Properties

Label 81.9.d.d.26.1
Level $81$
Weight $9$
Character 81.26
Analytic conductor $32.998$
Analytic rank $0$
Dimension $4$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,9,Mod(26,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.26");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 81.d (of order \(6\), degree \(2\), not 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: \(32.9976674150\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-14})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 14x^{2} + 196 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 3)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.1
Root \(-3.24037 - 1.87083i\) of defining polynomial
Character \(\chi\) \(=\) 81.26
Dual form 81.9.d.d.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-19.4422 - 11.2250i) q^{2} +(124.000 + 214.774i) q^{4} +(-194.422 + 112.250i) q^{5} +(875.000 - 1515.54i) q^{7} +179.600i q^{8} +O(q^{10})\) \(q+(-19.4422 - 11.2250i) q^{2} +(124.000 + 214.774i) q^{4} +(-194.422 + 112.250i) q^{5} +(875.000 - 1515.54i) q^{7} +179.600i q^{8} +5040.00 q^{10} +(-6027.09 - 3479.74i) q^{11} +(-12865.0 - 22282.8i) q^{13} +(-34023.9 + 19643.7i) q^{14} +(33760.0 - 58474.0i) q^{16} +74893.0i q^{17} +18938.0 q^{19} +(-48216.7 - 27837.9i) q^{20} +(78120.0 + 135308. i) q^{22} +(-407431. + 235231. i) q^{23} +(-170112. + 294643. i) q^{25} +577637. i q^{26} +434000. q^{28} +(-399149. - 230449. i) q^{29} +(175739. + 304389. i) q^{31} +(-1.27292e6 + 734921. i) q^{32} +(840672. - 1.45609e6i) q^{34} +392874. i q^{35} +1.33517e6 q^{37} +(-368197. - 212579. i) q^{38} +(-20160.0 - 34918.1i) q^{40} +(1.62420e6 - 937734. i) q^{41} +(1.76308e6 - 3.05374e6i) q^{43} -1.72595e6i q^{44} +1.05618e7 q^{46} +(3.53428e6 + 2.04052e6i) q^{47} +(1.35115e6 + 2.34026e6i) q^{49} +(6.61473e6 - 3.81902e6i) q^{50} +(3.19052e6 - 5.52614e6i) q^{52} -6.60177e6i q^{53} +1.56240e6 q^{55} +(272191. + 157150. i) q^{56} +(5.17356e6 + 8.96087e6i) q^{58} +(1.18774e7 - 6.85745e6i) q^{59} +(-376801. + 652638. i) q^{61} -7.89066e6i q^{62} +1.57128e7 q^{64} +(5.00248e6 + 2.88819e6i) q^{65} +(-1.13444e6 - 1.96492e6i) q^{67} +(-1.60851e7 + 9.28673e6i) q^{68} +(4.41000e6 - 7.63834e6i) q^{70} +1.70220e7i q^{71} +2.76728e7 q^{73} +(-2.59587e7 - 1.49872e7i) q^{74} +(2.34831e6 + 4.06740e6i) q^{76} +(-1.05474e7 + 6.08955e6i) q^{77} +(1.14905e7 - 1.99021e7i) q^{79} +1.51582e7i q^{80} -4.21042e7 q^{82} +(4.01794e7 + 2.31976e7i) q^{83} +(-8.40672e6 - 1.45609e7i) q^{85} +(-6.85562e7 + 3.95809e7i) q^{86} +(624960. - 1.08246e6i) q^{88} +7.26152e7i q^{89} -4.50275e7 q^{91} +(-1.01043e8 - 5.83372e7i) q^{92} +(-4.58096e7 - 7.93445e7i) q^{94} +(-3.68197e6 + 2.12579e6i) q^{95} +(-7.36355e7 + 1.27540e8i) q^{97} -6.06665e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 496 q^{4} + 3500 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 496 q^{4} + 3500 q^{7} + 20160 q^{10} - 51460 q^{13} + 135040 q^{16} + 75752 q^{19} + 312480 q^{22} - 680450 q^{25} + 1736000 q^{28} + 702956 q^{31} + 3362688 q^{34} + 5340680 q^{37} - 80640 q^{40} + 7052300 q^{43} + 42247296 q^{46} + 5404602 q^{49} + 12762080 q^{52} + 6249600 q^{55} + 20694240 q^{58} - 1507204 q^{61} + 62851072 q^{64} - 4537780 q^{67} + 17640000 q^{70} + 110691080 q^{73} + 9393248 q^{76} + 45961964 q^{79} - 168416640 q^{82} - 33626880 q^{85} + 2499840 q^{88} - 180110000 q^{91} - 183238272 q^{94} - 294542020 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −19.4422 11.2250i −1.21514 0.701561i −0.251265 0.967918i \(-0.580846\pi\)
−0.963874 + 0.266358i \(0.914180\pi\)
\(3\) 0 0
\(4\) 124.000 + 214.774i 0.484375 + 0.838962i
\(5\) −194.422 + 112.250i −0.311076 + 0.179600i −0.647408 0.762144i \(-0.724147\pi\)
0.336332 + 0.941743i \(0.390814\pi\)
\(6\) 0 0
\(7\) 875.000 1515.54i 0.364431 0.631214i −0.624253 0.781222i \(-0.714597\pi\)
0.988685 + 0.150008i \(0.0479300\pi\)
\(8\) 179.600i 0.0438475i
\(9\) 0 0
\(10\) 5040.00 0.504000
\(11\) −6027.09 3479.74i −0.411658 0.237671i 0.279844 0.960046i \(-0.409717\pi\)
−0.691502 + 0.722375i \(0.743051\pi\)
\(12\) 0 0
\(13\) −12865.0 22282.8i −0.450439 0.780184i 0.547974 0.836495i \(-0.315399\pi\)
−0.998413 + 0.0563115i \(0.982066\pi\)
\(14\) −34023.9 + 19643.7i −0.885670 + 0.511342i
\(15\) 0 0
\(16\) 33760.0 58474.0i 0.515137 0.892243i
\(17\) 74893.0i 0.896697i 0.893859 + 0.448348i \(0.147988\pi\)
−0.893859 + 0.448348i \(0.852012\pi\)
\(18\) 0 0
\(19\) 18938.0 0.145318 0.0726590 0.997357i \(-0.476852\pi\)
0.0726590 + 0.997357i \(0.476852\pi\)
\(20\) −48216.7 27837.9i −0.301354 0.173987i
\(21\) 0 0
\(22\) 78120.0 + 135308.i 0.333481 + 0.577607i
\(23\) −407431. + 235231.i −1.45594 + 0.840586i −0.998808 0.0488134i \(-0.984456\pi\)
−0.457130 + 0.889400i \(0.651123\pi\)
\(24\) 0 0
\(25\) −170112. + 294643.i −0.435488 + 0.754287i
\(26\) 577637.i 1.26404i
\(27\) 0 0
\(28\) 434000. 0.706086
\(29\) −399149. 230449.i −0.564343 0.325823i 0.190544 0.981679i \(-0.438975\pi\)
−0.754887 + 0.655855i \(0.772308\pi\)
\(30\) 0 0
\(31\) 175739. + 304389.i 0.190292 + 0.329596i 0.945347 0.326066i \(-0.105723\pi\)
−0.755055 + 0.655662i \(0.772390\pi\)
\(32\) −1.27292e6 + 734921.i −1.21395 + 0.700876i
\(33\) 0 0
\(34\) 840672. 1.45609e6i 0.629087 1.08961i
\(35\) 392874.i 0.261807i
\(36\) 0 0
\(37\) 1.33517e6 0.712409 0.356205 0.934408i \(-0.384071\pi\)
0.356205 + 0.934408i \(0.384071\pi\)
\(38\) −368197. 212579.i −0.176582 0.101949i
\(39\) 0 0
\(40\) −20160.0 34918.1i −0.00787500 0.0136399i
\(41\) 1.62420e6 937734.i 0.574784 0.331852i −0.184274 0.982875i \(-0.558993\pi\)
0.759058 + 0.651023i \(0.225660\pi\)
\(42\) 0 0
\(43\) 1.76308e6 3.05374e6i 0.515700 0.893218i −0.484134 0.874994i \(-0.660865\pi\)
0.999834 0.0182245i \(-0.00580135\pi\)
\(44\) 1.72595e6i 0.460488i
\(45\) 0 0
\(46\) 1.05618e7 2.35889
\(47\) 3.53428e6 + 2.04052e6i 0.724286 + 0.418167i 0.816328 0.577588i \(-0.196006\pi\)
−0.0920421 + 0.995755i \(0.529339\pi\)
\(48\) 0 0
\(49\) 1.35115e6 + 2.34026e6i 0.234379 + 0.405957i
\(50\) 6.61473e6 3.81902e6i 1.05836 0.611043i
\(51\) 0 0
\(52\) 3.19052e6 5.52614e6i 0.436363 0.755803i
\(53\) 6.60177e6i 0.836675i −0.908292 0.418337i \(-0.862613\pi\)
0.908292 0.418337i \(-0.137387\pi\)
\(54\) 0 0
\(55\) 1.56240e6 0.170742
\(56\) 272191. + 157150.i 0.0276772 + 0.0159794i
\(57\) 0 0
\(58\) 5.17356e6 + 8.96087e6i 0.457170 + 0.791841i
\(59\) 1.18774e7 6.85745e6i 0.980201 0.565919i 0.0778701 0.996964i \(-0.475188\pi\)
0.902331 + 0.431044i \(0.141855\pi\)
\(60\) 0 0
\(61\) −376801. + 652638.i −0.0272140 + 0.0471361i −0.879312 0.476247i \(-0.841997\pi\)
0.852098 + 0.523383i \(0.175330\pi\)
\(62\) 7.89066e6i 0.534007i
\(63\) 0 0
\(64\) 1.57128e7 0.936554
\(65\) 5.00248e6 + 2.88819e6i 0.280241 + 0.161797i
\(66\) 0 0
\(67\) −1.13444e6 1.96492e6i −0.0562969 0.0975090i 0.836504 0.547962i \(-0.184596\pi\)
−0.892800 + 0.450453i \(0.851263\pi\)
\(68\) −1.60851e7 + 9.28673e6i −0.752295 + 0.434338i
\(69\) 0 0
\(70\) 4.41000e6 7.63834e6i 0.183673 0.318132i
\(71\) 1.70220e7i 0.669849i 0.942245 + 0.334925i \(0.108711\pi\)
−0.942245 + 0.334925i \(0.891289\pi\)
\(72\) 0 0
\(73\) 2.76728e7 0.974454 0.487227 0.873275i \(-0.338008\pi\)
0.487227 + 0.873275i \(0.338008\pi\)
\(74\) −2.59587e7 1.49872e7i −0.865676 0.499799i
\(75\) 0 0
\(76\) 2.34831e6 + 4.06740e6i 0.0703885 + 0.121916i
\(77\) −1.05474e7 + 6.08955e6i −0.300042 + 0.173230i
\(78\) 0 0
\(79\) 1.14905e7 1.99021e7i 0.295006 0.510965i −0.679981 0.733230i \(-0.738012\pi\)
0.974986 + 0.222265i \(0.0713452\pi\)
\(80\) 1.51582e7i 0.370073i
\(81\) 0 0
\(82\) −4.21042e7 −0.931257
\(83\) 4.01794e7 + 2.31976e7i 0.846625 + 0.488799i 0.859511 0.511118i \(-0.170768\pi\)
−0.0128855 + 0.999917i \(0.504102\pi\)
\(84\) 0 0
\(85\) −8.40672e6 1.45609e7i −0.161046 0.278940i
\(86\) −6.85562e7 + 3.95809e7i −1.25329 + 0.723589i
\(87\) 0 0
\(88\) 624960. 1.08246e6i 0.0104213 0.0180502i
\(89\) 7.26152e7i 1.15736i 0.815555 + 0.578679i \(0.196432\pi\)
−0.815555 + 0.578679i \(0.803568\pi\)
\(90\) 0 0
\(91\) −4.50275e7 −0.656617
\(92\) −1.01043e8 5.83372e7i −1.41044 0.814318i
\(93\) 0 0
\(94\) −4.58096e7 7.93445e7i −0.586739 1.01626i
\(95\) −3.68197e6 + 2.12579e6i −0.0452049 + 0.0260991i
\(96\) 0 0
\(97\) −7.36355e7 + 1.27540e8i −0.831764 + 1.44066i 0.0648734 + 0.997894i \(0.479336\pi\)
−0.896638 + 0.442765i \(0.853998\pi\)
\(98\) 6.06665e7i 0.657726i
\(99\) 0 0
\(100\) −8.43758e7 −0.843758
\(101\) 8.96724e7 + 5.17724e7i 0.861734 + 0.497522i 0.864593 0.502474i \(-0.167577\pi\)
−0.00285856 + 0.999996i \(0.500910\pi\)
\(102\) 0 0
\(103\) 8.30318e7 + 1.43815e8i 0.737726 + 1.27778i 0.953517 + 0.301340i \(0.0974339\pi\)
−0.215790 + 0.976440i \(0.569233\pi\)
\(104\) 4.00199e6 2.31055e6i 0.0342092 0.0197507i
\(105\) 0 0
\(106\) −7.41046e7 + 1.28353e8i −0.586978 + 1.01668i
\(107\) 2.25540e7i 0.172063i −0.996292 0.0860316i \(-0.972581\pi\)
0.996292 0.0860316i \(-0.0274186\pi\)
\(108\) 0 0
\(109\) −1.09975e8 −0.779091 −0.389546 0.921007i \(-0.627368\pi\)
−0.389546 + 0.921007i \(0.627368\pi\)
\(110\) −3.03765e7 1.75379e7i −0.207476 0.119786i
\(111\) 0 0
\(112\) −5.90800e7 1.02330e8i −0.375464 0.650323i
\(113\) 2.49197e8 1.43874e8i 1.52837 0.882405i 0.528941 0.848659i \(-0.322589\pi\)
0.999430 0.0337466i \(-0.0107439\pi\)
\(114\) 0 0
\(115\) 5.28091e7 9.14681e7i 0.301938 0.522972i
\(116\) 1.14303e8i 0.631283i
\(117\) 0 0
\(118\) −3.07899e8 −1.58811
\(119\) 1.13504e8 + 6.55314e7i 0.566007 + 0.326785i
\(120\) 0 0
\(121\) −8.29622e7 1.43695e8i −0.387025 0.670347i
\(122\) 1.46517e7 8.45916e6i 0.0661376 0.0381846i
\(123\) 0 0
\(124\) −4.35833e7 + 7.54884e7i −0.184346 + 0.319296i
\(125\) 1.64075e8i 0.672053i
\(126\) 0 0
\(127\) 2.75994e8 1.06092 0.530462 0.847708i \(-0.322018\pi\)
0.530462 + 0.847708i \(0.322018\pi\)
\(128\) 2.03767e7 + 1.17645e7i 0.0759091 + 0.0438261i
\(129\) 0 0
\(130\) −6.48396e7 1.12305e8i −0.227021 0.393213i
\(131\) 2.50383e8 1.44559e8i 0.850198 0.490862i −0.0105194 0.999945i \(-0.503348\pi\)
0.860718 + 0.509082i \(0.170015\pi\)
\(132\) 0 0
\(133\) 1.65708e7 2.87014e7i 0.0529585 0.0917268i
\(134\) 5.09365e7i 0.157983i
\(135\) 0 0
\(136\) −1.34508e7 −0.0393180
\(137\) 1.79754e8 + 1.03781e8i 0.510266 + 0.294602i 0.732943 0.680290i \(-0.238146\pi\)
−0.222677 + 0.974892i \(0.571479\pi\)
\(138\) 0 0
\(139\) 7.13341e7 + 1.23554e8i 0.191090 + 0.330978i 0.945612 0.325297i \(-0.105464\pi\)
−0.754522 + 0.656275i \(0.772131\pi\)
\(140\) −8.43792e7 + 4.87164e7i −0.219646 + 0.126813i
\(141\) 0 0
\(142\) 1.91071e8 3.30945e8i 0.469940 0.813960i
\(143\) 1.79067e8i 0.428226i
\(144\) 0 0
\(145\) 1.03471e8 0.234071
\(146\) −5.38020e8 3.10626e8i −1.18410 0.683638i
\(147\) 0 0
\(148\) 1.65561e8 + 2.86760e8i 0.345073 + 0.597685i
\(149\) −7.09479e8 + 4.09618e8i −1.43944 + 0.831063i −0.997811 0.0661339i \(-0.978934\pi\)
−0.441632 + 0.897196i \(0.645600\pi\)
\(150\) 0 0
\(151\) −2.11930e8 + 3.67074e8i −0.407648 + 0.706067i −0.994626 0.103536i \(-0.966984\pi\)
0.586978 + 0.809603i \(0.300318\pi\)
\(152\) 3.40126e6i 0.00637184i
\(153\) 0 0
\(154\) 2.73420e8 0.486124
\(155\) −6.83351e7 3.94533e7i −0.118391 0.0683528i
\(156\) 0 0
\(157\) 3.79925e8 + 6.58050e8i 0.625316 + 1.08308i 0.988480 + 0.151354i \(0.0483633\pi\)
−0.363163 + 0.931725i \(0.618303\pi\)
\(158\) −4.46801e8 + 2.57961e8i −0.716945 + 0.413929i
\(159\) 0 0
\(160\) 1.64989e8 2.85770e8i 0.251754 0.436051i
\(161\) 8.23307e8i 1.22534i
\(162\) 0 0
\(163\) 6.68160e8 0.946520 0.473260 0.880923i \(-0.343077\pi\)
0.473260 + 0.880923i \(0.343077\pi\)
\(164\) 4.02802e8 + 2.32558e8i 0.556822 + 0.321482i
\(165\) 0 0
\(166\) −5.20785e8 9.02026e8i −0.685845 1.18792i
\(167\) 1.70006e8 9.81529e7i 0.218574 0.126194i −0.386716 0.922199i \(-0.626391\pi\)
0.605290 + 0.796005i \(0.293057\pi\)
\(168\) 0 0
\(169\) 7.68489e7 1.33106e8i 0.0942087 0.163174i
\(170\) 3.77461e8i 0.451935i
\(171\) 0 0
\(172\) 8.74485e8 0.999168
\(173\) −8.86111e8 5.11596e8i −0.989245 0.571141i −0.0841963 0.996449i \(-0.526832\pi\)
−0.905048 + 0.425308i \(0.860166\pi\)
\(174\) 0 0
\(175\) 2.97697e8 + 5.15626e8i 0.317411 + 0.549772i
\(176\) −4.06949e8 + 2.34952e8i −0.424121 + 0.244866i
\(177\) 0 0
\(178\) 8.15104e8 1.41180e9i 0.811957 1.40635i
\(179\) 1.28895e9i 1.25552i −0.778408 0.627759i \(-0.783972\pi\)
0.778408 0.627759i \(-0.216028\pi\)
\(180\) 0 0
\(181\) 4.71707e8 0.439499 0.219749 0.975556i \(-0.429476\pi\)
0.219749 + 0.975556i \(0.429476\pi\)
\(182\) 8.75435e8 + 5.05432e8i 0.797881 + 0.460657i
\(183\) 0 0
\(184\) −4.22473e7 7.31745e7i −0.0368576 0.0638393i
\(185\) −2.59587e8 + 1.49872e8i −0.221613 + 0.127948i
\(186\) 0 0
\(187\) 2.60608e8 4.51387e8i 0.213119 0.369133i
\(188\) 1.01210e9i 0.810198i
\(189\) 0 0
\(190\) 9.54475e7 0.0732403
\(191\) 1.40112e8 + 8.08934e7i 0.105279 + 0.0607827i 0.551715 0.834033i \(-0.313974\pi\)
−0.446436 + 0.894815i \(0.647307\pi\)
\(192\) 0 0
\(193\) 7.94199e8 + 1.37559e9i 0.572401 + 0.991427i 0.996319 + 0.0857264i \(0.0273211\pi\)
−0.423918 + 0.905701i \(0.639346\pi\)
\(194\) 2.86328e9 1.65311e9i 2.02142 1.16707i
\(195\) 0 0
\(196\) −3.35085e8 + 5.80385e8i −0.227055 + 0.393271i
\(197\) 5.37769e8i 0.357052i −0.983935 0.178526i \(-0.942867\pi\)
0.983935 0.178526i \(-0.0571328\pi\)
\(198\) 0 0
\(199\) 6.47586e8 0.412938 0.206469 0.978453i \(-0.433803\pi\)
0.206469 + 0.978453i \(0.433803\pi\)
\(200\) −5.29178e7 3.05521e7i −0.0330737 0.0190951i
\(201\) 0 0
\(202\) −1.16229e9 2.01314e9i −0.698084 1.20912i
\(203\) −6.98510e8 + 4.03285e8i −0.411328 + 0.237481i
\(204\) 0 0
\(205\) −2.10521e8 + 3.64633e8i −0.119201 + 0.206462i
\(206\) 3.72812e9i 2.07024i
\(207\) 0 0
\(208\) −1.73729e9 −0.928152
\(209\) −1.14141e8 6.58993e7i −0.0598214 0.0345379i
\(210\) 0 0
\(211\) −2.90552e7 5.03250e7i −0.0146586 0.0253895i 0.858603 0.512641i \(-0.171333\pi\)
−0.873262 + 0.487252i \(0.837999\pi\)
\(212\) 1.41789e9 8.18619e8i 0.701938 0.405264i
\(213\) 0 0
\(214\) −2.53168e8 + 4.38499e8i −0.120713 + 0.209081i
\(215\) 7.91619e8i 0.370478i
\(216\) 0 0
\(217\) 6.15086e8 0.277394
\(218\) 2.13816e9 + 1.23447e9i 0.946704 + 0.546580i
\(219\) 0 0
\(220\) 1.93738e8 + 3.35563e8i 0.0827034 + 0.143246i
\(221\) 1.66883e9 9.63499e8i 0.699588 0.403908i
\(222\) 0 0
\(223\) −2.20100e9 + 3.81224e9i −0.890021 + 1.54156i −0.0501724 + 0.998741i \(0.515977\pi\)
−0.839848 + 0.542821i \(0.817356\pi\)
\(224\) 2.57222e9i 1.02168i
\(225\) 0 0
\(226\) −6.45992e9 −2.47624
\(227\) −3.06220e9 1.76796e9i −1.15327 0.665839i −0.203586 0.979057i \(-0.565260\pi\)
−0.949681 + 0.313218i \(0.898593\pi\)
\(228\) 0 0
\(229\) 9.32847e8 + 1.61574e9i 0.339210 + 0.587529i 0.984284 0.176591i \(-0.0565070\pi\)
−0.645074 + 0.764120i \(0.723174\pi\)
\(230\) −2.05345e9 + 1.18556e9i −0.733793 + 0.423656i
\(231\) 0 0
\(232\) 4.13885e7 7.16870e7i 0.0142866 0.0247450i
\(233\) 2.72132e9i 0.923328i −0.887055 0.461664i \(-0.847253\pi\)
0.887055 0.461664i \(-0.152747\pi\)
\(234\) 0 0
\(235\) −9.16191e8 −0.300410
\(236\) 2.94561e9 + 1.70065e9i 0.949570 + 0.548234i
\(237\) 0 0
\(238\) −1.47118e9 2.54815e9i −0.458518 0.794177i
\(239\) −1.96987e9 + 1.13730e9i −0.603734 + 0.348566i −0.770509 0.637429i \(-0.779998\pi\)
0.166775 + 0.985995i \(0.446665\pi\)
\(240\) 0 0
\(241\) 8.73336e8 1.51266e9i 0.258889 0.448408i −0.707056 0.707158i \(-0.749977\pi\)
0.965945 + 0.258749i \(0.0833104\pi\)
\(242\) 3.72500e9i 1.08609i
\(243\) 0 0
\(244\) −1.86893e8 −0.0527272
\(245\) −5.25387e8 3.03333e8i −0.145819 0.0841889i
\(246\) 0 0
\(247\) −2.43637e8 4.21992e8i −0.0654570 0.113375i
\(248\) −5.46681e7 + 3.15626e7i −0.0144520 + 0.00834385i
\(249\) 0 0
\(250\) −1.84174e9 + 3.18999e9i −0.471486 + 0.816638i
\(251\) 1.37549e9i 0.346547i 0.984874 + 0.173274i \(0.0554345\pi\)
−0.984874 + 0.173274i \(0.944566\pi\)
\(252\) 0 0
\(253\) 3.27417e9 0.799132
\(254\) −5.36594e9 3.09802e9i −1.28917 0.744303i
\(255\) 0 0
\(256\) −2.27535e9 3.94102e9i −0.529770 0.917589i
\(257\) −6.87340e9 + 3.96836e9i −1.57558 + 0.909659i −0.580110 + 0.814538i \(0.696990\pi\)
−0.995466 + 0.0951209i \(0.969676\pi\)
\(258\) 0 0
\(259\) 1.16827e9 2.02351e9i 0.259624 0.449683i
\(260\) 1.43254e9i 0.313483i
\(261\) 0 0
\(262\) −6.49068e9 −1.37748
\(263\) −2.79340e8 1.61277e8i −0.0583863 0.0337093i 0.470523 0.882388i \(-0.344065\pi\)
−0.528909 + 0.848679i \(0.677399\pi\)
\(264\) 0 0
\(265\) 7.41046e8 + 1.28353e9i 0.150266 + 0.260269i
\(266\) −6.44344e8 + 3.72012e8i −0.128704 + 0.0743072i
\(267\) 0 0
\(268\) 2.81342e8 4.87299e8i 0.0545376 0.0944619i
\(269\) 3.47314e9i 0.663304i 0.943402 + 0.331652i \(0.107606\pi\)
−0.943402 + 0.331652i \(0.892394\pi\)
\(270\) 0 0
\(271\) −1.44216e9 −0.267385 −0.133693 0.991023i \(-0.542683\pi\)
−0.133693 + 0.991023i \(0.542683\pi\)
\(272\) 4.37930e9 + 2.52839e9i 0.800071 + 0.461921i
\(273\) 0 0
\(274\) −2.32988e9 4.03547e9i −0.413363 0.715966i
\(275\) 2.05057e9 1.18390e9i 0.358544 0.207006i
\(276\) 0 0
\(277\) −1.69023e9 + 2.92757e9i −0.287096 + 0.497265i −0.973115 0.230318i \(-0.926023\pi\)
0.686019 + 0.727583i \(0.259357\pi\)
\(278\) 3.20289e9i 0.536245i
\(279\) 0 0
\(280\) −7.05600e7 −0.0114796
\(281\) −3.48369e9 2.01131e9i −0.558745 0.322592i 0.193896 0.981022i \(-0.437887\pi\)
−0.752642 + 0.658430i \(0.771221\pi\)
\(282\) 0 0
\(283\) 5.21264e9 + 9.02856e9i 0.812666 + 1.40758i 0.910992 + 0.412424i \(0.135318\pi\)
−0.0983264 + 0.995154i \(0.531349\pi\)
\(284\) −3.65589e9 + 2.11073e9i −0.561978 + 0.324458i
\(285\) 0 0
\(286\) 2.01003e9 3.48147e9i 0.300426 0.520354i
\(287\) 3.28207e9i 0.483749i
\(288\) 0 0
\(289\) 1.36679e9 0.195935
\(290\) −2.01171e9 1.16146e9i −0.284429 0.164215i
\(291\) 0 0
\(292\) 3.43142e9 + 5.94340e9i 0.472001 + 0.817530i
\(293\) 9.00032e9 5.19634e9i 1.22120 0.705061i 0.256028 0.966669i \(-0.417586\pi\)
0.965174 + 0.261608i \(0.0842528\pi\)
\(294\) 0 0
\(295\) −1.53949e9 + 2.66648e9i −0.203278 + 0.352087i
\(296\) 2.39796e8i 0.0312374i
\(297\) 0 0
\(298\) 1.83918e10 2.33216
\(299\) 1.04832e10 + 6.05248e9i 1.31162 + 0.757266i
\(300\) 0 0
\(301\) −3.08538e9 5.34404e9i −0.375874 0.651034i
\(302\) 8.24079e9 4.75782e9i 0.990698 0.571980i
\(303\) 0 0
\(304\) 6.39347e8 1.10738e9i 0.0748587 0.129659i
\(305\) 1.69183e8i 0.0195505i
\(306\) 0 0
\(307\) −2.99309e9 −0.336951 −0.168476 0.985706i \(-0.553884\pi\)
−0.168476 + 0.985706i \(0.553884\pi\)
\(308\) −2.61576e9 1.51021e9i −0.290666 0.167816i
\(309\) 0 0
\(310\) 8.85725e8 + 1.53412e9i 0.0959074 + 0.166116i
\(311\) 5.58441e9 3.22416e9i 0.596947 0.344647i −0.170893 0.985290i \(-0.554665\pi\)
0.767840 + 0.640642i \(0.221332\pi\)
\(312\) 0 0
\(313\) −1.63869e7 + 2.83829e7i −0.00170733 + 0.00295719i −0.866878 0.498521i \(-0.833877\pi\)
0.865170 + 0.501478i \(0.167210\pi\)
\(314\) 1.70586e10i 1.75479i
\(315\) 0 0
\(316\) 5.69928e9 0.571573
\(317\) 1.02015e10 + 5.88983e9i 1.01024 + 0.583264i 0.911263 0.411825i \(-0.135108\pi\)
0.0989806 + 0.995089i \(0.468442\pi\)
\(318\) 0 0
\(319\) 1.60380e9 + 2.77787e9i 0.154878 + 0.268256i
\(320\) −3.05491e9 + 1.76375e9i −0.291339 + 0.168205i
\(321\) 0 0
\(322\) 9.24160e9 1.60069e10i 0.859654 1.48896i
\(323\) 1.41832e9i 0.130306i
\(324\) 0 0
\(325\) 8.75399e9 0.784644
\(326\) −1.29905e10 7.50008e9i −1.15015 0.664042i
\(327\) 0 0
\(328\) 1.68417e8 + 2.91706e8i 0.0145509 + 0.0252029i
\(329\) 6.18500e9 3.57091e9i 0.527905 0.304786i
\(330\) 0 0
\(331\) 6.00499e9 1.04009e10i 0.500265 0.866484i −0.499735 0.866178i \(-0.666569\pi\)
1.00000 0.000305936i \(-9.73825e-5\pi\)
\(332\) 1.15060e10i 0.947049i
\(333\) 0 0
\(334\) −4.40705e9 −0.354130
\(335\) 4.41123e8 + 2.54682e8i 0.0350252 + 0.0202218i
\(336\) 0 0
\(337\) −7.96069e9 1.37883e10i −0.617207 1.06903i −0.989993 0.141117i \(-0.954931\pi\)
0.372786 0.927917i \(-0.378403\pi\)
\(338\) −2.98823e9 + 1.72525e9i −0.228953 + 0.132186i
\(339\) 0 0
\(340\) 2.08487e9 3.61109e9i 0.156014 0.270224i
\(341\) 2.44611e9i 0.180908i
\(342\) 0 0
\(343\) 1.48174e10 1.07052
\(344\) 5.48450e8 + 3.16647e8i 0.0391654 + 0.0226122i
\(345\) 0 0
\(346\) 1.14853e10 + 1.98931e10i 0.801380 + 1.38803i
\(347\) −4.28503e9 + 2.47396e9i −0.295553 + 0.170638i −0.640444 0.768005i \(-0.721249\pi\)
0.344890 + 0.938643i \(0.387916\pi\)
\(348\) 0 0
\(349\) 3.64784e9 6.31824e9i 0.245886 0.425887i −0.716494 0.697593i \(-0.754254\pi\)
0.962380 + 0.271706i \(0.0875878\pi\)
\(350\) 1.33666e10i 0.890733i
\(351\) 0 0
\(352\) 1.02293e10 0.666311
\(353\) 6.00913e9 + 3.46938e9i 0.387002 + 0.223436i 0.680860 0.732413i \(-0.261606\pi\)
−0.293858 + 0.955849i \(0.594939\pi\)
\(354\) 0 0
\(355\) −1.91071e9 3.30945e9i −0.120305 0.208374i
\(356\) −1.55959e10 + 9.00429e9i −0.970980 + 0.560595i
\(357\) 0 0
\(358\) −1.44684e10 + 2.50600e10i −0.880822 + 1.52563i
\(359\) 1.60096e10i 0.963838i 0.876216 + 0.481919i \(0.160060\pi\)
−0.876216 + 0.481919i \(0.839940\pi\)
\(360\) 0 0
\(361\) −1.66249e10 −0.978883
\(362\) −9.17102e9 5.29489e9i −0.534052 0.308335i
\(363\) 0 0
\(364\) −5.58341e9 9.67075e9i −0.318049 0.550877i
\(365\) −5.38020e9 + 3.10626e9i −0.303129 + 0.175011i
\(366\) 0 0
\(367\) −6.81822e9 + 1.18095e10i −0.375843 + 0.650980i −0.990453 0.137852i \(-0.955980\pi\)
0.614610 + 0.788831i \(0.289314\pi\)
\(368\) 3.17655e10i 1.73207i
\(369\) 0 0
\(370\) 6.72926e9 0.359054
\(371\) −1.00053e10 5.77654e9i −0.528121 0.304911i
\(372\) 0 0
\(373\) 1.22031e10 + 2.11364e10i 0.630427 + 1.09193i 0.987464 + 0.157842i \(0.0504536\pi\)
−0.357037 + 0.934090i \(0.616213\pi\)
\(374\) −1.01336e10 + 5.85064e9i −0.517938 + 0.299032i
\(375\) 0 0
\(376\) −3.66477e8 + 6.34756e8i −0.0183356 + 0.0317582i
\(377\) 1.18589e10i 0.587055i
\(378\) 0 0
\(379\) −1.98392e10 −0.961542 −0.480771 0.876846i \(-0.659643\pi\)
−0.480771 + 0.876846i \(0.659643\pi\)
\(380\) −9.13128e8 5.27195e8i −0.0437923 0.0252835i
\(381\) 0 0
\(382\) −1.81605e9 3.14550e9i −0.0852855 0.147719i
\(383\) −1.30885e10 + 7.55663e9i −0.608266 + 0.351183i −0.772287 0.635274i \(-0.780887\pi\)
0.164020 + 0.986457i \(0.447554\pi\)
\(384\) 0 0
\(385\) 1.36710e9 2.36789e9i 0.0622239 0.107775i
\(386\) 3.56594e10i 1.60630i
\(387\) 0 0
\(388\) −3.65232e10 −1.61154
\(389\) 1.55877e10 + 8.99957e9i 0.680744 + 0.393028i 0.800135 0.599819i \(-0.204761\pi\)
−0.119391 + 0.992847i \(0.538094\pi\)
\(390\) 0 0
\(391\) −1.76171e10 3.05138e10i −0.753751 1.30554i
\(392\) −4.20310e8 + 2.42666e8i −0.0178002 + 0.0102770i
\(393\) 0 0
\(394\) −6.03645e9 + 1.04554e10i −0.250494 + 0.433867i
\(395\) 5.15922e9i 0.211931i
\(396\) 0 0
\(397\) −2.35673e10 −0.948739 −0.474370 0.880326i \(-0.657324\pi\)
−0.474370 + 0.880326i \(0.657324\pi\)
\(398\) −1.25905e10 7.26914e9i −0.501778 0.289701i
\(399\) 0 0
\(400\) 1.14860e10 + 1.98943e10i 0.448672 + 0.777122i
\(401\) 1.19245e10 6.88461e9i 0.461172 0.266257i −0.251365 0.967892i \(-0.580880\pi\)
0.712537 + 0.701635i \(0.247546\pi\)
\(402\) 0 0
\(403\) 4.52176e9 7.83193e9i 0.171430 0.296926i
\(404\) 2.56791e10i 0.963950i
\(405\) 0 0
\(406\) 1.81075e10 0.666428
\(407\) −8.04719e9 4.64605e9i −0.293269 0.169319i
\(408\) 0 0
\(409\) −1.79240e10 3.10452e10i −0.640533 1.10944i −0.985314 0.170752i \(-0.945380\pi\)
0.344781 0.938683i \(-0.387953\pi\)
\(410\) 8.18598e9 4.72618e9i 0.289691 0.167253i
\(411\) 0 0
\(412\) −2.05919e10 + 3.56662e10i −0.714672 + 1.23785i
\(413\) 2.40011e10i 0.824955i
\(414\) 0 0
\(415\) −1.04157e10 −0.351153
\(416\) 3.27523e10 + 1.89095e10i 1.09362 + 0.631404i
\(417\) 0 0
\(418\) 1.47944e9 + 2.56246e9i 0.0484609 + 0.0839367i
\(419\) 1.93987e10 1.11998e10i 0.629384 0.363375i −0.151130 0.988514i \(-0.548291\pi\)
0.780513 + 0.625139i \(0.214958\pi\)
\(420\) 0 0
\(421\) 7.47674e9 1.29501e10i 0.238004 0.412235i −0.722138 0.691750i \(-0.756840\pi\)
0.960141 + 0.279515i \(0.0901736\pi\)
\(422\) 1.30457e9i 0.0411357i
\(423\) 0 0
\(424\) 1.18567e9 0.0366861
\(425\) −2.20667e10 1.27402e10i −0.676367 0.390501i
\(426\) 0 0
\(427\) 6.59402e8 + 1.14212e9i 0.0198353 + 0.0343557i
\(428\) 4.84401e9 2.79669e9i 0.144355 0.0833431i
\(429\) 0 0
\(430\) 8.88590e9 1.53908e10i 0.259913 0.450182i
\(431\) 6.40436e10i 1.85595i −0.372640 0.927976i \(-0.621547\pi\)
0.372640 0.927976i \(-0.378453\pi\)
\(432\) 0 0
\(433\) −5.22954e9 −0.148769 −0.0743843 0.997230i \(-0.523699\pi\)
−0.0743843 + 0.997230i \(0.523699\pi\)
\(434\) −1.19586e10 6.90433e9i −0.337072 0.194609i
\(435\) 0 0
\(436\) −1.36369e10 2.36198e10i −0.377372 0.653628i
\(437\) −7.71593e9 + 4.45480e9i −0.211574 + 0.122152i
\(438\) 0 0
\(439\) −2.17401e10 + 3.76549e10i −0.585332 + 1.01383i 0.409501 + 0.912309i \(0.365703\pi\)
−0.994834 + 0.101516i \(0.967631\pi\)
\(440\) 2.80606e8i 0.00748664i
\(441\) 0 0
\(442\) −4.32610e10 −1.13346
\(443\) 3.27996e10 + 1.89368e10i 0.851634 + 0.491691i 0.861202 0.508263i \(-0.169712\pi\)
−0.00956760 + 0.999954i \(0.503046\pi\)
\(444\) 0 0
\(445\) −8.15104e9 1.41180e10i −0.207861 0.360026i
\(446\) 8.55846e10 4.94123e10i 2.16300 1.24881i
\(447\) 0 0
\(448\) 1.37487e10 2.38134e10i 0.341310 0.591166i
\(449\) 2.95505e10i 0.727076i 0.931579 + 0.363538i \(0.118431\pi\)
−0.931579 + 0.363538i \(0.881569\pi\)
\(450\) 0 0
\(451\) −1.30523e10 −0.315486
\(452\) 6.18008e10 + 3.56807e10i 1.48061 + 0.854830i
\(453\) 0 0
\(454\) 3.96906e10 + 6.87462e10i 0.934253 + 1.61817i
\(455\) 8.75435e9 5.05432e9i 0.204258 0.117928i
\(456\) 0 0
\(457\) 1.01091e10 1.75094e10i 0.231764 0.401427i −0.726563 0.687100i \(-0.758884\pi\)
0.958327 + 0.285672i \(0.0922169\pi\)
\(458\) 4.18847e10i 0.951905i
\(459\) 0 0
\(460\) 2.61933e10 0.585005
\(461\) −6.07799e10 3.50913e10i −1.34573 0.776955i −0.358085 0.933689i \(-0.616570\pi\)
−0.987641 + 0.156734i \(0.949903\pi\)
\(462\) 0 0
\(463\) −2.08004e9 3.60274e9i −0.0452635 0.0783987i 0.842506 0.538687i \(-0.181079\pi\)
−0.887770 + 0.460288i \(0.847746\pi\)
\(464\) −2.69505e10 + 1.55599e10i −0.581427 + 0.335687i
\(465\) 0 0
\(466\) −3.05467e10 + 5.29085e10i −0.647770 + 1.12197i
\(467\) 2.88138e10i 0.605806i 0.953021 + 0.302903i \(0.0979558\pi\)
−0.953021 + 0.302903i \(0.902044\pi\)
\(468\) 0 0
\(469\) −3.97056e9 −0.0820654
\(470\) 1.78128e10 + 1.02842e10i 0.365040 + 0.210756i
\(471\) 0 0
\(472\) 1.23159e9 + 2.13318e9i 0.0248142 + 0.0429794i
\(473\) −2.12524e10 + 1.22701e10i −0.424584 + 0.245134i
\(474\) 0 0
\(475\) −3.22159e9 + 5.57996e9i −0.0632843 + 0.109612i
\(476\) 3.25036e10i 0.633145i
\(477\) 0 0
\(478\) 5.10649e10 0.978161
\(479\) −3.87242e10 2.23574e10i −0.735598 0.424698i 0.0848686 0.996392i \(-0.472953\pi\)
−0.820467 + 0.571694i \(0.806286\pi\)
\(480\) 0 0
\(481\) −1.71770e10 2.97514e10i −0.320897 0.555810i
\(482\) −3.39592e10 + 1.96063e10i −0.629172 + 0.363252i
\(483\) 0 0
\(484\) 2.05746e10 3.56363e10i 0.374930 0.649399i
\(485\) 3.30623e10i 0.597538i
\(486\) 0 0
\(487\) 5.72836e10 1.01839 0.509195 0.860651i \(-0.329943\pi\)
0.509195 + 0.860651i \(0.329943\pi\)
\(488\) −1.17214e8 6.76733e7i −0.00206680 0.00119327i
\(489\) 0 0
\(490\) 6.80980e9 + 1.17949e10i 0.118127 + 0.204602i
\(491\) −6.28095e10 + 3.62631e10i −1.08069 + 0.623934i −0.931081 0.364812i \(-0.881133\pi\)
−0.149604 + 0.988746i \(0.547800\pi\)
\(492\) 0 0
\(493\) 1.72590e10 2.98935e10i 0.292165 0.506044i
\(494\) 1.09393e10i 0.183688i
\(495\) 0 0
\(496\) 2.37318e10 0.392106
\(497\) 2.57976e10 + 1.48942e10i 0.422818 + 0.244114i
\(498\) 0 0
\(499\) 1.32184e10 + 2.28949e10i 0.213195 + 0.369264i 0.952713 0.303873i \(-0.0982798\pi\)
−0.739518 + 0.673137i \(0.764946\pi\)
\(500\) 3.52392e10 2.03454e10i 0.563827 0.325526i
\(501\) 0 0
\(502\) 1.54398e10 2.67426e10i 0.243124 0.421103i
\(503\) 7.52828e10i 1.17604i 0.808845 + 0.588022i \(0.200093\pi\)
−0.808845 + 0.588022i \(0.799907\pi\)
\(504\) 0 0
\(505\) −2.32457e10 −0.357419
\(506\) −6.36571e10 3.67524e10i −0.971056 0.560640i
\(507\) 0 0
\(508\) 3.42232e10 + 5.92764e10i 0.513886 + 0.890076i
\(509\) −5.58746e10 + 3.22592e10i −0.832421 + 0.480599i −0.854681 0.519154i \(-0.826247\pi\)
0.0222598 + 0.999752i \(0.492914\pi\)
\(510\) 0 0
\(511\) 2.42137e10 4.19393e10i 0.355122 0.615089i
\(512\) 9.61394e10i 1.39901i
\(513\) 0 0
\(514\) 1.78179e11 2.55272
\(515\) −3.22864e10 1.86406e10i −0.458977 0.264991i
\(516\) 0 0
\(517\) −1.42010e10 2.45968e10i −0.198772 0.344284i
\(518\) −4.54277e10 + 2.62277e10i −0.630959 + 0.364285i
\(519\) 0 0
\(520\) −5.18717e8 + 8.98444e8i −0.00709442 + 0.0122879i
\(521\) 7.65146e10i 1.03847i −0.854632 0.519235i \(-0.826217\pi\)
0.854632 0.519235i \(-0.173783\pi\)
\(522\) 0 0
\(523\) −8.46771e10 −1.13177 −0.565886 0.824483i \(-0.691466\pi\)
−0.565886 + 0.824483i \(0.691466\pi\)
\(524\) 6.20951e10 + 3.58506e10i 0.823630 + 0.475523i
\(525\) 0 0
\(526\) 3.62067e9 + 6.27118e9i 0.0472983 + 0.0819231i
\(527\) −2.27966e10 + 1.31616e10i −0.295548 + 0.170635i
\(528\) 0 0
\(529\) 7.15113e10 1.23861e11i 0.913171 1.58166i
\(530\) 3.32729e10i 0.421684i
\(531\) 0 0
\(532\) 8.21909e9 0.102607
\(533\) −4.17907e10 2.41279e10i −0.517811 0.298958i
\(534\) 0 0
\(535\) 2.53168e9 + 4.38499e9i 0.0309025 + 0.0535247i
\(536\) 3.52898e8 2.03746e8i 0.00427553 0.00246848i
\(537\) 0 0
\(538\) 3.89859e10 6.75255e10i 0.465348 0.806007i
\(539\) 1.88066e10i 0.222821i
\(540\) 0 0
\(541\) 1.43470e11 1.67483 0.837415 0.546568i \(-0.184066\pi\)
0.837415 + 0.546568i \(0.184066\pi\)
\(542\) 2.80389e10 + 1.61883e10i 0.324910 + 0.187587i
\(543\) 0 0
\(544\) −5.50405e10 9.53329e10i −0.628473 1.08855i
\(545\) 2.13816e10 1.23447e10i 0.242356 0.139924i
\(546\) 0 0
\(547\) −8.20857e10 + 1.42177e11i −0.916892 + 1.58810i −0.112786 + 0.993619i \(0.535977\pi\)
−0.804107 + 0.594485i \(0.797356\pi\)
\(548\) 5.14755e10i 0.570792i
\(549\) 0 0
\(550\) −5.31568e10 −0.580908
\(551\) −7.55908e9 4.36424e9i −0.0820092 0.0473480i
\(552\) 0 0
\(553\) −2.01084e10 3.48287e10i −0.215019 0.372423i
\(554\) 6.57237e10 3.79456e10i 0.697723 0.402831i
\(555\) 0 0
\(556\) −1.76909e10 + 3.06415e10i −0.185119 + 0.320635i
\(557\) 1.54420e11i 1.60429i 0.597130 + 0.802145i \(0.296308\pi\)
−0.597130 + 0.802145i \(0.703692\pi\)
\(558\) 0 0
\(559\) −9.07278e10 −0.929166
\(560\) 2.29729e10 + 1.32634e10i 0.233595 + 0.134866i
\(561\) 0 0
\(562\) 4.51538e10 + 7.82086e10i 0.452636 + 0.783988i
\(563\) 1.33907e11 7.73112e10i 1.33281 0.769500i 0.347084 0.937834i \(-0.387172\pi\)
0.985730 + 0.168334i \(0.0538386\pi\)
\(564\) 0 0
\(565\) −3.22996e10 + 5.59446e10i −0.316959 + 0.548990i
\(566\) 2.34047e11i 2.28054i
\(567\) 0 0
\(568\) −3.05714e9 −0.0293712
\(569\) 9.99216e10 + 5.76898e10i 0.953258 + 0.550364i 0.894092 0.447884i \(-0.147822\pi\)
0.0591666 + 0.998248i \(0.481156\pi\)
\(570\) 0 0
\(571\) 8.17051e10 + 1.41517e11i 0.768608 + 1.33127i 0.938318 + 0.345774i \(0.112384\pi\)
−0.169710 + 0.985494i \(0.554283\pi\)
\(572\) −3.84591e10 + 2.22044e10i −0.359265 + 0.207422i
\(573\) 0 0
\(574\) −3.68411e10 + 6.38107e10i −0.339379 + 0.587822i
\(575\) 1.60063e11i 1.46426i
\(576\) 0 0
\(577\) 7.42282e10 0.669678 0.334839 0.942275i \(-0.391318\pi\)
0.334839 + 0.942275i \(0.391318\pi\)
\(578\) −2.65735e10 1.53422e10i −0.238088 0.137460i
\(579\) 0 0
\(580\) 1.28304e10 + 2.22230e10i 0.113378 + 0.196377i
\(581\) 7.03140e10 4.05958e10i 0.617074 0.356268i
\(582\) 0 0
\(583\) −2.29724e10 + 3.97894e10i −0.198853 + 0.344424i
\(584\) 4.97002e9i 0.0427274i
\(585\) 0 0
\(586\) −2.33315e11 −1.97857
\(587\) 5.82728e10 + 3.36438e10i 0.490810 + 0.283369i 0.724911 0.688843i \(-0.241881\pi\)
−0.234100 + 0.972212i \(0.575214\pi\)
\(588\) 0 0
\(589\) 3.32815e9 + 5.76452e9i 0.0276529 + 0.0478963i
\(590\) 5.98623e10 3.45615e10i 0.494021 0.285223i
\(591\) 0 0
\(592\) 4.50753e10 7.80728e10i 0.366988 0.635642i
\(593\) 2.36444e10i 0.191210i −0.995419 0.0956048i \(-0.969521\pi\)
0.995419 0.0956048i \(-0.0304785\pi\)
\(594\) 0 0
\(595\) −2.94235e10 −0.234761
\(596\) −1.75951e11 1.01585e11i −1.39446 0.805092i
\(597\) 0 0
\(598\) −1.35878e11 2.35347e11i −1.06254 1.84037i
\(599\) 2.62726e10 1.51685e10i 0.204078 0.117825i −0.394478 0.918905i \(-0.629075\pi\)
0.598556 + 0.801081i \(0.295741\pi\)
\(600\) 0 0
\(601\) −1.68956e10 + 2.92640e10i −0.129501 + 0.224303i −0.923484 0.383638i \(-0.874671\pi\)
0.793982 + 0.607941i \(0.208004\pi\)
\(602\) 1.38533e11i 1.05480i
\(603\) 0 0
\(604\) −1.05117e11 −0.789818
\(605\) 3.22594e10 + 1.86250e10i 0.240788 + 0.139019i
\(606\) 0 0
\(607\) 1.91183e10 + 3.31139e10i 0.140830 + 0.243925i 0.927809 0.373055i \(-0.121690\pi\)
−0.786979 + 0.616979i \(0.788356\pi\)
\(608\) −2.41066e10 + 1.39179e10i −0.176409 + 0.101850i
\(609\) 0 0
\(610\) −1.89908e9 + 3.28930e9i −0.0137159 + 0.0237566i
\(611\) 1.05005e11i 0.753435i
\(612\) 0 0
\(613\) 1.08066e11 0.765330 0.382665 0.923887i \(-0.375006\pi\)
0.382665 + 0.923887i \(0.375006\pi\)
\(614\) 5.81924e10 + 3.35974e10i 0.409442 + 0.236392i
\(615\) 0 0
\(616\) −1.09368e9 1.89431e9i −0.00759569 0.0131561i
\(617\) −4.09230e9 + 2.36269e9i −0.0282375 + 0.0163029i −0.514052 0.857759i \(-0.671856\pi\)
0.485815 + 0.874062i \(0.338523\pi\)
\(618\) 0 0
\(619\) −1.14923e10 + 1.99052e10i −0.0782786 + 0.135583i −0.902507 0.430674i \(-0.858276\pi\)
0.824229 + 0.566257i \(0.191609\pi\)
\(620\) 1.95688e10i 0.132434i
\(621\) 0 0
\(622\) −1.44764e11 −0.967165
\(623\) 1.10052e11 + 6.35383e10i 0.730540 + 0.421778i
\(624\) 0 0
\(625\) −4.80328e10 8.31952e10i −0.314788 0.545228i
\(626\) 6.37194e8 3.67884e8i 0.00414930 0.00239560i
\(627\) 0 0
\(628\) −9.42215e10 + 1.63196e11i −0.605775 + 1.04923i
\(629\) 9.99949e10i 0.638815i
\(630\) 0 0
\(631\) −1.01892e11 −0.642722 −0.321361 0.946957i \(-0.604140\pi\)
−0.321361 + 0.946957i \(0.604140\pi\)
\(632\) 3.57441e9 + 2.06369e9i 0.0224045 + 0.0129353i
\(633\) 0 0
\(634\) −1.32226e11 2.29023e11i −0.818391 1.41749i
\(635\) −5.36594e10 + 3.09802e10i −0.330028 + 0.190542i
\(636\) 0 0
\(637\) 3.47651e10 6.02149e10i 0.211147 0.365718i
\(638\) 7.20106e10i 0.434624i
\(639\) 0 0
\(640\) −5.28224e9 −0.0314846
\(641\) −1.02021e11 5.89017e10i −0.604305 0.348896i 0.166428 0.986054i \(-0.446777\pi\)
−0.770733 + 0.637158i \(0.780110\pi\)
\(642\) 0 0
\(643\) 1.31340e10 + 2.27488e10i 0.0768339 + 0.133080i 0.901882 0.431982i \(-0.142186\pi\)
−0.825048 + 0.565062i \(0.808852\pi\)
\(644\) −1.76825e11 + 1.02090e11i −1.02802 + 0.593526i
\(645\) 0 0
\(646\) 1.59206e10 2.75754e10i 0.0914178 0.158340i
\(647\) 3.10527e11i 1.77208i 0.463612 + 0.886038i \(0.346553\pi\)
−0.463612 + 0.886038i \(0.653447\pi\)
\(648\) 0 0
\(649\) −9.54486e10 −0.538010
\(650\) −1.70197e11 9.82633e10i −0.953451 0.550475i
\(651\) 0 0
\(652\) 8.28518e10 + 1.43504e11i 0.458471 + 0.794095i
\(653\) 3.01676e10 1.74172e10i 0.165916 0.0957914i −0.414743 0.909939i \(-0.636128\pi\)
0.580659 + 0.814147i \(0.302795\pi\)
\(654\) 0 0
\(655\) −3.24534e10 + 5.62109e10i −0.176317 + 0.305390i
\(656\) 1.26632e11i 0.683796i
\(657\) 0 0
\(658\) −1.60333e11 −0.855304
\(659\) −3.26595e10 1.88560e10i −0.173168 0.0999787i 0.410911 0.911676i \(-0.365211\pi\)
−0.584079 + 0.811697i \(0.698544\pi\)
\(660\) 0 0
\(661\) 6.98094e10 + 1.20913e11i 0.365686 + 0.633387i 0.988886 0.148676i \(-0.0475011\pi\)
−0.623200 + 0.782062i \(0.714168\pi\)
\(662\) −2.33501e11 + 1.34812e11i −1.21578 + 0.701932i
\(663\) 0 0
\(664\) −4.16628e9 + 7.21620e9i −0.0214327 + 0.0371224i
\(665\) 7.44025e9i 0.0380453i
\(666\) 0 0
\(667\) 2.16834e11 1.09553
\(668\) 4.21614e10 + 2.43419e10i 0.211743 + 0.122250i
\(669\) 0 0
\(670\) −5.71760e9 9.90318e9i −0.0283736 0.0491446i
\(671\) 4.54203e9 2.62234e9i 0.0224058 0.0129360i
\(672\) 0 0
\(673\) 6.48916e10 1.12396e11i 0.316321 0.547884i −0.663396 0.748268i \(-0.730886\pi\)
0.979717 + 0.200384i \(0.0642190\pi\)
\(674\) 3.57434e11i 1.73203i
\(675\) 0 0
\(676\) 3.81171e10 0.182529
\(677\) 2.95009e11 + 1.70324e11i 1.40437 + 0.810813i 0.994837 0.101483i \(-0.0323588\pi\)
0.409532 + 0.912296i \(0.365692\pi\)
\(678\) 0 0
\(679\) 1.28862e11 + 2.23196e11i 0.606242 + 1.05004i
\(680\) 2.61513e9 1.50984e9i 0.0122309 0.00706149i
\(681\) 0 0
\(682\) −2.74575e10 + 4.75577e10i −0.126918 + 0.219828i
\(683\) 1.02876e11i 0.472750i 0.971662 + 0.236375i \(0.0759593\pi\)
−0.971662 + 0.236375i \(0.924041\pi\)
\(684\) 0 0
\(685\) −4.65976e10 −0.211642
\(686\) −2.88084e11 1.66325e11i −1.30084 0.751038i
\(687\) 0 0
\(688\) −1.19043e11 2.06188e11i −0.531312 0.920259i
\(689\) −1.47106e11 + 8.49317e10i −0.652760 + 0.376871i
\(690\) 0 0
\(691\) −1.79130e11 + 3.10262e11i −0.785698 + 1.36087i 0.142884 + 0.989740i \(0.454363\pi\)
−0.928581 + 0.371129i \(0.878971\pi\)
\(692\) 2.53752e11i 1.10659i
\(693\) 0 0
\(694\) 1.11081e11 0.478851
\(695\) −2.77379e10 1.60145e10i −0.118887 0.0686394i
\(696\) 0 0
\(697\) 7.02297e10 + 1.21641e11i 0.297571 + 0.515407i
\(698\) −1.41844e11 + 8.18937e10i −0.597571 + 0.345008i
\(699\) 0 0
\(700\) −7.38288e10 + 1.27875e11i −0.307492 + 0.532592i
\(701\) 2.49323e11i 1.03250i −0.856438 0.516250i \(-0.827327\pi\)
0.856438 0.516250i \(-0.172673\pi\)
\(702\) 0 0
\(703\) 2.52854e10 0.103526
\(704\) −9.47022e10 5.46764e10i −0.385540 0.222592i
\(705\) 0 0
\(706\) −7.78873e10 1.34905e11i −0.313507 0.543011i
\(707\) 1.56927e11 9.06017e10i 0.628086 0.362626i
\(708\) 0 0
\(709\) 1.94437e11 3.36775e11i 0.769474 1.33277i −0.168374 0.985723i \(-0.553852\pi\)
0.937848 0.347045i \(-0.112815\pi\)
\(710\) 8.57909e10i 0.337604i
\(711\) 0 0
\(712\) −1.30417e10 −0.0507473
\(713\) −1.43203e11 8.26784e10i −0.554108 0.319914i
\(714\) 0 0
\(715\) −2.01003e10 3.48147e10i −0.0769091 0.133211i
\(716\) 2.76833e11 1.59829e11i 1.05333 0.608142i
\(717\) 0 0
\(718\) 1.79708e11 3.11263e11i 0.676191 1.17120i
\(719\) 3.35735e10i 0.125626i 0.998025 + 0.0628132i \(0.0200072\pi\)
−0.998025 + 0.0628132i \(0.979993\pi\)
\(720\) 0 0
\(721\) 2.90611e11 1.07540
\(722\) 3.23225e11 + 1.86614e11i 1.18948 + 0.686746i
\(723\) 0 0
\(724\) 5.84916e10 + 1.01310e11i 0.212882 + 0.368723i
\(725\) 1.35800e11 7.84044e10i 0.491529 0.283784i
\(726\) 0 0
\(727\) −1.26557e11 + 2.19202e11i −0.453051 + 0.784707i −0.998574 0.0533888i \(-0.982998\pi\)
0.545523 + 0.838096i \(0.316331\pi\)
\(728\) 8.08692e9i 0.0287911i
\(729\) 0 0
\(730\) 1.39471e11 0.491125
\(731\) 2.28703e11 + 1.32042e11i 0.800946 + 0.462426i
\(732\) 0 0
\(733\) −1.03801e11 1.79789e11i −0.359572 0.622797i 0.628317 0.777957i \(-0.283744\pi\)
−0.987889 + 0.155160i \(0.950411\pi\)
\(734\) 2.65123e11 1.53069e11i 0.913403 0.527354i
\(735\) 0 0
\(736\) 3.45752e11 5.98860e11i 1.17829 2.04086i
\(737\) 1.57903e10i 0.0535205i
\(738\) 0 0
\(739\) 4.15014e11 1.39151 0.695753 0.718281i \(-0.255071\pi\)
0.695753 + 0.718281i \(0.255071\pi\)
\(740\) −6.43775e10 3.71684e10i −0.214688 0.123950i
\(741\) 0 0
\(742\) 1.29683e11 + 2.24618e11i 0.427827 + 0.741017i
\(743\) −2.86386e11 + 1.65345e11i −0.939715 + 0.542545i −0.889871 0.456212i \(-0.849206\pi\)
−0.0498441 + 0.998757i \(0.515872\pi\)
\(744\) 0 0
\(745\) 9.19590e10 1.59278e11i 0.298517 0.517046i
\(746\) 5.47918e11i 1.76913i
\(747\) 0 0
\(748\) 1.29262e11 0.412918
\(749\) −3.41816e10 1.97347e10i −0.108609 0.0627053i
\(750\) 0 0
\(751\) 2.38989e11 + 4.13941e11i 0.751308 + 1.30130i 0.947189 + 0.320676i \(0.103910\pi\)
−0.195881 + 0.980628i \(0.562757\pi\)
\(752\) 2.38635e11 1.37776e11i 0.746213 0.430826i
\(753\) 0 0
\(754\) 1.33116e11 2.30563e11i 0.411855 0.713353i
\(755\) 9.51565e10i 0.292854i
\(756\) 0 0
\(757\) −8.95066e10 −0.272566 −0.136283 0.990670i \(-0.543516\pi\)
−0.136283 + 0.990670i \(0.543516\pi\)
\(758\) 3.85719e11 + 2.22695e11i 1.16841 + 0.674580i
\(759\) 0 0
\(760\) −3.81790e8 6.61280e8i −0.00114438 0.00198212i
\(761\) 4.94910e11 2.85737e11i 1.47567 0.851976i 0.476042 0.879422i \(-0.342071\pi\)
0.999623 + 0.0274462i \(0.00873751\pi\)
\(762\) 0 0
\(763\) −9.62282e10 + 1.66672e11i −0.283925 + 0.491773i
\(764\) 4.01231e10i 0.117766i
\(765\) 0 0
\(766\) 3.39292e11 0.985504
\(767\) −3.05607e11 1.76442e11i −0.883042 0.509825i
\(768\) 0 0
\(769\) −1.28097e11 2.21871e11i −0.366298 0.634447i 0.622686 0.782472i \(-0.286042\pi\)
−0.988984 + 0.148026i \(0.952708\pi\)
\(770\)