# 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

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: $$x^{4} - 14x^{2} + 196$$ x^4 - 14*x^2 + 196 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)

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

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −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 $$0.952708\pi$$
$$770$$