Properties

Label 21.30.e.a.4.19
Level $21$
Weight $30$
Character 21.4
Analytic conductor $111.884$
Analytic rank $0$
Dimension $38$
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: \(38\)
Relative dimension: \(19\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.19
Character \(\chi\) \(=\) 21.4
Dual form 21.30.e.a.16.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(21714.1 + 37610.0i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(-6.74573e8 + 1.16839e9i) q^{4} +(-9.42284e9 - 1.63208e10i) q^{5} +2.07716e11 q^{6} +(-1.27489e12 - 1.26276e12i) q^{7} -3.52757e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\) \(q+(21714.1 + 37610.0i) q^{2} +(2.39148e6 - 4.14217e6i) q^{3} +(-6.74573e8 + 1.16839e9i) q^{4} +(-9.42284e9 - 1.63208e10i) q^{5} +2.07716e11 q^{6} +(-1.27489e12 - 1.26276e12i) q^{7} -3.52757e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(4.09218e14 - 7.08786e14i) q^{10} +(-8.08847e14 + 1.40096e15i) q^{11} +(3.22646e15 + 5.58840e15i) q^{12} -1.38940e16 q^{13} +(1.98090e16 - 7.53684e16i) q^{14} -9.01383e16 q^{15} +(-4.03824e17 - 6.99444e17i) q^{16} +(-8.45403e16 + 1.46428e17i) q^{17} +(4.96750e17 - 8.60396e17i) q^{18} +(-2.66809e18 - 4.62127e18i) q^{19} +2.54256e19 q^{20} +(-8.27944e18 + 2.26097e18i) q^{21} -7.02537e19 q^{22} +(3.07854e19 + 5.33218e19i) q^{23} +(-8.43614e19 + 1.46118e20i) q^{24} +(-8.44476e19 + 1.46268e20i) q^{25} +(-3.01697e20 - 5.22554e20i) q^{26} -1.09419e20 q^{27} +(2.33541e21 - 6.37759e20i) q^{28} +2.73312e21 q^{29} +(-1.95728e21 - 3.39010e21i) q^{30} +(3.23980e21 - 5.61150e21i) q^{31} +(8.06813e21 - 1.39744e22i) q^{32} +(3.86869e21 + 6.70077e21i) q^{33} -7.34288e21 q^{34} +(-8.59610e21 + 3.27061e22i) q^{35} +3.08641e22 q^{36} +(4.02829e22 + 6.97721e22i) q^{37} +(1.15871e23 - 2.00694e23i) q^{38} +(-3.32273e22 + 5.75514e22i) q^{39} +(3.32398e23 + 5.75730e23i) q^{40} +5.71205e22 q^{41} +(-2.64816e23 - 2.62295e23i) q^{42} -4.57813e23 q^{43} +(-1.09125e24 - 1.89011e24i) q^{44} +(-2.15564e23 + 3.73368e23i) q^{45} +(-1.33696e24 + 2.31568e24i) q^{46} +(8.12934e23 + 1.40804e24i) q^{47} -3.86296e24 q^{48} +(3.08038e22 + 3.21976e24i) q^{49} -7.33483e24 q^{50} +(4.04354e23 + 7.00361e23i) q^{51} +(9.37252e24 - 1.62337e25i) q^{52} +(-5.82157e24 + 1.00832e25i) q^{53} +(-2.37594e24 - 4.11525e24i) q^{54} +3.04866e25 q^{55} +(4.49728e25 + 4.45446e25i) q^{56} -2.55228e25 q^{57} +(5.93475e25 + 1.02793e26i) q^{58} +(4.87466e24 - 8.44315e24i) q^{59} +(6.08049e25 - 1.05317e26i) q^{60} +(2.38613e24 + 4.13290e24i) q^{61} +2.81398e26 q^{62} +(-1.04348e25 + 3.97019e25i) q^{63} +2.67168e26 q^{64} +(1.30921e26 + 2.26762e26i) q^{65} +(-1.68011e26 + 2.91003e26i) q^{66} +(1.55446e26 - 2.69240e26i) q^{67} +(-1.14057e26 - 1.97553e26i) q^{68} +2.94491e26 q^{69} +(-1.41673e27 + 3.86885e26i) q^{70} +2.89398e26 q^{71} +(4.03498e26 + 6.98879e26i) q^{72} +(-6.70869e25 + 1.16198e26i) q^{73} +(-1.74942e27 + 3.03008e27i) q^{74} +(4.03910e26 + 6.99593e26i) q^{75} +7.19929e27 q^{76} +(2.80027e27 - 7.64705e26i) q^{77} -2.88601e27 q^{78} +(-2.17720e27 - 3.77102e27i) q^{79} +(-7.61034e27 + 1.31815e28i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(1.24032e27 + 2.14830e27i) q^{82} +5.93368e27 q^{83} +(2.94338e27 - 1.11988e28i) q^{84} +3.18644e27 q^{85} +(-9.94103e27 - 1.72184e28i) q^{86} +(6.53623e27 - 1.13211e28i) q^{87} +(2.85327e28 - 4.94201e28i) q^{88} +(1.18492e28 + 2.05234e28i) q^{89} -1.87232e28 q^{90} +(1.77134e28 + 1.75447e28i) q^{91} -8.30679e28 q^{92} +(-1.54959e28 - 2.68396e28i) q^{93} +(-3.53043e28 + 6.11489e28i) q^{94} +(-5.02820e28 + 8.70909e28i) q^{95} +(-3.85896e28 - 6.68392e28i) q^{96} +3.54082e28 q^{97} +(-1.20426e29 + 7.10728e28i) q^{98} +3.70077e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9} - 226333527764279 q^{10} + 968182184010316 q^{11} + 26\!\cdots\!77 q^{12}+ \cdots - 44\!\cdots\!52 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 21714.1 + 37610.0i 0.937147 + 1.62319i 0.770759 + 0.637127i \(0.219877\pi\)
0.166388 + 0.986060i \(0.446790\pi\)
\(3\) 2.39148e6 4.14217e6i 0.288675 0.500000i
\(4\) −6.74573e8 + 1.16839e9i −1.25649 + 2.17631i
\(5\) −9.42284e9 1.63208e10i −0.690425 1.19585i −0.971699 0.236224i \(-0.924090\pi\)
0.281273 0.959628i \(-0.409243\pi\)
\(6\) 2.07716e11 1.08212
\(7\) −1.27489e12 1.26276e12i −0.710481 0.703716i
\(8\) −3.52757e13 −2.83577
\(9\) −1.14384e13 1.98119e13i −0.166667 0.288675i
\(10\) 4.09218e14 7.08786e14i 1.29406 2.24138i
\(11\) −8.08847e14 + 1.40096e15i −0.642203 + 1.11233i 0.342737 + 0.939432i \(0.388646\pi\)
−0.984940 + 0.172897i \(0.944687\pi\)
\(12\) 3.22646e15 + 5.58840e15i 0.725435 + 1.25649i
\(13\) −1.38940e16 −0.978698 −0.489349 0.872088i \(-0.662766\pi\)
−0.489349 + 0.872088i \(0.662766\pi\)
\(14\) 1.98090e16 7.53684e16i 0.476438 1.81273i
\(15\) −9.01383e16 −0.797235
\(16\) −4.03824e17 6.99444e17i −1.40105 2.42668i
\(17\) −8.45403e16 + 1.46428e17i −0.121774 + 0.210919i −0.920467 0.390820i \(-0.872192\pi\)
0.798693 + 0.601738i \(0.205525\pi\)
\(18\) 4.96750e17 8.60396e17i 0.312382 0.541062i
\(19\) −2.66809e18 4.62127e18i −0.766078 1.32689i −0.939675 0.342070i \(-0.888872\pi\)
0.173596 0.984817i \(-0.444461\pi\)
\(20\) 2.54256e19 3.47005
\(21\) −8.27944e18 + 2.26097e18i −0.556956 + 0.152095i
\(22\) −7.02537e19 −2.40736
\(23\) 3.07854e19 + 5.33218e19i 0.553721 + 0.959072i 0.998002 + 0.0631849i \(0.0201258\pi\)
−0.444281 + 0.895887i \(0.646541\pi\)
\(24\) −8.43614e19 + 1.46118e20i −0.818617 + 1.41789i
\(25\) −8.44476e19 + 1.46268e20i −0.453375 + 0.785268i
\(26\) −3.01697e20 5.22554e20i −0.917185 1.58861i
\(27\) −1.09419e20 −0.192450
\(28\) 2.33541e21 6.37759e20i 2.42421 0.662011i
\(29\) 2.73312e21 1.70564 0.852822 0.522201i \(-0.174889\pi\)
0.852822 + 0.522201i \(0.174889\pi\)
\(30\) −1.95728e21 3.39010e21i −0.747126 1.29406i
\(31\) 3.23980e21 5.61150e21i 0.768729 1.33148i −0.169523 0.985526i \(-0.554223\pi\)
0.938252 0.345952i \(-0.112444\pi\)
\(32\) 8.06813e21 1.39744e22i 1.20809 2.09247i
\(33\) 3.86869e21 + 6.70077e21i 0.370776 + 0.642203i
\(34\) −7.34288e21 −0.456481
\(35\) −8.59610e21 + 3.27061e22i −0.351006 + 1.33549i
\(36\) 3.08641e22 0.837660
\(37\) 4.02829e22 + 6.97721e22i 0.734846 + 1.27279i 0.954791 + 0.297278i \(0.0960788\pi\)
−0.219945 + 0.975512i \(0.570588\pi\)
\(38\) 1.15871e23 2.00694e23i 1.43586 2.48698i
\(39\) −3.32273e22 + 5.75514e22i −0.282526 + 0.489349i
\(40\) 3.32398e23 + 5.75730e23i 1.95789 + 3.39116i
\(41\) 5.71205e22 0.235194 0.117597 0.993061i \(-0.462481\pi\)
0.117597 + 0.993061i \(0.462481\pi\)
\(42\) −2.64816e23 2.62295e23i −0.768829 0.761509i
\(43\) −4.57813e23 −0.944922 −0.472461 0.881352i \(-0.656634\pi\)
−0.472461 + 0.881352i \(0.656634\pi\)
\(44\) −1.09125e24 1.89011e24i −1.61384 2.79526i
\(45\) −2.15564e23 + 3.73368e23i −0.230142 + 0.398617i
\(46\) −1.33696e24 + 2.31568e24i −1.03784 + 1.79758i
\(47\) 8.12934e23 + 1.40804e24i 0.461994 + 0.800197i 0.999060 0.0433431i \(-0.0138009\pi\)
−0.537066 + 0.843540i \(0.680468\pi\)
\(48\) −3.86296e24 −1.61779
\(49\) 3.08038e22 + 3.21976e24i 0.00956669 + 0.999954i
\(50\) −7.33483e24 −1.69952
\(51\) 4.04354e23 + 7.00361e23i 0.0703062 + 0.121774i
\(52\) 9.37252e24 1.62337e25i 1.22973 2.12995i
\(53\) −5.82157e24 + 1.00832e25i −0.579482 + 1.00369i 0.416057 + 0.909338i \(0.363412\pi\)
−0.995539 + 0.0943531i \(0.969922\pi\)
\(54\) −2.37594e24 4.11525e24i −0.180354 0.312382i
\(55\) 3.04866e25 1.77357
\(56\) 4.49728e25 + 4.45446e25i 2.01476 + 1.99558i
\(57\) −2.55228e25 −0.884591
\(58\) 5.93475e25 + 1.02793e26i 1.59844 + 2.76858i
\(59\) 4.87466e24 8.44315e24i 0.102468 0.177480i −0.810233 0.586108i \(-0.800659\pi\)
0.912701 + 0.408628i \(0.133993\pi\)
\(60\) 6.08049e25 1.05317e26i 1.00172 1.73503i
\(61\) 2.38613e24 + 4.13290e24i 0.0309322 + 0.0535762i 0.881077 0.472973i \(-0.156819\pi\)
−0.850145 + 0.526549i \(0.823486\pi\)
\(62\) 2.81398e26 2.88165
\(63\) −1.04348e25 + 3.97019e25i −0.0847319 + 0.322384i
\(64\) 2.67168e26 1.72653
\(65\) 1.30921e26 + 2.26762e26i 0.675718 + 1.17038i
\(66\) −1.68011e26 + 2.91003e26i −0.694944 + 1.20368i
\(67\) 1.55446e26 2.69240e26i 0.517005 0.895480i −0.482800 0.875731i \(-0.660380\pi\)
0.999805 0.0197488i \(-0.00628664\pi\)
\(68\) −1.14057e26 1.97553e26i −0.306016 0.530035i
\(69\) 2.94491e26 0.639382
\(70\) −1.41673e27 + 3.86885e26i −2.49670 + 0.681806i
\(71\) 2.89398e26 0.415193 0.207596 0.978215i \(-0.433436\pi\)
0.207596 + 0.978215i \(0.433436\pi\)
\(72\) 4.03498e26 + 6.98879e26i 0.472629 + 0.818617i
\(73\) −6.70869e25 + 1.16198e26i −0.0643363 + 0.111434i −0.896399 0.443247i \(-0.853826\pi\)
0.832063 + 0.554681i \(0.187160\pi\)
\(74\) −1.74942e27 + 3.03008e27i −1.37732 + 2.38558i
\(75\) 4.03910e26 + 6.99593e26i 0.261756 + 0.453375i
\(76\) 7.19929e27 3.85028
\(77\) 2.80027e27 7.64705e26i 1.23904 0.338360i
\(78\) −2.88601e27 −1.05907
\(79\) −2.17720e27 3.77102e27i −0.664209 1.15044i −0.979499 0.201449i \(-0.935435\pi\)
0.315290 0.948995i \(-0.397898\pi\)
\(80\) −7.61034e27 + 1.31815e28i −1.93464 + 3.35089i
\(81\) −2.61674e26 + 4.53232e26i −0.0555556 + 0.0962250i
\(82\) 1.24032e27 + 2.14830e27i 0.220411 + 0.381764i
\(83\) 5.93368e27 0.884487 0.442244 0.896895i \(-0.354183\pi\)
0.442244 + 0.896895i \(0.354183\pi\)
\(84\) 2.94338e27 1.11988e28i 0.368805 1.40321i
\(85\) 3.18644e27 0.336303
\(86\) −9.94103e27 1.72184e28i −0.885531 1.53378i
\(87\) 6.53623e27 1.13211e28i 0.492377 0.852822i
\(88\) 2.85327e28 4.94201e28i 1.82114 3.15431i
\(89\) 1.18492e28 + 2.05234e28i 0.641997 + 1.11197i 0.984986 + 0.172633i \(0.0552274\pi\)
−0.342989 + 0.939340i \(0.611439\pi\)
\(90\) −1.87232e28 −0.862707
\(91\) 1.77134e28 + 1.75447e28i 0.695347 + 0.688726i
\(92\) −8.30679e28 −2.78298
\(93\) −1.54959e28 2.68396e28i −0.443826 0.768729i
\(94\) −3.53043e28 + 6.11489e28i −0.865913 + 1.49980i
\(95\) −5.02820e28 + 8.70909e28i −1.05784 + 1.83223i
\(96\) −3.85896e28 6.68392e28i −0.697489 1.20809i
\(97\) 3.54082e28 0.550698 0.275349 0.961344i \(-0.411207\pi\)
0.275349 + 0.961344i \(0.411207\pi\)
\(98\) −1.20426e29 + 7.10728e28i −1.61415 + 0.952633i
\(99\) 3.70077e28 0.428136
\(100\) −1.13932e29 1.97336e29i −1.13932 1.97336i
\(101\) −9.28603e27 + 1.60839e28i −0.0803841 + 0.139229i −0.903415 0.428767i \(-0.858948\pi\)
0.823031 + 0.567997i \(0.192281\pi\)
\(102\) −1.75604e28 + 3.04155e28i −0.131775 + 0.228240i
\(103\) −1.05967e29 1.83541e29i −0.690290 1.19562i −0.971743 0.236043i \(-0.924150\pi\)
0.281452 0.959575i \(-0.409184\pi\)
\(104\) 4.90121e29 2.77537
\(105\) 1.14917e29 + 1.13823e29i 0.566420 + 0.561027i
\(106\) −5.05641e29 −2.17224
\(107\) −5.59441e28 9.68980e28i −0.209744 0.363287i 0.741890 0.670522i \(-0.233930\pi\)
−0.951634 + 0.307235i \(0.900596\pi\)
\(108\) 7.38111e28 1.27845e29i 0.241812 0.418830i
\(109\) 1.73977e29 3.01337e29i 0.498664 0.863712i −0.501335 0.865253i \(-0.667157\pi\)
0.999999 + 0.00154181i \(0.000490773\pi\)
\(110\) 6.61990e29 + 1.14660e30i 1.66210 + 2.87884i
\(111\) 3.85344e29 0.848527
\(112\) −3.68393e29 + 1.40165e30i −0.712280 + 2.71005i
\(113\) 1.98404e29 0.337220 0.168610 0.985683i \(-0.446072\pi\)
0.168610 + 0.985683i \(0.446072\pi\)
\(114\) −5.54205e29 9.59912e29i −0.828992 1.43586i
\(115\) 5.80171e29 1.00489e30i 0.764606 1.32434i
\(116\) −1.84369e30 + 3.19337e30i −2.14313 + 3.71200i
\(117\) 1.58925e29 + 2.75266e29i 0.163116 + 0.282526i
\(118\) 4.23396e29 0.384112
\(119\) 2.92683e29 7.99266e28i 0.234945 0.0641594i
\(120\) 3.17970e30 2.26078
\(121\) −5.15313e29 8.92548e29i −0.324850 0.562657i
\(122\) −1.03626e29 + 1.79485e29i −0.0579761 + 0.100418i
\(123\) 1.36603e29 2.36603e29i 0.0678946 0.117597i
\(124\) 4.37096e30 + 7.57073e30i 1.93180 + 3.34598i
\(125\) −3.27336e29 −0.128765
\(126\) −1.71977e30 + 4.69640e29i −0.602696 + 0.164586i
\(127\) −2.22463e30 −0.695190 −0.347595 0.937645i \(-0.613002\pi\)
−0.347595 + 0.937645i \(0.613002\pi\)
\(128\) 1.46977e30 + 2.54572e30i 0.409926 + 0.710013i
\(129\) −1.09485e30 + 1.89634e30i −0.272775 + 0.472461i
\(130\) −5.68568e30 + 9.84788e30i −1.26650 + 2.19363i
\(131\) −2.70016e30 4.67681e30i −0.538214 0.932215i −0.999000 0.0447034i \(-0.985766\pi\)
0.460786 0.887511i \(-0.347568\pi\)
\(132\) −1.04389e31 −1.86351
\(133\) −2.43400e30 + 9.26077e30i −0.389468 + 1.48183i
\(134\) 1.35015e31 1.93804
\(135\) 1.03104e30 + 1.78581e30i 0.132872 + 0.230142i
\(136\) 2.98222e30 5.16536e30i 0.345323 0.598117i
\(137\) −3.63450e29 + 6.29514e29i −0.0378439 + 0.0655476i −0.884327 0.466868i \(-0.845382\pi\)
0.846483 + 0.532416i \(0.178716\pi\)
\(138\) 6.39462e30 + 1.10758e31i 0.599195 + 1.03784i
\(139\) 1.55274e31 1.31034 0.655170 0.755482i \(-0.272597\pi\)
0.655170 + 0.755482i \(0.272597\pi\)
\(140\) −3.24149e31 3.21063e31i −2.46541 2.44193i
\(141\) 7.77647e30 0.533465
\(142\) 6.28404e30 + 1.08843e31i 0.389097 + 0.673936i
\(143\) 1.12381e31 1.94650e31i 0.628523 1.08863i
\(144\) −9.23820e30 + 1.60010e31i −0.467015 + 0.808894i
\(145\) −2.57538e31 4.46069e31i −1.17762 2.03970i
\(146\) −5.82694e30 −0.241171
\(147\) 1.34105e31 + 7.57241e30i 0.502739 + 0.283879i
\(148\) −1.08695e32 −3.69331
\(149\) −9.04511e29 1.56666e30i −0.0278749 0.0482807i 0.851751 0.523946i \(-0.175541\pi\)
−0.879626 + 0.475665i \(0.842207\pi\)
\(150\) −1.75411e31 + 3.03821e31i −0.490608 + 0.849758i
\(151\) −8.01935e30 + 1.38899e31i −0.203692 + 0.352805i −0.949715 0.313115i \(-0.898627\pi\)
0.746023 + 0.665920i \(0.231961\pi\)
\(152\) 9.41188e31 + 1.63019e32i 2.17242 + 3.76275i
\(153\) 3.86802e30 0.0811827
\(154\) 8.95660e31 + 8.87132e31i 1.71038 + 1.69410i
\(155\) −1.22112e32 −2.12300
\(156\) −4.48285e31 7.76452e31i −0.709982 1.22973i
\(157\) −6.71474e30 + 1.16303e31i −0.0969358 + 0.167898i −0.910415 0.413696i \(-0.864237\pi\)
0.813479 + 0.581594i \(0.197571\pi\)
\(158\) 9.45520e31 1.63769e32i 1.24492 2.15627i
\(159\) 2.78444e31 + 4.82279e31i 0.334564 + 0.579482i
\(160\) −3.04099e32 −3.33638
\(161\) 2.80843e31 1.06854e32i 0.281507 1.07106i
\(162\) −2.27281e31 −0.208255
\(163\) 9.04456e31 + 1.56656e32i 0.757996 + 1.31289i 0.943871 + 0.330315i \(0.107155\pi\)
−0.185875 + 0.982573i \(0.559512\pi\)
\(164\) −3.85320e31 + 6.67393e31i −0.295519 + 0.511854i
\(165\) 7.29081e31 1.26281e32i 0.511987 0.886787i
\(166\) 1.28845e32 + 2.23166e32i 0.828895 + 1.43569i
\(167\) −1.60739e32 −0.947837 −0.473919 0.880569i \(-0.657161\pi\)
−0.473919 + 0.880569i \(0.657161\pi\)
\(168\) 2.92063e32 7.97574e31i 1.57940 0.431307i
\(169\) −8.49474e30 −0.0421496
\(170\) 6.91908e31 + 1.19842e32i 0.315166 + 0.545883i
\(171\) −6.10373e31 + 1.05720e32i −0.255359 + 0.442296i
\(172\) 3.08829e32 5.34907e32i 1.18729 2.05644i
\(173\) 1.21507e32 + 2.10456e32i 0.429470 + 0.743863i 0.996826 0.0796089i \(-0.0253671\pi\)
−0.567356 + 0.823472i \(0.692034\pi\)
\(174\) 5.67714e32 1.84572
\(175\) 2.92362e32 7.98390e31i 0.874720 0.238871i
\(176\) 1.30653e33 3.59903
\(177\) −2.33153e31 4.03833e31i −0.0591601 0.102468i
\(178\) −5.14590e32 + 8.91296e32i −1.20329 + 2.08416i
\(179\) 6.30264e31 1.09165e32i 0.135879 0.235350i −0.790054 0.613038i \(-0.789947\pi\)
0.925933 + 0.377688i \(0.123281\pi\)
\(180\) −2.90828e32 5.03729e32i −0.578342 1.00172i
\(181\) −3.66789e32 −0.673095 −0.336548 0.941666i \(-0.609259\pi\)
−0.336548 + 0.941666i \(0.609259\pi\)
\(182\) −2.75226e32 + 1.04717e33i −0.466289 + 1.77412i
\(183\) 2.28256e31 0.0357175
\(184\) −1.08598e33 1.88097e33i −1.57023 2.71971i
\(185\) 7.59160e32 1.31490e33i 1.01471 1.75753i
\(186\) 6.72959e32 1.16560e33i 0.831861 1.44083i
\(187\) −1.36760e32 2.36876e32i −0.156407 0.270905i
\(188\) −2.19353e33 −2.32196
\(189\) 1.39498e32 + 1.38169e32i 0.136732 + 0.135430i
\(190\) −4.36732e33 −3.96541
\(191\) 8.57412e32 + 1.48508e33i 0.721449 + 1.24959i 0.960419 + 0.278559i \(0.0898568\pi\)
−0.238970 + 0.971027i \(0.576810\pi\)
\(192\) 6.38927e32 1.10665e33i 0.498406 0.863265i
\(193\) −1.37516e32 + 2.38184e32i −0.0994881 + 0.172318i −0.911473 0.411360i \(-0.865054\pi\)
0.811985 + 0.583679i \(0.198387\pi\)
\(194\) 7.68858e32 + 1.33170e33i 0.516085 + 0.893885i
\(195\) 1.25238e33 0.780252
\(196\) −3.78273e33 2.13597e33i −2.18823 1.23561i
\(197\) −1.52551e33 −0.819702 −0.409851 0.912152i \(-0.634419\pi\)
−0.409851 + 0.912152i \(0.634419\pi\)
\(198\) 8.03590e32 + 1.39186e33i 0.401226 + 0.694944i
\(199\) 1.00784e33 1.74563e33i 0.467759 0.810183i −0.531562 0.847019i \(-0.678395\pi\)
0.999321 + 0.0368366i \(0.0117281\pi\)
\(200\) 2.97895e33 5.15970e33i 1.28567 2.22684i
\(201\) −7.43494e32 1.28777e33i −0.298493 0.517005i
\(202\) −8.06553e32 −0.301327
\(203\) −3.48444e33 3.45127e33i −1.21183 1.20029i
\(204\) −1.09106e33 −0.353356
\(205\) −5.38237e32 9.32255e32i −0.162384 0.281257i
\(206\) 4.60198e33 7.97086e33i 1.29381 2.24094i
\(207\) 7.04270e32 1.21983e33i 0.184574 0.319691i
\(208\) 5.61073e33 + 9.71807e33i 1.37120 + 2.37499i
\(209\) 8.63231e33 1.96791
\(210\) −1.78555e33 + 6.79358e33i −0.379833 + 1.44517i
\(211\) 9.20405e33 1.82761 0.913805 0.406154i \(-0.133130\pi\)
0.913805 + 0.406154i \(0.133130\pi\)
\(212\) −7.85414e33 1.36038e34i −1.45623 2.52226i
\(213\) 6.92092e32 1.19874e33i 0.119856 0.207596i
\(214\) 2.42956e33 4.20812e33i 0.393122 0.680907i
\(215\) 4.31390e33 + 7.47190e33i 0.652398 + 1.12999i
\(216\) 3.85984e33 0.545745
\(217\) −1.12163e34 + 3.06299e33i −1.48315 + 0.405023i
\(218\) 1.51111e34 1.86929
\(219\) 3.20875e32 + 5.55771e32i 0.0371446 + 0.0643363i
\(220\) −2.05654e34 + 3.56203e34i −2.22848 + 3.85984i
\(221\) 1.17460e33 2.03447e33i 0.119180 0.206426i
\(222\) 8.36742e33 + 1.44928e34i 0.795195 + 1.37732i
\(223\) −6.10299e33 −0.543403 −0.271702 0.962382i \(-0.587586\pi\)
−0.271702 + 0.962382i \(0.587586\pi\)
\(224\) −2.79323e34 + 7.62782e33i −2.33083 + 0.636508i
\(225\) 3.86378e33 0.302250
\(226\) 4.30818e33 + 7.46198e33i 0.316025 + 0.547371i
\(227\) −1.15761e34 + 2.00503e34i −0.796500 + 1.37958i 0.125383 + 0.992108i \(0.459984\pi\)
−0.921882 + 0.387470i \(0.873349\pi\)
\(228\) 1.72170e34 2.98207e34i 1.11148 1.92514i
\(229\) 6.64258e33 + 1.15053e34i 0.402460 + 0.697081i 0.994022 0.109178i \(-0.0348220\pi\)
−0.591562 + 0.806259i \(0.701489\pi\)
\(230\) 5.03917e34 2.86619
\(231\) 3.52926e33 1.34280e34i 0.188499 0.717195i
\(232\) −9.64130e34 −4.83682
\(233\) 1.44302e33 + 2.49939e33i 0.0680161 + 0.117807i 0.898028 0.439938i \(-0.145000\pi\)
−0.830012 + 0.557746i \(0.811666\pi\)
\(234\) −6.90185e33 + 1.19544e34i −0.305728 + 0.529537i
\(235\) 1.53203e34 2.65355e34i 0.637945 1.10495i
\(236\) 6.57662e33 + 1.13910e34i 0.257501 + 0.446005i
\(237\) −2.08269e34 −0.766963
\(238\) 9.36140e33 + 9.27227e33i 0.324321 + 0.321233i
\(239\) 8.59862e33 0.280323 0.140162 0.990129i \(-0.455238\pi\)
0.140162 + 0.990129i \(0.455238\pi\)
\(240\) 3.64000e34 + 6.30467e34i 1.11696 + 1.93464i
\(241\) 1.37703e34 2.38509e34i 0.397829 0.689060i −0.595629 0.803260i \(-0.703097\pi\)
0.993458 + 0.114200i \(0.0364305\pi\)
\(242\) 2.23792e34 3.87618e34i 0.608865 1.05458i
\(243\) 1.25158e33 + 2.16780e33i 0.0320750 + 0.0555556i
\(244\) −6.43847e33 −0.155464
\(245\) 5.22589e34 3.08420e34i 1.18919 0.701834i
\(246\) 1.18649e34 0.254509
\(247\) 3.70704e34 + 6.42079e34i 0.749760 + 1.29862i
\(248\) −1.14286e35 + 1.97950e35i −2.17994 + 3.77577i
\(249\) 1.41903e34 2.45783e34i 0.255329 0.442244i
\(250\) −7.10783e33 1.23111e34i −0.120672 0.209010i
\(251\) 7.50851e34 1.20305 0.601526 0.798853i \(-0.294559\pi\)
0.601526 + 0.798853i \(0.294559\pi\)
\(252\) −3.93485e34 3.89739e34i −0.595142 0.589475i
\(253\) −9.96026e34 −1.42240
\(254\) −4.83059e34 8.36683e34i −0.651495 1.12842i
\(255\) 7.62032e33 1.31988e34i 0.0970824 0.168152i
\(256\) 7.88749e33 1.36615e34i 0.0949422 0.164445i
\(257\) 1.60817e34 + 2.78544e34i 0.182938 + 0.316857i 0.942880 0.333134i \(-0.108106\pi\)
−0.759942 + 0.649991i \(0.774773\pi\)
\(258\) −9.50953e34 −1.02252
\(259\) 3.67486e34 1.39820e35i 0.373589 1.42142i
\(260\) −3.53263e35 −3.39613
\(261\) −3.12626e34 5.41484e34i −0.284274 0.492377i
\(262\) 1.17263e35 2.03106e35i 1.00877 1.74725i
\(263\) 5.32885e34 9.22983e34i 0.433785 0.751338i −0.563410 0.826177i \(-0.690511\pi\)
0.997196 + 0.0748391i \(0.0238443\pi\)
\(264\) −1.36471e35 2.36375e35i −1.05144 1.82114i
\(265\) 2.19423e35 1.60036
\(266\) −4.01150e35 + 1.09547e35i −2.77027 + 0.756514i
\(267\) 1.13349e35 0.741315
\(268\) 2.09719e35 + 3.63245e35i 1.29922 + 2.25032i
\(269\) −1.13451e35 + 1.96504e35i −0.665889 + 1.15335i 0.313155 + 0.949702i \(0.398614\pi\)
−0.979044 + 0.203651i \(0.934719\pi\)
\(270\) −4.47762e34 + 7.75547e34i −0.249042 + 0.431354i
\(271\) 1.10556e35 + 1.91489e35i 0.582812 + 1.00946i 0.995144 + 0.0984267i \(0.0313810\pi\)
−0.412332 + 0.911034i \(0.635286\pi\)
\(272\) 1.36558e35 0.682444
\(273\) 1.15035e35 3.14139e34i 0.545092 0.148855i
\(274\) −3.15680e34 −0.141861
\(275\) −1.36610e35 2.36616e35i −0.582317 1.00860i
\(276\) −1.98656e35 + 3.44082e35i −0.803377 + 1.39149i
\(277\) 2.61093e34 4.52225e34i 0.100193 0.173540i −0.811571 0.584254i \(-0.801387\pi\)
0.911764 + 0.410714i \(0.134721\pi\)
\(278\) 3.37164e35 + 5.83985e35i 1.22798 + 2.12693i
\(279\) −1.48232e35 −0.512486
\(280\) 3.03234e35 1.15373e36i 0.995374 3.78716i
\(281\) 5.45159e35 1.69935 0.849673 0.527310i \(-0.176799\pi\)
0.849673 + 0.527310i \(0.176799\pi\)
\(282\) 1.68860e35 + 2.92473e35i 0.499935 + 0.865913i
\(283\) 1.06644e35 1.84713e35i 0.299940 0.519511i −0.676182 0.736735i \(-0.736367\pi\)
0.976122 + 0.217224i \(0.0697001\pi\)
\(284\) −1.95220e35 + 3.38132e35i −0.521686 + 0.903586i
\(285\) 2.40497e35 + 4.16553e35i 0.610744 + 1.05784i
\(286\) 9.76105e35 2.35608
\(287\) −7.28226e34 7.21292e34i −0.167101 0.165510i
\(288\) −3.69146e35 −0.805391
\(289\) 2.26690e35 + 3.92639e35i 0.470342 + 0.814657i
\(290\) 1.11844e36 1.93720e36i 2.20721 3.82300i
\(291\) 8.46781e34 1.46667e35i 0.158973 0.275349i
\(292\) −9.05101e34 1.56768e35i −0.161676 0.280031i
\(293\) 1.70067e35 0.289095 0.144547 0.989498i \(-0.453827\pi\)
0.144547 + 0.989498i \(0.453827\pi\)
\(294\) 6.39846e33 + 6.68796e35i 0.0103523 + 1.08208i
\(295\) −1.83732e35 −0.282987
\(296\) −1.42101e36 2.46126e36i −2.08386 3.60934i
\(297\) 8.85032e34 1.53292e35i 0.123592 0.214068i
\(298\) 3.92814e34 6.80373e34i 0.0522457 0.0904923i
\(299\) −4.27732e35 7.40854e35i −0.541925 0.938642i
\(300\) −1.08987e36 −1.31558
\(301\) 5.83664e35 + 5.78106e35i 0.671349 + 0.664957i
\(302\) −6.96534e35 −0.763557
\(303\) 4.44148e34 + 7.69287e34i 0.0464098 + 0.0803841i
\(304\) −2.15488e36 + 3.73236e36i −2.14662 + 3.71806i
\(305\) 4.49682e34 7.78873e34i 0.0427128 0.0739808i
\(306\) 8.39908e34 + 1.45476e35i 0.0760801 + 0.131775i
\(307\) 1.55033e36 1.33942 0.669712 0.742621i \(-0.266417\pi\)
0.669712 + 0.742621i \(0.266417\pi\)
\(308\) −9.95509e35 + 3.78767e36i −0.820465 + 3.12167i
\(309\) −1.01368e36 −0.797079
\(310\) −2.65157e36 4.59265e36i −1.98957 3.44603i
\(311\) 1.04321e36 1.80689e36i 0.747044 1.29392i −0.202190 0.979346i \(-0.564806\pi\)
0.949234 0.314572i \(-0.101861\pi\)
\(312\) 1.17212e36 2.03017e36i 0.801179 1.38768i
\(313\) −8.83342e35 1.52999e36i −0.576416 0.998381i −0.995886 0.0906125i \(-0.971118\pi\)
0.419470 0.907769i \(-0.362216\pi\)
\(314\) −5.83219e35 −0.363373
\(315\) 7.46295e35 2.03800e35i 0.444025 0.121256i
\(316\) 5.87471e36 3.33829
\(317\) −8.41517e34 1.45755e35i −0.0456776 0.0791159i 0.842283 0.539036i \(-0.181211\pi\)
−0.887960 + 0.459920i \(0.847878\pi\)
\(318\) −1.20923e36 + 2.09445e36i −0.627071 + 1.08612i
\(319\) −2.21068e36 + 3.82901e36i −1.09537 + 1.89724i
\(320\) −2.51748e36 4.36040e36i −1.19204 2.06467i
\(321\) −5.35158e35 −0.242192
\(322\) 4.62861e36 1.26399e36i 2.00235 0.546808i
\(323\) 9.02245e35 0.373154
\(324\) −3.53036e35 6.11477e35i −0.139610 0.241812i
\(325\) 1.17332e36 2.03224e36i 0.443717 0.768540i
\(326\) −3.92790e36 + 6.80332e36i −1.42071 + 2.46074i
\(327\) −8.32128e35 1.44129e36i −0.287904 0.498664i
\(328\) −2.01497e36 −0.666956
\(329\) 7.41609e35 2.82164e36i 0.234874 0.893637i
\(330\) 6.33255e36 1.91923
\(331\) 2.89989e36 + 5.02275e36i 0.841153 + 1.45692i 0.888920 + 0.458062i \(0.151456\pi\)
−0.0477668 + 0.998859i \(0.515210\pi\)
\(332\) −4.00270e36 + 6.93288e36i −1.11135 + 1.92491i
\(333\) 9.21545e35 1.59616e36i 0.244949 0.424263i
\(334\) −3.49032e36 6.04541e36i −0.888263 1.53852i
\(335\) −5.85897e36 −1.42781
\(336\) 4.92486e36 + 4.87797e36i 1.14941 + 1.13846i
\(337\) −8.14069e36 −1.81982 −0.909909 0.414808i \(-0.863849\pi\)
−0.909909 + 0.414808i \(0.863849\pi\)
\(338\) −1.84456e35 3.19487e35i −0.0395003 0.0684166i
\(339\) 4.74480e35 8.21824e35i 0.0973470 0.168610i
\(340\) −2.14949e36 + 3.72302e36i −0.422562 + 0.731899i
\(341\) 5.24100e36 + 9.07769e36i 0.987361 + 1.71016i
\(342\) −5.30149e36 −0.957238
\(343\) 4.02650e36 4.14375e36i 0.696887 0.717181i
\(344\) 1.61497e37 2.67958
\(345\) −2.77494e36 4.80634e36i −0.441445 0.764606i
\(346\) −5.27684e36 + 9.13975e36i −0.804953 + 1.39422i
\(347\) 1.56512e36 2.71087e36i 0.228966 0.396580i −0.728536 0.685007i \(-0.759799\pi\)
0.957502 + 0.288427i \(0.0931323\pi\)
\(348\) 8.81833e36 + 1.52738e37i 1.23733 + 2.14313i
\(349\) −4.47326e36 −0.602081 −0.301041 0.953611i \(-0.597334\pi\)
−0.301041 + 0.953611i \(0.597334\pi\)
\(350\) 9.35113e36 + 9.26210e36i 1.20747 + 1.19598i
\(351\) 1.52027e36 0.188351
\(352\) 1.30518e37 + 2.26063e37i 1.55167 + 2.68758i
\(353\) 1.25779e36 2.17856e36i 0.143508 0.248563i −0.785307 0.619106i \(-0.787495\pi\)
0.928815 + 0.370543i \(0.120828\pi\)
\(354\) 1.01255e36 1.75378e36i 0.110884 0.192056i
\(355\) −2.72695e36 4.72322e36i −0.286660 0.496509i
\(356\) −3.19726e37 −3.22665
\(357\) 3.68877e35 1.40349e36i 0.0357431 0.135994i
\(358\) 5.47426e36 0.509356
\(359\) 1.66766e35 + 2.88847e35i 0.0149018 + 0.0258106i 0.873380 0.487039i \(-0.161923\pi\)
−0.858478 + 0.512850i \(0.828590\pi\)
\(360\) 7.60419e36 1.31708e37i 0.652630 1.13039i
\(361\) −8.17249e36 + 1.41552e37i −0.673752 + 1.16697i
\(362\) −7.96450e36 1.37949e37i −0.630789 1.09256i
\(363\) −4.92945e36 −0.375105
\(364\) −3.24481e37 + 8.86103e36i −2.37257 + 0.647909i
\(365\) 2.52860e36 0.177678
\(366\) 4.95638e35 + 8.58470e35i 0.0334725 + 0.0579761i
\(367\) −4.48710e36 + 7.77188e36i −0.291278 + 0.504508i −0.974112 0.226065i \(-0.927414\pi\)
0.682834 + 0.730573i \(0.260747\pi\)
\(368\) 2.48637e37 4.30653e37i 1.55158 2.68741i
\(369\) −6.53367e35 1.13166e36i −0.0391990 0.0678946i
\(370\) 6.59380e37 3.80374
\(371\) 2.01546e37 5.50386e36i 1.11802 0.305313i
\(372\) 4.18124e37 2.23065
\(373\) −1.14122e36 1.97665e36i −0.0585586 0.101426i 0.835260 0.549855i \(-0.185317\pi\)
−0.893819 + 0.448429i \(0.851984\pi\)
\(374\) 5.93927e36 1.02871e37i 0.293153 0.507757i
\(375\) −7.82819e35 + 1.35588e36i −0.0371713 + 0.0643826i
\(376\) −2.86768e37 4.96697e37i −1.31011 2.26918i
\(377\) −3.79741e37 −1.66931
\(378\) −2.16748e36 + 8.24674e36i −0.0916905 + 0.348860i
\(379\) −3.27860e37 −1.33481 −0.667405 0.744695i \(-0.732595\pi\)
−0.667405 + 0.744695i \(0.732595\pi\)
\(380\) −6.78377e37 1.17498e38i −2.65833 4.60437i
\(381\) −5.32016e36 + 9.21479e36i −0.200684 + 0.347595i
\(382\) −3.72359e37 + 6.44945e37i −1.35221 + 2.34209i
\(383\) 2.15189e37 + 3.72719e37i 0.752382 + 1.30316i 0.946665 + 0.322219i \(0.104429\pi\)
−0.194283 + 0.980946i \(0.562238\pi\)
\(384\) 1.40598e37 0.473342
\(385\) −3.88671e37 3.84971e37i −1.26009 1.24809i
\(386\) −1.19441e37 −0.372940
\(387\) 5.23665e36 + 9.07014e36i 0.157487 + 0.272775i
\(388\) −2.38854e37 + 4.13707e37i −0.691946 + 1.19849i
\(389\) 1.99416e37 3.45399e37i 0.556533 0.963944i −0.441249 0.897385i \(-0.645465\pi\)
0.997782 0.0665591i \(-0.0212021\pi\)
\(390\) 2.71944e37 + 4.71021e37i 0.731211 + 1.26650i
\(391\) −1.04104e37 −0.269715
\(392\) −1.08663e36 1.13579e38i −0.0271289 2.83564i
\(393\) −2.58295e37 −0.621476
\(394\) −3.31252e37 5.73746e37i −0.768182 1.33053i
\(395\) −4.10308e37 + 7.10674e37i −0.917174 + 1.58859i
\(396\) −2.49644e37 + 4.32396e37i −0.537948 + 0.931754i
\(397\) 4.09203e37 + 7.08760e37i 0.850112 + 1.47244i 0.881107 + 0.472917i \(0.156799\pi\)
−0.0309953 + 0.999520i \(0.509868\pi\)
\(398\) 8.75376e37 1.75344
\(399\) 3.25388e37 + 3.22290e37i 0.628485 + 0.622501i
\(400\) 1.36408e38 2.54079
\(401\) −2.33849e37 4.05038e37i −0.420089 0.727616i 0.575859 0.817549i \(-0.304668\pi\)
−0.995948 + 0.0899335i \(0.971335\pi\)
\(402\) 3.22887e37 5.59256e37i 0.559464 0.969021i
\(403\) −4.50138e37 + 7.79662e37i −0.752354 + 1.30312i
\(404\) −1.25282e37 2.16995e37i −0.202004 0.349881i
\(405\) 9.86284e36 0.153428
\(406\) 5.41405e37 2.05991e38i 0.812633 3.09187i
\(407\) −1.30331e38 −1.88768
\(408\) −1.42639e37 2.47058e37i −0.199372 0.345323i
\(409\) 3.61774e37 6.26611e37i 0.488033 0.845299i −0.511872 0.859062i \(-0.671048\pi\)
0.999905 + 0.0137631i \(0.00438107\pi\)
\(410\) 2.33747e37 4.04862e37i 0.304355 0.527159i
\(411\) 1.73837e36 + 3.01094e36i 0.0218492 + 0.0378439i
\(412\) 2.85931e38 3.46937
\(413\) −1.68763e37 + 4.60863e36i −0.197698 + 0.0539878i
\(414\) 6.11705e37 0.691890
\(415\) −5.59121e37 9.68426e37i −0.610672 1.05772i
\(416\) −1.12099e38 + 1.94161e38i −1.18235 + 2.04790i
\(417\) 3.71335e37 6.43171e37i 0.378262 0.655170i
\(418\) 1.87443e38 + 3.24661e38i 1.84422 + 3.19429i
\(419\) −1.52469e38 −1.44904 −0.724518 0.689256i \(-0.757937\pi\)
−0.724518 + 0.689256i \(0.757937\pi\)
\(420\) −2.10510e38 + 5.74865e37i −1.93267 + 0.527778i
\(421\) 1.01030e38 0.896110 0.448055 0.894006i \(-0.352117\pi\)
0.448055 + 0.894006i \(0.352117\pi\)
\(422\) 1.99858e38 + 3.46164e38i 1.71274 + 2.96655i
\(423\) 1.85973e37 3.22115e37i 0.153998 0.266732i
\(424\) 2.05360e38 3.55694e38i 1.64328 2.84624i
\(425\) −1.42785e37 2.47310e37i −0.110418 0.191250i
\(426\) 6.01127e37 0.449290
\(427\) 2.17678e36 8.28210e36i 0.0157257 0.0598324i
\(428\) 1.50954e38 1.05417
\(429\) −5.37516e37 9.31005e37i −0.362878 0.628523i
\(430\) −1.87345e38 + 3.24492e38i −1.22279 + 2.11793i
\(431\) −1.07362e38 + 1.85957e38i −0.677535 + 1.17352i 0.298186 + 0.954508i \(0.403618\pi\)
−0.975721 + 0.219017i \(0.929715\pi\)
\(432\) 4.41860e37 + 7.65324e37i 0.269631 + 0.467015i
\(433\) 7.64526e37 0.451147 0.225573 0.974226i \(-0.427574\pi\)
0.225573 + 0.974226i \(0.427574\pi\)
\(434\) −3.58753e38 3.55337e38i −2.04736 2.02786i
\(435\) −2.46359e38 −1.35980
\(436\) 2.34721e38 + 4.06548e38i 1.25313 + 2.17049i
\(437\) 1.64276e38 2.84535e38i 0.848387 1.46945i
\(438\) −1.39350e37 + 2.41362e37i −0.0696199 + 0.120585i
\(439\) −3.04880e37 5.28068e37i −0.147365 0.255243i 0.782888 0.622163i \(-0.213746\pi\)
−0.930253 + 0.366919i \(0.880412\pi\)
\(440\) −1.07544e39 −5.02945
\(441\) 6.34371e37 3.74392e37i 0.287067 0.169421i
\(442\) 1.02022e38 0.446757
\(443\) 1.82985e38 + 3.16939e38i 0.775463 + 1.34314i 0.934534 + 0.355874i \(0.115817\pi\)
−0.159071 + 0.987267i \(0.550850\pi\)
\(444\) −2.59943e38 + 4.50234e38i −1.06617 + 1.84665i
\(445\) 2.23306e38 3.86777e38i 0.886503 1.53547i
\(446\) −1.32521e38 2.29534e38i −0.509249 0.882045i
\(447\) −8.65250e36 −0.0321871
\(448\) −3.40610e38 3.37367e38i −1.22667 1.21499i
\(449\) 5.43886e37 0.189642 0.0948212 0.995494i \(-0.469772\pi\)
0.0948212 + 0.995494i \(0.469772\pi\)
\(450\) 8.38987e37 + 1.45317e38i 0.283253 + 0.490608i
\(451\) −4.62018e37 + 8.00238e37i −0.151042 + 0.261613i
\(452\) −1.33838e38 + 2.31814e38i −0.423714 + 0.733894i
\(453\) 3.83563e37 + 6.64351e37i 0.117602 + 0.203692i
\(454\) −1.00546e39 −2.98575
\(455\) 1.19434e38 4.54418e38i 0.343529 1.30705i
\(456\) 9.00335e38 2.50850
\(457\) −3.17203e38 5.49411e38i −0.856154 1.48290i −0.875570 0.483091i \(-0.839514\pi\)
0.0194157 0.999811i \(-0.493819\pi\)
\(458\) −2.88476e38 + 4.99655e38i −0.754328 + 1.30653i
\(459\) 9.25032e36 1.60220e37i 0.0234354 0.0405913i
\(460\) 7.82736e38 + 1.35574e39i 1.92144 + 3.32803i
\(461\) 3.00121e38 0.713893 0.356946 0.934125i \(-0.383818\pi\)
0.356946 + 0.934125i \(0.383818\pi\)
\(462\) 5.81661e38 1.58842e38i 1.34079 0.366147i
\(463\) 4.97745e38 1.11194 0.555972 0.831201i \(-0.312346\pi\)
0.555972 + 0.831201i \(0.312346\pi\)
\(464\) −1.10370e39 1.91167e39i −2.38969 4.13906i
\(465\) −2.92030e38 + 5.05811e38i −0.612858 + 1.06150i
\(466\) −6.26679e37 + 1.08544e38i −0.127482 + 0.220806i
\(467\) 3.48861e38 + 6.04245e38i 0.687951 + 1.19157i 0.972500 + 0.232905i \(0.0748231\pi\)
−0.284548 + 0.958662i \(0.591844\pi\)
\(468\) −4.28827e38 −0.819817
\(469\) −5.38162e38 + 1.46963e38i −0.997486 + 0.272396i
\(470\) 1.33067e39 2.39139
\(471\) 3.21164e37 + 5.56272e37i 0.0559659 + 0.0969358i
\(472\) −1.71957e38 + 2.97838e38i −0.290577 + 0.503294i
\(473\) 3.70301e38 6.41380e38i 0.606832 1.05106i
\(474\) −4.52239e38 7.83301e38i −0.718757 1.24492i
\(475\) 9.01255e38 1.38928
\(476\) −1.04050e38 + 3.95886e38i −0.155576 + 0.591928i
\(477\) 2.66357e38 0.386321
\(478\) 1.86712e38 + 3.23394e38i 0.262704 + 0.455017i
\(479\) 8.43445e37 1.46089e38i 0.115131 0.199412i −0.802701 0.596381i \(-0.796605\pi\)
0.917832 + 0.396969i \(0.129938\pi\)
\(480\) −7.27248e38 + 1.25963e39i −0.963129 + 1.66819i
\(481\) −5.59691e38 9.69414e38i −0.719192 1.24568i
\(482\) 1.19604e39 1.49130
\(483\) −3.75445e38 3.71870e38i −0.454268 0.449943i
\(484\) 1.39046e39 1.63268
\(485\) −3.33645e38 5.77891e38i −0.380216 0.658553i
\(486\) −5.43539e37 + 9.41437e37i −0.0601180 + 0.104127i
\(487\) −2.90597e38 + 5.03328e38i −0.311975 + 0.540357i −0.978790 0.204866i \(-0.934324\pi\)
0.666814 + 0.745224i \(0.267657\pi\)
\(488\) −8.41725e37 1.45791e38i −0.0877168 0.151930i
\(489\) 8.65197e38 0.875259
\(490\) 2.29473e39 + 1.29575e39i 2.25366 + 1.27256i
\(491\) 1.21858e39 1.16191 0.580954 0.813936i \(-0.302679\pi\)
0.580954 + 0.813936i \(0.302679\pi\)
\(492\) 1.84297e38 + 3.19212e38i 0.170618 + 0.295519i
\(493\) −2.31059e38 + 4.00206e38i −0.207703 + 0.359752i
\(494\) −1.60991e39 + 2.78844e39i −1.40527 + 2.43400i
\(495\) −3.48717e38 6.03996e38i −0.295596 0.511987i
\(496\) −5.23323e39 −4.30810
\(497\) −3.68952e38 3.65439e38i −0.294987 0.292178i
\(498\) 1.23252e39 0.957125
\(499\) −1.03697e39 1.79609e39i −0.782183 1.35478i −0.930667 0.365867i \(-0.880773\pi\)
0.148484 0.988915i \(-0.452561\pi\)
\(500\) 2.20812e38 3.82458e38i 0.161792 0.280233i
\(501\) −3.84406e38 + 6.65811e38i −0.273617 + 0.473919i
\(502\) 1.63041e39 + 2.82395e39i 1.12744 + 1.95278i
\(503\) −7.36308e38 −0.494680 −0.247340 0.968929i \(-0.579556\pi\)
−0.247340 + 0.968929i \(0.579556\pi\)
\(504\) 3.68096e38 1.40052e39i 0.240280 0.914208i
\(505\) 3.50003e38 0.221997
\(506\) −2.16279e39 3.74606e39i −1.33300 2.30883i
\(507\) −2.03150e37 + 3.51867e37i −0.0121675 + 0.0210748i
\(508\) 1.50067e39 2.59924e39i 0.873499 1.51294i
\(509\) −6.31699e38 1.09414e39i −0.357357 0.618961i 0.630161 0.776464i \(-0.282989\pi\)
−0.987518 + 0.157504i \(0.949655\pi\)
\(510\) 6.61875e38 0.363922
\(511\) 2.32258e38 6.34257e37i 0.124128 0.0338971i
\(512\) 2.26324e39 1.17575
\(513\) 2.91940e38 + 5.05654e38i 0.147432 + 0.255359i
\(514\) −6.98403e38 + 1.20967e39i −0.342879 + 0.593884i
\(515\) −1.99702e39 + 3.45895e39i −0.953188 + 1.65097i
\(516\) −1.47712e39 2.55844e39i −0.685479 1.18729i
\(517\) −2.63016e39 −1.18678
\(518\) 6.05658e39 1.65395e39i 2.65733 0.725671i
\(519\) 1.16233e39 0.495909
\(520\) −4.61834e39 7.99919e39i −1.91618 3.31893i
\(521\) 8.29921e38 1.43746e39i 0.334880 0.580030i −0.648582 0.761145i \(-0.724637\pi\)
0.983462 + 0.181116i \(0.0579708\pi\)
\(522\) 1.35768e39 2.35157e39i 0.532813 0.922860i
\(523\) −1.17190e39 2.02979e39i −0.447317 0.774776i 0.550893 0.834576i \(-0.314287\pi\)
−0.998210 + 0.0597999i \(0.980954\pi\)
\(524\) 7.28582e39 2.70504
\(525\) 3.68472e38 1.40195e39i 0.133074 0.506316i
\(526\) 4.62845e39 1.62608
\(527\) 5.47787e38 + 9.48795e38i 0.187223 + 0.324279i
\(528\) 3.12454e39 5.41186e39i 1.03895 1.79951i
\(529\) −3.49948e38 + 6.06128e38i −0.113213 + 0.196091i
\(530\) 4.76458e39 + 8.25249e39i 1.49977 + 2.59768i
\(531\) −2.23033e38 −0.0683123
\(532\) −9.17833e39 9.09094e39i −2.73555 2.70950i
\(533\) −7.93633e38 −0.230184
\(534\) 2.46127e39 + 4.26304e39i 0.694721 + 1.20329i
\(535\) −1.05430e39 + 1.82611e39i −0.289625 + 0.501646i
\(536\) −5.48347e39 + 9.49766e39i −1.46611 + 2.53938i
\(537\) −3.01453e38 5.22133e38i −0.0784500 0.135879i
\(538\) −9.85400e39 −2.49614
\(539\) −4.53568e39 2.56114e39i −1.11842 0.631533i
\(540\) −2.78204e39 −0.667812
\(541\) 4.02158e39 + 6.96558e39i 0.939802 + 1.62779i 0.765838 + 0.643033i \(0.222324\pi\)
0.173964 + 0.984752i \(0.444342\pi\)
\(542\) −4.80127e39 + 8.31604e39i −1.09236 + 1.89203i
\(543\) −8.77169e38 + 1.51930e39i −0.194306 + 0.336548i
\(544\) 1.36416e39 + 2.36280e39i 0.294227 + 0.509616i
\(545\) −6.55744e39 −1.37716
\(546\) 3.67936e39 + 3.64432e39i 0.752452 + 0.745287i
\(547\) 3.08330e39 0.614043 0.307022 0.951703i \(-0.400668\pi\)
0.307022 + 0.951703i \(0.400668\pi\)
\(548\) −4.90347e38 8.49306e38i −0.0951011 0.164720i
\(549\) 5.45870e37 9.45474e37i 0.0103107 0.0178587i
\(550\) 5.93276e39 1.02758e40i 1.09143 1.89042i
\(551\) −7.29222e39 1.26305e40i −1.30666 2.26320i
\(552\) −1.03884e40 −1.81314
\(553\) −1.98617e39 + 7.55691e39i −0.337678 + 1.28478i
\(554\) 2.26776e39 0.375583
\(555\) −3.63104e39 6.28914e39i −0.585845 1.01471i
\(556\) −1.04744e40 + 1.81421e40i −1.64643 + 2.85170i
\(557\) 5.31143e39 9.19967e39i 0.813414 1.40887i −0.0970478 0.995280i \(-0.530940\pi\)
0.910461 0.413594i \(-0.135727\pi\)
\(558\) −3.21874e39 5.57502e39i −0.480275 0.831861i
\(559\) 6.36086e39 0.924793
\(560\) 2.63474e40 7.19501e39i 3.73260 1.01931i
\(561\) −1.30824e39 −0.180604
\(562\) 1.18377e40 + 2.05035e40i 1.59254 + 2.75836i
\(563\) 4.63872e39 8.03450e39i 0.608172 1.05338i −0.383370 0.923595i \(-0.625237\pi\)
0.991542 0.129789i \(-0.0414302\pi\)
\(564\) −5.24580e39 + 9.08599e39i −0.670293 + 1.16098i
\(565\) −1.86953e39 3.23812e39i −0.232825 0.403265i
\(566\) 9.26276e39 1.12435
\(567\) 9.05928e38 2.47393e38i 0.107186 0.0292707i
\(568\) −1.02087e40 −1.17739
\(569\) 7.82720e39 + 1.35571e40i 0.879992 + 1.52419i 0.851348 + 0.524601i \(0.175785\pi\)
0.0286437 + 0.999590i \(0.490881\pi\)
\(570\) −1.04444e40 + 1.80902e40i −1.14471 + 1.98270i
\(571\) 1.66507e38 2.88398e38i 0.0177913 0.0308154i −0.856993 0.515329i \(-0.827670\pi\)
0.874784 + 0.484513i \(0.161003\pi\)
\(572\) 1.51619e40 + 2.62611e40i 1.57947 + 2.73572i
\(573\) 8.20195e39 0.833057
\(574\) 1.13150e39 4.30508e39i 0.112055 0.426343i
\(575\) −1.03990e40 −1.00417
\(576\) −3.05597e39 5.29309e39i −0.287755 0.498406i
\(577\) −5.92622e39 + 1.02645e40i −0.544162 + 0.942517i 0.454497 + 0.890748i \(0.349819\pi\)
−0.998659 + 0.0517684i \(0.983514\pi\)
\(578\) −9.84477e39 + 1.70516e40i −0.881560 + 1.52691i
\(579\) 6.57733e38 + 1.13923e39i 0.0574395 + 0.0994881i
\(580\) 6.94913e40 5.91867
\(581\) −7.56481e39 7.49278e39i −0.628411 0.622428i
\(582\) 7.35485e39 0.595923
\(583\) −9.41751e39 1.63116e40i −0.744290 1.28915i
\(584\) 2.36654e39 4.09897e39i 0.182443 0.316001i
\(585\) 2.99505e39 5.18758e39i 0.225239 0.390126i
\(586\) 3.69287e39 + 6.39623e39i 0.270924 + 0.469255i
\(587\) −9.72926e39 −0.696350 −0.348175 0.937430i \(-0.613198\pi\)
−0.348175 + 0.937430i \(0.613198\pi\)
\(588\) −1.78939e40 + 1.05606e40i −1.24949 + 0.737422i
\(589\) −3.45763e40 −2.35563
\(590\) −3.98959e39 6.91018e39i −0.265201 0.459341i
\(591\) −3.64824e39 + 6.31894e39i −0.236628 + 0.409851i
\(592\) 3.25344e40 5.63513e40i 2.05911 3.56648i
\(593\) 6.50407e39 + 1.12654e40i 0.401691 + 0.695750i 0.993930 0.110013i \(-0.0350892\pi\)
−0.592239 + 0.805762i \(0.701756\pi\)
\(594\) 7.68709e39 0.463296
\(595\) −4.06237e39 4.02369e39i −0.238937 0.236662i
\(596\) 2.44064e39 0.140098
\(597\) −4.82047e39 8.34930e39i −0.270061 0.467759i
\(598\) 1.85757e40 3.21740e40i 1.01573 1.75929i
\(599\) −1.01171e40 + 1.75233e40i −0.539967 + 0.935250i 0.458938 + 0.888468i \(0.348230\pi\)
−0.998905 + 0.0467820i \(0.985103\pi\)
\(600\) −1.42482e40 2.46787e40i −0.742280 1.28567i
\(601\) −8.89478e39 −0.452330 −0.226165 0.974089i \(-0.572619\pi\)
−0.226165 + 0.974089i \(0.572619\pi\)
\(602\) −9.06883e39 + 3.45047e40i −0.450196 + 1.71289i
\(603\) −7.11221e39 −0.344670
\(604\) −1.08193e40 1.87395e40i −0.511874 0.886591i
\(605\) −9.71142e39 + 1.68207e40i −0.448570 + 0.776945i
\(606\) −1.92886e39 + 3.34088e39i −0.0869856 + 0.150663i
\(607\) −1.39696e40 2.41961e40i −0.615104 1.06539i −0.990366 0.138472i \(-0.955781\pi\)
0.375262 0.926919i \(-0.377553\pi\)
\(608\) −8.61060e40 −3.70196
\(609\) −2.26287e40 + 6.17952e39i −0.949970 + 0.259420i
\(610\) 3.90579e39 0.160113
\(611\) −1.12949e40 1.95634e40i −0.452153 0.783151i
\(612\) −2.60926e39 + 4.51938e39i −0.102005 + 0.176678i
\(613\) −1.12027e40 + 1.94037e40i −0.427707 + 0.740811i −0.996669 0.0815534i \(-0.974012\pi\)
0.568962 + 0.822364i \(0.307345\pi\)
\(614\) 3.36641e40 + 5.83080e40i 1.25524 + 2.17414i
\(615\) −5.14875e39 −0.187505
\(616\) −9.87816e40 + 2.69755e40i −3.51363 + 0.959511i
\(617\) −8.54137e39 −0.296751 −0.148376 0.988931i \(-0.547405\pi\)
−0.148376 + 0.988931i \(0.547405\pi\)
\(618\) −2.20111e40 3.81244e40i −0.746980 1.29381i
\(619\) −3.91526e39 + 6.78143e39i −0.129791 + 0.224805i −0.923596 0.383368i \(-0.874764\pi\)
0.793804 + 0.608173i \(0.208097\pi\)
\(620\) 8.23738e40 1.42676e41i 2.66753 4.62030i
\(621\) −3.36850e39 5.83442e39i −0.106564 0.184574i
\(622\) 9.06097e40 2.80036
\(623\) 1.08096e40 4.11278e40i 0.326386 1.24182i
\(624\) 5.36719e40 1.58333
\(625\) 1.88140e40 + 3.25869e40i 0.542277 + 0.939252i
\(626\) 3.83620e40 6.64450e40i 1.08037 1.87126i
\(627\) 2.06440e40 3.57565e40i 0.568087 0.983956i
\(628\) −9.05917e39 1.56909e40i −0.243598 0.421924i
\(629\) −1.36221e40 −0.357940
\(630\) 2.38701e40 + 2.36428e40i 0.612937 + 0.607101i
\(631\) 5.23641e40 1.31404 0.657019 0.753874i \(-0.271817\pi\)
0.657019 + 0.753874i \(0.271817\pi\)
\(632\) 7.68022e40 + 1.33025e41i 1.88355 + 3.26240i
\(633\) 2.20113e40 3.81248e40i 0.527585 0.913805i
\(634\) 3.65456e39 6.32989e39i 0.0856133 0.148287i
\(635\) 2.09623e40 + 3.63078e40i 0.479977 + 0.831344i
\(636\) −7.51322e40 −1.68151
\(637\) −4.27989e38 4.47353e40i −0.00936290 0.978654i
\(638\) −1.92012e41 −4.10609
\(639\) −3.31025e39 5.73353e39i −0.0691988 0.119856i
\(640\) 2.76989e40 4.79759e40i 0.566047 0.980423i
\(641\) −1.69811e39 + 2.94121e39i −0.0339253 + 0.0587603i −0.882490 0.470332i \(-0.844134\pi\)
0.848564 + 0.529092i \(0.177467\pi\)
\(642\) −1.16205e40 2.01273e40i −0.226969 0.393122i
\(643\) 4.75524e39 0.0908057 0.0454028 0.998969i \(-0.485543\pi\)
0.0454028 + 0.998969i \(0.485543\pi\)
\(644\) 1.05903e41 + 1.04894e41i 1.97725 + 1.95843i
\(645\) 4.12665e40 0.753324
\(646\) 1.95915e40 + 3.39334e40i 0.349700 + 0.605698i
\(647\) 5.17763e40 8.96793e40i 0.903690 1.56524i 0.0810230 0.996712i \(-0.474181\pi\)
0.822667 0.568524i \(-0.192485\pi\)
\(648\) 9.23074e39 1.59881e40i 0.157543 0.272872i
\(649\) 7.88570e39 + 1.36584e40i 0.131611 + 0.227957i
\(650\) 1.01910e41 1.66331
\(651\) −1.41363e40 + 5.37851e40i −0.225637 + 0.858495i
\(652\) −2.44049e41 −3.80966
\(653\) 3.27693e40 + 5.67580e40i 0.500294 + 0.866535i 1.00000 0.000339848i \(0.000108177\pi\)
−0.499706 + 0.866195i \(0.666558\pi\)
\(654\) 3.61379e40 6.25927e40i 0.539617 0.934644i
\(655\) −5.08863e40 + 8.81377e40i −0.743194 + 1.28725i
\(656\) −2.30666e40 3.99526e40i −0.329517 0.570741i
\(657\) 3.06947e39 0.0428909
\(658\) 1.22225e41 3.33776e40i 1.67065 0.456226i
\(659\) −8.41104e40 −1.12463 −0.562317 0.826922i \(-0.690090\pi\)
−0.562317 + 0.826922i \(0.690090\pi\)
\(660\) 9.83637e40 + 1.70371e41i 1.28661 + 2.22848i
\(661\) −1.90498e39 + 3.29952e39i −0.0243763 + 0.0422211i −0.877956 0.478741i \(-0.841093\pi\)
0.853580 + 0.520962i \(0.174427\pi\)
\(662\) −1.25937e41 + 2.18130e41i −1.57657 + 2.73070i
\(663\) −5.61809e39 9.73082e39i −0.0688086 0.119180i
\(664\) −2.09315e41 −2.50820
\(665\) 1.74079e41 4.75379e40i 2.04095 0.557347i
\(666\) 8.00422e40 0.918212
\(667\) 8.41403e40 + 1.45735e41i 0.944451 + 1.63584i
\(668\) 1.08431e41 1.87807e41i 1.19095 2.06278i
\(669\) −1.45952e40 + 2.52796e40i −0.156867 + 0.271702i
\(670\) −1.27223e41 2.20356e41i −1.33807 2.31761i
\(671\) −7.72006e39 −0.0794591
\(672\) −3.52039e40 + 1.33942e41i −0.354598 + 1.34916i
\(673\) 7.99687e40 0.788318 0.394159 0.919042i \(-0.371036\pi\)
0.394159 + 0.919042i \(0.371036\pi\)
\(674\) −1.76768e41 3.06172e41i −1.70544 2.95390i
\(675\) 9.24017e39 1.60044e40i 0.0872520 0.151125i
\(676\) 5.73033e39 9.92521e39i 0.0529605 0.0917303i
\(677\) −3.22406e40 5.58424e40i −0.291654 0.505159i 0.682547 0.730841i \(-0.260872\pi\)
−0.974201 + 0.225682i \(0.927539\pi\)
\(678\) 4.12118e40 0.364914
\(679\) −4.51417e40 4.47118e40i −0.391260 0.387535i
\(680\) −1.12404e41 −0.953680
\(681\) 5.53679e40 + 9.59000e40i 0.459859 + 0.796500i
\(682\) −2.27608e41 + 3.94228e41i −1.85061 + 3.20534i
\(683\) 5.37304e39 9.30638e39i 0.0427681 0.0740766i −0.843849 0.536581i \(-0.819716\pi\)
0.886617 + 0.462504i \(0.153049\pi\)
\(684\) −8.23483e40 1.42631e41i −0.641713 1.11148i
\(685\) 1.36989e40 0.104514
\(686\) 2.43278e41 + 6.14586e40i 1.81720 + 0.459074i
\(687\) 6.35425e40 0.464721
\(688\) 1.84876e41 + 3.20215e41i 1.32388 + 2.29303i
\(689\) 8.08849e40 1.40097e41i 0.567138 0.982311i
\(690\) 1.20511e41 2.08731e41i 0.827399 1.43310i
\(691\) 9.81289e40 + 1.69964e41i 0.659729 + 1.14268i 0.980686 + 0.195590i \(0.0626622\pi\)
−0.320957 + 0.947094i \(0.604005\pi\)
\(692\) −3.27861e41 −2.15850
\(693\) −4.71808e40 4.67316e40i −0.304182 0.301286i
\(694\) 1.35941e41 0.858298
\(695\) −1.46312e41 2.53420e41i −0.904692 1.56697i
\(696\) −2.30570e41 + 3.99359e41i −1.39627 + 2.41841i
\(697\) −4.82899e39 + 8.36405e39i −0.0286405 + 0.0496068i
\(698\) −9.71329e40 1.68239e41i −0.564239 0.977290i
\(699\) 1.38038e40 0.0785382
\(700\) −1.03936e41 + 3.95451e41i −0.579221 + 2.20380i
\(701\) −3.13665e40 −0.171220 −0.0856101 0.996329i \(-0.527284\pi\)
−0.0856101 + 0.996329i \(0.527284\pi\)
\(702\) 3.30113e40 + 5.71773e40i 0.176512 + 0.305728i
\(703\) 2.14957e41 3.72316e41i 1.12590 1.95011i
\(704\) −2.16098e41 + 3.74292e41i −1.10878 + 1.92047i
\(705\) −7.32765e40 1.26919e41i −0.368318 0.637945i
\(706\) 1.09248e41 0.537953
\(707\) 3.21487e40 8.77925e39i 0.155089 0.0423522i
\(708\) 6.29116e40 0.297337
\(709\) 4.43041e39 + 7.67370e39i 0.0205151 + 0.0355332i 0.876101 0.482128i \(-0.160136\pi\)
−0.855586 + 0.517661i \(0.826803\pi\)
\(710\) 1.18427e41 2.05122e41i 0.537285 0.930605i
\(711\) −4.98073e40 + 8.62687e40i −0.221403 + 0.383481i
\(712\) −4.17989e41 7.23978e41i −1.82056 3.15330i
\(713\) 3.98954e41 1.70265
\(714\) 6.07950e40 1.66021e40i 0.254240 0.0694285i
\(715\) −4.23580e41 −1.73579
\(716\) 8.50318e40 + 1.47279e41i 0.341462 + 0.591430i
\(717\) 2.05635e40 3.56170e40i 0.0809224 0.140162i
\(718\) −7.24236e39 + 1.25441e40i −0.0279303 + 0.0483767i
\(719\) 1.78235e41 + 3.08711e41i 0.673632 + 1.16677i 0.976867 + 0.213850i \(0.0686002\pi\)
−0.303234 + 0.952916i \(0.598066\pi\)
\(720\) 3.48200e41 1.28976
\(721\) −9.66699e40 + 3.67805e41i −0.350938 + 1.33523i
\(722\) −7.09835e41 −2.52562
\(723\) −6.58629e40 1.14078e41i −0.229687 0.397829i
\(724\) 2.47426e41 4.28554e41i 0.845738 1.46486i
\(725\) −2.30806e41 + 3.99767e41i −0.773296 + 1.33939i
\(726\) −1.07039e41 1.85397e41i −0.351528 0.608865i
\(727\) −1.42583e41 −0.459007 −0.229503 0.973308i \(-0.573710\pi\)
−0.229503 + 0.973308i \(0.573710\pi\)
\(728\) −6.24853e41 6.18903e41i −1.97184 1.95307i
\(729\) 1.19725e40 0.0370370
\(730\) 5.49063e40 + 9.51006e40i 0.166510 + 0.288404i
\(731\) 3.87037e40 6.70368e40i 0.115067 0.199302i
\(732\) −1.53975e40 + 2.66693e40i −0.0448787 + 0.0777321i
\(733\) 1.58916e40 + 2.75251e40i 0.0454110 + 0.0786542i 0.887838 0.460157i \(-0.152207\pi\)
−0.842426 + 0.538811i \(0.818874\pi\)
\(734\) −3.89734e41 −1.09188
\(735\) −2.77661e39 2.90224e41i −0.00762689 0.797198i
\(736\) 9.93521e41 2.67577
\(737\) 2.51464e41 + 4.35549e41i 0.664045 + 1.15016i
\(738\) 2.83746e40 4.91463e40i 0.0734705 0.127255i
\(739\) −5.35725e40 + 9.27904e40i −0.136018 + 0.235591i −0.925986 0.377558i \(-0.876764\pi\)
0.789968 + 0.613149i \(0.210097\pi\)
\(740\) 1.02422e42 + 1.77400e42i 2.54995 + 4.41665i
\(741\) 3.54614e41 0.865748
\(742\) 6.44639e41 + 6.38501e41i 1.54333 + 1.52864i
\(743\) 1.31136e41 0.307882 0.153941 0.988080i \(-0.450803\pi\)
0.153941 + 0.988080i \(0.450803\pi\)
\(744\) 5.46628e41 + 9.46787e41i 1.25859 + 2.17994i
\(745\) −1.70461e40 + 2.95248e40i −0.0384911 + 0.0666685i
\(746\) 4.95611e40 8.58424e40i 0.109756 0.190103i
\(747\) −6.78717e40 1.17557e41i −0.147415 0.255329i
\(748\) 3.69020e41 0.786097
\(749\) −5.10357e40 + 1.94178e41i −0.106632 + 0.405709i
\(750\) −6.79930e40 −0.139340
\(751\) 3.47278e41 + 6.01504e41i 0.698069 + 1.20909i 0.969135 + 0.246531i \(0.0792906\pi\)
−0.271066 + 0.962561i \(0.587376\pi\)
\(752\) 6.56564e41 1.13720e42i 1.29455 2.24223i
\(753\) 1.79565e41 3.11015e41i 0.347291 0.601526i
\(754\) −8.24574e41 1.42820e42i −1.56439 2.70960i
\(755\) 3.02260e41 0.562536
\(756\) −2.55538e41 + 6.97829e40i −0.466540 + 0.127404i
\(757\) 8.15155e41 1.45999 0.729995 0.683453i \(-0.239522\pi\)
0.729995 + 0.683453i \(0.239522\pi\)
\(758\) −7.11919e41 1.23308e42i −1.25091 2.16665i
\(759\) −2.38198e41 + 4.12571e41i −0.410613 + 0.711202i
\(760\) 1.77373e42 3.07220e42i 2.99979 5.19579i
\(761\) −2.56566e41 4.44386e41i −0.425718 0.737365i 0.570769 0.821111i \(-0.306645\pi\)
−0.996487 + 0.0837454i \(0.973312\pi\)
\(762\) −4.62091e41 −0.752282
\(763\) −6.02318e41 + 1.64483e41i −0.962099 + 0.262733i
\(764\) −2.31355e42 −3.62597
\(765\) −3.64478e40 6.31294e40i −0.0560506 0.0970824i
\(766\) −9.34531e41 + 1.61866e42i −1.41019 + 2.44251i
\(767\) −6.77285e40 + 1.17309e41i −0.100286 + 0.173700i
\(768\) −3.77256e40 6.53427e40i −0.0548149 0.0949422i
\(769\) 2.52785e41 0.360428 0.180214 0.983627i \(-0.442321\pi\)
0.180214 + 0.983627i \(0.442321\pi\)
\(770\) 6.03908e41 2.29772e42i 0.844997 3.21501i
\(771\) 1.53837e41 0.211238
\(772\) −1.85529e41 3.21345e41i −0.250012 0.433033i
\(773\) −1.59707e41 + 2.76621e41i −0.211214 + 0.365833i −0.952095 0.305803i \(-0.901075\pi\)
0.740881 + 0.671637i \(0.234408\pi\)
\(774\) −2.27419e41 + 3.93901e41i −0.295177 + 0.511262i
\(775\) 5.47187e41 + 9.47755e41i 0.697045 + 1.20732i
\(776\) −1.24905e42 −1.56165
\(777\) −4.91273e41 4.86595e41i −0.602862 0.597122i
\(778\) 1.73206e42 2.08621
\(779\) −1.52403e41 2.63969e41i −0.180177 0.312076i
\(780\) −8.44823e41 + 1.46328e42i −0.980379 + 1.69807i
\(781\) −2.34079e41 + 4.05437e41i −0.266638 + 0.461831i
\(782\) −2.26053e41 3.91536e41i −0.252763 0.437798i
\(783\) −2.99056e41 −0.328251
\(784\) 2.23960e42 1.32176e42i 2.41317 1.42420i
\(785\) 2.53088e41 0.267708
\(786\) −5.60866e41 9.71449e41i −0.582415 1.00877i
\(787\) −6.81611e41 + 1.18058e42i −0.694869 + 1.20355i 0.275356 + 0.961342i \(0.411204\pi\)
−0.970225 + 0.242206i \(0.922129\pi\)
\(788\) 1.02907e42 1.78240e42i 1.02995 1.78392i
\(789\) −2.54877e41 4.41460e41i −0.250446 0.433785i
\(790\) −3.56379e42 −3.43811
\(791\) −2.52944e41 2.50536e41i −0.239588 0.237307i
\(792\) −1.30547e42 −1.21409
\(793\) −3.31529e40 5.74225e40i −0.0302733 0.0524349i
\(794\) −1.77710e42 + 3.07802e42i −1.59336 + 2.75978i
\(795\) 5.24746e41 9.08887e41i 0.461983 0.800178i
\(796\) 1.35972e42 + 2.35511e42i 1.17547 + 2.03597i
\(797\) −1.11273e42 −0.944592 −0.472296 0.881440i \(-0.656575\pi\)
−0.472296 + 0.881440i \(0.656575\pi\)
\(798\) −5.05581e41 + 1.92361e42i −0.421452 + 1.60352i
\(799\) −2.74903e41 −0.225035
\(800\) 1.36267e42 + 2.36021e42i 1.09543 + 1.89734i
\(801\) 2.71071e41 4.69509e41i 0.213999 0.370657i
\(802\) 1.01557e42 1.75901e42i 0.787371 1.36377i
\(803\) −1.08526e41 1.87973e41i −0.0826340 0.143126i
\(804\) 2.00616e42 1.50022
\(805\) −2.00858e42 + 5.48509e41i −1.47519 + 0.402850i
\(806\) −3.90974e42 −2.82027
\(807\) 5.42634e41 + 9.39870e41i 0.384451 + 0.665889i
\(808\) 3.27571e41 5.67370e41i 0.227951 0.394823i
\(809\) 8.18087e41 1.41697e42i 0.559172 0.968515i −0.438393 0.898783i \(-0.644452\pi\)
0.997566 0.0697318i \(-0.0222144\pi\)
\(810\) 2.14163e41 + 3.70942e41i 0.143785 + 0.249042i
\(811\) −8.50334e41 −0.560773 −0.280387 0.959887i \(-0.590463\pi\)
−0.280387 + 0.959887i \(0.590463\pi\)
\(812\) 6.38296e42 1.74307e42i 4.13485 1.12916i
\(813\) 1.05757e42 0.672974
\(814\) −2.83003e42 4.90175e42i −1.76904 3.06406i
\(815\) 1.70451e42 2.95230e42i 1.04668 1.81290i
\(816\) 3.26575e41 5.65645e41i 0.197005 0.341222i
\(817\) 1.22149e42 + 2.11568e42i 0.723884 + 1.25380i
\(818\) 3.14225e42 1.82944
\(819\) 1.44981e41 5.51619e41i 0.0829270 0.315517i
\(820\) 1.45232e42 0.816135
\(821\) 3.42755e41 + 5.93669e41i 0.189238 + 0.327770i 0.944996 0.327081i \(-0.106065\pi\)
−0.755758 + 0.654850i \(0.772732\pi\)
\(822\) −7.54944e40 + 1.30760e41i −0.0409519 + 0.0709307i
\(823\) −1.12138e42 + 1.94229e42i −0.597661 + 1.03518i 0.395504 + 0.918464i \(0.370570\pi\)
−0.993165 + 0.116715i \(0.962764\pi\)
\(824\) 3.73807e42 + 6.47453e42i 1.95751 + 3.39050i
\(825\) −1.30681e42 −0.672402
\(826\) −5.39785e41 5.34646e41i −0.272904 0.270306i
\(827\) −1.18761e42 −0.589991 −0.294996 0.955499i \(-0.595318\pi\)
−0.294996 + 0.955499i \(0.595318\pi\)
\(828\) 9.50164e41 + 1.64573e42i 0.463830 + 0.803377i
\(829\) −1.79163e42 + 3.10319e42i −0.859423 + 1.48856i 0.0130567 + 0.999915i \(0.495844\pi\)
−0.872480 + 0.488650i \(0.837490\pi\)
\(830\) 2.42817e42 4.20571e42i 1.14458 1.98247i
\(831\) −1.24880e41 2.16298e41i −0.0578465 0.100193i
\(832\) −3.71203e42 −1.68975
\(833\) −4.74067e41 2.67689e41i −0.212074 0.119751i
\(834\) 3.22529e42 1.41795
\(835\) 1.51462e42 + 2.62340e42i 0.654411 + 1.13347i
\(836\) −5.82312e42 + 1.00859e43i −2.47266 + 4.28278i
\(837\) −3.54496e41 + 6.14004e41i −0.147942 + 0.256243i
\(838\) −3.31074e42 5.73437e42i −1.35796 2.35206i
\(839\) −7.09530e41 −0.286037 −0.143019 0.989720i \(-0.545681\pi\)
−0.143019 + 0.989720i \(0.545681\pi\)
\(840\) −4.05378e42 4.01518e42i −1.60624 1.59094i
\(841\) 4.90229e42 1.90922
\(842\) 2.19379e42 + 3.79975e42i 0.839787 + 1.45455i
\(843\) 1.30374e42 2.25814e42i 0.490559 0.849673i
\(844\) −6.20881e42 + 1.07540e43i −2.29637 + 3.97744i
\(845\) 8.00446e40 + 1.38641e41i 0.0291011 + 0.0504046i
\(846\) 1.61530e42 0.577275
\(847\) −4.70100e41 + 1.78862e42i −0.165151 + 0.628359i
\(848\) 9.40355e42 3.24752
\(849\) −5.10076e41 8.83478e41i −0.173170 0.299940i
\(850\) 6.20089e41 1.07403e42i 0.206957 0.358460i
\(851\) −2.48025e42 + 4.29592e42i −0.813799 + 1.40954i
\(852\) 9.33733e41 + 1.61727e42i 0.301195 + 0.521686i
\(853\) −2.88917e42 −0.916247 −0.458124 0.888888i \(-0.651478\pi\)
−0.458124 + 0.888888i \(0.651478\pi\)
\(854\) 3.58757e41 9.79703e40i 0.111856 0.0305461i
\(855\) 2.30058e42 0.705227
\(856\) 1.97347e42 + 3.41815e42i 0.594786 + 1.03020i
\(857\) 8.43568e41 1.46110e42i 0.249976 0.432971i −0.713543 0.700612i \(-0.752911\pi\)
0.963519 + 0.267640i \(0.0862439\pi\)
\(858\) 2.33434e42 4.04320e42i 0.680141 1.17804i
\(859\) 2.57071e41 + 4.45260e41i 0.0736465 + 0.127560i 0.900497 0.434862i \(-0.143203\pi\)
−0.826850 + 0.562422i \(0.809870\pi\)
\(860\) −1.16402e43 −3.27893
\(861\) −4.72926e41 + 1.29148e41i −0.130993 + 0.0357719i
\(862\) −9.32513e42 −2.53980
\(863\) −2.60198e42 4.50676e42i −0.696864 1.20700i −0.969548 0.244900i \(-0.921245\pi\)
0.272685 0.962103i \(-0.412088\pi\)
\(864\) −8.82807e41 + 1.52907e42i −0.232496 + 0.402696i
\(865\) 2.28988e42 3.96619e42i 0.593034 1.02716i
\(866\) 1.66010e42 + 2.87538e42i 0.422791 + 0.732296i
\(867\) 2.16850e42 0.543104
\(868\) 3.98746e42 1.51713e43i 0.982112 3.73670i
\(869\) 7.04408e42 1.70623
\(870\) −5.34948e42 9.26557e42i −1.27433 2.20721i
\(871\) −2.15977e42 + 3.74083e42i −0.505992 + 0.876404i
\(872\) −6.13717e42 + 1.06299e43i −1.41410 + 2.44929i
\(873\) −4.05013e41 7.01502e41i −0.0917829 0.158973i
\(874\) 1.42685e43 3.18025
\(875\) 4.17319e41 + 4.13345e41i 0.0914853 + 0.0906142i
\(876\) −8.65814e41 −0.186687
\(877\) −1.00135e42 1.73439e42i −0.212369 0.367835i 0.740086 0.672512i \(-0.234785\pi\)
−0.952456 + 0.304677i \(0.901451\pi\)
\(878\) 1.32404e42 2.29331e42i 0.276205 0.478401i
\(879\) 4.06713e41 7.04448e41i 0.0834545 0.144547i
\(880\) −1.23112e43 2.13236e43i −2.48486 4.30390i
\(881\) 4.09835e41 0.0813690 0.0406845 0.999172i \(-0.487046\pi\)
0.0406845 + 0.999172i \(0.487046\pi\)
\(882\) 2.78557e42 + 1.57291e42i 0.544026 + 0.307192i
\(883\) 2.50159e42 0.480603 0.240301 0.970698i \(-0.422754\pi\)
0.240301 + 0.970698i \(0.422754\pi\)
\(884\) 1.58471e42 + 2.74480e42i 0.299497 + 0.518744i
\(885\) −4.39393e41 + 7.61052e41i −0.0816913 + 0.141494i
\(886\) −7.94672e42 + 1.37641e43i −1.45345 + 2.51744i
\(887\) −2.73597e42 4.73884e42i −0.492288 0.852668i 0.507673 0.861550i \(-0.330506\pi\)
−0.999961 + 0.00888247i \(0.997173\pi\)
\(888\) −1.35933e43 −2.40623
\(889\) 2.83616e42 + 2.80916e42i 0.493919 + 0.489216i
\(890\) 1.93956e43 3.32314
\(891\) −4.23308e41 7.33191e41i −0.0713559 0.123592i
\(892\) 4.11691e42 7.13070e42i 0.682781 1.18261i
\(893\) 4.33796e42 7.51357e42i 0.707847 1.22603i
\(894\) −1.87882e41 3.25421e41i −0.0301641 0.0522457i
\(895\) −2.37555e42 −0.375258
\(896\) 1.34082e42 5.10149e42i 0.208403 0.792923i
\(897\) −4.09166e42 −0.625762
\(898\) 1.18100e42 + 2.04555e42i 0.177723 + 0.307825i
\(899\) 8.85478e42 1.53369e43i 1.31118 2.27103i
\(900\) −2.60640e42 + 4.51442e42i −0.379774 + 0.657788i
\(901\) −9.84314e41 1.70488e42i −0.141132 0.244447i
\(902\) −4.01293e42 −0.566196
\(903\) 3.79044e42 1.03510e42i 0.526280 0.143718i
\(904\) −6.99885e42 −0.956279
\(905\) 3.45619e42 + 5.98630e42i 0.464722 + 0.804922i
\(906\) −1.66575e42 + 2.88516e42i −0.220420 + 0.381779i
\(907\) −4.14929e41 + 7.18679e41i −0.0540342 + 0.0935899i −0.891777 0.452475i \(-0.850541\pi\)
0.837743 + 0.546065i \(0.183875\pi\)
\(908\) −1.56178e43 2.70508e43i −2.00159 3.46685i
\(909\) 4.24869e41 0.0535894
\(910\) 1.96841e43 5.37539e42i 2.44352 0.667282i
\(911\) 1.06552e42 0.130180 0.0650902 0.997879i \(-0.479267\pi\)
0.0650902 + 0.997879i \(0.479267\pi\)
\(912\) 1.03067e43 + 1.78517e43i 1.23935 + 2.14662i
\(913\) −4.79944e42 + 8.31287e42i −0.568021 + 0.983840i
\(914\) 1.37756e43 2.38600e43i 1.60469 2.77940i
\(915\) −2.15082e41 3.72532e41i −0.0246603 0.0427128i
\(916\) −1.79236e43 −2.02275
\(917\) −2.46325e42 + 9.37208e42i −0.273624 + 1.04107i
\(918\) 8.03451e41 0.0878498
\(919\) 5.25162e41 + 9.09606e41i 0.0565221 + 0.0978991i 0.892902 0.450251i \(-0.148666\pi\)
−0.836380 + 0.548150i \(0.815332\pi\)
\(920\) −2.04660e43 + 3.54481e43i −2.16825 + 3.75551i
\(921\) 3.70759e42 6.42174e42i 0.386658 0.669712i
\(922\) 6.51687e42 + 1.12876e43i 0.669022 + 1.15878i
\(923\) −4.02090e42 −0.406349
\(924\) 1.33084e43 + 1.31817e43i 1.32399 + 1.31138i
\(925\) −1.36072e43 −1.33264
\(926\) 1.08081e43 + 1.87202e43i 1.04206 + 1.80489i
\(927\) −2.42419e42 + 4.19882e42i −0.230097 + 0.398539i
\(928\) 2.20512e43 3.81938e43i 2.06057 3.56901i
\(929\) 2.58205e42 + 4.47224e42i 0.237540 + 0.411432i 0.960008 0.279973i \(-0.0903255\pi\)
−0.722468 + 0.691405i \(0.756992\pi\)
\(930\) −2.53647e43 −2.29735
\(931\) 1.47972e43 8.73296e42i 1.31950 0.778737i
\(932\) −3.89369e42 −0.341846
\(933\) −4.98964e42 8.64231e42i −0.431306 0.747044i
\(934\) −1.51504e43 + 2.62413e43i −1.28942 + 2.23335i
\(935\) −2.57734e42 + 4.46409e42i −0.215975 + 0.374080i
\(936\) −5.60620e42 9.71023e42i −0.462561 0.801179i
\(937\) 7.82828e42 0.635978 0.317989 0.948094i \(-0.396992\pi\)
0.317989 + 0.948094i \(0.396992\pi\)
\(938\) −1.72130e43 1.70491e43i −1.37694 1.36383i
\(939\) −8.44999e42 −0.665588
\(940\) 2.06693e43 + 3.58003e43i 1.60314 + 2.77672i
\(941\) 1.48890e42 2.57885e42i 0.113715 0.196959i −0.803551 0.595236i \(-0.797058\pi\)
0.917265 + 0.398277i \(0.130392\pi\)
\(942\) −1.39476e42 + 2.41580e42i −0.104897 + 0.181686i
\(943\) 1.75848e42 + 3.04577e42i 0.130232 + 0.225568i
\(944\) −7.87401e42 −0.574252
\(945\) 9.40577e41 3.57867e42i 0.0675512 0.257016i
\(946\) 3.21631e43 2.27476
\(947\) −3.01465e42 5.22153e42i −0.209972 0.363683i 0.741733 0.670695i \(-0.234004\pi\)
−0.951706 + 0.307012i \(0.900671\pi\)
\(948\) 1.40493e43 2.43341e43i 0.963681 1.66915i
\(949\) 9.32106e41 1.61446e42i 0.0629659 0.109060i
\(950\) 1.95700e43 + 3.38962e43i 1.30196 + 2.25506i
\(951\) −8.04990e41 −0.0527440
\(952\) −1.03246e43 + 2.81947e42i −0.666251 + 0.181942i
\(953\) −1.15157e43 −0.731889 −0.365944 0.930637i \(-0.619254\pi\)
−0.365944 + 0.930637i \(0.619254\pi\)
\(954\) 5.78373e42 + 1.00177e43i 0.362040 + 0.627071i
\(955\) 1.61585e43 2.79874e43i 0.996213 1.72549i
\(956\) −5.80040e42 + 1.00466e43i −0.352224 + 0.610069i
\(957\) 1.05736e43 + 1.83140e43i 0.632412 + 1.09537i
\(958\) 7.32587e42 0.431578
\(959\) 1.25828e42 3.43615e41i 0.0730143 0.0199389i
\(960\) −2.40820e43 −1.37645
\(961\) −1.21117e43 2.09780e43i −0.681890 1.18107i
\(962\) 2.43064e43 4.21000e43i 1.34798 2.33477i
\(963\) −1.27982e42 + 2.21672e42i −0.0699147 + 0.121096i
\(964\) 1.85781e43 + 3.21783e43i 0.999736 + 1.73159i
\(965\) 5.18315e42 0.274757
\(966\) 5.83357e42 2.21953e43i 0.304625 1.15903i
\(967\) 6.54044e42 0.336452 0.168226 0.985748i \(-0.446196\pi\)
0.168226 + 0.985748i \(0.446196\pi\)
\(968\) 1.81780e43 + 3.14853e43i 0.921201 + 1.59557i
\(969\) 2.15770e42 3.73725e42i 0.107720 0.186577i
\(970\) 1.44897e43 2.50968e43i 0.712636 1.23432i
\(971\) −9.88553e42 1.71222e43i −0.478984 0.829625i 0.520726 0.853724i \(-0.325662\pi\)
−0.999710 + 0.0240994i \(0.992328\pi\)
\(972\) −3.37712e42 −0.161208
\(973\) −1.97958e43 1.96073e43i −0.930971 0.922107i
\(974\) −2.52402e43 −1.16947
\(975\) −5.61193e42 9.72015e42i −0.256180 0.443717i
\(976\) 1.92715e42 3.33793e42i 0.0866750 0.150125i
\(977\) −1.52185e43 + 2.63592e43i −0.674374 + 1.16805i 0.302277 + 0.953220i \(0.402253\pi\)
−0.976651 + 0.214830i \(0.931080\pi\)
\(978\) 1.87870e43 + 3.25401e43i 0.820246 + 1.42071i
\(979\) −3.83367e43 −1.64917
\(980\) 7.83205e41 + 8.18642e43i 0.0331969 + 3.46989i
\(981\) −7.96008e42 −0.332443
\(982\) 2.64604e43 + 4.58308e43i 1.08888 + 1.88600i
\(983\) −8.70235e42 + 1.50729e43i −0.352867 + 0.611183i −0.986750 0.162245i \(-0.948126\pi\)
0.633884 + 0.773428i \(0.281460\pi\)
\(984\) −4.81876e42 + 8.34635e42i −0.192534 + 0.333478i
\(985\) 1.43747e43 + 2.48977e43i 0.565943 + 0.980242i
\(986\) −2.00690e43 −0.778594
\(987\) −9.91418e42 9.81978e42i −0.379016 0.375408i
\(988\) −1.00027e44 −3.76826
\(989\) −1.40940e43 2.44114e43i −0.523223 0.906248i
\(990\) 1.51442e43 2.62305e43i 0.554033 0.959614i
\(991\) 1.57034e42 2.71991e42i 0.0566143 0.0980588i −0.836329 0.548227i \(-0.815303\pi\)
0.892944 + 0.450169i \(0.148636\pi\)
\(992\) −5.22782e43 9.05486e43i −1.85738 3.21708i
\(993\) 2.77401e43 0.971280
\(994\) 5.73269e42 2.18115e43i 0.197814 0.752632i
\(995\) −3.79869e43 −1.29181
\(996\) 1.91448e43 + 3.31597e43i 0.641638 + 1.11135i
\(997\) −4.87869e42 + 8.45015e42i −0.161148 + 0.279116i −0.935281 0.353907i \(-0.884853\pi\)
0.774133 + 0.633023i \(0.218186\pi\)
\(998\) 4.50339e43 7.80010e43i 1.46604 2.53926i
\(999\) −4.40772e42 7.63439e42i −0.141421 0.244949i
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.a.4.19 38
7.2 even 3 inner 21.30.e.a.16.19 yes 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.30.e.a.4.19 38 1.1 even 1 trivial
21.30.e.a.16.19 yes 38 7.2 even 3 inner