# Properties

 Label 162.11.d.d.53.1 Level $162$ Weight $11$ Character 162.53 Analytic conductor $102.928$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$11$$ Character orbit: $$[\chi]$$ $$=$$ 162.d (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$102.927874933$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.17318914560000.97 Defining polynomial: $$x^{8} - 4x^{7} - 82x^{6} + 260x^{5} + 2477x^{4} - 5392x^{3} - 31616x^{2} + 34356x + 161859$$ x^8 - 4*x^7 - 82*x^6 + 260*x^5 + 2477*x^4 - 5392*x^3 - 31616*x^2 + 34356*x + 161859 Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$2^{24}\cdot 3^{16}$$ Twist minimal: no (minimal twist has level 6) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 53.1 Root $$-5.33452 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 162.53 Dual form 162.11.d.d.107.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-19.5959 + 11.3137i) q^{2} +(256.000 - 443.405i) q^{4} +(-3144.08 - 1815.24i) q^{5} +(11613.3 + 20114.8i) q^{7} +11585.2i q^{8} +O(q^{10})$$ $$q+(-19.5959 + 11.3137i) q^{2} +(256.000 - 443.405i) q^{4} +(-3144.08 - 1815.24i) q^{5} +(11613.3 + 20114.8i) q^{7} +11585.2i q^{8} +82148.2 q^{10} +(-54076.9 + 31221.3i) q^{11} +(85080.3 - 147363. i) q^{13} +(-455145. - 262778. i) q^{14} +(-131072. - 227023. i) q^{16} +2.66626e6i q^{17} +766825. q^{19} +(-1.60977e6 + 929401. i) q^{20} +(706458. - 1.22362e6i) q^{22} +(1.21526e6 + 701633. i) q^{23} +(1.70736e6 + 2.95723e6i) q^{25} +3.85029e6i q^{26} +1.18920e7 q^{28} +(-4.18503e6 + 2.41623e6i) q^{29} +(2.09149e7 - 3.62256e7i) q^{31} +(5.13695e6 + 2.96582e6i) q^{32} +(-3.01653e7 - 5.22478e7i) q^{34} -8.43233e7i q^{35} +5.01619e7 q^{37} +(-1.50266e7 + 8.67564e6i) q^{38} +(2.10299e7 - 3.64249e7i) q^{40} +(-1.29245e8 - 7.46194e7i) q^{41} +(9.93595e7 + 1.72096e8i) q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} +(1.34285e8 - 7.75293e7i) q^{47} +(-1.28498e8 + 2.22565e8i) q^{49} +(-6.69144e7 - 3.86331e7i) q^{50} +(-4.35611e7 - 7.54501e7i) q^{52} -4.21541e7i q^{53} +2.26696e8 q^{55} +(-2.33034e8 + 1.34542e8i) q^{56} +(5.46730e7 - 9.46964e7i) q^{58} +(2.52902e8 + 1.46013e8i) q^{59} +(2.65363e8 + 4.59623e8i) q^{61} +9.46499e8i q^{62} -1.34218e8 q^{64} +(-5.34999e8 + 3.08882e8i) q^{65} +(-2.61047e8 + 4.52146e8i) q^{67} +(1.18223e9 + 6.82563e8i) q^{68} +(9.54009e8 + 1.65239e9i) q^{70} -5.71364e8i q^{71} +2.18588e9 q^{73} +(-9.82968e8 + 5.67517e8i) q^{74} +(1.96307e8 - 3.40014e8i) q^{76} +(-1.25602e9 - 7.25163e8i) q^{77} +(-9.82961e8 - 1.70254e9i) q^{79} +9.51707e8i q^{80} +3.37689e9 q^{82} +(1.89277e9 - 1.09279e9i) q^{83} +(4.83989e9 - 8.38294e9i) q^{85} +(-3.89408e9 - 2.24825e9i) q^{86} +(-3.61707e8 - 6.26494e8i) q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} +(6.22215e8 - 3.59236e8i) q^{92} +(-1.75429e9 + 3.03852e9i) q^{94} +(-2.41096e9 - 1.39197e9i) q^{95} +(4.42056e9 + 7.65664e9i) q^{97} -5.81517e9i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 2048 q^{4} + 45112 q^{7}+O(q^{10})$$ 8 * q + 2048 * q^4 + 45112 * q^7 $$8 q + 2048 q^{4} + 45112 q^{7} - 107520 q^{10} - 275240 q^{13} - 1048576 q^{16} - 3137456 q^{19} - 7730688 q^{22} + 33732380 q^{25} + 46194688 q^{28} + 21785848 q^{31} - 151087104 q^{34} - 142028336 q^{37} - 27525120 q^{40} + 470688664 q^{43} + 377628672 q^{46} + 50058420 q^{49} + 140922880 q^{52} + 5402718720 q^{55} + 1564177920 q^{58} + 1184038744 q^{61} - 1073741824 q^{64} + 297365848 q^{67} + 3962250240 q^{70} + 13068538000 q^{73} - 803188736 q^{76} - 199282568 q^{79} + 16757336064 q^{82} + 12880512000 q^{85} + 3958112256 q^{88} + 16634464160 q^{91} - 8505477120 q^{94} + 39176355064 q^{97}+O(q^{100})$$ 8 * q + 2048 * q^4 + 45112 * q^7 - 107520 * q^10 - 275240 * q^13 - 1048576 * q^16 - 3137456 * q^19 - 7730688 * q^22 + 33732380 * q^25 + 46194688 * q^28 + 21785848 * q^31 - 151087104 * q^34 - 142028336 * q^37 - 27525120 * q^40 + 470688664 * q^43 + 377628672 * q^46 + 50058420 * q^49 + 140922880 * q^52 + 5402718720 * q^55 + 1564177920 * q^58 + 1184038744 * q^61 - 1073741824 * q^64 + 297365848 * q^67 + 3962250240 * q^70 + 13068538000 * q^73 - 803188736 * q^76 - 199282568 * q^79 + 16757336064 * q^82 + 12880512000 * q^85 + 3958112256 * q^88 + 16634464160 * q^91 - 8505477120 * q^94 + 39176355064 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$$.

 $$n$$ $$83$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −19.5959 + 11.3137i −0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 256.000 443.405i 0.250000 0.433013i
$$5$$ −3144.08 1815.24i −1.00611 0.580876i −0.0960570 0.995376i $$-0.530623\pi$$
−0.910049 + 0.414500i $$0.863956\pi$$
$$6$$ 0 0
$$7$$ 11613.3 + 20114.8i 0.690978 + 1.19681i 0.971518 + 0.236966i $$0.0761531\pi$$
−0.280540 + 0.959842i $$0.590514\pi$$
$$8$$ 11585.2i 0.353553i
$$9$$ 0 0
$$10$$ 82148.2 0.821482
$$11$$ −54076.9 + 31221.3i −0.335775 + 0.193860i −0.658402 0.752666i $$-0.728767\pi$$
0.322627 + 0.946526i $$0.395434\pi$$
$$12$$ 0 0
$$13$$ 85080.3 147363.i 0.229146 0.396892i −0.728409 0.685142i $$-0.759740\pi$$
0.957555 + 0.288250i $$0.0930734\pi$$
$$14$$ −455145. 262778.i −0.846272 0.488595i
$$15$$ 0 0
$$16$$ −131072. 227023.i −0.125000 0.216506i
$$17$$ 2.66626e6i 1.87784i 0.344139 + 0.938919i $$0.388171\pi$$
−0.344139 + 0.938919i $$0.611829\pi$$
$$18$$ 0 0
$$19$$ 766825. 0.309691 0.154845 0.987939i $$-0.450512\pi$$
0.154845 + 0.987939i $$0.450512\pi$$
$$20$$ −1.60977e6 + 929401.i −0.503053 + 0.290438i
$$21$$ 0 0
$$22$$ 706458. 1.22362e6i 0.137080 0.237429i
$$23$$ 1.21526e6 + 701633.i 0.188813 + 0.109011i 0.591427 0.806359i $$-0.298565\pi$$
−0.402614 + 0.915370i $$0.631898\pi$$
$$24$$ 0 0
$$25$$ 1.70736e6 + 2.95723e6i 0.174833 + 0.302820i
$$26$$ 3.85029e6i 0.324061i
$$27$$ 0 0
$$28$$ 1.18920e7 0.690978
$$29$$ −4.18503e6 + 2.41623e6i −0.204037 + 0.117801i −0.598537 0.801095i $$-0.704251\pi$$
0.394500 + 0.918896i $$0.370918\pi$$
$$30$$ 0 0
$$31$$ 2.09149e7 3.62256e7i 0.730544 1.26534i −0.226106 0.974103i $$-0.572600\pi$$
0.956651 0.291237i $$-0.0940670\pi$$
$$32$$ 5.13695e6 + 2.96582e6i 0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ −3.01653e7 5.22478e7i −0.663916 1.14994i
$$35$$ 8.43233e7i 1.60549i
$$36$$ 0 0
$$37$$ 5.01619e7 0.723378 0.361689 0.932299i $$-0.382200\pi$$
0.361689 + 0.932299i $$0.382200\pi$$
$$38$$ −1.50266e7 + 8.67564e6i −0.189646 + 0.109492i
$$39$$ 0 0
$$40$$ 2.10299e7 3.64249e7i 0.205371 0.355712i
$$41$$ −1.29245e8 7.46194e7i −1.11556 0.644069i −0.175296 0.984516i $$-0.556088\pi$$
−0.940264 + 0.340447i $$0.889422\pi$$
$$42$$ 0 0
$$43$$ 9.93595e7 + 1.72096e8i 0.675876 + 1.17065i 0.976212 + 0.216818i $$0.0695680\pi$$
−0.300336 + 0.953834i $$0.597099\pi$$
$$44$$ 3.19706e7i 0.193860i
$$45$$ 0 0
$$46$$ −3.17523e7 −0.154165
$$47$$ 1.34285e8 7.75293e7i 0.585514 0.338047i −0.177808 0.984065i $$-0.556901\pi$$
0.763322 + 0.646019i $$0.223567\pi$$
$$48$$ 0 0
$$49$$ −1.28498e8 + 2.22565e8i −0.454901 + 0.787911i
$$50$$ −6.69144e7 3.86331e7i −0.214126 0.123626i
$$51$$ 0 0
$$52$$ −4.35611e7 7.54501e7i −0.114573 0.198446i
$$53$$ 4.21541e7i 0.100800i −0.998729 0.0503999i $$-0.983950\pi$$
0.998729 0.0503999i $$-0.0160496\pi$$
$$54$$ 0 0
$$55$$ 2.26696e8 0.450434
$$56$$ −2.33034e8 + 1.34542e8i −0.423136 + 0.244298i
$$57$$ 0 0
$$58$$ 5.46730e7 9.46964e7i 0.0832976 0.144276i
$$59$$ 2.52902e8 + 1.46013e8i 0.353746 + 0.204236i 0.666334 0.745653i $$-0.267862\pi$$
−0.312588 + 0.949889i $$0.601196\pi$$
$$60$$ 0 0
$$61$$ 2.65363e8 + 4.59623e8i 0.314190 + 0.544192i 0.979265 0.202584i $$-0.0649339\pi$$
−0.665075 + 0.746776i $$0.731601\pi$$
$$62$$ 9.46499e8i 1.03315i
$$63$$ 0 0
$$64$$ −1.34218e8 −0.125000
$$65$$ −5.34999e8 + 3.08882e8i −0.461090 + 0.266211i
$$66$$ 0 0
$$67$$ −2.61047e8 + 4.52146e8i −0.193350 + 0.334892i −0.946358 0.323119i $$-0.895269\pi$$
0.753008 + 0.658011i $$0.228602\pi$$
$$68$$ 1.18223e9 + 6.82563e8i 0.813128 + 0.469459i
$$69$$ 0 0
$$70$$ 9.54009e8 + 1.65239e9i 0.567626 + 0.983157i
$$71$$ 5.71364e8i 0.316681i −0.987385 0.158340i $$-0.949386\pi$$
0.987385 0.158340i $$-0.0506143\pi$$
$$72$$ 0 0
$$73$$ 2.18588e9 1.05441 0.527207 0.849737i $$-0.323239\pi$$
0.527207 + 0.849737i $$0.323239\pi$$
$$74$$ −9.82968e8 + 5.67517e8i −0.442977 + 0.255753i
$$75$$ 0 0
$$76$$ 1.96307e8 3.40014e8i 0.0774227 0.134100i
$$77$$ −1.25602e9 7.25163e8i −0.464026 0.267906i
$$78$$ 0 0
$$79$$ −9.82961e8 1.70254e9i −0.319449 0.553301i 0.660924 0.750452i $$-0.270164\pi$$
−0.980373 + 0.197151i $$0.936831\pi$$
$$80$$ 9.51707e8i 0.290438i
$$81$$ 0 0
$$82$$ 3.37689e9 0.910851
$$83$$ 1.89277e9 1.09279e9i 0.480514 0.277425i −0.240116 0.970744i $$-0.577186\pi$$
0.720631 + 0.693319i $$0.243852\pi$$
$$84$$ 0 0
$$85$$ 4.83989e9 8.38294e9i 1.09079 1.88930i
$$86$$ −3.89408e9 2.24825e9i −0.827776 0.477917i
$$87$$ 0 0
$$88$$ −3.61707e8 6.26494e8i −0.0685398 0.118714i
$$89$$ 2.38742e8i 0.0427542i 0.999771 + 0.0213771i $$0.00680506\pi$$
−0.999771 + 0.0213771i $$0.993195\pi$$
$$90$$ 0 0
$$91$$ 3.95224e9 0.633339
$$92$$ 6.22215e8 3.59236e8i 0.0944064 0.0545056i
$$93$$ 0 0
$$94$$ −1.75429e9 + 3.03852e9i −0.239035 + 0.414021i
$$95$$ −2.41096e9 1.39197e9i −0.311582 0.179892i
$$96$$ 0 0
$$97$$ 4.42056e9 + 7.65664e9i 0.514776 + 0.891619i 0.999853 + 0.0171473i $$0.00545843\pi$$
−0.485076 + 0.874472i $$0.661208\pi$$
$$98$$ 5.81517e9i 0.643327i
$$99$$ 0 0
$$100$$ 1.74833e9 0.174833
$$101$$ −1.45430e10 + 8.39641e9i −1.38372 + 0.798890i −0.992598 0.121450i $$-0.961246\pi$$
−0.391120 + 0.920340i $$0.627912\pi$$
$$102$$ 0 0
$$103$$ −4.18432e9 + 7.24746e9i −0.360944 + 0.625173i −0.988116 0.153708i $$-0.950879\pi$$
0.627173 + 0.778880i $$0.284212\pi$$
$$104$$ 1.70724e9 + 9.85675e8i 0.140323 + 0.0810153i
$$105$$ 0 0
$$106$$ 4.76919e8 + 8.26048e8i 0.0356381 + 0.0617271i
$$107$$ 1.43555e10i 1.02353i 0.859126 + 0.511764i $$0.171008\pi$$
−0.859126 + 0.511764i $$0.828992\pi$$
$$108$$ 0 0
$$109$$ −4.72564e9 −0.307134 −0.153567 0.988138i $$-0.549076\pi$$
−0.153567 + 0.988138i $$0.549076\pi$$
$$110$$ −4.44233e9 + 2.56478e9i −0.275833 + 0.159253i
$$111$$ 0 0
$$112$$ 3.04435e9 5.27296e9i 0.172744 0.299202i
$$113$$ −1.14452e10 6.60792e9i −0.621202 0.358651i 0.156135 0.987736i $$-0.450097\pi$$
−0.777337 + 0.629084i $$0.783430\pi$$
$$114$$ 0 0
$$115$$ −2.54726e9 4.41199e9i −0.126644 0.219354i
$$116$$ 2.47422e9i 0.117801i
$$117$$ 0 0
$$118$$ −6.60779e9 −0.288833
$$119$$ −5.36312e10 + 3.09640e10i −2.24741 + 1.29754i
$$120$$ 0 0
$$121$$ −1.10192e10 + 1.90858e10i −0.424837 + 0.735839i
$$122$$ −1.04001e10 6.00449e9i −0.384802 0.222166i
$$123$$ 0 0
$$124$$ −1.07084e10 1.85475e10i −0.365272 0.632670i
$$125$$ 2.30568e10i 0.755526i
$$126$$ 0 0
$$127$$ −3.17814e10 −0.961953 −0.480976 0.876733i $$-0.659718\pi$$
−0.480976 + 0.876733i $$0.659718\pi$$
$$128$$ 2.63012e9 1.51850e9i 0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ 6.98920e9 1.21056e10i 0.188239 0.326040i
$$131$$ −4.33960e10 2.50547e10i −1.12485 0.649430i −0.182213 0.983259i $$-0.558326\pi$$
−0.942634 + 0.333829i $$0.891659\pi$$
$$132$$ 0 0
$$133$$ 8.90535e9 + 1.54245e10i 0.213990 + 0.370641i
$$134$$ 1.18136e10i 0.273438i
$$135$$ 0 0
$$136$$ −3.08893e10 −0.663916
$$137$$ 2.37935e10 1.37372e10i 0.493010 0.284639i −0.232812 0.972522i $$-0.574793\pi$$
0.725822 + 0.687882i $$0.241460\pi$$
$$138$$ 0 0
$$139$$ −3.16244e10 + 5.47751e10i −0.609464 + 1.05562i 0.381865 + 0.924218i $$0.375282\pi$$
−0.991329 + 0.131405i $$0.958051\pi$$
$$140$$ −3.73894e10 2.15868e10i −0.695197 0.401372i
$$141$$ 0 0
$$142$$ 6.46425e9 + 1.11964e10i 0.111963 + 0.193926i
$$143$$ 1.06253e10i 0.177689i
$$144$$ 0 0
$$145$$ 1.75441e10 0.273710
$$146$$ −4.28342e10 + 2.47304e10i −0.645694 + 0.372792i
$$147$$ 0 0
$$148$$ 1.28414e10 2.22420e10i 0.180845 0.313232i
$$149$$ 2.93131e10 + 1.69239e10i 0.399145 + 0.230446i 0.686115 0.727493i $$-0.259315\pi$$
−0.286970 + 0.957940i $$0.592648\pi$$
$$150$$ 0 0
$$151$$ −6.11931e10 1.05990e11i −0.779503 1.35014i −0.932229 0.361870i $$-0.882139\pi$$
0.152726 0.988269i $$-0.451195\pi$$
$$152$$ 8.88385e9i 0.109492i
$$153$$ 0 0
$$154$$ 3.28171e10 0.378876
$$155$$ −1.31516e11 + 7.59309e10i −1.47001 + 0.848711i
$$156$$ 0 0
$$157$$ 7.94857e10 1.37673e11i 0.833279 1.44328i −0.0621448 0.998067i $$-0.519794\pi$$
0.895424 0.445215i $$-0.146873\pi$$
$$158$$ 3.85241e10 + 2.22419e10i 0.391243 + 0.225884i
$$159$$ 0 0
$$160$$ −1.07673e10 1.86496e10i −0.102685 0.177856i
$$161$$ 3.25930e10i 0.301297i
$$162$$ 0 0
$$163$$ −9.20831e10 −0.800280 −0.400140 0.916454i $$-0.631038\pi$$
−0.400140 + 0.916454i $$0.631038\pi$$
$$164$$ −6.61732e10 + 3.82051e10i −0.557780 + 0.322034i
$$165$$ 0 0
$$166$$ −2.47270e10 + 4.28284e10i −0.196169 + 0.339775i
$$167$$ −1.83958e11 1.06208e11i −1.41623 0.817663i −0.420269 0.907400i $$-0.638064\pi$$
−0.995966 + 0.0897362i $$0.971398\pi$$
$$168$$ 0 0
$$169$$ 5.44519e10 + 9.43135e10i 0.394984 + 0.684133i
$$170$$ 2.19029e11i 1.54261i
$$171$$ 0 0
$$172$$ 1.01744e11 0.675876
$$173$$ −2.63386e11 + 1.52066e11i −1.69966 + 0.981300i −0.753590 + 0.657345i $$0.771680\pi$$
−0.946072 + 0.323956i $$0.894987\pi$$
$$174$$ 0 0
$$175$$ −3.96560e10 + 6.86861e10i −0.241612 + 0.418484i
$$176$$ 1.41759e10 + 8.18449e9i 0.0839438 + 0.0484650i
$$177$$ 0 0
$$178$$ −2.70106e9 4.67837e9i −0.0151159 0.0261815i
$$179$$ 7.07114e9i 0.0384791i −0.999815 0.0192395i $$-0.993875\pi$$
0.999815 0.0192395i $$-0.00612451\pi$$
$$180$$ 0 0
$$181$$ −1.27309e11 −0.655337 −0.327669 0.944793i $$-0.606263\pi$$
−0.327669 + 0.944793i $$0.606263\pi$$
$$182$$ −7.74478e10 + 4.47145e10i −0.387839 + 0.223919i
$$183$$ 0 0
$$184$$ −8.12859e9 + 1.40791e10i −0.0385413 + 0.0667554i
$$185$$ −1.57713e11 9.10557e10i −0.727795 0.420193i
$$186$$ 0 0
$$187$$ −8.32442e10 1.44183e11i −0.364037 0.630531i
$$188$$ 7.93900e10i 0.338047i
$$189$$ 0 0
$$190$$ 6.29934e10 0.254406
$$191$$ 1.78799e11 1.03230e11i 0.703394 0.406105i −0.105216 0.994449i $$-0.533553\pi$$
0.808610 + 0.588345i $$0.200220\pi$$
$$192$$ 0 0
$$193$$ −1.55803e11 + 2.69859e11i −0.581821 + 1.00774i 0.413442 + 0.910530i $$0.364326\pi$$
−0.995264 + 0.0972136i $$0.969007\pi$$
$$194$$ −1.73250e11 1.00026e11i −0.630470 0.364002i
$$195$$ 0 0
$$196$$ 6.57911e10 + 1.13954e11i 0.227450 + 0.393956i
$$197$$ 1.51694e11i 0.511255i 0.966775 + 0.255628i $$0.0822821\pi$$
−0.966775 + 0.255628i $$0.917718\pi$$
$$198$$ 0 0
$$199$$ −1.11692e11 −0.357895 −0.178947 0.983859i $$-0.557269\pi$$
−0.178947 + 0.983859i $$0.557269\pi$$
$$200$$ −3.42602e10 + 1.97801e10i −0.107063 + 0.0618129i
$$201$$ 0 0
$$202$$ 1.89989e11 3.29071e11i 0.564901 0.978436i
$$203$$ −9.72037e10 5.61206e10i −0.281970 0.162795i
$$204$$ 0 0
$$205$$ 2.70904e11 + 4.69219e11i 0.748248 + 1.29600i
$$206$$ 1.89361e11i 0.510451i
$$207$$ 0 0
$$208$$ −4.46066e10 −0.114573
$$209$$ −4.14676e10 + 2.39413e10i −0.103987 + 0.0600367i
$$210$$ 0 0
$$211$$ −7.65329e10 + 1.32559e11i −0.182994 + 0.316954i −0.942899 0.333080i $$-0.891912\pi$$
0.759905 + 0.650034i $$0.225245\pi$$
$$212$$ −1.86913e10 1.07914e10i −0.0436476 0.0252000i
$$213$$ 0 0
$$214$$ −1.62414e11 2.81310e11i −0.361872 0.626781i
$$215$$ 7.21444e11i 1.57040i
$$216$$ 0 0
$$217$$ 9.71560e11 2.01916
$$218$$ 9.26033e10 5.34645e10i 0.188081 0.108588i
$$219$$ 0 0
$$220$$ 5.80343e10 1.00518e11i 0.112609 0.195044i
$$221$$ 3.92909e11 + 2.26846e11i 0.745300 + 0.430299i
$$222$$ 0 0
$$223$$ 3.02880e11 + 5.24603e11i 0.549219 + 0.951276i 0.998328 + 0.0577987i $$0.0184082\pi$$
−0.449109 + 0.893477i $$0.648259\pi$$
$$224$$ 1.37771e11i 0.244298i
$$225$$ 0 0
$$226$$ 2.99040e11 0.507210
$$227$$ −5.80746e11 + 3.35294e11i −0.963512 + 0.556284i −0.897252 0.441519i $$-0.854440\pi$$
−0.0662598 + 0.997802i $$0.521107\pi$$
$$228$$ 0 0
$$229$$ −1.76678e11 + 3.06015e11i −0.280547 + 0.485921i −0.971520 0.236960i $$-0.923849\pi$$
0.690973 + 0.722881i $$0.257182\pi$$
$$230$$ 9.98318e10 + 5.76379e10i 0.155106 + 0.0895508i
$$231$$ 0 0
$$232$$ −2.79926e10 4.84845e10i −0.0416488 0.0721379i
$$233$$ 1.12390e12i 1.63662i 0.574779 + 0.818309i $$0.305088\pi$$
−0.574779 + 0.818309i $$0.694912\pi$$
$$234$$ 0 0
$$235$$ −5.62936e11 −0.785452
$$236$$ 1.29486e11 7.47586e10i 0.176873 0.102118i
$$237$$ 0 0
$$238$$ 7.00635e11 1.21354e12i 0.917502 1.58916i
$$239$$ −2.29153e11 1.32302e11i −0.293857 0.169658i 0.345823 0.938300i $$-0.387600\pi$$
−0.639680 + 0.768641i $$0.720933\pi$$
$$240$$ 0 0
$$241$$ −4.43384e11 7.67964e11i −0.545375 0.944617i −0.998583 0.0532121i $$-0.983054\pi$$
0.453209 0.891404i $$-0.350279\pi$$
$$242$$ 4.98671e11i 0.600810i
$$243$$ 0 0
$$244$$ 2.71732e11 0.314190
$$245$$ 8.08018e11 4.66509e11i 0.915357 0.528482i
$$246$$ 0 0
$$247$$ 6.52417e10 1.13002e11i 0.0709644 0.122914i
$$248$$ 4.19682e11 + 2.42304e11i 0.447365 + 0.258286i
$$249$$ 0 0
$$250$$ −2.60858e11 4.51820e11i −0.267119 0.462663i
$$251$$ 8.59494e11i 0.862729i 0.902178 + 0.431364i $$0.141968\pi$$
−0.902178 + 0.431364i $$0.858032\pi$$
$$252$$ 0 0
$$253$$ −8.76237e10 −0.0845316
$$254$$ 6.22785e11 3.59565e11i 0.589073 0.340102i
$$255$$ 0 0
$$256$$ −3.43597e10 + 5.95128e10i −0.0312500 + 0.0541266i
$$257$$ 1.88707e12 + 1.08950e12i 1.68315 + 0.971764i 0.959549 + 0.281540i $$0.0908453\pi$$
0.723596 + 0.690224i $$0.242488\pi$$
$$258$$ 0 0
$$259$$ 5.82543e11 + 1.00899e12i 0.499838 + 0.865745i
$$260$$ 3.16295e11i 0.266211i
$$261$$ 0 0
$$262$$ 1.13385e12 0.918433
$$263$$ 1.19461e12 6.89708e11i 0.949395 0.548134i 0.0565021 0.998402i $$-0.482005\pi$$
0.892893 + 0.450269i $$0.148672\pi$$
$$264$$ 0 0
$$265$$ −7.65196e10 + 1.32536e11i −0.0585522 + 0.101415i
$$266$$ −3.49017e11 2.01505e11i −0.262083 0.151313i
$$267$$ 0 0
$$268$$ 1.33656e11 + 2.31499e11i 0.0966750 + 0.167446i
$$269$$ 1.18129e12i 0.838680i −0.907829 0.419340i $$-0.862262\pi$$
0.907829 0.419340i $$-0.137738\pi$$
$$270$$ 0 0
$$271$$ −1.42251e12 −0.973213 −0.486606 0.873621i $$-0.661765\pi$$
−0.486606 + 0.873621i $$0.661765\pi$$
$$272$$ 6.05304e11 3.49472e11i 0.406564 0.234730i
$$273$$ 0 0
$$274$$ −3.10837e11 + 5.38385e11i −0.201270 + 0.348611i
$$275$$ −1.84657e11 1.06612e11i −0.117409 0.0677863i
$$276$$ 0 0
$$277$$ −2.64980e11 4.58959e11i −0.162485 0.281433i 0.773274 0.634072i $$-0.218618\pi$$
−0.935759 + 0.352639i $$0.885284\pi$$
$$278$$ 1.43116e12i 0.861913i
$$279$$ 0 0
$$280$$ 9.76905e11 0.567626
$$281$$ 1.97835e12 1.14220e12i 1.12920 0.651946i 0.185469 0.982650i $$-0.440619\pi$$
0.943735 + 0.330704i $$0.107286\pi$$
$$282$$ 0 0
$$283$$ −1.15637e12 + 2.00289e12i −0.637038 + 1.10338i 0.349042 + 0.937107i $$0.386507\pi$$
−0.986079 + 0.166275i $$0.946826\pi$$
$$284$$ −2.53346e11 1.46269e11i −0.137127 0.0791701i
$$285$$ 0 0
$$286$$ −1.20211e11 2.08212e11i −0.0628225 0.108812i
$$287$$ 3.46630e12i 1.78015i
$$288$$ 0 0
$$289$$ −5.09295e12 −2.52627
$$290$$ −3.43793e11 + 1.98489e11i −0.167613 + 0.0967712i
$$291$$ 0 0
$$292$$ 5.59584e11 9.69228e11i 0.263604 0.456575i
$$293$$ 9.17894e11 + 5.29947e11i 0.425064 + 0.245411i 0.697242 0.716836i $$-0.254410\pi$$
−0.272177 + 0.962247i $$0.587744\pi$$
$$294$$ 0 0
$$295$$ −5.30096e11 9.18153e11i −0.237271 0.410965i
$$296$$ 5.81138e11i 0.255753i
$$297$$ 0 0
$$298$$ −7.65890e11 −0.325900
$$299$$ 2.06790e11 1.19390e11i 0.0865314 0.0499589i
$$300$$ 0 0
$$301$$ −2.30778e12 + 3.99719e12i −0.934031 + 1.61779i
$$302$$ 2.39827e12 + 1.38464e12i 0.954692 + 0.551192i
$$303$$ 0 0
$$304$$ −1.00509e11 1.74087e11i −0.0387114 0.0670501i
$$305$$ 1.92679e12i 0.730020i
$$306$$ 0 0
$$307$$ 6.89209e11 0.252731 0.126366 0.991984i $$-0.459669\pi$$
0.126366 + 0.991984i $$0.459669\pi$$
$$308$$ −6.43082e11 + 3.71284e11i −0.232013 + 0.133953i
$$309$$ 0 0
$$310$$ 1.71812e12 2.97587e12i 0.600129 1.03945i
$$311$$ −1.69458e12 9.78369e11i −0.582454 0.336280i 0.179654 0.983730i $$-0.442502\pi$$
−0.762108 + 0.647450i $$0.775835\pi$$
$$312$$ 0 0
$$313$$ 1.24410e11 + 2.15485e11i 0.0414128 + 0.0717291i 0.885989 0.463707i $$-0.153481\pi$$
−0.844576 + 0.535436i $$0.820147\pi$$
$$314$$ 3.59711e12i 1.17843i
$$315$$ 0 0
$$316$$ −1.00655e12 −0.319449
$$317$$ 4.01555e12 2.31838e12i 1.25444 0.724249i 0.282448 0.959283i $$-0.408853\pi$$
0.971987 + 0.235034i $$0.0755201\pi$$
$$318$$ 0 0
$$319$$ 1.50876e11 2.61324e11i 0.0456737 0.0791091i
$$320$$ 4.21992e11 + 2.43637e11i 0.125763 + 0.0726095i
$$321$$ 0 0
$$322$$ −3.68748e11 6.38690e11i −0.106525 0.184506i
$$323$$ 2.04456e12i 0.581549i
$$324$$ 0 0
$$325$$ 5.81050e11 0.160249
$$326$$ 1.80445e12 1.04180e12i 0.490069 0.282942i
$$327$$ 0 0
$$328$$ 8.64483e11 1.49733e12i 0.227713 0.394410i
$$329$$ 3.11897e12 + 1.80074e12i 0.809154 + 0.467165i
$$330$$ 0 0
$$331$$ 7.07216e11 + 1.22493e12i 0.177997 + 0.308300i 0.941194 0.337866i $$-0.109705\pi$$
−0.763197 + 0.646165i $$0.776372\pi$$
$$332$$ 1.11902e12i 0.277425i
$$333$$ 0 0
$$334$$ 4.80642e12 1.15635
$$335$$ 1.64150e12 9.47723e11i 0.389061 0.224625i
$$336$$ 0 0
$$337$$ −4.33878e11 + 7.51498e11i −0.0998201 + 0.172893i −0.911610 0.411056i $$-0.865160\pi$$
0.811790 + 0.583949i $$0.198493\pi$$
$$338$$ −2.13407e12 1.23211e12i −0.483755 0.279296i
$$339$$ 0 0
$$340$$ −2.47803e12 4.29207e12i −0.545395 0.944652i
$$341$$ 2.61196e12i 0.566493i
$$342$$ 0 0
$$343$$ 5.91785e11 0.124650
$$344$$ −1.99377e12 + 1.15110e12i −0.413888 + 0.238958i
$$345$$ 0 0
$$346$$ 3.44086e12 5.95975e12i 0.693884 1.20184i
$$347$$ 4.50950e12 + 2.60356e12i 0.896357 + 0.517512i 0.876017 0.482281i $$-0.160192\pi$$
0.0203407 + 0.999793i $$0.493525\pi$$
$$348$$ 0 0
$$349$$ −5.59765e11 9.69541e11i −0.108113 0.187257i 0.806893 0.590698i $$-0.201148\pi$$
−0.915006 + 0.403441i $$0.867814\pi$$
$$350$$ 1.79462e12i 0.341691i
$$351$$ 0 0
$$352$$ −3.70388e11 −0.0685398
$$353$$ −3.23852e12 + 1.86976e12i −0.590844 + 0.341124i −0.765431 0.643518i $$-0.777474\pi$$
0.174587 + 0.984642i $$0.444141\pi$$
$$354$$ 0 0
$$355$$ −1.03716e12 + 1.79642e12i −0.183952 + 0.318614i
$$356$$ 1.05859e11 + 6.11180e10i 0.0185131 + 0.0106886i
$$357$$ 0 0
$$358$$ 8.00009e10 + 1.38566e11i 0.0136044 + 0.0235635i
$$359$$ 3.54489e12i 0.594471i −0.954804 0.297235i $$-0.903935\pi$$
0.954804 0.297235i $$-0.0960646\pi$$
$$360$$ 0 0
$$361$$ −5.54305e12 −0.904092
$$362$$ 2.49473e12 1.44033e12i 0.401310 0.231697i
$$363$$ 0 0
$$364$$ 1.01177e12 1.75244e12i 0.158335 0.274244i
$$365$$ −6.87257e12 3.96788e12i −1.06085 0.612484i
$$366$$ 0 0
$$367$$ 5.05807e12 + 8.76083e12i 0.759722 + 1.31588i 0.942992 + 0.332814i $$0.107998\pi$$
−0.183271 + 0.983062i $$0.558669\pi$$
$$368$$ 3.67858e11i 0.0545056i
$$369$$ 0 0
$$370$$ 4.12071e12 0.594242
$$371$$ 8.47919e11 4.89546e11i 0.120638 0.0696505i
$$372$$ 0 0
$$373$$ −1.90528e12 + 3.30004e12i −0.263885 + 0.457062i −0.967271 0.253746i $$-0.918337\pi$$
0.703386 + 0.710808i $$0.251670\pi$$
$$374$$ 3.26249e12 + 1.88360e12i 0.445853 + 0.257413i
$$375$$ 0 0
$$376$$ 8.98195e11 + 1.55572e12i 0.119518 + 0.207010i
$$377$$ 8.22293e11i 0.107974i
$$378$$ 0 0
$$379$$ 1.11052e13 1.42014 0.710069 0.704132i $$-0.248664\pi$$
0.710069 + 0.704132i $$0.248664\pi$$
$$380$$ −1.23441e12 + 7.12688e11i −0.155791 + 0.0899460i
$$381$$ 0 0
$$382$$ −2.33582e12 + 4.04576e12i −0.287159 + 0.497375i
$$383$$ 3.71671e12 + 2.14585e12i 0.450988 + 0.260378i 0.708247 0.705964i $$-0.249486\pi$$
−0.257259 + 0.966342i $$0.582819\pi$$
$$384$$ 0 0
$$385$$ 2.63269e12 + 4.55995e12i 0.311240 + 0.539083i
$$386$$ 7.05084e12i 0.822820i
$$387$$ 0 0
$$388$$ 4.52665e12 0.514776
$$389$$ −1.30384e13 + 7.52771e12i −1.46378 + 0.845113i −0.999183 0.0404106i $$-0.987133\pi$$
−0.464595 + 0.885523i $$0.653800\pi$$
$$390$$ 0 0
$$391$$ −1.87074e12 + 3.24021e12i −0.204705 + 0.354560i
$$392$$ −2.57847e12 1.48868e12i −0.278569 0.160832i
$$393$$ 0 0
$$394$$ −1.71622e12 2.97259e12i −0.180756 0.313079i
$$395$$ 7.13723e12i 0.742240i
$$396$$ 0 0
$$397$$ −1.11669e13 −1.13235 −0.566174 0.824286i $$-0.691577\pi$$
−0.566174 + 0.824286i $$0.691577\pi$$
$$398$$ 2.18870e12 1.26365e12i 0.219165 0.126535i
$$399$$ 0 0
$$400$$ 4.47573e11 7.75220e11i 0.0437083 0.0757050i
$$401$$ −1.00186e13 5.78426e12i −0.966243 0.557861i −0.0681541 0.997675i $$-0.521711\pi$$
−0.898089 + 0.439814i $$0.855044\pi$$
$$402$$ 0 0
$$403$$ −3.55889e12 6.16417e12i −0.334803 0.579895i
$$404$$ 8.59793e12i 0.798890i
$$405$$ 0 0
$$406$$ 2.53973e12 0.230227
$$407$$ −2.71260e12 + 1.56612e12i −0.242892 + 0.140234i
$$408$$ 0 0
$$409$$ 5.37056e12 9.30209e12i 0.469249 0.812763i −0.530133 0.847914i $$-0.677858\pi$$
0.999382 + 0.0351516i $$0.0111914\pi$$
$$410$$ −1.06172e13 6.12985e12i −0.916413 0.529091i
$$411$$ 0 0
$$412$$ 2.14237e12 + 3.71070e12i 0.180472 + 0.312586i
$$413$$ 6.78275e12i 0.564489i
$$414$$ 0 0
$$415$$ −7.93468e12 −0.644598
$$416$$ 8.74107e11 5.04666e11i 0.0701613 0.0405077i
$$417$$ 0 0
$$418$$ 5.41730e11 9.38304e11i 0.0424523 0.0735296i
$$419$$ −7.63589e12 4.40859e12i −0.591275 0.341373i 0.174326 0.984688i $$-0.444225\pi$$
−0.765602 + 0.643315i $$0.777559\pi$$
$$420$$ 0 0
$$421$$ 2.84871e12 + 4.93410e12i 0.215396 + 0.373076i 0.953395 0.301725i $$-0.0975625\pi$$
−0.737999 + 0.674802i $$0.764229\pi$$
$$422$$ 3.46348e12i 0.258792i
$$423$$ 0 0
$$424$$ 4.88365e11 0.0356381
$$425$$ −7.88474e12 + 4.55226e12i −0.568647 + 0.328309i
$$426$$ 0 0
$$427$$ −6.16347e12 + 1.06754e13i −0.434196 + 0.752050i
$$428$$ 6.36531e12 + 3.67501e12i 0.443201 + 0.255882i
$$429$$ 0 0
$$430$$ 8.16221e12 + 1.41374e13i 0.555220 + 0.961670i
$$431$$ 1.80323e13i 1.21245i 0.795293 + 0.606226i $$0.207317\pi$$
−0.795293 + 0.606226i $$0.792683\pi$$
$$432$$ 0 0
$$433$$ 2.06339e13 1.35563 0.677816 0.735232i $$-0.262927\pi$$
0.677816 + 0.735232i $$0.262927\pi$$
$$434$$ −1.90386e13 + 1.09919e13i −1.23648 + 0.713881i
$$435$$ 0 0
$$436$$ −1.20976e12 + 2.09537e12i −0.0767836 + 0.132993i
$$437$$ 9.31896e11 + 5.38030e11i 0.0584736 + 0.0337598i
$$438$$ 0 0
$$439$$ −9.76567e12 1.69146e13i −0.598935 1.03739i −0.992979 0.118294i $$-0.962258\pi$$
0.394044 0.919092i $$-0.371076\pi$$
$$440$$ 2.62633e12i 0.159253i
$$441$$ 0 0
$$442$$ −1.02659e13 −0.608535
$$443$$ −2.57616e13 + 1.48735e13i −1.50992 + 0.871753i −0.509987 + 0.860182i $$0.670350\pi$$
−0.999933 + 0.0115703i $$0.996317\pi$$
$$444$$ 0 0
$$445$$ 4.33373e11 7.50625e11i 0.0248349 0.0430153i
$$446$$ −1.18704e13 6.85338e12i −0.672653 0.388357i
$$447$$ 0 0
$$448$$ −1.55871e12 2.69976e12i −0.0863722 0.149601i
$$449$$ 1.37505e13i 0.753509i −0.926313 0.376754i $$-0.877040\pi$$
0.926313 0.376754i $$-0.122960\pi$$
$$450$$ 0 0
$$451$$ 9.31887e12 0.499437
$$452$$ −5.85997e12 + 3.38325e12i −0.310601 + 0.179326i
$$453$$ 0 0
$$454$$ 7.58684e12 1.31408e13i 0.393352 0.681306i
$$455$$ −1.24262e13 7.17425e12i −0.637207 0.367891i
$$456$$ 0 0
$$457$$ −2.05112e11 3.55265e11i −0.0102899 0.0178226i 0.860835 0.508885i $$-0.169942\pi$$
−0.871124 + 0.491062i $$0.836609\pi$$
$$458$$ 7.99554e12i 0.396753i
$$459$$ 0 0
$$460$$ −2.60840e12 −0.126644
$$461$$ −1.82657e11 + 1.05457e11i −0.00877266 + 0.00506490i −0.504380 0.863482i $$-0.668279\pi$$
0.495607 + 0.868547i $$0.334946\pi$$
$$462$$ 0 0
$$463$$ 9.83688e12 1.70380e13i 0.462330 0.800779i −0.536746 0.843744i $$-0.680347\pi$$
0.999077 + 0.0429642i $$0.0136801\pi$$
$$464$$ 1.09708e12 + 6.33399e11i 0.0510092 + 0.0294502i
$$465$$ 0 0
$$466$$ −1.27155e13 2.20238e13i −0.578632 1.00222i
$$467$$ 1.21902e13i 0.548815i −0.961614 0.274407i $$-0.911518\pi$$
0.961614 0.274407i $$-0.0884817\pi$$
$$468$$ 0 0
$$469$$ −1.21264e13 −0.534402
$$470$$ 1.10312e13 6.36889e12i 0.480989 0.277699i
$$471$$ 0 0
$$472$$ −1.69159e12 + 2.92993e12i −0.0722082 + 0.125068i
$$473$$ −1.07461e13 6.20427e12i −0.453885 0.262051i
$$474$$ 0 0
$$475$$ 1.30924e12 + 2.26768e12i 0.0541443 + 0.0937806i
$$476$$ 3.17071e13i 1.29754i
$$477$$ 0 0
$$478$$ 5.98729e12 0.239933
$$479$$ 4.33780e12 2.50443e12i 0.172025 0.0993187i −0.411515 0.911403i $$-0.635000\pi$$
0.583540 + 0.812084i $$0.301667\pi$$
$$480$$ 0 0
$$481$$ 4.26779e12 7.39203e12i 0.165759 0.287103i
$$482$$ 1.73770e13 + 1.00326e13i 0.667945 + 0.385638i
$$483$$ 0 0
$$484$$ 5.64181e12 + 9.77191e12i 0.212418 + 0.367919i
$$485$$ 3.20975e13i 1.19608i
$$486$$ 0 0
$$487$$ −4.17000e13 −1.52227 −0.761134 0.648595i $$-0.775357\pi$$
−0.761134 + 0.648595i $$0.775357\pi$$
$$488$$ −5.32484e12 + 3.07430e12i −0.192401 + 0.111083i
$$489$$ 0 0
$$490$$ −1.05559e13 + 1.82834e13i −0.373693 + 0.647255i
$$491$$ 1.82160e12 + 1.05170e12i 0.0638331 + 0.0368540i 0.531577 0.847010i $$-0.321600\pi$$
−0.467744 + 0.883864i $$0.654933\pi$$
$$492$$ 0 0
$$493$$ −6.44229e12 1.11584e13i −0.221211 0.383148i
$$494$$ 2.95250e12i 0.100359i
$$495$$ 0 0
$$496$$ −1.09654e13 −0.365272
$$497$$ 1.14929e13 6.63541e12i 0.379006 0.218819i
$$498$$ 0 0
$$499$$ −1.37241e13 + 2.37708e13i −0.443589 + 0.768319i −0.997953 0.0639553i $$-0.979628\pi$$
0.554363 + 0.832275i $$0.312962\pi$$
$$500$$ 1.02235e13 + 5.90255e12i 0.327152 + 0.188881i
$$501$$ 0 0
$$502$$ −9.72406e12 1.68426e13i −0.305021 0.528311i
$$503$$ 2.26985e13i 0.704949i 0.935822 + 0.352474i $$0.114660\pi$$
−0.935822 + 0.352474i $$0.885340\pi$$
$$504$$ 0 0
$$505$$ 6.09659e13 1.85622
$$506$$ 1.71707e12 9.91349e11i 0.0517648 0.0298864i
$$507$$ 0 0
$$508$$ −8.13603e12 + 1.40920e13i −0.240488 + 0.416538i
$$509$$ −3.64995e13 2.10730e13i −1.06831 0.616791i −0.140593 0.990068i $$-0.544901\pi$$
−0.927720 + 0.373277i $$0.878234\pi$$
$$510$$ 0 0
$$511$$ 2.53852e13 + 4.39684e13i 0.728577 + 1.26193i
$$512$$ 1.55494e12i 0.0441942i
$$513$$ 0 0
$$514$$ −4.93051e13 −1.37428
$$515$$ 2.63117e13 1.51911e13i 0.726295 0.419327i
$$516$$ 0 0
$$517$$ −4.84114e12 + 8.38509e12i −0.131067 + 0.227015i
$$518$$ −2.28309e13 1.31815e13i −0.612174 0.353439i
$$519$$ 0 0
$$520$$ −3.57847e12 6.19809e12i −0.0941197 0.163020i
$$521$$ 6.54420e13i 1.70478i 0.522907 + 0.852390i $$0.324848\pi$$
−0.522907 + 0.852390i $$0.675152\pi$$
$$522$$ 0 0
$$523$$ −6.14531e13 −1.57049 −0.785245 0.619185i $$-0.787463\pi$$
−0.785245 + 0.619185i $$0.787463\pi$$
$$524$$ −2.22188e13 + 1.28280e13i −0.562423 + 0.324715i
$$525$$ 0 0
$$526$$ −1.56063e13 + 2.70309e13i −0.387589 + 0.671324i
$$527$$ 9.65869e13 + 5.57645e13i 2.37610 + 1.37184i
$$528$$ 0 0
$$529$$ −1.97287e13 3.41711e13i −0.476233 0.824860i
$$530$$ 3.46288e12i 0.0828053i
$$531$$ 0 0
$$532$$ 9.11907e12 0.213990
$$533$$ −2.19923e13 + 1.26973e13i −0.511252 + 0.295172i
$$534$$ 0 0
$$535$$ 2.60587e13 4.51349e13i 0.594543 1.02978i
$$536$$ −5.23822e12 3.02429e12i −0.118402 0.0683595i
$$537$$ 0 0
$$538$$ 1.33648e13 + 2.31485e13i 0.296518 + 0.513584i
$$539$$ 1.60475e13i 0.352748i
$$540$$ 0 0
$$541$$ 1.50207e13 0.324118 0.162059 0.986781i $$-0.448187\pi$$
0.162059 + 0.986781i $$0.448187\pi$$
$$542$$ 2.78753e13 1.60938e13i 0.595969 0.344083i
$$543$$ 0 0
$$544$$ −7.90765e12 + 1.36965e13i −0.165979 + 0.287484i
$$545$$ 1.48578e13 + 8.57816e12i 0.309010 + 0.178407i
$$546$$ 0 0
$$547$$ −3.57548e13 6.19292e13i −0.730127 1.26462i −0.956829 0.290652i $$-0.906128\pi$$
0.226702 0.973964i $$-0.427206\pi$$
$$548$$ 1.40669e13i 0.284639i
$$549$$ 0 0
$$550$$ 4.82470e12 0.0958644
$$551$$ −3.20919e12 + 1.85282e12i −0.0631883 + 0.0364818i
$$552$$ 0 0
$$553$$ 2.28308e13 3.95441e13i 0.441464 0.764638i
$$554$$ 1.03851e13 + 5.99581e12i 0.199003 + 0.114894i
$$555$$ 0 0
$$556$$ 1.61917e13 + 2.80448e13i 0.304732 + 0.527811i
$$557$$ 7.34107e13i 1.36925i −0.728895 0.684626i $$-0.759966\pi$$
0.728895 0.684626i $$-0.240034\pi$$
$$558$$ 0 0
$$559$$ 3.38141e13 0.619497
$$560$$ −1.91434e13 + 1.10524e13i −0.347599 + 0.200686i
$$561$$ 0 0
$$562$$ −2.58451e13 + 4.47650e13i −0.460996 + 0.798468i
$$563$$ −4.13394e13 2.38673e13i −0.730840 0.421951i 0.0878892 0.996130i $$-0.471988\pi$$
−0.818729 + 0.574179i $$0.805321\pi$$
$$564$$ 0 0
$$565$$ 2.39899e13 + 4.15517e13i 0.416664 + 0.721683i
$$566$$ 5.23314e13i 0.900907i
$$567$$ 0 0
$$568$$ 6.61939e12 0.111963
$$569$$ 1.65369e13 9.54756e12i 0.277263 0.160078i −0.354921 0.934896i $$-0.615492\pi$$
0.632184 + 0.774819i $$0.282159\pi$$
$$570$$ 0 0
$$571$$ 1.04724e13 1.81387e13i 0.172530 0.298831i −0.766774 0.641918i $$-0.778139\pi$$
0.939304 + 0.343087i $$0.111472\pi$$
$$572$$ 4.71130e12 + 2.72007e12i 0.0769415 + 0.0444222i
$$573$$ 0 0
$$574$$ 3.92167e13 + 6.79253e13i 0.629378 + 1.09011i
$$575$$ 4.79175e12i 0.0762351i
$$576$$ 0 0
$$577$$ 3.56688e13 0.557711 0.278855 0.960333i $$-0.410045\pi$$
0.278855 + 0.960333i $$0.410045\pi$$
$$578$$ 9.98011e13 5.76202e13i 1.54702 0.893173i
$$579$$ 0 0
$$580$$ 4.49129e12 7.77914e12i 0.0684275 0.118520i
$$581$$ 4.39624e13 + 2.53817e13i 0.664050 + 0.383389i
$$582$$ 0 0
$$583$$ 1.31611e12 + 2.27956e12i 0.0195411 + 0.0338461i
$$584$$ 2.53239e13i 0.372792i
$$585$$ 0 0
$$586$$ −2.39826e13 −0.347064
$$587$$ 1.12079e14 6.47090e13i 1.60818 0.928483i 0.618402 0.785862i $$-0.287780\pi$$
0.989777 0.142621i $$-0.0455532\pi$$
$$588$$ 0 0
$$589$$ 1.60381e13 2.77787e13i 0.226243 0.391864i
$$590$$ 2.07754e13 + 1.19947e13i 0.290596 + 0.167776i
$$591$$ 0 0
$$592$$ −6.57482e12 1.13879e13i −0.0904223 0.156616i
$$593$$ 3.96596e13i 0.540848i −0.962741 0.270424i $$-0.912836\pi$$
0.962741 0.270424i $$-0.0871639\pi$$
$$594$$ 0 0
$$595$$ 2.24828e14 3.01485
$$596$$ 1.50083e13 8.66505e12i 0.199572 0.115223i
$$597$$ 0 0
$$598$$ −2.70150e12 + 4.67913e12i −0.0353263 + 0.0611870i
$$599$$ −3.96254e13 2.28777e13i −0.513854 0.296674i 0.220562 0.975373i $$-0.429211\pi$$
−0.734416 + 0.678699i $$0.762544\pi$$
$$600$$ 0 0
$$601$$ −5.30165e13 9.18273e13i −0.676143 1.17111i −0.976133 0.217172i $$-0.930317\pi$$
0.299990 0.953942i $$-0.403017\pi$$
$$602$$ 1.04438e14i 1.32092i
$$603$$ 0 0
$$604$$ −6.26617e13 −0.779503
$$605$$ 6.92903e13 4.00048e13i 0.854862 0.493555i
$$606$$ 0 0
$$607$$ 4.77534e13 8.27112e13i 0.579509 1.00374i −0.416026 0.909353i $$-0.636578\pi$$
0.995536 0.0943870i $$-0.0300891\pi$$
$$608$$ 3.93915e12 + 2.27427e12i 0.0474115 + 0.0273731i
$$609$$ 0 0
$$610$$ 2.17991e13 + 3.77572e13i 0.258101 + 0.447044i
$$611$$ 2.63849e13i 0.309848i
$$612$$ 0 0
$$613$$ −5.18411e13 −0.598924 −0.299462 0.954108i $$-0.596807\pi$$
−0.299462 + 0.954108i $$0.596807\pi$$
$$614$$ −1.35057e13 + 7.79751e12i −0.154766 + 0.0893540i
$$615$$ 0 0
$$616$$ 8.40119e12 1.45513e13i 0.0947190 0.164058i
$$617$$ 6.97534e13 + 4.02721e13i 0.780081 + 0.450380i 0.836459 0.548030i $$-0.184622\pi$$
−0.0563782 + 0.998409i $$0.517955\pi$$
$$618$$ 0 0
$$619$$ 2.57473e13 + 4.45957e13i 0.283321 + 0.490726i 0.972201 0.234149i $$-0.0752305\pi$$
−0.688880 + 0.724876i $$0.741897\pi$$
$$620$$ 7.77532e13i 0.848711i
$$621$$ 0 0
$$622$$ 4.42759e13 0.475571
$$623$$ −4.80224e12 + 2.77257e12i −0.0511686 + 0.0295422i
$$624$$ 0 0
$$625$$ 5.85270e13 1.01372e14i 0.613700 1.06296i
$$626$$ −4.87587e12 2.81508e12i −0.0507201 0.0292833i
$$627$$ 0 0
$$628$$ −4.06967e13 7.04887e13i −0.416640 0.721641i
$$629$$ 1.33745e14i 1.35839i
$$630$$ 0 0
$$631$$ −1.02922e13 −0.102887 −0.0514435 0.998676i $$-0.516382\pi$$
−0.0514435 + 0.998676i $$0.516382\pi$$
$$632$$ 1.97243e13 1.13878e13i 0.195622 0.112942i
$$633$$ 0 0
$$634$$ −5.24589e13 + 9.08614e13i −0.512121 + 0.887020i
$$635$$ 9.99232e13 + 5.76907e13i 0.967827 + 0.558775i
$$636$$ 0 0
$$637$$ 2.18653e13 + 3.78719e13i 0.208477 + 0.361093i
$$638$$ 6.82785e12i 0.0645923i
$$639$$ 0 0
$$640$$ −1.10257e13 −0.102685
$$641$$ 4.00494e13 2.31225e13i 0.370089 0.213671i −0.303408 0.952861i $$-0.598125\pi$$
0.673497 + 0.739190i $$0.264791\pi$$
$$642$$ 0 0
$$643$$ −1.36551e13 + 2.36514e13i −0.124234 + 0.215180i −0.921433 0.388537i $$-0.872981\pi$$
0.797199 + 0.603716i $$0.206314\pi$$
$$644$$ 1.44519e13 + 8.34381e12i 0.130466 + 0.0753243i
$$645$$ 0 0
$$646$$ −2.31315e13 4.00650e13i −0.205609 0.356125i
$$647$$ 1.34984e13i 0.119059i −0.998227 0.0595293i $$-0.981040\pi$$
0.998227 0.0595293i $$-0.0189600\pi$$
$$648$$ 0 0
$$649$$ −1.82349e13 −0.158372
$$650$$ −1.13862e13 + 6.57382e12i −0.0981323 + 0.0566567i
$$651$$ 0 0
$$652$$ −2.35733e13 + 4.08301e13i −0.200070 + 0.346531i
$$653$$ 7.29055e13 + 4.20920e13i 0.614037 + 0.354514i 0.774544 0.632520i $$-0.217980\pi$$
−0.160507 + 0.987035i $$0.551313\pi$$
$$654$$ 0 0
$$655$$ 9.09604e13 + 1.57548e14i 0.754477 + 1.30679i
$$656$$ 3.91220e13i 0.322034i
$$657$$ 0 0
$$658$$ −8.14920e13 −0.660672
$$659$$ −1.43296e14 + 8.27319e13i −1.15294 + 0.665650i −0.949602 0.313458i $$-0.898512\pi$$
−0.203338 + 0.979109i $$0.565179\pi$$
$$660$$ 0 0
$$661$$ −1.00840e14 + 1.74661e14i −0.799148 + 1.38416i 0.121024 + 0.992650i $$0.461382\pi$$
−0.920172 + 0.391515i $$0.871951\pi$$
$$662$$ −2.77171e13 1.60025e13i −0.218001 0.125863i
$$663$$ 0 0
$$664$$ 1.26602e13 + 2.19281e13i 0.0980846 + 0.169887i
$$665$$ 6.46612e13i 0.497205i
$$666$$ 0 0
$$667$$ −6.78122e12 −0.0513664
$$668$$ −9.41862e13 + 5.43785e13i −0.708117 + 0.408832i
$$669$$ 0 0
$$670$$ −2.14445e13 + 3.71430e13i −0.158834 + 0.275108i
$$671$$ −2.87001e13 1.65700e13i −0.210994 0.121818i
$$672$$ 0 0
$$673$$ −3.02184e12 5.23398e12i −0.0218875 0.0379103i 0.854874 0.518835i $$-0.173634\pi$$
−0.876762 + 0.480925i $$0.840301\pi$$
$$674$$ 1.96351e13i 0.141167i
$$675$$ 0 0
$$676$$ 5.57588e13 0.394984
$$677$$ 1.05200e14 6.07372e13i 0.739727 0.427082i −0.0822428 0.996612i $$-0.526208\pi$$
0.821970 + 0.569530i $$0.192875\pi$$
$$678$$ 0 0
$$679$$ −1.02674e14 + 1.77837e14i −0.711398 + 1.23218i
$$680$$ 9.71184e13 + 5.60713e13i 0.667970 + 0.385653i
$$681$$ 0 0
$$682$$ −2.95510e13 5.11838e13i −0.200286 0.346905i
$$683$$ 1.51629e14i 1.02019i −0.860119 0.510094i $$-0.829611\pi$$
0.860119 0.510094i $$-0.170389\pi$$
$$684$$ 0 0
$$685$$ −9.97450e13 −0.661360
$$686$$ −1.15966e13 + 6.69528e12i −0.0763324 + 0.0440705i
$$687$$ 0 0
$$688$$ 2.60465e13 4.51139e13i 0.168969 0.292663i
$$689$$ −6.21197e12 3.58648e12i −0.0400067 0.0230979i
$$690$$ 0 0
$$691$$ −3.31124e13 5.73524e13i −0.210185 0.364051i 0.741588 0.670856i $$-0.234073\pi$$
−0.951772 + 0.306806i $$0.900740\pi$$
$$692$$ 1.55716e14i 0.981300i
$$693$$ 0 0
$$694$$ −1.17824e14 −0.731873
$$695$$ 1.98859e14 1.14812e14i 1.22637 0.708046i
$$696$$ 0 0
$$697$$ 1.98955e14 3.44600e14i 1.20946 2.09484i
$$698$$ 2.19382e13 + 1.26660e13i 0.132411 + 0.0764475i
$$699$$ 0 0
$$700$$ 2.03039e13 + 3.51673e13i 0.120806 + 0.209242i
$$701$$ 5.78990e13i 0.342043i 0.985267 + 0.171022i $$0.0547068\pi$$
−0.985267 + 0.171022i $$0.945293\pi$$
$$702$$ 0 0
$$703$$ 3.84654e13 0.224024
$$704$$ 7.25808e12 4.19046e12i 0.0419719 0.0242325i
$$705$$ 0 0
$$706$$ 4.23078e13 7.32793e13i 0.241211 0.417790i
$$707$$ −3.37784e14 1.95020e14i −1.91224 1.10403i
$$708$$ 0 0
$$709$$ −1.35039e14 2.33894e14i −0.753750 1.30553i −0.945994 0.324186i $$-0.894910\pi$$
0.192244 0.981347i $$-0.438424\pi$$
$$710$$ 4.69366e13i 0.260148i
$$711$$ 0 0
$$712$$ −2.76588e12 −0.0151159
$$713$$ 5.08342e13 2.93491e13i 0.275872 0.159275i
$$714$$ 0 0
$$715$$ 1.92874e13 3.34068e13i 0.103215 0.178774i
$$716$$ −3.13538e12 1.81021e12i −0.0166619 0.00961977i
$$717$$ 0 0
$$718$$ 4.01059e13 + 6.94654e13i 0.210177 + 0.364038i
$$719$$ 1.48102e14i 0.770755i −0.922759 0.385377i $$-0.874071\pi$$
0.922759 0.385377i $$-0.125929\pi$$
$$720$$ 0 0
$$721$$ −1.94375e14 −0.997616
$$722$$ 1.08621e14 6.27124e13i 0.553641 0.319645i
$$723$$ 0 0
$$724$$ −3.25910e13 + 5.64493e13i −0.163834 + 0.283769i
$$725$$ −1.42907e13 8.25072e12i −0.0713448 0.0411910i
$$726$$ 0 0
$$727$$ −2.60801e13 4.51720e13i −0.128421 0.222432i 0.794644 0.607076i $$-0.207658\pi$$
−0.923065 + 0.384644i $$0.874324\pi$$
$$728$$ 4.57876e13i 0.223919i
$$729$$ 0 0
$$730$$ 1.79566e14 0.866183
$$731$$ −4.58852e14 + 2.64918e14i −2.19829 + 1.26919i
$$732$$ 0 0
$$733$$ −1.60891e14 + 2.78671e14i −0.760346 + 1.31696i 0.182326 + 0.983238i $$0.441637\pi$$
−0.942672 + 0.333720i $$0.891696\pi$$
$$734$$ −1.98235e14 1.14451e14i −0.930465 0.537204i
$$735$$ 0 0
$$736$$ 4.16184e12 + 7.20851e12i 0.0192706 + 0.0333777i
$$737$$ 3.26009e13i 0.149931i
$$738$$ 0 0
$$739$$ 1.66542e14 0.755617 0.377809 0.925884i $$-0.376678\pi$$
0.377809 + 0.925884i $$0.376678\pi$$
$$740$$ −8.07491e13 + 4.66205e13i −0.363898 + 0.210096i
$$741$$ 0 0
$$742$$ −1.10772e13 + 1.91862e13i −0.0492503 + 0.0853041i
$$743$$ −9.84071e13 5.68154e13i −0.434593 0.250912i 0.266708 0.963777i $$-0.414064\pi$$
−0.701301 + 0.712865i $$0.747397\pi$$
$$744$$ 0 0
$$745$$ −6.14419e13 1.06420e14i −0.267721 0.463707i
$$746$$ 8.62230e13i 0.373189i
$$747$$ 0 0
$$748$$ −8.52421e13 −0.364037
$$749$$ −2.88758e14 + 1.66714e14i −1.22497 + 0.707236i
$$750$$ 0 0
$$751$$ 8.24781e13 1.42856e14i 0.345254 0.597998i −0.640146 0.768253i $$-0.721126\pi$$
0.985400 + 0.170256i $$0.0544594\pi$$
$$752$$ −3.52019e13 2.03238e13i −0.146378 0.0845116i
$$753$$ 0 0
$$754$$ −9.30319e12 1.61136e13i −0.0381746 0.0661204i
$$755$$ 4.44320e14i 1.81118i
$$756$$ 0 0
$$757$$ −2.67990e14 −1.07805 −0.539026 0.842289i $$-0.681207\pi$$
−0.539026 + 0.842289i $$0.681207\pi$$
$$758$$ −2.17617e14 + 1.25641e14i −0.869653 + 0.502095i
$$759$$ 0 0
$$760$$ 1.61263e13 2.79316e13i 0.0636014 0.110161i
$$761$$ 1.12405e14 + 6.48973e13i 0.440417 + 0.254275i 0.703774 0.710423i $$-0.251497\pi$$
−0.263358 + 0.964698i $$0.584830\pi$$
$$762$$ 0 0
$$763$$ −5.48801e13 9.50552e13i −0.212223 0.367581i
$$764$$ 1.05707e14i 0.406105i
$$765$$ 0 0
$$766$$ −9.71099e13 −0.368230
$$767$$ 4.30339e13 2.48456e13i 0.162119 0.0935995i
$$768$$ 0 0
$$769$$ 1.09593e14 1.89820e14i 0.407521 0.705846i −0.587091 0.809521i $$-0.699727\pi$$
0.994611 + 0.103675i $$0.0330601\pi$$
$$770$$ −1.03180e14 5.95709e13i −0.381190 0.220080i
$$771$$ 0 0
$$772$$ 7.97712e13 + 1.38168e14i 0.290911