Properties

Label 12.20.b.a.11.34
Level $12$
Weight $20$
Character 12.11
Analytic conductor $27.458$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [12,20,Mod(11,12)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(12, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 20, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.11");
 
S:= CuspForms(chi, 20);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 12.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(27.4580035868\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.34
Character \(\chi\) \(=\) 12.11
Dual form 12.20.b.a.11.33

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(706.401 + 159.015i) q^{2} +(32549.6 - 10138.3i) q^{3} +(473717. + 224656. i) q^{4} -5.54418e6i q^{5} +(2.46052e7 - 1.98584e6i) q^{6} +1.49965e8i q^{7} +(2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +O(q^{10})\) \(q+(706.401 + 159.015i) q^{2} +(32549.6 - 10138.3i) q^{3} +(473717. + 224656. i) q^{4} -5.54418e6i q^{5} +(2.46052e7 - 1.98584e6i) q^{6} +1.49965e8i q^{7} +(2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +(8.81605e8 - 3.91641e9i) q^{10} +2.49508e6 q^{11} +(1.76969e10 + 2.50978e9i) q^{12} +4.88082e10 q^{13} +(-2.38467e10 + 1.05936e11i) q^{14} +(-5.62085e10 - 1.80461e11i) q^{15} +(1.73937e11 + 2.12847e11i) q^{16} -4.51471e11i q^{17} +(7.80757e11 - 3.14093e11i) q^{18} -6.03024e11i q^{19} +(1.24553e12 - 2.62637e12i) q^{20} +(1.52039e12 + 4.88132e12i) q^{21} +(1.76253e9 + 3.96754e8i) q^{22} -7.40098e12 q^{23} +(1.21020e13 + 4.58698e12i) q^{24} -1.16644e13 q^{25} +(3.44782e13 + 7.76122e12i) q^{26} +(2.44487e13 - 3.11818e13i) q^{27} +(-3.36906e13 + 7.10412e13i) q^{28} -1.10755e14i q^{29} +(-1.10099e13 - 1.36416e14i) q^{30} +2.18703e14i q^{31} +(8.90238e13 + 1.78014e14i) q^{32} +(8.12138e10 - 2.52958e10i) q^{33} +(7.17904e13 - 3.18919e14i) q^{34} +8.31435e14 q^{35} +(6.01473e14 - 9.77241e13i) q^{36} +4.99785e14 q^{37} +(9.58896e13 - 4.25977e14i) q^{38} +(1.58869e15 - 4.94832e14i) q^{39} +(1.29748e15 - 1.65721e15i) q^{40} -1.26797e13i q^{41} +(2.97808e14 + 3.68993e15i) q^{42} +3.26952e15i q^{43} +(1.18196e12 + 5.60534e11i) q^{44} +(-3.65913e15 - 5.30407e15i) q^{45} +(-5.22806e15 - 1.17686e15i) q^{46} -1.12738e16 q^{47} +(7.81949e15 + 5.16465e15i) q^{48} -1.10907e16 q^{49} +(-8.23976e15 - 1.85481e15i) q^{50} +(-4.57714e15 - 1.46952e16i) q^{51} +(2.31213e16 + 1.09651e16i) q^{52} +3.23098e16i q^{53} +(2.22289e16 - 1.81391e16i) q^{54} -1.38332e13i q^{55} +(-3.50957e16 + 4.48262e16i) q^{56} +(-6.11364e15 - 1.96282e16i) q^{57} +(1.76117e16 - 7.82375e16i) q^{58} -6.67474e16 q^{59} +(1.39147e16 - 9.81149e16i) q^{60} -1.62842e17 q^{61} +(-3.47770e16 + 1.54492e17i) q^{62} +(9.89764e16 + 1.43471e17i) q^{63} +(3.45797e16 + 1.39905e17i) q^{64} -2.70602e17i q^{65} +(6.13919e13 - 4.95483e12i) q^{66} +4.88693e15i q^{67} +(1.01426e17 - 2.13869e17i) q^{68} +(-2.40899e17 + 7.50333e16i) q^{69} +(5.87327e17 + 1.32210e17i) q^{70} +2.98345e17 q^{71} +(4.40420e17 + 2.66105e16i) q^{72} -9.07454e17 q^{73} +(3.53049e17 + 7.94731e16i) q^{74} +(-3.79672e17 + 1.18257e17i) q^{75} +(1.35473e17 - 2.85663e17i) q^{76} +3.74176e14i q^{77} +(1.20094e18 - 9.69254e16i) q^{78} +3.92004e17i q^{79} +(1.18006e18 - 9.64339e17i) q^{80} +(4.79666e17 - 1.26282e18i) q^{81} +(2.01625e15 - 8.95693e15i) q^{82} +8.04463e17 q^{83} +(-3.76381e17 + 2.65393e18i) q^{84} -2.50303e18 q^{85} +(-5.19901e17 + 2.30959e18i) q^{86} +(-1.12287e18 - 3.60503e18i) q^{87} +(7.45805e14 + 5.83911e14i) q^{88} -1.37583e18i q^{89} +(-1.74139e18 - 4.32865e18i) q^{90} +7.31955e18i q^{91} +(-3.50597e18 - 1.66267e18i) q^{92} +(2.21728e18 + 7.11870e18i) q^{93} +(-7.96384e18 - 1.79270e18i) q^{94} -3.34327e18 q^{95} +(4.70244e18 + 4.89172e18i) q^{96} -1.68560e18 q^{97} +(-7.83452e18 - 1.76359e18i) q^{98} +(2.38702e15 - 1.64674e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 11\!\cdots\!16 q^{36}+ \cdots + 12\!\cdots\!88 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 706.401 + 159.015i 0.975588 + 0.219610i
\(3\) 32549.6 10138.3i 0.954759 0.297381i
\(4\) 473717. + 224656.i 0.903543 + 0.428497i
\(5\) 5.54418e6i 1.26947i −0.772730 0.634735i \(-0.781109\pi\)
0.772730 0.634735i \(-0.218891\pi\)
\(6\) 2.46052e7 1.98584e6i 0.996759 0.0804466i
\(7\) 1.49965e8i 1.40462i 0.711870 + 0.702312i \(0.247849\pi\)
−0.711870 + 0.702312i \(0.752151\pi\)
\(8\) 2.98910e8 + 2.34025e8i 0.787383 + 0.616464i
\(9\) 9.56692e8 6.59995e8i 0.823129 0.567854i
\(10\) 8.81605e8 3.91641e9i 0.278788 1.23848i
\(11\) 2.49508e6 0.000319046 0.000159523 1.00000i \(-0.499949\pi\)
0.000159523 1.00000i \(0.499949\pi\)
\(12\) 1.76969e10 + 2.50978e9i 0.990093 + 0.140415i
\(13\) 4.88082e10 1.27653 0.638265 0.769816i \(-0.279652\pi\)
0.638265 + 0.769816i \(0.279652\pi\)
\(14\) −2.38467e10 + 1.05936e11i −0.308469 + 1.37033i
\(15\) −5.62085e10 1.80461e11i −0.377516 1.21204i
\(16\) 1.73937e11 + 2.12847e11i 0.632780 + 0.774332i
\(17\) 4.51471e11i 0.923347i −0.887050 0.461673i \(-0.847249\pi\)
0.887050 0.461673i \(-0.152751\pi\)
\(18\) 7.80757e11 3.14093e11i 0.927741 0.373224i
\(19\) 6.03024e11i 0.428722i −0.976755 0.214361i \(-0.931233\pi\)
0.976755 0.214361i \(-0.0687669\pi\)
\(20\) 1.24553e12 2.62637e12i 0.543964 1.14702i
\(21\) 1.52039e12 + 4.88132e12i 0.417708 + 1.34108i
\(22\) 1.76253e9 + 3.96754e8i 0.000311258 + 7.00657e-5i
\(23\) −7.40098e12 −0.856791 −0.428395 0.903591i \(-0.640921\pi\)
−0.428395 + 0.903591i \(0.640921\pi\)
\(24\) 1.21020e13 + 4.58698e12i 0.935086 + 0.354422i
\(25\) −1.16644e13 −0.611552
\(26\) 3.44782e13 + 7.76122e12i 1.24537 + 0.280339i
\(27\) 2.44487e13 3.11818e13i 0.617021 0.786946i
\(28\) −3.36906e13 + 7.10412e13i −0.601877 + 1.26914i
\(29\) 1.10755e14i 1.41770i −0.705362 0.708848i \(-0.749215\pi\)
0.705362 0.708848i \(-0.250785\pi\)
\(30\) −1.10099e13 1.36416e14i −0.102124 1.26535i
\(31\) 2.18703e14i 1.48566i 0.669481 + 0.742829i \(0.266517\pi\)
−0.669481 + 0.742829i \(0.733483\pi\)
\(32\) 8.90238e13 + 1.78014e14i 0.447282 + 0.894393i
\(33\) 8.12138e10 2.52958e10i 0.000304612 9.48782e-5i
\(34\) 7.17904e13 3.18919e14i 0.202776 0.900806i
\(35\) 8.31435e14 1.78313
\(36\) 6.01473e14 9.77241e13i 0.987057 0.160372i
\(37\) 4.99785e14 0.632218 0.316109 0.948723i \(-0.397623\pi\)
0.316109 + 0.948723i \(0.397623\pi\)
\(38\) 9.58896e13 4.25977e14i 0.0941515 0.418256i
\(39\) 1.58869e15 4.94832e14i 1.21878 0.379616i
\(40\) 1.29748e15 1.65721e15i 0.782582 0.999559i
\(41\) 1.26797e13i 0.00604869i −0.999995 0.00302435i \(-0.999037\pi\)
0.999995 0.00302435i \(-0.000962681\pi\)
\(42\) 2.97808e14 + 3.68993e15i 0.112997 + 1.40007i
\(43\) 3.26952e15i 0.992050i 0.868308 + 0.496025i \(0.165208\pi\)
−0.868308 + 0.496025i \(0.834792\pi\)
\(44\) 1.18196e12 + 5.60534e11i 0.000288272 + 0.000136710i
\(45\) −3.65913e15 5.30407e15i −0.720873 1.04494i
\(46\) −5.22806e15 1.17686e15i −0.835874 0.188160i
\(47\) −1.12738e16 −1.46940 −0.734702 0.678390i \(-0.762678\pi\)
−0.734702 + 0.678390i \(0.762678\pi\)
\(48\) 7.81949e15 + 5.16465e15i 0.834424 + 0.551123i
\(49\) −1.10907e16 −0.972967
\(50\) −8.23976e15 1.85481e15i −0.596622 0.134303i
\(51\) −4.57714e15 1.46952e16i −0.274586 0.881574i
\(52\) 2.31213e16 + 1.09651e16i 1.15340 + 0.546990i
\(53\) 3.23098e16i 1.34497i 0.740109 + 0.672487i \(0.234774\pi\)
−0.740109 + 0.672487i \(0.765226\pi\)
\(54\) 2.22289e16 1.81391e16i 0.774780 0.632231i
\(55\) 1.38332e13i 0.000405019i
\(56\) −3.50957e16 + 4.48262e16i −0.865899 + 1.10598i
\(57\) −6.11364e15 1.96282e16i −0.127494 0.409326i
\(58\) 1.76117e16 7.82375e16i 0.311340 1.38309i
\(59\) −6.67474e16 −1.00309 −0.501545 0.865132i \(-0.667235\pi\)
−0.501545 + 0.865132i \(0.667235\pi\)
\(60\) 1.39147e16 9.81149e16i 0.178253 1.25689i
\(61\) −1.62842e17 −1.78293 −0.891464 0.453091i \(-0.850321\pi\)
−0.891464 + 0.453091i \(0.850321\pi\)
\(62\) −3.47770e16 + 1.54492e17i −0.326265 + 1.44939i
\(63\) 9.89764e16 + 1.43471e17i 0.797621 + 1.15619i
\(64\) 3.45797e16 + 1.39905e17i 0.239945 + 0.970786i
\(65\) 2.70602e17i 1.62052i
\(66\) 6.13919e13 4.95483e12i 0.000318012 2.56662e-5i
\(67\) 4.88693e15i 0.0219445i 0.999940 + 0.0109723i \(0.00349265\pi\)
−0.999940 + 0.0109723i \(0.996507\pi\)
\(68\) 1.01426e17 2.13869e17i 0.395652 0.834284i
\(69\) −2.40899e17 + 7.50333e16i −0.818028 + 0.254793i
\(70\) 5.87327e17 + 1.32210e17i 1.73960 + 0.391592i
\(71\) 2.98345e17 0.772261 0.386131 0.922444i \(-0.373811\pi\)
0.386131 + 0.922444i \(0.373811\pi\)
\(72\) 4.40420e17 + 2.66105e16i 0.998180 + 0.0603107i
\(73\) −9.07454e17 −1.80409 −0.902044 0.431645i \(-0.857933\pi\)
−0.902044 + 0.431645i \(0.857933\pi\)
\(74\) 3.53049e17 + 7.94731e16i 0.616784 + 0.138841i
\(75\) −3.79672e17 + 1.18257e17i −0.583885 + 0.181864i
\(76\) 1.35473e17 2.85663e17i 0.183706 0.387369i
\(77\) 3.74176e14i 0.000448140i
\(78\) 1.20094e18 9.69254e16i 1.27239 0.102693i
\(79\) 3.92004e17i 0.367987i 0.982927 + 0.183994i \(0.0589026\pi\)
−0.982927 + 0.183994i \(0.941097\pi\)
\(80\) 1.18006e18 9.64339e17i 0.982990 0.803295i
\(81\) 4.79666e17 1.26282e18i 0.355084 0.934834i
\(82\) 2.01625e15 8.95693e15i 0.00132835 0.00590103i
\(83\) 8.04463e17 0.472350 0.236175 0.971711i \(-0.424106\pi\)
0.236175 + 0.971711i \(0.424106\pi\)
\(84\) −3.76381e17 + 2.65393e18i −0.197231 + 1.39071i
\(85\) −2.50303e18 −1.17216
\(86\) −5.19901e17 + 2.30959e18i −0.217864 + 0.967832i
\(87\) −1.12287e18 3.60503e18i −0.421595 1.35356i
\(88\) 7.45805e14 + 5.83911e14i 0.000251212 + 0.000196680i
\(89\) 1.37583e18i 0.416255i −0.978102 0.208127i \(-0.933263\pi\)
0.978102 0.208127i \(-0.0667368\pi\)
\(90\) −1.74139e18 4.32865e18i −0.473796 1.17774i
\(91\) 7.31955e18i 1.79305i
\(92\) −3.50597e18 1.66267e18i −0.774147 0.367132i
\(93\) 2.21728e18 + 7.11870e18i 0.441806 + 1.41845i
\(94\) −7.96384e18 1.79270e18i −1.43353 0.322696i
\(95\) −3.34327e18 −0.544249
\(96\) 4.70244e18 + 4.89172e18i 0.693022 + 0.720917i
\(97\) −1.68560e18 −0.225125 −0.112562 0.993645i \(-0.535906\pi\)
−0.112562 + 0.993645i \(0.535906\pi\)
\(98\) −7.83452e18 1.76359e18i −0.949215 0.213673i
\(99\) 2.38702e15 1.64674e15i 0.000262616 0.000181172i
\(100\) −5.52563e18 2.62048e18i −0.552563 0.262048i
\(101\) 2.15370e18i 0.195944i 0.995189 + 0.0979722i \(0.0312356\pi\)
−0.995189 + 0.0979722i \(0.968764\pi\)
\(102\) −8.96549e17 1.11085e19i −0.0742801 0.920354i
\(103\) 2.29597e19i 1.73385i −0.498438 0.866926i \(-0.666093\pi\)
0.498438 0.866926i \(-0.333907\pi\)
\(104\) 1.45893e19 + 1.14224e19i 1.00512 + 0.786935i
\(105\) 2.70629e19 8.42933e18i 1.70246 0.530267i
\(106\) −5.13773e18 + 2.28237e19i −0.295370 + 1.31214i
\(107\) −5.85665e18 −0.307967 −0.153983 0.988073i \(-0.549210\pi\)
−0.153983 + 0.988073i \(0.549210\pi\)
\(108\) 1.85869e19 9.27878e18i 0.894710 0.446648i
\(109\) 2.20095e19 0.970641 0.485321 0.874336i \(-0.338703\pi\)
0.485321 + 0.874336i \(0.338703\pi\)
\(110\) 2.19967e15 9.77176e15i 8.89462e−5 0.000395132i
\(111\) 1.62678e19 5.06697e18i 0.603616 0.188009i
\(112\) −3.19196e19 + 2.60846e19i −1.08764 + 0.888818i
\(113\) 3.71474e19i 1.16328i 0.813447 + 0.581639i \(0.197588\pi\)
−0.813447 + 0.581639i \(0.802412\pi\)
\(114\) −1.19751e18 1.48375e19i −0.0344892 0.427332i
\(115\) 4.10323e19i 1.08767i
\(116\) 2.48818e19 5.24666e19i 0.607479 1.28095i
\(117\) 4.66944e19 3.22132e19i 1.05075 0.724883i
\(118\) −4.71504e19 1.06138e19i −0.978603 0.220288i
\(119\) 6.77050e19 1.29695
\(120\) 2.54310e19 6.70958e19i 0.449927 1.18706i
\(121\) −6.11591e19 −1.00000
\(122\) −1.15032e20 2.58943e19i −1.73940 0.391549i
\(123\) −1.28550e17 4.12718e17i −0.00179876 0.00577504i
\(124\) −4.91330e19 + 1.03603e20i −0.636601 + 1.34236i
\(125\) 4.10772e19i 0.493123i
\(126\) 4.71031e19 + 1.17087e20i 0.524239 + 1.30313i
\(127\) 7.81349e18i 0.0806695i −0.999186 0.0403348i \(-0.987158\pi\)
0.999186 0.0403348i \(-0.0128424\pi\)
\(128\) 2.18021e18 + 1.04328e20i 0.0208932 + 0.999782i
\(129\) 3.31473e19 + 1.06422e20i 0.295016 + 0.947168i
\(130\) 4.30296e19 1.91153e20i 0.355881 1.58096i
\(131\) −8.54542e19 −0.657138 −0.328569 0.944480i \(-0.606566\pi\)
−0.328569 + 0.944480i \(0.606566\pi\)
\(132\) 4.41552e16 + 6.26211e15i 0.000315885 + 4.47990e-5i
\(133\) 9.04328e19 0.602193
\(134\) −7.77093e17 + 3.45213e18i −0.00481923 + 0.0214088i
\(135\) −1.72877e20 1.35548e20i −0.999004 0.783289i
\(136\) 1.05655e20 1.34949e20i 0.569210 0.727028i
\(137\) 1.34424e20i 0.675512i −0.941234 0.337756i \(-0.890332\pi\)
0.941234 0.337756i \(-0.109668\pi\)
\(138\) −1.82103e20 + 1.46972e19i −0.854014 + 0.0689259i
\(139\) 3.67041e19i 0.160722i 0.996766 + 0.0803608i \(0.0256073\pi\)
−0.996766 + 0.0803608i \(0.974393\pi\)
\(140\) 3.93865e20 + 1.86787e20i 1.61113 + 0.764065i
\(141\) −3.66958e20 + 1.14297e20i −1.40293 + 0.436973i
\(142\) 2.10751e20 + 4.74412e19i 0.753409 + 0.169596i
\(143\) 1.21780e17 0.000407272
\(144\) 3.06882e20 + 8.88309e19i 0.960567 + 0.278048i
\(145\) −6.14046e20 −1.79972
\(146\) −6.41027e20 1.44298e20i −1.76005 0.396195i
\(147\) −3.60999e20 + 1.12441e20i −0.928949 + 0.289342i
\(148\) 2.36757e20 + 1.12280e20i 0.571236 + 0.270904i
\(149\) 7.43168e19i 0.168197i 0.996457 + 0.0840983i \(0.0268010\pi\)
−0.996457 + 0.0840983i \(0.973199\pi\)
\(150\) −2.87006e20 + 2.31637e19i −0.609570 + 0.0491973i
\(151\) 1.53578e20i 0.306231i 0.988208 + 0.153115i \(0.0489306\pi\)
−0.988208 + 0.153115i \(0.951069\pi\)
\(152\) 1.41123e20 1.80250e20i 0.264291 0.337568i
\(153\) −2.97968e20 4.31918e20i −0.524326 0.760034i
\(154\) −5.94993e16 + 2.64318e17i −9.84159e−5 + 0.000437200i
\(155\) 1.21253e21 1.88600
\(156\) 8.63756e20 + 1.22498e20i 1.26388 + 0.179245i
\(157\) 4.76448e20 0.656098 0.328049 0.944661i \(-0.393609\pi\)
0.328049 + 0.944661i \(0.393609\pi\)
\(158\) −6.23343e19 + 2.76912e20i −0.0808137 + 0.359004i
\(159\) 3.27566e20 + 1.05167e21i 0.399969 + 1.28413i
\(160\) 9.86939e20 4.93564e20i 1.13540 0.567810i
\(161\) 1.10989e21i 1.20347i
\(162\) 5.39643e20 8.15785e20i 0.551714 0.834033i
\(163\) 5.72589e20i 0.552155i −0.961135 0.276077i \(-0.910965\pi\)
0.961135 0.276077i \(-0.0890346\pi\)
\(164\) 2.84856e18 6.00657e18i 0.00259185 0.00546525i
\(165\) −1.40245e17 4.50264e17i −0.000120445 0.000386696i
\(166\) 5.68273e20 + 1.27921e20i 0.460819 + 0.103733i
\(167\) 9.88977e19 0.0757495 0.0378747 0.999282i \(-0.487941\pi\)
0.0378747 + 0.999282i \(0.487941\pi\)
\(168\) −6.87889e20 + 1.81489e21i −0.497829 + 1.31344i
\(169\) 9.20324e20 0.629531
\(170\) −1.76815e21 3.98019e20i −1.14355 0.257418i
\(171\) −3.97993e20 5.76908e20i −0.243451 0.352894i
\(172\) −7.34517e20 + 1.54883e21i −0.425091 + 0.896360i
\(173\) 2.94806e21i 1.61473i 0.590055 + 0.807363i \(0.299106\pi\)
−0.590055 + 0.807363i \(0.700894\pi\)
\(174\) −2.19942e20 2.72515e21i −0.114049 1.41310i
\(175\) 1.74926e21i 0.859000i
\(176\) 4.33987e17 + 5.31069e17i 0.000201886 + 0.000247048i
\(177\) −2.17260e21 + 6.76704e20i −0.957709 + 0.298300i
\(178\) 2.18777e20 9.71886e20i 0.0914136 0.406093i
\(179\) −9.70172e20 −0.384366 −0.192183 0.981359i \(-0.561557\pi\)
−0.192183 + 0.981359i \(0.561557\pi\)
\(180\) −5.41800e20 3.33467e21i −0.203587 1.25304i
\(181\) 3.97411e21 1.41675 0.708375 0.705836i \(-0.249429\pi\)
0.708375 + 0.705836i \(0.249429\pi\)
\(182\) −1.16391e21 + 5.17054e21i −0.393770 + 1.74927i
\(183\) −5.30045e21 + 1.65094e21i −1.70227 + 0.530209i
\(184\) −2.21223e21 1.73201e21i −0.674623 0.528180i
\(185\) 2.77090e21i 0.802581i
\(186\) 4.34310e20 + 5.38124e21i 0.119516 + 1.48084i
\(187\) 1.12645e18i 0.000294590i
\(188\) −5.34060e21 2.53273e21i −1.32767 0.629636i
\(189\) 4.67619e21 + 3.66646e21i 1.10536 + 0.866683i
\(190\) −2.36169e21 5.31629e20i −0.530963 0.119522i
\(191\) 5.34922e21 1.14412 0.572062 0.820210i \(-0.306144\pi\)
0.572062 + 0.820210i \(0.306144\pi\)
\(192\) 2.54395e21 + 4.20328e21i 0.517783 + 0.855512i
\(193\) 2.15483e21 0.417464 0.208732 0.977973i \(-0.433066\pi\)
0.208732 + 0.977973i \(0.433066\pi\)
\(194\) −1.19071e21 2.68035e20i −0.219629 0.0494396i
\(195\) −2.74344e21 8.80797e21i −0.481910 1.54720i
\(196\) −5.25387e21 2.49160e21i −0.879117 0.416914i
\(197\) 2.73703e20i 0.0436365i −0.999762 0.0218182i \(-0.993054\pi\)
0.999762 0.0218182i \(-0.00694551\pi\)
\(198\) 1.94805e18 7.83687e17i 0.000295992 0.000119076i
\(199\) 5.79917e21i 0.839965i 0.907532 + 0.419983i \(0.137964\pi\)
−0.907532 + 0.419983i \(0.862036\pi\)
\(200\) −3.48662e21 2.72977e21i −0.481526 0.376999i
\(201\) 4.95451e19 + 1.59068e20i 0.00652587 + 0.0209517i
\(202\) −3.42470e20 + 1.52138e21i −0.0430313 + 0.191161i
\(203\) 1.66094e22 1.99133
\(204\) 1.13309e21 7.98964e21i 0.129652 0.914199i
\(205\) −7.02984e19 −0.00767863
\(206\) 3.65092e21 1.62187e22i 0.380771 1.69152i
\(207\) −7.08045e21 + 4.88461e21i −0.705249 + 0.486532i
\(208\) 8.48957e21 + 1.03887e22i 0.807763 + 0.988458i
\(209\) 1.50459e18i 0.000136782i
\(210\) 2.04576e22 1.65110e21i 1.77735 0.143446i
\(211\) 6.69519e21i 0.556006i 0.960580 + 0.278003i \(0.0896725\pi\)
−0.960580 + 0.278003i \(0.910328\pi\)
\(212\) −7.25860e21 + 1.53057e22i −0.576318 + 1.21524i
\(213\) 9.71101e21 3.02471e21i 0.737323 0.229656i
\(214\) −4.13715e21 9.31293e20i −0.300448 0.0676325i
\(215\) 1.81268e22 1.25938
\(216\) 1.46053e22 3.59895e21i 0.970956 0.239257i
\(217\) −3.27979e22 −2.08679
\(218\) 1.55475e22 + 3.49983e21i 0.946946 + 0.213162i
\(219\) −2.95373e22 + 9.20004e21i −1.72247 + 0.536501i
\(220\) 3.10770e18 6.55300e18i 0.000173550 0.000365952i
\(221\) 2.20355e22i 1.17868i
\(222\) 1.22973e22 9.92494e20i 0.630169 0.0508598i
\(223\) 3.42488e22i 1.68170i −0.541265 0.840852i \(-0.682055\pi\)
0.541265 0.840852i \(-0.317945\pi\)
\(224\) −2.66959e22 + 1.33505e22i −1.25629 + 0.628262i
\(225\) −1.11593e22 + 7.69846e21i −0.503386 + 0.347272i
\(226\) −5.90698e21 + 2.62410e22i −0.255467 + 1.13488i
\(227\) −9.15468e21 −0.379662 −0.189831 0.981817i \(-0.560794\pi\)
−0.189831 + 0.981817i \(0.560794\pi\)
\(228\) 1.51346e21 1.06717e22i 0.0601991 0.424474i
\(229\) −2.34552e22 −0.894957 −0.447479 0.894295i \(-0.647678\pi\)
−0.447479 + 0.894295i \(0.647678\pi\)
\(230\) −6.52474e21 + 2.89853e22i −0.238863 + 1.06112i
\(231\) 3.79350e18 + 1.21793e19i 0.000133268 + 0.000427866i
\(232\) 2.59195e22 3.31059e22i 0.873958 1.11627i
\(233\) 7.75371e21i 0.250974i −0.992095 0.125487i \(-0.959951\pi\)
0.992095 0.125487i \(-0.0400493\pi\)
\(234\) 3.81074e22 1.53303e22i 1.18429 0.476432i
\(235\) 6.25041e22i 1.86536i
\(236\) −3.16193e22 1.49952e22i −0.906335 0.429821i
\(237\) 3.97425e21 + 1.27596e22i 0.109432 + 0.351339i
\(238\) 4.78269e22 + 1.07661e22i 1.26529 + 0.284824i
\(239\) −5.58610e21 −0.142013 −0.0710066 0.997476i \(-0.522621\pi\)
−0.0710066 + 0.997476i \(0.522621\pi\)
\(240\) 2.86337e22 4.33526e22i 0.699634 1.05928i
\(241\) −7.82487e21 −0.183787 −0.0918935 0.995769i \(-0.529292\pi\)
−0.0918935 + 0.995769i \(0.529292\pi\)
\(242\) −4.32028e22 9.72518e21i −0.975588 0.219610i
\(243\) 2.81006e21 4.59674e22i 0.0610177 0.998137i
\(244\) −7.71412e22 3.65835e22i −1.61095 0.763980i
\(245\) 6.14891e22i 1.23515i
\(246\) −2.51798e19 3.11986e20i −0.000486597 0.00602909i
\(247\) 2.94326e22i 0.547277i
\(248\) −5.11820e22 + 6.53727e22i −0.915855 + 1.16978i
\(249\) 2.61849e22 8.15588e21i 0.450981 0.140468i
\(250\) 6.53186e21 2.90169e22i 0.108295 0.481085i
\(251\) 5.35960e22 0.855523 0.427762 0.903892i \(-0.359302\pi\)
0.427762 + 0.903892i \(0.359302\pi\)
\(252\) 1.46552e22 + 9.02001e22i 0.225262 + 1.38644i
\(253\) −1.84660e19 −0.000273356
\(254\) 1.24246e21 5.51945e21i 0.0177158 0.0787002i
\(255\) −8.14728e22 + 2.53765e22i −1.11913 + 0.348578i
\(256\) −1.50495e22 + 7.40439e22i −0.199179 + 0.979963i
\(257\) 9.24681e22i 1.17931i −0.807656 0.589654i \(-0.799264\pi\)
0.807656 0.589654i \(-0.200736\pi\)
\(258\) 6.49274e21 + 8.04472e22i 0.0798070 + 0.988834i
\(259\) 7.49505e22i 0.888028i
\(260\) 6.07923e22 1.28189e23i 0.694387 1.46421i
\(261\) −7.30978e22 1.05958e23i −0.805044 1.16695i
\(262\) −6.03650e22 1.35885e22i −0.641095 0.144314i
\(263\) 7.84375e22 0.803423 0.401712 0.915766i \(-0.368415\pi\)
0.401712 + 0.915766i \(0.368415\pi\)
\(264\) 3.01955e19 + 1.14449e19i 0.000298336 + 0.000113077i
\(265\) 1.79131e23 1.70740
\(266\) 6.38818e22 + 1.43801e22i 0.587492 + 0.132247i
\(267\) −1.39485e22 4.47826e22i −0.123786 0.397423i
\(268\) −1.09788e21 + 2.31502e21i −0.00940316 + 0.0198278i
\(269\) 1.45532e23i 1.20313i 0.798824 + 0.601565i \(0.205456\pi\)
−0.798824 + 0.601565i \(0.794544\pi\)
\(270\) −1.00567e23 1.23241e23i −0.802598 0.983559i
\(271\) 1.50170e23i 1.15711i −0.815642 0.578557i \(-0.803616\pi\)
0.815642 0.578557i \(-0.196384\pi\)
\(272\) 9.60940e22 7.85276e22i 0.714977 0.584275i
\(273\) 7.42077e22 + 2.38248e23i 0.533217 + 1.71193i
\(274\) 2.13754e22 9.49575e22i 0.148349 0.659021i
\(275\) −2.91036e19 −0.000195113
\(276\) −1.30975e23 1.85749e22i −0.848302 0.120307i
\(277\) 2.52142e23 1.57793 0.788964 0.614439i \(-0.210618\pi\)
0.788964 + 0.614439i \(0.210618\pi\)
\(278\) −5.83649e21 + 2.59278e22i −0.0352960 + 0.156798i
\(279\) 1.44343e23 + 2.09232e23i 0.843637 + 1.22289i
\(280\) 2.48525e23 + 1.94577e23i 1.40400 + 1.09923i
\(281\) 1.28348e23i 0.700935i −0.936575 0.350467i \(-0.886023\pi\)
0.936575 0.350467i \(-0.113977\pi\)
\(282\) −2.77395e23 + 2.23880e22i −1.46464 + 0.118209i
\(283\) 2.88031e23i 1.47051i −0.677789 0.735256i \(-0.737062\pi\)
0.677789 0.735256i \(-0.262938\pi\)
\(284\) 1.41331e23 + 6.70250e22i 0.697771 + 0.330912i
\(285\) −1.08822e23 + 3.38951e22i −0.519627 + 0.161849i
\(286\) 8.60258e19 + 1.93648e19i 0.000397330 + 8.94410e-5i
\(287\) 1.90151e21 0.00849613
\(288\) 2.02656e23 + 1.11549e23i 0.876055 + 0.482211i
\(289\) 3.52466e22 0.147431
\(290\) −4.33763e23 9.76422e22i −1.75578 0.395236i
\(291\) −5.48657e22 + 1.70891e22i −0.214940 + 0.0669478i
\(292\) −4.29876e23 2.03865e23i −1.63007 0.773047i
\(293\) 3.47250e23i 1.27468i −0.770584 0.637338i \(-0.780036\pi\)
0.770584 0.637338i \(-0.219964\pi\)
\(294\) −2.72890e23 + 2.20245e22i −0.969813 + 0.0782719i
\(295\) 3.70059e23i 1.27339i
\(296\) 1.49391e23 + 1.16962e23i 0.497798 + 0.389739i
\(297\) 6.10014e19 7.78010e19i 0.000196858 0.000251072i
\(298\) −1.18174e22 + 5.24975e22i −0.0369376 + 0.164091i
\(299\) −3.61229e23 −1.09372
\(300\) −2.06424e23 2.92752e22i −0.605493 0.0858713i
\(301\) −4.90315e23 −1.39346
\(302\) −2.44212e22 + 1.08488e23i −0.0672513 + 0.298755i
\(303\) 2.18349e22 + 7.01022e22i 0.0582701 + 0.187080i
\(304\) 1.28352e23 1.04888e23i 0.331973 0.271287i
\(305\) 9.02827e23i 2.26337i
\(306\) −1.41804e23 3.52489e23i −0.344615 0.856627i
\(307\) 1.16531e23i 0.274554i −0.990533 0.137277i \(-0.956165\pi\)
0.990533 0.137277i \(-0.0438351\pi\)
\(308\) −8.40608e19 + 1.77253e20i −0.000192027 + 0.000404914i
\(309\) −2.32772e23 7.47328e23i −0.515614 1.65541i
\(310\) 8.56532e23 + 1.92810e23i 1.83996 + 0.414184i
\(311\) −6.98423e23 −1.45511 −0.727553 0.686051i \(-0.759343\pi\)
−0.727553 + 0.686051i \(0.759343\pi\)
\(312\) 5.90679e23 + 2.23882e23i 1.19367 + 0.452430i
\(313\) −5.99952e22 −0.117610 −0.0588052 0.998269i \(-0.518729\pi\)
−0.0588052 + 0.998269i \(0.518729\pi\)
\(314\) 3.36564e23 + 7.57622e22i 0.640082 + 0.144086i
\(315\) 7.95427e23 5.48743e23i 1.46774 1.01256i
\(316\) −8.80660e22 + 1.85699e23i −0.157682 + 0.332492i
\(317\) 4.40158e23i 0.764796i 0.923998 + 0.382398i \(0.124902\pi\)
−0.923998 + 0.382398i \(0.875098\pi\)
\(318\) 6.41622e22 + 7.94990e23i 0.108199 + 1.34061i
\(319\) 2.76343e20i 0.000452310i
\(320\) 7.75659e23 1.91716e23i 1.23238 0.304603i
\(321\) −1.90632e23 + 5.93765e22i −0.294034 + 0.0915834i
\(322\) 1.76489e23 7.84028e23i 0.264293 1.17409i
\(323\) −2.72248e23 −0.395859
\(324\) 5.10926e23 4.90461e23i 0.721408 0.692511i
\(325\) −5.69320e23 −0.780665
\(326\) 9.10500e22 4.04478e23i 0.121259 0.538676i
\(327\) 7.16401e23 2.23139e23i 0.926728 0.288650i
\(328\) 2.96736e21 3.79009e21i 0.00372880 0.00476264i
\(329\) 1.69068e24i 2.06396i
\(330\) −2.74705e19 3.40368e20i −3.25824e−5 0.000403707i
\(331\) 1.20541e24i 1.38921i 0.719392 + 0.694604i \(0.244420\pi\)
−0.719392 + 0.694604i \(0.755580\pi\)
\(332\) 3.81088e23 + 1.80727e23i 0.426789 + 0.202401i
\(333\) 4.78140e23 3.29855e23i 0.520397 0.359007i
\(334\) 6.98614e22 + 1.57262e22i 0.0739003 + 0.0166353i
\(335\) 2.70940e22 0.0278579
\(336\) −7.74519e23 + 1.17265e24i −0.774121 + 1.17205i
\(337\) −5.16565e23 −0.501928 −0.250964 0.967996i \(-0.580748\pi\)
−0.250964 + 0.967996i \(0.580748\pi\)
\(338\) 6.50118e23 + 1.46345e23i 0.614163 + 0.138251i
\(339\) 3.76612e23 + 1.20913e24i 0.345937 + 1.11065i
\(340\) −1.18573e24 5.62322e23i −1.05910 0.502268i
\(341\) 5.45682e20i 0.000473994i
\(342\) −1.89406e23 4.70815e23i −0.160009 0.397743i
\(343\) 4.62114e22i 0.0379713i
\(344\) −7.65149e23 + 9.77293e23i −0.611563 + 0.781123i
\(345\) 4.15998e23 + 1.33559e24i 0.323452 + 1.03846i
\(346\) −4.68785e23 + 2.08252e24i −0.354610 + 1.57531i
\(347\) −1.44732e23 −0.106521 −0.0532603 0.998581i \(-0.516961\pi\)
−0.0532603 + 0.998581i \(0.516961\pi\)
\(348\) 2.77971e23 1.96002e24i 0.199066 1.40365i
\(349\) −7.90825e23 −0.551110 −0.275555 0.961285i \(-0.588862\pi\)
−0.275555 + 0.961285i \(0.588862\pi\)
\(350\) 2.78158e23 1.23568e24i 0.188645 0.838030i
\(351\) 1.19330e24 1.52193e24i 0.787647 1.00456i
\(352\) 2.22121e20 + 4.44158e20i 0.000142704 + 0.000285353i
\(353\) 3.64188e23i 0.227754i 0.993495 + 0.113877i \(0.0363270\pi\)
−0.993495 + 0.113877i \(0.963673\pi\)
\(354\) −1.64233e24 + 1.32550e23i −0.999839 + 0.0806952i
\(355\) 1.65408e24i 0.980362i
\(356\) 3.09088e23 6.51753e23i 0.178364 0.376104i
\(357\) 2.20377e24 6.86413e23i 1.23828 0.385689i
\(358\) −6.85330e23 1.54271e23i −0.374983 0.0844105i
\(359\) −5.80491e23 −0.309313 −0.154657 0.987968i \(-0.549427\pi\)
−0.154657 + 0.987968i \(0.549427\pi\)
\(360\) 1.47533e23 2.44177e24i 0.0765625 1.26716i
\(361\) 1.61478e24 0.816198
\(362\) 2.80731e24 + 6.31941e23i 1.38216 + 0.311132i
\(363\) −1.99070e24 + 6.20049e23i −0.954759 + 0.297381i
\(364\) −1.64438e24 + 3.46739e24i −0.768315 + 1.62009i
\(365\) 5.03109e24i 2.29023i
\(366\) −4.00677e24 + 3.23379e23i −1.77715 + 0.143431i
\(367\) 7.29018e23i 0.315073i 0.987513 + 0.157536i \(0.0503551\pi\)
−0.987513 + 0.157536i \(0.949645\pi\)
\(368\) −1.28731e24 1.57527e24i −0.542160 0.663440i
\(369\) −8.36852e21 1.21305e22i −0.00343477 0.00497886i
\(370\) 4.40613e23 1.95736e24i 0.176255 0.782988i
\(371\) −4.84536e24 −1.88918
\(372\) −5.48898e23 + 3.87037e24i −0.208609 + 1.47094i
\(373\) 2.85996e24 1.05956 0.529781 0.848135i \(-0.322274\pi\)
0.529781 + 0.848135i \(0.322274\pi\)
\(374\) 1.79123e20 7.95729e20i 6.46949e−5 0.000287399i
\(375\) −4.16452e23 1.33705e24i −0.146645 0.470814i
\(376\) −3.36986e24 2.63836e24i −1.15698 0.905835i
\(377\) 5.40576e24i 1.80973i
\(378\) 2.72025e24 + 3.33357e24i 0.888047 + 1.08827i
\(379\) 4.82016e24i 1.53458i −0.641301 0.767290i \(-0.721605\pi\)
0.641301 0.767290i \(-0.278395\pi\)
\(380\) −1.58376e24 7.51087e23i −0.491752 0.233209i
\(381\) −7.92154e22 2.54326e23i −0.0239896 0.0770200i
\(382\) 3.77869e24 + 8.50603e23i 1.11619 + 0.251261i
\(383\) 5.48430e24 1.58028 0.790138 0.612929i \(-0.210009\pi\)
0.790138 + 0.612929i \(0.210009\pi\)
\(384\) 1.12867e24 + 3.37372e24i 0.317264 + 0.948337i
\(385\) 2.07450e21 0.000568900
\(386\) 1.52217e24 + 3.42649e23i 0.407273 + 0.0916791i
\(387\) 2.15786e24 + 3.12792e24i 0.563339 + 0.816585i
\(388\) −7.98498e23 3.78681e23i −0.203410 0.0964654i
\(389\) 3.68660e24i 0.916442i 0.888838 + 0.458221i \(0.151513\pi\)
−0.888838 + 0.458221i \(0.848487\pi\)
\(390\) −5.37372e23 6.65821e24i −0.130365 1.61526i
\(391\) 3.34133e24i 0.791115i
\(392\) −3.31514e24 2.59551e24i −0.766098 0.599799i
\(393\) −2.78150e24 + 8.66360e23i −0.627408 + 0.195420i
\(394\) 4.35227e22 1.93344e23i 0.00958300 0.0425712i
\(395\) 2.17334e24 0.467149
\(396\) 1.50072e21 2.43829e20i 0.000314917 5.11660e-5i
\(397\) 4.75450e24 0.974082 0.487041 0.873379i \(-0.338076\pi\)
0.487041 + 0.873379i \(0.338076\pi\)
\(398\) −9.22152e23 + 4.09654e24i −0.184465 + 0.819460i
\(399\) 2.94355e24 9.16834e23i 0.574949 0.179081i
\(400\) −2.02888e24 2.48273e24i −0.386978 0.473544i
\(401\) 1.08639e24i 0.202356i −0.994868 0.101178i \(-0.967739\pi\)
0.994868 0.101178i \(-0.0322611\pi\)
\(402\) 9.70467e21 + 1.20244e23i 0.00176536 + 0.0218734i
\(403\) 1.06745e25i 1.89649i
\(404\) −4.83842e23 + 1.02025e24i −0.0839616 + 0.177044i
\(405\) −7.00131e24 2.65935e24i −1.18674 0.450768i
\(406\) 1.17329e25 + 2.64114e24i 1.94271 + 0.437315i
\(407\) 1.24700e21 0.000201707
\(408\) 2.07089e24 5.46371e24i 0.327254 0.863409i
\(409\) −7.66016e24 −1.18268 −0.591338 0.806423i \(-0.701400\pi\)
−0.591338 + 0.806423i \(0.701400\pi\)
\(410\) −4.96588e22 1.11785e22i −0.00749117 0.00168630i
\(411\) −1.36283e24 4.37546e24i −0.200884 0.644951i
\(412\) 5.15803e24 1.08764e25i 0.742951 1.56661i
\(413\) 1.00098e25i 1.40896i
\(414\) −5.77836e24 + 2.32460e24i −0.794880 + 0.319775i
\(415\) 4.46009e24i 0.599634i
\(416\) 4.34509e24 + 8.68853e24i 0.570969 + 1.14172i
\(417\) 3.72117e23 + 1.19470e24i 0.0477955 + 0.153450i
\(418\) 2.39252e20 1.06285e21i 3.00387e−5 0.000133443i
\(419\) 3.13837e24 0.385186 0.192593 0.981279i \(-0.438310\pi\)
0.192593 + 0.981279i \(0.438310\pi\)
\(420\) 1.47138e25 + 2.08672e24i 1.76546 + 0.250378i
\(421\) 3.70615e24 0.434753 0.217377 0.976088i \(-0.430250\pi\)
0.217377 + 0.976088i \(0.430250\pi\)
\(422\) −1.06463e24 + 4.72949e24i −0.122104 + 0.542432i
\(423\) −1.07856e25 + 7.44066e24i −1.20951 + 0.834407i
\(424\) −7.56131e24 + 9.65775e24i −0.829128 + 1.05901i
\(425\) 5.26615e24i 0.564674i
\(426\) 7.34084e24 5.92466e23i 0.769758 0.0621258i
\(427\) 2.44207e25i 2.50434i
\(428\) −2.77440e24 1.31573e24i −0.278261 0.131963i
\(429\) 3.96390e21 1.23464e21i 0.000388847 0.000121115i
\(430\) 1.28048e25 + 2.88242e24i 1.22863 + 0.276571i
\(431\) 3.09919e24 0.290880 0.145440 0.989367i \(-0.453540\pi\)
0.145440 + 0.989367i \(0.453540\pi\)
\(432\) 1.08895e25 2.19848e23i 0.999796 0.0201849i
\(433\) −1.37245e25 −1.23271 −0.616355 0.787468i \(-0.711391\pi\)
−0.616355 + 0.787468i \(0.711391\pi\)
\(434\) −2.31685e25 5.21535e24i −2.03585 0.458280i
\(435\) −1.99870e25 + 6.22538e24i −1.71830 + 0.535202i
\(436\) 1.04263e25 + 4.94457e24i 0.877016 + 0.415917i
\(437\) 4.46297e24i 0.367325i
\(438\) −2.23281e25 + 1.80206e24i −1.79824 + 0.145133i
\(439\) 1.81655e25i 1.43164i 0.698283 + 0.715822i \(0.253948\pi\)
−0.698283 + 0.715822i \(0.746052\pi\)
\(440\) 3.23731e21 4.13488e21i 0.000249680 0.000318905i
\(441\) −1.06104e25 + 7.31984e24i −0.800878 + 0.552503i
\(442\) 3.50396e24 1.55659e25i 0.258850 1.14991i
\(443\) −5.94482e24 −0.429836 −0.214918 0.976632i \(-0.568948\pi\)
−0.214918 + 0.976632i \(0.568948\pi\)
\(444\) 8.84465e24 + 1.25435e24i 0.625954 + 0.0887731i
\(445\) −7.62783e24 −0.528422
\(446\) 5.44606e24 2.41934e25i 0.369319 1.64065i
\(447\) 7.53445e23 + 2.41898e24i 0.0500185 + 0.160587i
\(448\) −2.09809e25 + 5.18576e24i −1.36359 + 0.337032i
\(449\) 5.95675e24i 0.379026i −0.981878 0.189513i \(-0.939309\pi\)
0.981878 0.189513i \(-0.0606909\pi\)
\(450\) −9.10708e24 + 3.66372e24i −0.567362 + 0.228246i
\(451\) 3.16368e19i 1.92981e-6i
\(452\) −8.34539e24 + 1.75974e25i −0.498462 + 1.05107i
\(453\) 1.55702e24 + 4.99891e24i 0.0910672 + 0.292377i
\(454\) −6.46687e24 1.45573e24i −0.370394 0.0833776i
\(455\) 4.05809e25 2.27622
\(456\) 2.76606e24 7.29782e24i 0.151948 0.400892i
\(457\) 2.63035e25 1.41517 0.707587 0.706626i \(-0.249784\pi\)
0.707587 + 0.706626i \(0.249784\pi\)
\(458\) −1.65688e25 3.72972e24i −0.873109 0.196541i
\(459\) −1.40777e25 1.10379e25i −0.726625 0.569725i
\(460\) −9.21816e24 + 1.94377e25i −0.466063 + 0.982756i
\(461\) 1.31846e25i 0.652991i −0.945199 0.326495i \(-0.894132\pi\)
0.945199 0.326495i \(-0.105868\pi\)
\(462\) 7.43053e20 + 9.20667e21i 3.60513e−5 + 0.000446687i
\(463\) 1.17965e24i 0.0560706i −0.999607 0.0280353i \(-0.991075\pi\)
0.999607 0.0280353i \(-0.00892508\pi\)
\(464\) 2.35739e25 1.92644e25i 1.09777 0.897089i
\(465\) 3.94674e25 1.22930e25i 1.80067 0.560859i
\(466\) 1.23295e24 5.47723e24i 0.0551163 0.244847i
\(467\) 1.27273e25 0.557475 0.278737 0.960367i \(-0.410084\pi\)
0.278737 + 0.960367i \(0.410084\pi\)
\(468\) 2.93568e25 4.76974e24i 1.26001 0.204719i
\(469\) −7.32871e23 −0.0308238
\(470\) −9.93905e24 + 4.41529e25i −0.409652 + 1.81983i
\(471\) 1.55082e25 4.83037e24i 0.626416 0.195111i
\(472\) −1.99515e25 1.56206e25i −0.789816 0.618369i
\(473\) 8.15770e21i 0.000316510i
\(474\) 7.78457e23 + 9.64534e24i 0.0296033 + 0.366795i
\(475\) 7.03393e24i 0.262186i
\(476\) 3.20730e25 + 1.52103e25i 1.17185 + 0.555742i
\(477\) 2.13243e25 + 3.09105e25i 0.763749 + 1.10709i
\(478\) −3.94603e24 8.88272e23i −0.138546 0.0311875i
\(479\) 1.58667e25 0.546135 0.273067 0.961995i \(-0.411962\pi\)
0.273067 + 0.961995i \(0.411962\pi\)
\(480\) 2.71206e25 2.60712e25i 0.915182 0.879769i
\(481\) 2.43936e25 0.807046
\(482\) −5.52749e24 1.24427e24i −0.179300 0.0403614i
\(483\) −1.12524e25 3.61265e25i −0.357888 1.14902i
\(484\) −2.89721e25 1.37398e25i −0.903543 0.428497i
\(485\) 9.34527e24i 0.285789i
\(486\) 9.29451e24 3.20246e25i 0.278729 0.960370i
\(487\) 2.17055e25i 0.638329i 0.947699 + 0.319165i \(0.103402\pi\)
−0.947699 + 0.319165i \(0.896598\pi\)
\(488\) −4.86753e25 3.81092e25i −1.40385 1.09911i
\(489\) −5.80508e24 1.86376e25i −0.164200 0.527175i
\(490\) −9.77766e24 + 4.34359e25i −0.271251 + 1.20500i
\(491\) −5.61079e25 −1.52669 −0.763343 0.645994i \(-0.776443\pi\)
−0.763343 + 0.645994i \(0.776443\pi\)
\(492\) 3.18232e22 2.24391e23i 0.000849329 0.00598877i
\(493\) −5.00027e25 −1.30902
\(494\) 4.68020e24 2.07912e25i 0.120187 0.533916i
\(495\) −9.12981e21 1.32341e22i −0.000229992 0.000333383i
\(496\) −4.65502e25 + 3.80406e25i −1.15039 + 0.940095i
\(497\) 4.47414e25i 1.08474i
\(498\) 1.97940e25 1.59754e24i 0.470819 0.0379990i
\(499\) 4.70657e25i 1.09837i 0.835700 + 0.549186i \(0.185062\pi\)
−0.835700 + 0.549186i \(0.814938\pi\)
\(500\) 9.22823e24 1.94589e25i 0.211302 0.445558i
\(501\) 3.21908e24 1.00265e24i 0.0723225 0.0225264i
\(502\) 3.78603e25 + 8.52254e24i 0.834638 + 0.187881i
\(503\) 1.83438e25 0.396821 0.198410 0.980119i \(-0.436422\pi\)
0.198410 + 0.980119i \(0.436422\pi\)
\(504\) −3.99066e24 + 6.60479e25i −0.0847138 + 1.40207i
\(505\) 1.19405e25 0.248745
\(506\) −1.30444e22 2.93636e21i −0.000266683 6.00316e-5i
\(507\) 2.99562e25 9.33051e24i 0.601050 0.187210i
\(508\) 1.75535e24 3.70138e24i 0.0345667 0.0728884i
\(509\) 6.09000e25i 1.17706i −0.808475 0.588530i \(-0.799707\pi\)
0.808475 0.588530i \(-0.200293\pi\)
\(510\) −6.15877e25 + 4.97063e24i −1.16836 + 0.0942963i
\(511\) 1.36087e26i 2.53406i
\(512\) −2.24051e25 + 4.99116e25i −0.409526 + 0.912298i
\(513\) −1.88034e25 1.47432e25i −0.337381 0.264530i
\(514\) 1.47038e25 6.53196e25i 0.258988 1.15052i
\(515\) −1.27292e26 −2.20107
\(516\) −8.20579e24 + 5.78604e25i −0.139299 + 0.982221i
\(517\) −2.81291e22 −0.000468808
\(518\) −1.19182e25 + 5.29451e25i −0.195020 + 0.866349i
\(519\) 2.98883e25 + 9.59583e25i 0.480188 + 1.54167i
\(520\) 6.33276e25 8.08856e25i 0.998990 1.27597i
\(521\) 8.86506e25i 1.37317i 0.727051 + 0.686584i \(0.240890\pi\)
−0.727051 + 0.686584i \(0.759110\pi\)
\(522\) −3.47874e25 8.64728e25i −0.529118 1.31525i
\(523\) 2.41404e25i 0.360561i 0.983615 + 0.180280i \(0.0577005\pi\)
−0.983615 + 0.180280i \(0.942299\pi\)
\(524\) −4.04811e25 1.91978e25i −0.593752 0.281582i
\(525\) −1.77345e25 5.69377e25i −0.255450 0.820138i
\(526\) 5.54084e25 + 1.24727e25i 0.783810 + 0.176440i
\(527\) 9.87381e25 1.37178
\(528\) 1.95102e22 + 1.28862e22i 0.000266220 + 0.000175834i
\(529\) −1.98410e25 −0.265910
\(530\) 1.26539e26 + 2.84845e25i 1.66572 + 0.374962i
\(531\) −6.38566e25 + 4.40529e25i −0.825673 + 0.569609i
\(532\) 4.28395e25 + 2.03163e25i 0.544107 + 0.258038i
\(533\) 6.18873e23i 0.00772134i
\(534\) −2.73218e24 3.38525e25i −0.0334863 0.414905i
\(535\) 3.24703e25i 0.390954i
\(536\) −1.14366e24 + 1.46076e24i −0.0135280 + 0.0172787i
\(537\) −3.15787e25 + 9.83589e24i −0.366977 + 0.114303i
\(538\) −2.31417e25 + 1.02804e26i −0.264219 + 1.17376i
\(539\) −2.76723e22 −0.000310421
\(540\) −5.14432e25 1.03049e26i −0.567006 1.13581i
\(541\) −6.84884e25 −0.741725 −0.370862 0.928688i \(-0.620938\pi\)
−0.370862 + 0.928688i \(0.620938\pi\)
\(542\) 2.38793e25 1.06080e26i 0.254113 1.12887i
\(543\) 1.29356e26 4.02907e25i 1.35265 0.421314i
\(544\) 8.03680e25 4.01916e25i 0.825835 0.412996i
\(545\) 1.22025e26i 1.23220i
\(546\) 1.45355e25 + 1.80099e26i 0.144244 + 1.78723i
\(547\) 4.11723e25i 0.401537i −0.979639 0.200768i \(-0.935656\pi\)
0.979639 0.200768i \(-0.0643438\pi\)
\(548\) 3.01993e25 6.36791e25i 0.289455 0.610354i
\(549\) −1.55790e26 + 1.07475e26i −1.46758 + 1.01244i
\(550\) −2.05588e22 4.62790e21i −0.000190350 4.28488e-5i
\(551\) −6.67880e25 −0.607797
\(552\) −8.95669e25 3.39481e25i −0.801173 0.303665i
\(553\) −5.87870e25 −0.516884
\(554\) 1.78113e26 + 4.00942e25i 1.53941 + 0.346529i
\(555\) −2.80922e25 9.01916e25i −0.238672 0.766272i
\(556\) −8.24580e24 + 1.73874e25i −0.0688688 + 0.145219i
\(557\) 1.60444e26i 1.31734i −0.752431 0.658671i \(-0.771119\pi\)
0.752431 0.658671i \(-0.228881\pi\)
\(558\) 6.86932e25 + 1.70754e26i 0.554484 + 1.37831i
\(559\) 1.59579e26i 1.26638i
\(560\) 1.44618e26 + 1.76968e26i 1.12833 + 1.38073i
\(561\) −1.14203e22 3.66657e22i −8.76055e−5 0.000281263i
\(562\) 2.04091e25 9.06648e25i 0.153932 0.683823i
\(563\) −1.71090e26 −1.26881 −0.634403 0.773002i \(-0.718754\pi\)
−0.634403 + 0.773002i \(0.718754\pi\)
\(564\) −1.99512e26 2.82949e25i −1.45485 0.206327i
\(565\) 2.05952e26 1.47675
\(566\) 4.58012e25 2.03466e26i 0.322939 1.43461i
\(567\) 1.89380e26 + 7.19333e25i 1.31309 + 0.498759i
\(568\) 8.91784e25 + 6.98202e25i 0.608066 + 0.476071i
\(569\) 1.43332e26i 0.961115i 0.876963 + 0.480558i \(0.159566\pi\)
−0.876963 + 0.480558i \(0.840434\pi\)
\(570\) −8.22619e25 + 6.63921e24i −0.542485 + 0.0437830i
\(571\) 8.93301e25i 0.579368i −0.957122 0.289684i \(-0.906450\pi\)
0.957122 0.289684i \(-0.0935502\pi\)
\(572\) 5.76894e22 + 2.73587e22i 0.000367988 + 0.000174515i
\(573\) 1.74115e26 5.42319e25i 1.09236 0.340241i
\(574\) 1.34323e24 + 3.02368e23i 0.00828872 + 0.00186583i
\(575\) 8.63282e25 0.523972
\(576\) 1.25419e26 + 1.11024e26i 0.748771 + 0.662829i
\(577\) 1.67041e26 0.980961 0.490481 0.871452i \(-0.336821\pi\)
0.490481 + 0.871452i \(0.336821\pi\)
\(578\) 2.48982e25 + 5.60472e24i 0.143831 + 0.0323772i
\(579\) 7.01389e25 2.18463e25i 0.398577 0.124146i
\(580\) −2.90884e26 1.37949e26i −1.62612 0.771175i
\(581\) 1.20642e26i 0.663474i
\(582\) −4.14746e25 + 3.34734e24i −0.224395 + 0.0181105i
\(583\) 8.06155e22i 0.000429109i
\(584\) −2.71248e26 2.12367e26i −1.42051 1.11215i
\(585\) −1.78596e26 2.58882e26i −0.920217 1.33389i
\(586\) 5.52178e25 2.45298e26i 0.279931 1.24356i
\(587\) −1.96328e26 −0.979311 −0.489656 0.871916i \(-0.662878\pi\)
−0.489656 + 0.871916i \(0.662878\pi\)
\(588\) −1.96272e26 2.78354e25i −0.963327 0.136619i
\(589\) 1.31883e26 0.636934
\(590\) −5.88448e25 + 2.61410e26i −0.279649 + 1.24231i
\(591\) −2.77488e24 8.90891e24i −0.0129766 0.0416623i
\(592\) 8.69312e25 + 1.06378e26i 0.400055 + 0.489546i
\(593\) 3.26171e26i 1.47715i 0.674170 + 0.738577i \(0.264502\pi\)
−0.674170 + 0.738577i \(0.735498\pi\)
\(594\) 5.54630e22 4.52586e22i 0.000247191 0.000201711i
\(595\) 3.75369e26i 1.64644i
\(596\) −1.66957e25 + 3.52051e25i −0.0720718 + 0.151973i
\(597\) 5.87936e25 + 1.88761e26i 0.249790 + 0.801964i
\(598\) −2.55172e26 5.74406e25i −1.06702 0.240192i
\(599\) 1.67035e26 0.687468 0.343734 0.939067i \(-0.388308\pi\)
0.343734 + 0.939067i \(0.388308\pi\)
\(600\) −1.41163e26 5.35045e25i −0.571853 0.216747i
\(601\) −1.82808e26 −0.728932 −0.364466 0.931217i \(-0.618749\pi\)
−0.364466 + 0.931217i \(0.618749\pi\)
\(602\) −3.46359e26 7.79672e25i −1.35944 0.306017i
\(603\) 3.22535e24 + 4.67529e24i 0.0124613 + 0.0180632i
\(604\) −3.45023e25 + 7.27526e25i −0.131219 + 0.276693i
\(605\) 3.39077e26i 1.26947i
\(606\) 4.27691e24 + 5.29923e25i 0.0157631 + 0.195309i
\(607\) 5.20544e26i 1.88871i 0.328933 + 0.944353i \(0.393311\pi\)
−0.328933 + 0.944353i \(0.606689\pi\)
\(608\) 1.07347e26 5.36835e25i 0.383446 0.191759i
\(609\) 5.40631e26 1.68391e26i 1.90124 0.592183i
\(610\) −1.43563e26 + 6.37758e26i −0.497059 + 2.20812i
\(611\) −5.50255e26 −1.87574
\(612\) −4.41196e25 2.71547e26i −0.148079 0.911396i
\(613\) 2.77002e26 0.915396 0.457698 0.889108i \(-0.348674\pi\)
0.457698 + 0.889108i \(0.348674\pi\)
\(614\) 1.85302e25 8.23179e25i 0.0602948 0.267852i
\(615\) −2.28818e24 + 7.12705e23i −0.00733124 + 0.00228348i
\(616\) −8.75665e22 + 1.11845e23i −0.000276262 + 0.000352858i
\(617\) 6.18374e26i 1.92106i −0.278169 0.960532i \(-0.589727\pi\)
0.278169 0.960532i \(-0.410273\pi\)
\(618\) −4.55942e25 5.64927e26i −0.139482 1.72823i
\(619\) 2.78796e26i 0.839897i −0.907548 0.419948i \(-0.862048\pi\)
0.907548 0.419948i \(-0.137952\pi\)
\(620\) 5.74396e26 + 2.72402e26i 1.70408 + 0.808145i
\(621\) −1.80944e26 + 2.30776e26i −0.528658 + 0.674248i
\(622\) −4.93367e26 1.11059e26i −1.41958 0.319556i
\(623\) 2.06327e26 0.584681
\(624\) 3.81656e26 + 2.52077e26i 1.06517 + 0.703526i
\(625\) −4.50220e26 −1.23756
\(626\) −4.23807e25 9.54011e24i −0.114739 0.0258284i
\(627\) −1.52540e22 4.89739e22i −4.06764e−5 0.000130594i
\(628\) 2.25702e26 + 1.07037e26i 0.592813 + 0.281136i
\(629\) 2.25638e26i 0.583756i
\(630\) 6.49149e26 2.61148e26i 1.65428 0.665505i
\(631\) 2.48783e26i 0.624514i −0.949998 0.312257i \(-0.898915\pi\)
0.949998 0.312257i \(-0.101085\pi\)
\(632\) −9.17387e25 + 1.17174e26i −0.226851 + 0.289747i
\(633\) 6.78777e25 + 2.17926e26i 0.165345 + 0.530852i
\(634\) −6.99915e25 + 3.10928e26i −0.167957 + 0.746125i
\(635\) −4.33194e25 −0.102407
\(636\) −8.10907e25 + 5.71784e26i −0.188855 + 1.33165i
\(637\) −5.41320e26 −1.24202
\(638\) 4.39425e22 1.95209e23i 9.93318e−5 0.000441268i
\(639\) 2.85424e26 1.96906e26i 0.635671 0.438532i
\(640\) 5.78412e26 1.20875e25i 1.26919 0.0265232i
\(641\) 3.31518e26i 0.716730i −0.933581 0.358365i \(-0.883334\pi\)
0.933581 0.358365i \(-0.116666\pi\)
\(642\) −1.44104e26 + 1.16304e25i −0.306968 + 0.0247749i
\(643\) 3.39062e26i 0.711665i 0.934550 + 0.355832i \(0.115803\pi\)
−0.934550 + 0.355832i \(0.884197\pi\)
\(644\) 2.49344e26 5.25774e26i 0.515683 1.08739i
\(645\) 5.90020e26 1.83775e26i 1.20240 0.374514i
\(646\) −1.92316e26 4.32914e25i −0.386195 0.0869345i
\(647\) 9.61083e26 1.90182 0.950912 0.309463i \(-0.100149\pi\)
0.950912 + 0.309463i \(0.100149\pi\)
\(648\) 4.38909e26 2.65217e26i 0.855879 0.517177i
\(649\) −1.66540e23 −0.000320032
\(650\) −4.02168e26 9.05301e25i −0.761607 0.171442i
\(651\) −1.06756e27 + 3.32515e26i −1.99238 + 0.620572i
\(652\) 1.28636e26 2.71245e26i 0.236597 0.498896i
\(653\) 4.95688e26i 0.898531i 0.893398 + 0.449265i \(0.148314\pi\)
−0.893398 + 0.449265i \(0.851686\pi\)
\(654\) 5.41549e26 4.37074e25i 0.967495 0.0780848i
\(655\) 4.73774e26i 0.834216i
\(656\) 2.69883e24 2.20547e24i 0.00468369 0.00382749i
\(657\) −8.68154e26 + 5.98915e26i −1.48500 + 1.02446i
\(658\) 2.68843e26 1.19430e27i 0.453266 2.01357i
\(659\) 1.20198e27 1.99750 0.998749 0.0500136i \(-0.0159265\pi\)
0.998749 + 0.0500136i \(0.0159265\pi\)
\(660\) 3.47182e22 2.44804e23i 5.68709e−5 0.000401007i
\(661\) −2.59952e26 −0.419739 −0.209870 0.977729i \(-0.567304\pi\)
−0.209870 + 0.977729i \(0.567304\pi\)
\(662\) −1.91677e26 + 8.51500e26i −0.305084 + 1.35529i
\(663\) −2.23402e26 7.17247e26i −0.350517 1.12536i
\(664\) 2.40462e26 + 1.88265e26i 0.371921 + 0.291187i
\(665\) 5.01376e26i 0.764465i
\(666\) 3.90210e26 1.56979e26i 0.586535 0.235959i
\(667\) 8.19696e26i 1.21467i
\(668\) 4.68495e25 + 2.22180e25i 0.0684429 + 0.0324584i
\(669\) −3.47225e26 1.11479e27i −0.500106 1.60562i
\(670\) 1.91392e25 + 4.30834e24i 0.0271778 + 0.00611786i
\(671\) −4.06304e23 −0.000568837
\(672\) −7.33590e26 + 7.05204e26i −1.01262 + 0.973434i
\(673\) 1.96867e26 0.267935 0.133968 0.990986i \(-0.457228\pi\)
0.133968 + 0.990986i \(0.457228\pi\)
\(674\) −3.64902e26 8.21414e25i −0.489675 0.110228i
\(675\) −2.85180e26 + 3.63718e26i −0.377340 + 0.481259i
\(676\) 4.35973e26 + 2.06756e26i 0.568808 + 0.269752i
\(677\) 6.59183e26i 0.848035i −0.905654 0.424018i \(-0.860619\pi\)
0.905654 0.424018i \(-0.139381\pi\)
\(678\) 7.37689e25 + 9.14020e26i 0.0935818 + 1.15951i
\(679\) 2.52782e26i 0.316216i
\(680\) −7.48183e26 5.85773e26i −0.922940 0.722594i
\(681\) −2.97981e26 + 9.28128e25i −0.362486 + 0.112904i
\(682\) −8.67713e22 + 3.85470e23i −0.000104094 + 0.000462423i
\(683\) −1.37366e27 −1.62511 −0.812554 0.582886i \(-0.801923\pi\)
−0.812554 + 0.582886i \(0.801923\pi\)
\(684\) −5.89300e25 3.62703e26i −0.0687548 0.423173i
\(685\) −7.45273e26 −0.857541
\(686\) −7.34829e24 + 3.26438e25i −0.00833887 + 0.0370443i
\(687\) −7.63458e26 + 2.37796e26i −0.854468 + 0.266143i
\(688\) −6.95906e26 + 5.68691e26i −0.768175 + 0.627749i
\(689\) 1.57699e27i 1.71690i
\(690\) 8.14837e25 + 1.00961e27i 0.0874993 + 1.08414i
\(691\) 1.46759e27i 1.55440i −0.629253 0.777201i \(-0.716639\pi\)
0.629253 0.777201i \(-0.283361\pi\)
\(692\) −6.62300e26 + 1.39655e27i −0.691906 + 1.45897i
\(693\) 2.46954e23 + 3.57971e23i 0.000254478 + 0.000368877i
\(694\) −1.02239e26 2.30144e25i −0.103920 0.0233930i
\(695\) 2.03494e26 0.204031
\(696\) 5.08032e26 1.34036e27i 0.502462 1.32567i
\(697\) −5.72450e24 −0.00558504
\(698\) −5.58639e26 1.25753e26i −0.537657 0.121029i
\(699\) −7.86094e25 2.52380e26i −0.0746348 0.239619i
\(700\) 3.92982e26 8.28654e26i 0.368079 0.776143i
\(701\) 2.82602e25i 0.0261128i −0.999915 0.0130564i \(-0.995844\pi\)
0.999915 0.0130564i \(-0.00415610\pi\)
\(702\) 1.08496e27 8.85340e26i 0.989030 0.807063i
\(703\) 3.01382e26i 0.271046i
\(704\) 8.62791e22 + 3.49074e23i 7.65536e−5 + 0.000309726i
\(705\) 6.33684e26 + 2.03448e27i 0.554723 + 1.78097i
\(706\) −5.79111e25 + 2.57263e26i −0.0500170 + 0.222194i
\(707\) −3.22981e26 −0.275228
\(708\) −1.18122e27 1.67521e26i −0.993152 0.140849i
\(709\) 1.61811e27 1.34236 0.671181 0.741293i \(-0.265787\pi\)
0.671181 + 0.741293i \(0.265787\pi\)
\(710\) 2.63022e26 1.16844e27i 0.215297 0.956429i
\(711\) 2.58720e26 + 3.75027e26i 0.208963 + 0.302901i
\(712\) 3.21978e26 4.11249e26i 0.256606 0.327752i
\(713\) 1.61862e27i 1.27290i
\(714\) 1.66590e27 1.34451e26i 1.29275 0.104336i
\(715\) 6.75172e23i 0.000517020i
\(716\) −4.59587e26 2.17955e26i −0.347291 0.164700i
\(717\) −1.81825e26 + 5.66336e25i −0.135588 + 0.0422320i
\(718\) −4.10060e26 9.23065e25i −0.301762 0.0679282i
\(719\) 1.73484e27 1.25990 0.629948 0.776638i \(-0.283076\pi\)
0.629948 + 0.776638i \(0.283076\pi\)
\(720\) 4.92494e26 1.70141e27i 0.352974 1.21941i
\(721\) 3.44316e27 2.43541
\(722\) 1.14068e27 + 2.56774e26i 0.796272 + 0.179245i
\(723\) −2.54696e26 + 7.93308e25i −0.175472 + 0.0546547i
\(724\) 1.88260e27 + 8.92807e26i 1.28009 + 0.607073i
\(725\) 1.29189e27i 0.866994i
\(726\) −1.50483e27 + 1.21452e26i −0.996759 + 0.0804466i
\(727\) 4.19437e26i 0.274214i −0.990556 0.137107i \(-0.956220\pi\)
0.990556 0.137107i \(-0.0437804\pi\)
\(728\) −1.71296e27 + 2.18789e27i −1.10535 + 1.41181i
\(729\) −3.74564e26 1.52471e27i −0.238569 0.971125i
\(730\) −8.00016e26 + 3.55397e27i −0.502958 + 2.23432i
\(731\) 1.47609e27 0.916006
\(732\) −2.88181e27 4.08699e26i −1.76526 0.250351i
\(733\) −9.43357e26 −0.570411 −0.285206 0.958466i \(-0.592062\pi\)
−0.285206 + 0.958466i \(0.592062\pi\)
\(734\) −1.15924e26 + 5.14979e26i −0.0691931 + 0.307381i
\(735\) 6.23394e26 + 2.00145e27i 0.367310 + 1.17927i
\(736\) −6.58863e26 1.31747e27i −0.383227 0.766308i
\(737\) 1.21933e22i 7.00131e-6i
\(738\) −3.98260e24 9.89974e24i −0.00225752 0.00561162i
\(739\) 8.35344e26i 0.467459i −0.972302 0.233729i \(-0.924907\pi\)
0.972302 0.233729i \(-0.0750929\pi\)
\(740\) 6.22499e26 1.31262e27i 0.343904 0.725167i
\(741\) −2.98396e26 9.58018e26i −0.162750 0.522517i
\(742\) −3.42277e27 7.70482e26i −1.84306 0.414883i
\(743\) −2.64337e26 −0.140528 −0.0702642 0.997528i \(-0.522384\pi\)
−0.0702642 + 0.997528i \(0.522384\pi\)
\(744\) −1.00319e27 + 2.64675e27i −0.526550 + 1.38922i
\(745\) 4.12026e26 0.213520
\(746\) 2.02028e27 + 4.54775e26i 1.03370 + 0.232690i
\(747\) 7.69623e26 5.30941e26i 0.388805 0.268226i
\(748\) 2.53065e23 5.33621e23i 0.000126231 0.000266175i
\(749\) 8.78296e26i 0.432577i
\(750\) −8.15727e25 1.01071e27i −0.0396701 0.491525i
\(751\) 7.40863e26i 0.355761i 0.984052 + 0.177881i \(0.0569241\pi\)
−0.984052 + 0.177881i \(0.943076\pi\)
\(752\) −1.96094e27 2.39959e27i −0.929810 1.13781i
\(753\) 1.74453e27 5.43372e26i 0.816819 0.254416i
\(754\) 8.59595e26 3.81864e27i 0.397435 1.76555i
\(755\) 8.51466e26 0.388751
\(756\) 1.39150e27 + 2.78740e27i 0.627372 + 1.25673i
\(757\) 4.40332e26 0.196051 0.0980256 0.995184i \(-0.468747\pi\)
0.0980256 + 0.995184i \(0.468747\pi\)
\(758\) 7.66476e26 3.40497e27i 0.337009 1.49712i
\(759\) −6.01062e23 + 1.87214e23i −0.000260989 + 8.12908e-5i
\(760\) −9.99339e26 7.82410e26i −0.428533 0.335510i
\(761\) 9.18035e26i 0.388781i 0.980924 + 0.194391i \(0.0622729\pi\)
−0.980924 + 0.194391i \(0.937727\pi\)
\(762\) −1.55163e25 1.92252e26i −0.00648959 0.0804081i
\(763\) 3.30067e27i 1.36339i
\(764\) 2.53401e27 + 1.20173e27i 1.03377 + 0.490254i
\(765\) −2.39463e27 + 1.65199e27i −0.964840 + 0.665616i
\(766\) 3.87412e27 + 8.72084e26i 1.54170 + 0.347044i
\(767\) −3.25782e27 −1.28048
\(768\) 2.60823e26 + 2.56268e27i 0.101254 + 0.994861i
\(769\) −1.39213e27 −0.533803 −0.266902 0.963724i \(-0.586000\pi\)
−0.266902 + 0.963724i \(0.586000\pi\)
\(770\) 1.46543e24 + 3.29875e23i 0.000555012 + 0.000124936i
\(771\) −9.37469e26 3.00980e27i −0.350704 1.12596i
\(772\) 1.02078e27 + 4.84096e26i 0.377196 + 0.178882i
\(773\) 3.07759e27i 1.12333i 0.827366 + 0.561663i \(0.189838\pi\)
−0.827366 + 0.561663i \(0.810162\pi\)
\(774\) 1.02693e27 + 2.55270e27i 0.370257 + 0.920365i
\(775\) 2.55105e27i 0.908557i
\(776\) −5.03844e26 3.94473e26i −0.177260 0.138781i
\(777\) 7.59870e26 + 2.43961e27i 0.264082 + 0.847853i
\(778\) −5.86223e26 + 2.60422e27i −0.201260 + 0.894070i
\(779\) −7.64615e24 −0.00259321
\(780\) 6.79152e26 4.78881e27i 0.227545 1.60446i
\(781\) 7.44394e23 0.000246387
\(782\) −5.31319e26 + 2.36032e27i −0.173737 + 0.771802i
\(783\) −3.45354e27 2.70782e27i −1.11565 0.874748i
\(784\) −1.92909e27 2.36063e27i −0.615674 0.753399i
\(785\) 2.64151e27i 0.832897i
\(786\) −2.10262e27 + 1.69699e26i −0.655008 + 0.0528645i
\(787\) 1.17722e27i 0.362323i −0.983453 0.181162i \(-0.942014\pi\)
0.983453 0.181162i \(-0.0579857\pi\)
\(788\) 6.14889e25 1.29657e26i 0.0186981 0.0394274i
\(789\) 2.55311e27 7.95223e26i 0.767075 0.238923i
\(790\) 1.53525e27 + 3.45592e26i 0.455745 + 0.102590i
\(791\) −5.57083e27 −1.63397
\(792\) 1.09888e24 + 6.63953e22i 0.000318465 + 1.92419e-5i
\(793\) −7.94805e27 −2.27596
\(794\) 3.35859e27 + 7.56035e26i 0.950302 + 0.213918i
\(795\) 5.83066e27 1.81609e27i 1.63016 0.507749i
\(796\) −1.30282e27 + 2.74716e27i −0.359923 + 0.758945i
\(797\) 4.60115e27i 1.25606i −0.778187 0.628032i \(-0.783861\pi\)
0.778187 0.628032i \(-0.216139\pi\)
\(798\) 2.22512e27 1.79585e26i 0.600241 0.0484443i
\(799\) 5.08980e27i 1.35677i
\(800\) −1.03841e27 2.07643e27i −0.273536 0.546968i
\(801\) −9.08039e26 1.31624e27i −0.236372 0.342631i
\(802\) 1.72752e26 7.67429e26i 0.0444393 0.197416i
\(803\) −2.26417e24 −0.000575587
\(804\) −1.22651e25 + 8.64837e25i −0.00308134 + 0.0217271i
\(805\) −6.15343e27 −1.52777
\(806\) −1.69740e27 + 7.54049e27i −0.416488 + 1.85019i
\(807\) 1.47545e27 + 4.73702e27i 0.357788 + 1.14870i
\(808\) −5.04020e26 + 6.43764e26i −0.120793 + 0.154283i
\(809\) 3.58857e26i 0.0849984i −0.999097 0.0424992i \(-0.986468\pi\)
0.999097 0.0424992i \(-0.0135320\pi\)
\(810\) −4.52286e27 2.99188e27i −1.05878 0.700384i
\(811\) 4.33582e27i 1.00317i 0.865109 + 0.501583i \(0.167249\pi\)
−0.865109 + 0.501583i \(0.832751\pi\)
\(812\) 7.86817e27 + 3.73141e27i 1.79925 + 0.853279i
\(813\) −1.52247e27 4.88799e27i −0.344103 1.10476i
\(814\) 8.80884e23 + 1.98291e23i 0.000196783 + 4.42968e-5i
\(815\) −3.17454e27 −0.700944
\(816\) 2.33169e27 3.53027e27i 0.508878 0.770463i
\(817\) 1.97160e27 0.425313
\(818\) −5.41114e27 1.21808e27i −1.15381 0.259727i
\(819\) 4.83086e27 + 7.00255e27i 1.01819 + 1.47591i
\(820\) −3.33015e25 1.57930e25i −0.00693797 0.00329027i
\(821\) 5.12796e27i 1.05605i 0.849229 + 0.528025i \(0.177067\pi\)
−0.849229 + 0.528025i \(0.822933\pi\)
\(822\) −2.66946e26 3.30754e27i −0.0543426 0.673322i
\(823\) 6.26001e27i 1.25973i −0.776706 0.629864i \(-0.783111\pi\)
0.776706 0.629864i \(-0.216889\pi\)
\(824\) 5.37314e27 6.86288e27i 1.06886 1.36521i
\(825\) −9.47312e23 + 2.95061e23i −0.000186286 + 5.80229e-5i
\(826\) 1.59170e27 7.07093e27i 0.309422 1.37457i
\(827\) 1.47904e27 0.284235 0.142117 0.989850i \(-0.454609\pi\)
0.142117 + 0.989850i \(0.454609\pi\)
\(828\) −4.45149e27 + 7.23254e26i −0.845701 + 0.137405i
\(829\) 4.98144e27 0.935593 0.467797 0.883836i \(-0.345048\pi\)
0.467797 + 0.883836i \(0.345048\pi\)
\(830\) 7.09218e26 3.15061e27i 0.131686 0.584996i
\(831\) 8.20712e27 2.55629e27i 1.50654 0.469246i
\(832\) 1.68778e27 + 6.82852e27i 0.306297 + 1.23924i
\(833\) 5.00715e27i 0.898386i
\(834\) 7.28886e25 + 9.03113e26i 0.0129295 + 0.160201i
\(835\) 5.48306e26i 0.0961616i
\(836\) 3.38016e23 7.12751e23i 5.86108e−5 0.000123588i
\(837\) 6.81956e27 + 5.34701e27i 1.16913 + 0.916683i
\(838\) 2.21695e27 + 4.99046e26i 0.375783 + 0.0845906i
\(839\) 3.55811e27 0.596323 0.298161 0.954516i \(-0.403627\pi\)
0.298161 + 0.954516i \(0.403627\pi\)
\(840\) 1.00621e28 + 3.81378e27i 1.66738 + 0.631978i
\(841\) −6.16344e27 −1.00986
\(842\) 2.61803e27 + 5.89331e26i 0.424140 + 0.0954761i
\(843\) −1.30122e27 4.17766e27i −0.208444 0.669224i
\(844\) −1.50411e27 + 3.17162e27i −0.238247 + 0.502375i
\(845\) 5.10244e27i 0.799170i
\(846\) −8.80211e27 + 3.54103e27i −1.36323 + 0.548417i
\(847\) 9.17175e27i 1.40462i
\(848\) −6.87704e27 + 5.61988e27i −1.04146 + 0.851073i
\(849\) −2.92015e27 9.37531e27i −0.437302 1.40398i
\(850\) −8.37394e26 + 3.72001e27i −0.124008 + 0.550889i
\(851\) −3.69890e27 −0.541678
\(852\) 5.27979e27 + 7.48781e26i 0.764610 + 0.108437i
\(853\) 9.03837e27 1.29442 0.647209 0.762313i \(-0.275936\pi\)
0.647209 + 0.762313i \(0.275936\pi\)
\(854\) 3.88325e27 1.72508e28i 0.549978 2.44321i
\(855\) −3.19848e27 + 2.20654e27i −0.447987 + 0.309054i
\(856\) −1.75061e27 1.37060e27i −0.242488 0.189850i
\(857\) 2.45385e27i 0.336148i 0.985774 + 0.168074i \(0.0537547\pi\)
−0.985774 + 0.168074i \(0.946245\pi\)
\(858\) 2.99643e24 2.41836e23i 0.000405952 3.27637e-5i
\(859\) 9.67531e27i 1.29637i 0.761482 + 0.648186i \(0.224472\pi\)
−0.761482 + 0.648186i \(0.775528\pi\)
\(860\) 8.58696e27 + 4.07229e27i 1.13790 + 0.539639i
\(861\) 6.18935e25 1.92781e25i 0.00811176 0.00252659i
\(862\) 2.18927e27 + 4.92816e26i 0.283779 + 0.0638801i
\(863\) −1.31764e28 −1.68925 −0.844624 0.535361i \(-0.820176\pi\)
−0.844624 + 0.535361i \(0.820176\pi\)
\(864\) 7.72730e27 + 1.57628e27i 0.979822 + 0.199873i
\(865\) 1.63446e28 2.04984
\(866\) −9.69499e27 2.18239e27i −1.20262 0.270715i
\(867\) 1.14726e27 3.57340e26i 0.140761 0.0438430i
\(868\) −1.55369e28 7.36825e27i −1.88551 0.894184i
\(869\) 9.78080e23i 0.000117405i
\(870\) −1.51087e28 + 1.21940e27i −1.79389 + 0.144781i
\(871\) 2.38523e26i 0.0280128i
\(872\) 6.57887e27 + 5.15078e27i 0.764267 + 0.598365i
\(873\) −1.61260e27 + 1.11249e27i −0.185307 + 0.127838i
\(874\) −7.09677e26 + 3.15265e27i −0.0806681 + 0.358358i
\(875\) 6.16016e27 0.692652
\(876\) −1.60591e28 2.27751e27i −1.78621 0.253322i
\(877\) −6.64144e27 −0.730745 −0.365373 0.930861i \(-0.619058\pi\)
−0.365373 + 0.930861i \(0.619058\pi\)
\(878\) −2.88858e27 + 1.28321e28i −0.314403 + 1.39669i
\(879\) −3.52052e27 1.13028e28i −0.379064 1.21701i
\(880\) 2.94434e24 2.40610e24i 0.000313619 0.000256288i
\(881\) 8.95581e27i 0.943699i 0.881679 + 0.471850i \(0.156413\pi\)
−0.881679 + 0.471850i \(0.843587\pi\)
\(882\) −8.65917e27 + 3.48353e27i −0.902662 + 0.363135i
\(883\) 2.47145e27i 0.254873i −0.991847 0.127437i \(-0.959325\pi\)
0.991847 0.127437i \(-0.0406750\pi\)
\(884\) 4.95041e27 1.04386e28i 0.505062 1.06499i
\(885\) 3.75177e27 + 1.20453e28i 0.378682 + 1.21578i
\(886\) −4.19942e27 9.45312e26i −0.419343 0.0943963i
\(887\) −8.06467e27 −0.796732 −0.398366 0.917227i \(-0.630423\pi\)
−0.398366 + 0.917227i \(0.630423\pi\)
\(888\) 6.04841e27 + 2.29250e27i 0.591178 + 0.224072i
\(889\) 1.17175e27 0.113310
\(890\) −5.38831e27 1.21294e27i −0.515522 0.116047i
\(891\) 1.19680e24 3.15084e24i 0.000113288 0.000298255i
\(892\) 7.69420e27 1.62242e28i 0.720605 1.51949i
\(893\) 6.79839e27i 0.629966i
\(894\) 1.47581e26 + 1.82858e27i 0.0135308 + 0.167652i
\(895\) 5.37881e27i 0.487941i
\(896\) −1.56456e28 + 3.26957e26i −1.40432 + 0.0293470i
\(897\) −1.17579e28 + 3.66224e27i −1.04424 + 0.325251i
\(898\) 9.47210e26 4.20785e27i 0.0832379 0.369773i
\(899\) 2.42225e28 2.10621
\(900\) −7.01583e27 + 1.13989e27i −0.603636 + 0.0980756i
\(901\) 1.45869e28 1.24188
\(902\) 5.03071e21 2.23482e22i 4.23806e−7 1.88270e-6i
\(903\) −1.59596e28 + 4.97095e27i −1.33041 + 0.414387i
\(904\) −8.69343e27 + 1.11038e28i −0.717119 + 0.915946i
\(905\) 2.20332e28i 1.79852i
\(906\) 3.04982e26 + 3.77883e27i 0.0246352 + 0.305238i
\(907\) 1.25220e28i 1.00093i −0.865755 0.500467i \(-0.833162\pi\)
0.865755 0.500467i \(-0.166838\pi\)
\(908\) −4.33672e27 2.05665e27i −0.343041 0.162684i
\(909\) 1.42143e27 + 2.06043e27i 0.111268 + 0.161288i
\(910\) 2.86664e28 + 6.45295e27i 2.22065 + 0.499879i
\(911\) 1.09901e27 0.0842511 0.0421255 0.999112i \(-0.486587\pi\)
0.0421255 + 0.999112i \(0.486587\pi\)
\(912\) 3.11441e27 4.71534e27i 0.236279 0.357736i
\(913\) 2.00720e24 0.000150702
\(914\) 1.85808e28 + 4.18264e27i 1.38063 + 0.310786i
\(915\) 9.15312e27 + 2.93867e28i 0.673084 + 2.16098i
\(916\) −1.11111e28 5.26935e27i −0.808632 0.383487i
\(917\) 1.28152e28i 0.923031i
\(918\) −8.18929e27 1.00357e28i −0.583769 0.715390i
\(919\) 1.83014e27i 0.129118i −0.997914 0.0645591i \(-0.979436\pi\)
0.997914 0.0645591i \(-0.0205641\pi\)
\(920\) −9.60260e27 + 1.22650e28i −0.670509 + 0.856413i
\(921\) −1.18143e27 3.79305e27i −0.0816472 0.262133i
\(922\) 2.09654e27 9.31359e27i 0.143403 0.637050i
\(923\) 1.45617e28 0.985815
\(924\) −9.39100e23 + 6.62175e24i −6.29257e−5 + 0.000443700i
\(925\) −5.82970e27 −0.386634
\(926\) 1.87582e26 8.33308e26i 0.0123136 0.0547018i
\(927\) −1.51533e28 2.19653e28i −0.984574 1.42718i
\(928\) 1.97159e28 9.85984e27i 1.26798 0.634109i
\(929\) 2.18069e27i 0.138818i 0.997588 + 0.0694088i \(0.0221113\pi\)
−0.997588 + 0.0694088i \(0.977889\pi\)
\(930\) 2.98345e28 2.40789e27i 1.87989 0.151722i
\(931\) 6.68799e27i 0.417132i
\(932\) 1.74192e27 3.67306e27i 0.107542 0.226766i
\(933\) −2.27334e28 + 7.08082e27i −1.38928 + 0.432721i
\(934\) 8.99057e27 + 2.02382e27i 0.543866 + 0.122427i
\(935\) −6.24527e24 −0.000373973
\(936\) 2.14961e28 + 1.29881e27i 1.27421 + 0.0769884i
\(937\) 7.08161e27 0.415534 0.207767 0.978178i \(-0.433380\pi\)
0.207767 + 0.978178i \(0.433380\pi\)
\(938\) −5.17701e26 1.16537e26i −0.0300713 0.00676920i
\(939\) −1.95282e27 + 6.08249e26i −0.112290 + 0.0349750i
\(940\) −1.40419e28 + 2.96092e28i −0.799303 + 1.68544i
\(941\) 4.27735e27i 0.241031i −0.992711 0.120516i \(-0.961545\pi\)
0.992711 0.120516i \(-0.0384548\pi\)
\(942\) 1.17231e28 9.46150e26i 0.653972 0.0527809i
\(943\) 9.38420e25i 0.00518246i
\(944\) −1.16099e28 1.42070e28i −0.634735 0.776724i
\(945\) 2.03275e28 2.59256e28i 1.10023 1.40322i
\(946\) −1.29719e24 + 5.76261e24i −6.95086e−5 + 0.000308783i
\(947\) −9.95537e27 −0.528120 −0.264060 0.964506i \(-0.585062\pi\)
−0.264060 + 0.964506i \(0.585062\pi\)
\(948\) −9.83845e26 + 6.93726e27i −0.0516711 + 0.364342i
\(949\) −4.42912e28 −2.30297
\(950\) −1.11850e27 + 4.96878e27i −0.0575785 + 0.255785i
\(951\) 4.46245e27 + 1.43270e28i 0.227436 + 0.730196i
\(952\) 2.02377e28 + 1.58447e28i 1.02120 + 0.799525i
\(953\) 2.48300e28i 1.24049i 0.784406 + 0.620247i \(0.212968\pi\)
−0.784406 + 0.620247i \(0.787032\pi\)
\(954\) 1.01483e28 + 2.52261e28i 0.501977 + 1.24779i
\(955\) 2.96570e28i 1.45243i
\(956\) −2.64623e27 1.25495e27i −0.128315 0.0608523i
\(957\) −2.80164e24 8.99484e24i −0.000134508 0.000431847i
\(958\) 1.12083e28 + 2.52304e27i 0.532802 + 0.119937i
\(959\) 2.01590e28 0.948839
\(960\) 2.33037e28 1.41041e28i 1.08605 0.657309i
\(961\) −2.61604e28 −1.20718
\(962\) 1.72317e28 + 3.87894e27i 0.787344 + 0.177235i
\(963\) −5.60301e27 + 3.86536e27i −0.253496 + 0.174880i
\(964\) −3.70677e27 1.75790e27i −0.166060 0.0787523i
\(965\) 1.19468e28i 0.529957i
\(966\) −2.20407e27 2.73091e28i −0.0968149 1.19957i
\(967\) 4.29422e28i 1.86781i 0.357523 + 0.933904i \(0.383621\pi\)
−0.357523 + 0.933904i \(0.616379\pi\)
\(968\) −1.82811e28 1.43128e28i −0.787383 0.616464i
\(969\) −8.86156e27 + 2.76013e27i −0.377950 + 0.117721i
\(970\) −1.48603e27 + 6.60151e27i −0.0627621 + 0.278812i
\(971\) 2.21794e28 0.927614 0.463807 0.885936i \(-0.346483\pi\)
0.463807 + 0.885936i \(0.346483\pi\)
\(972\) 1.16580e28 2.11442e28i 0.482831 0.875714i
\(973\) −5.50435e27 −0.225753
\(974\) −3.45149e27 + 1.53328e28i −0.140183 + 0.622746i
\(975\) −1.85311e28 + 5.77193e27i −0.745347 + 0.232155i
\(976\) −2.83244e28 3.46605e28i −1.12820 1.38058i
\(977\) 1.59999e28i 0.631129i 0.948904 + 0.315565i \(0.102194\pi\)
−0.948904 + 0.315565i \(0.897806\pi\)
\(978\) −1.13707e27 1.40887e28i −0.0444190 0.550365i
\(979\) 3.43280e24i 0.000132804i
\(980\) −1.38139e28 + 2.91284e28i −0.529259 + 1.11601i
\(981\) 2.10563e28 1.45262e28i 0.798963 0.551182i
\(982\) −3.96346e28 8.92196e27i −1.48942 0.335275i
\(983\) −4.61641e28 −1.71809 −0.859045 0.511900i \(-0.828942\pi\)
−0.859045 + 0.511900i \(0.828942\pi\)
\(984\) 5.81614e25 1.53450e26i 0.00214379 0.00565605i
\(985\) −1.51746e27 −0.0553952
\(986\) −3.53220e28 7.95115e27i −1.27707 0.287475i
\(987\) −1.71406e28 5.50311e28i −0.613782 1.97058i
\(988\) 6.61220e27 1.39427e28i 0.234507 0.494488i
\(989\) 2.41976e28i 0.849979i
\(990\) −4.34490e24 1.08003e25i −0.000151163 0.000375753i
\(991\) 2.59012e28i 0.892525i 0.894902 + 0.446262i \(0.147245\pi\)
−0.894902 + 0.446262i \(0.852755\pi\)
\(992\) −3.89322e28 + 1.94698e28i −1.32876 + 0.664508i
\(993\) 1.22208e28 + 3.92355e28i 0.413124 + 1.32636i
\(994\) −7.11454e27 + 3.16054e28i −0.238219 + 1.05826i
\(995\) 3.21516e28 1.06631
\(996\) 1.42365e28 + 2.01903e27i 0.467671 + 0.0663252i
\(997\) 3.83937e28 1.24927 0.624635 0.780917i \(-0.285248\pi\)
0.624635 + 0.780917i \(0.285248\pi\)
\(998\) −7.48414e27 + 3.32473e28i −0.241213 + 1.07156i
\(999\) 1.22191e28 1.55842e28i 0.390092 0.497522i
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 12.20.b.a.11.34 yes 36
3.2 odd 2 inner 12.20.b.a.11.3 36
4.3 odd 2 inner 12.20.b.a.11.4 yes 36
12.11 even 2 inner 12.20.b.a.11.33 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.20.b.a.11.3 36 3.2 odd 2 inner
12.20.b.a.11.4 yes 36 4.3 odd 2 inner
12.20.b.a.11.33 yes 36 12.11 even 2 inner
12.20.b.a.11.34 yes 36 1.1 even 1 trivial