\pi\)
\(984\) −1.52652e43 + 2.64401e43i −0.609920 + 1.05641i
\(985\) 4.66719e42 + 8.08381e42i 0.183751 + 0.318266i
\(986\) 2.39510e43 0.929200
\(987\) 6.11651e42 + 4.01190e42i 0.233833 + 0.153374i
\(988\) −2.17837e43 −0.820646
\(989\) 1.21177e42 + 2.09885e42i 0.0449857 + 0.0779175i
\(990\) −1.89609e42 + 3.28412e42i −0.0693663 + 0.120146i
\(991\) 3.44445e42 5.96596e42i 0.124180 0.215086i −0.797232 0.603673i \(-0.793703\pi\)
0.921412 + 0.388587i \(0.127037\pi\)
\(992\) −9.04106e42 1.56596e43i −0.321218 0.556366i
\(993\) −6.55995e42 −0.229687
\(994\) 7.54442e41 1.32397e43i 0.0260330 0.456850i
\(995\) −4.11794e43 −1.40038
\(996\) −5.23063e42 9.05971e42i −0.175305 0.303636i
\(997\) 2.78815e43 4.82922e43i 0.920951 1.59513i 0.123004 0.992406i \(-0.460747\pi\)
0.797947 0.602727i \(-0.205919\pi\)
\(998\) 1.84170e43 3.18992e43i 0.599551 1.03845i
\(999\) −4.07476e42 7.05769e42i −0.130738 0.226445i
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 21.30.e.b.4.7 40
7.2 even 3 inner 21.30.e.b.16.7 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.30.e.b.4.7 40 1.1 even 1 trivial
21.30.e.b.16.7 yes 40 7.2 even 3 inner