# Properties

 Label 81.12.c.b.28.1 Level $81$ Weight $12$ Character 81.28 Analytic conductor $62.236$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$81 = 3^{4}$$ Weight: $$k$$ $$=$$ $$12$$ Character orbit: $$[\chi]$$ $$=$$ 81.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$62.2357976253$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 28.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 81.28 Dual form 81.12.c.b.55.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} +O(q^{10})$$ $$q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} -115920. q^{10} +(267306. + 462988. i) q^{11} +(288869. - 500336. i) q^{13} +(200928. - 348018. i) q^{14} +(-493568. - 854885. i) q^{16} +6.90593e6 q^{17} +1.06614e7 q^{19} +(-3.55488e6 - 6.15723e6i) q^{20} +(6.41534e6 - 1.11117e7i) q^{22} +(9.32164e6 - 1.61455e7i) q^{23} +(1.27496e7 + 2.20830e7i) q^{25} -1.38657e7 q^{26} +2.46472e7 q^{28} +(6.42033e7 + 1.11203e8i) q^{29} +(2.64216e7 - 4.57635e7i) q^{31} +(-9.83532e7 + 1.70353e8i) q^{32} +(-8.28712e7 - 1.43537e8i) q^{34} +8.08735e7 q^{35} -1.82213e8 q^{37} +(-1.27937e8 - 2.21593e8i) q^{38} +(-2.04019e8 + 3.53372e8i) q^{40} +(1.54060e8 - 2.66840e8i) q^{41} +(8.56285e6 + 1.48313e7i) q^{43} +7.86949e8 q^{44} -4.47439e8 q^{46} +(1.34367e9 + 2.32731e9i) q^{47} +(8.48483e8 - 1.46961e9i) q^{49} +(3.05991e8 - 5.29991e8i) q^{50} +(-4.25215e8 - 7.36494e8i) q^{52} +1.59606e9 q^{53} +2.58218e9 q^{55} +(-7.07267e8 - 1.22502e9i) q^{56} +(1.54088e9 - 2.66888e9i) q^{58} +(-2.59460e9 + 4.49398e9i) q^{59} +(-3.47824e9 - 6.02449e9i) q^{61} -1.26824e9 q^{62} +2.69930e9 q^{64} +(-1.39524e9 - 2.41662e9i) q^{65} +(7.74091e9 - 1.34077e10i) q^{67} +(5.08277e9 - 8.80361e9i) q^{68} +(-9.70482e8 - 1.68092e9i) q^{70} -9.79149e9 q^{71} +1.46379e9 q^{73} +(2.18656e9 + 3.78723e9i) q^{74} +(7.84681e9 - 1.35911e10i) q^{76} +(-4.47577e9 + 7.75226e9i) q^{77} +(-1.90584e10 - 3.30102e10i) q^{79} -4.76787e9 q^{80} -7.39489e9 q^{82} +(-1.46675e10 - 2.54049e10i) q^{83} +(1.66778e10 - 2.88868e10i) q^{85} +(2.05508e8 - 3.55951e8i) q^{86} +(-2.25820e10 - 3.91132e10i) q^{88} +2.49929e10 q^{89} +9.67365e9 q^{91} +(-1.37214e10 - 2.37662e10i) q^{92} +(3.22482e10 - 5.58555e10i) q^{94} +(2.57473e10 - 4.45957e10i) q^{95} +(-3.75068e10 - 6.49637e10i) q^{97} -4.07272e10 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 24q^{2} + 1472q^{4} + 4830q^{5} + 16744q^{7} - 168960q^{8} + O(q^{10})$$ $$2q - 24q^{2} + 1472q^{4} + 4830q^{5} + 16744q^{7} - 168960q^{8} - 231840q^{10} + 534612q^{11} + 577738q^{13} + 401856q^{14} - 987136q^{16} + 13811868q^{17} + 21322840q^{19} - 7109760q^{20} + 12830688q^{22} + 18643272q^{23} + 25499225q^{25} - 27731424q^{26} + 49294336q^{28} + 128406630q^{29} + 52843168q^{31} - 196706304q^{32} - 165742416q^{34} + 161747040q^{35} - 364426628q^{37} - 255874080q^{38} - 408038400q^{40} + 308120442q^{41} + 17125708q^{43} + 1573897728q^{44} - 894877056q^{46} + 2687348496q^{47} + 1696965207q^{49} + 611981400q^{50} - 850430336q^{52} + 3192111396q^{53} + 5164351920q^{55} - 1414533120q^{56} + 3081759120q^{58} - 5189203740q^{59} - 6956478662q^{61} - 2536472064q^{62} + 5398593536q^{64} - 2790474540q^{65} + 15481826884q^{67} + 10165534848q^{68} - 1940964480q^{70} - 19582970544q^{71} + 2927582644q^{73} + 4373119536q^{74} + 15693610240q^{76} - 8951543328q^{77} - 38116845680q^{79} - 9535733760q^{80} - 14789781216q^{82} - 29335099668q^{83} + 33355661220q^{85} + 411016992q^{86} - 45164021760q^{88} + 49985834220q^{89} + 19347290144q^{91} - 27442896384q^{92} + 64496363904q^{94} + 51494658600q^{95} - 75013568546q^{97} - 81454329936q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −12.0000 20.7846i −0.265165 0.459279i 0.702442 0.711741i $$-0.252093\pi$$
−0.967607 + 0.252462i $$0.918760\pi$$
$$3$$ 0 0
$$4$$ 736.000 1274.79i 0.359375 0.622456i
$$5$$ 2415.00 4182.90i 0.345607 0.598608i −0.639857 0.768494i $$-0.721006\pi$$
0.985464 + 0.169886i $$0.0543398\pi$$
$$6$$ 0 0
$$7$$ 8372.00 + 14500.7i 0.188274 + 0.326100i 0.944675 0.328008i $$-0.106377\pi$$
−0.756401 + 0.654108i $$0.773044\pi$$
$$8$$ −84480.0 −0.911505
$$9$$ 0 0
$$10$$ −115920. −0.366571
$$11$$ 267306. + 462988.i 0.500436 + 0.866781i 1.00000 0.000504048i $$0.000160443\pi$$
−0.499563 + 0.866277i $$0.666506\pi$$
$$12$$ 0 0
$$13$$ 288869. 500336.i 0.215781 0.373743i −0.737733 0.675092i $$-0.764104\pi$$
0.953514 + 0.301349i $$0.0974371\pi$$
$$14$$ 200928. 348018.i 0.0998473 0.172941i
$$15$$ 0 0
$$16$$ −493568. 854885.i −0.117676 0.203820i
$$17$$ 6.90593e6 1.17965 0.589825 0.807531i $$-0.299197\pi$$
0.589825 + 0.807531i $$0.299197\pi$$
$$18$$ 0 0
$$19$$ 1.06614e7 0.987803 0.493901 0.869518i $$-0.335570\pi$$
0.493901 + 0.869518i $$0.335570\pi$$
$$20$$ −3.55488e6 6.15723e6i −0.248405 0.430250i
$$21$$ 0 0
$$22$$ 6.41534e6 1.11117e7i 0.265397 0.459680i
$$23$$ 9.32164e6 1.61455e7i 0.301988 0.523058i −0.674599 0.738185i $$-0.735683\pi$$
0.976586 + 0.215127i $$0.0690166\pi$$
$$24$$ 0 0
$$25$$ 1.27496e7 + 2.20830e7i 0.261112 + 0.452259i
$$26$$ −1.38657e7 −0.228870
$$27$$ 0 0
$$28$$ 2.46472e7 0.270644
$$29$$ 6.42033e7 + 1.11203e8i 0.581257 + 1.00677i 0.995331 + 0.0965237i $$0.0307724\pi$$
−0.414073 + 0.910244i $$0.635894\pi$$
$$30$$ 0 0
$$31$$ 2.64216e7 4.57635e7i 0.165756 0.287098i −0.771167 0.636632i $$-0.780327\pi$$
0.936924 + 0.349534i $$0.113660\pi$$
$$32$$ −9.83532e7 + 1.70353e8i −0.518159 + 0.897478i
$$33$$ 0 0
$$34$$ −8.28712e7 1.43537e8i −0.312802 0.541789i
$$35$$ 8.08735e7 0.260275
$$36$$ 0 0
$$37$$ −1.82213e8 −0.431987 −0.215993 0.976395i $$-0.569299\pi$$
−0.215993 + 0.976395i $$0.569299\pi$$
$$38$$ −1.27937e8 2.21593e8i −0.261931 0.453677i
$$39$$ 0 0
$$40$$ −2.04019e8 + 3.53372e8i −0.315022 + 0.545634i
$$41$$ 1.54060e8 2.66840e8i 0.207673 0.359700i −0.743308 0.668949i $$-0.766744\pi$$
0.950981 + 0.309249i $$0.100078\pi$$
$$42$$ 0 0
$$43$$ 8.56285e6 + 1.48313e7i 0.00888264 + 0.0153852i 0.870433 0.492288i $$-0.163839\pi$$
−0.861550 + 0.507673i $$0.830506\pi$$
$$44$$ 7.86949e8 0.719377
$$45$$ 0 0
$$46$$ −4.47439e8 −0.320306
$$47$$ 1.34367e9 + 2.32731e9i 0.854586 + 1.48019i 0.877029 + 0.480438i $$0.159522\pi$$
−0.0224426 + 0.999748i $$0.507144\pi$$
$$48$$ 0 0
$$49$$ 8.48483e8 1.46961e9i 0.429106 0.743233i
$$50$$ 3.05991e8 5.29991e8i 0.138476 0.239847i
$$51$$ 0 0
$$52$$ −4.25215e8 7.36494e8i −0.155092 0.268628i
$$53$$ 1.59606e9 0.524241 0.262120 0.965035i $$-0.415578\pi$$
0.262120 + 0.965035i $$0.415578\pi$$
$$54$$ 0 0
$$55$$ 2.58218e9 0.691817
$$56$$ −7.07267e8 1.22502e9i −0.171613 0.297242i
$$57$$ 0 0
$$58$$ 1.54088e9 2.66888e9i 0.308258 0.533919i
$$59$$ −2.59460e9 + 4.49398e9i −0.472481 + 0.818362i −0.999504 0.0314895i $$-0.989975\pi$$
0.527023 + 0.849851i $$0.323308\pi$$
$$60$$ 0 0
$$61$$ −3.47824e9 6.02449e9i −0.527285 0.913284i −0.999494 0.0317979i $$-0.989877\pi$$
0.472209 0.881486i $$-0.343457\pi$$
$$62$$ −1.26824e9 −0.175811
$$63$$ 0 0
$$64$$ 2.69930e9 0.314240
$$65$$ −1.39524e9 2.41662e9i −0.149150 0.258336i
$$66$$ 0 0
$$67$$ 7.74091e9 1.34077e10i 0.700456 1.21323i −0.267851 0.963460i $$-0.586313\pi$$
0.968307 0.249765i $$-0.0803533\pi$$
$$68$$ 5.08277e9 8.80361e9i 0.423937 0.734280i
$$69$$ 0 0
$$70$$ −9.70482e8 1.68092e9i −0.0690158 0.119539i
$$71$$ −9.79149e9 −0.644062 −0.322031 0.946729i $$-0.604366\pi$$
−0.322031 + 0.946729i $$0.604366\pi$$
$$72$$ 0 0
$$73$$ 1.46379e9 0.0826425 0.0413212 0.999146i $$-0.486843\pi$$
0.0413212 + 0.999146i $$0.486843\pi$$
$$74$$ 2.18656e9 + 3.78723e9i 0.114548 + 0.198403i
$$75$$ 0 0
$$76$$ 7.84681e9 1.35911e10i 0.354992 0.614864i
$$77$$ −4.47577e9 + 7.75226e9i −0.188438 + 0.326385i
$$78$$ 0 0
$$79$$ −1.90584e10 3.30102e10i −0.696848 1.20698i −0.969554 0.244878i $$-0.921252\pi$$
0.272706 0.962097i $$-0.412081\pi$$
$$80$$ −4.76787e9 −0.162678
$$81$$ 0 0
$$82$$ −7.39489e9 −0.220270
$$83$$ −1.46675e10 2.54049e10i −0.408722 0.707927i 0.586025 0.810293i $$-0.300692\pi$$
−0.994747 + 0.102366i $$0.967359\pi$$
$$84$$ 0 0
$$85$$ 1.66778e10 2.88868e10i 0.407695 0.706149i
$$86$$ 2.05508e8 3.55951e8i 0.00471073 0.00815923i
$$87$$ 0 0
$$88$$ −2.25820e10 3.91132e10i −0.456150 0.790075i
$$89$$ 2.49929e10 0.474430 0.237215 0.971457i $$-0.423765\pi$$
0.237215 + 0.971457i $$0.423765\pi$$
$$90$$ 0 0
$$91$$ 9.67365e9 0.162503
$$92$$ −1.37214e10 2.37662e10i −0.217054 0.375948i
$$93$$ 0 0
$$94$$ 3.22482e10 5.58555e10i 0.453213 0.784987i
$$95$$ 2.57473e10 4.45957e10i 0.341391 0.591307i
$$96$$ 0 0
$$97$$ −3.75068e10 6.49637e10i −0.443471 0.768114i 0.554473 0.832202i $$-0.312920\pi$$
−0.997944 + 0.0640871i $$0.979586\pi$$
$$98$$ −4.07272e10 −0.455136
$$99$$ 0 0
$$100$$ 3.75349e10 0.375349
$$101$$ 4.08715e10 + 7.07915e10i 0.386948 + 0.670214i 0.992037 0.125944i $$-0.0401959\pi$$
−0.605089 + 0.796158i $$0.706863\pi$$
$$102$$ 0 0
$$103$$ 1.12878e11 1.95510e11i 0.959407 1.66174i 0.235463 0.971883i $$-0.424339\pi$$
0.723944 0.689858i $$-0.242327\pi$$
$$104$$ −2.44037e10 + 4.22684e10i −0.196685 + 0.340669i
$$105$$ 0 0
$$106$$ −1.91527e10 3.31734e10i −0.139010 0.240773i
$$107$$ −9.02413e10 −0.622006 −0.311003 0.950409i $$-0.600665\pi$$
−0.311003 + 0.950409i $$0.600665\pi$$
$$108$$ 0 0
$$109$$ 7.34827e10 0.457445 0.228723 0.973492i $$-0.426545\pi$$
0.228723 + 0.973492i $$0.426545\pi$$
$$110$$ −3.09861e10 5.36695e10i −0.183446 0.317737i
$$111$$ 0 0
$$112$$ 8.26430e9 1.43142e10i 0.0443105 0.0767481i
$$113$$ −4.25734e10 + 7.37393e10i −0.217374 + 0.376502i −0.954004 0.299793i $$-0.903082\pi$$
0.736630 + 0.676295i $$0.236416\pi$$
$$114$$ 0 0
$$115$$ −4.50235e10 7.79830e10i −0.208738 0.361545i
$$116$$ 1.89015e11 0.835557
$$117$$ 0 0
$$118$$ 1.24541e11 0.501142
$$119$$ 5.78165e10 + 1.00141e11i 0.222097 + 0.384684i
$$120$$ 0 0
$$121$$ −2.49160e8 + 4.31558e8i −0.000873290 + 0.00151258i
$$122$$ −8.34777e10 + 1.44588e11i −0.279635 + 0.484342i
$$123$$ 0 0
$$124$$ −3.88926e10 6.73639e10i −0.119137 0.206352i
$$125$$ 3.59001e11 1.05218
$$126$$ 0 0
$$127$$ −2.62717e11 −0.705615 −0.352808 0.935696i $$-0.614773\pi$$
−0.352808 + 0.935696i $$0.614773\pi$$
$$128$$ 1.69036e11 + 2.92778e11i 0.434834 + 0.753155i
$$129$$ 0 0
$$130$$ −3.34857e10 + 5.79989e10i −0.0790990 + 0.137003i
$$131$$ 3.15764e11 5.46920e11i 0.715107 1.23860i −0.247811 0.968808i $$-0.579711\pi$$
0.962918 0.269793i $$-0.0869554\pi$$
$$132$$ 0 0
$$133$$ 8.92574e10 + 1.54598e11i 0.185977 + 0.322122i
$$134$$ −3.71564e11 −0.742946
$$135$$ 0 0
$$136$$ −5.83413e11 −1.07526
$$137$$ −1.48599e11 2.57382e11i −0.263059 0.455632i 0.703994 0.710206i $$-0.251398\pi$$
−0.967053 + 0.254574i $$0.918065\pi$$
$$138$$ 0 0
$$139$$ −2.98397e11 + 5.16838e11i −0.487767 + 0.844838i −0.999901 0.0140679i $$-0.995522\pi$$
0.512134 + 0.858906i $$0.328855\pi$$
$$140$$ 5.95229e10 1.03097e11i 0.0935363 0.162010i
$$141$$ 0 0
$$142$$ 1.17498e11 + 2.03512e11i 0.170783 + 0.295804i
$$143$$ 3.08866e11 0.431938
$$144$$ 0 0
$$145$$ 6.20204e11 0.803546
$$146$$ −1.75655e10 3.04243e10i −0.0219139 0.0379560i
$$147$$ 0 0
$$148$$ −1.34109e11 + 2.32284e11i −0.155245 + 0.268893i
$$149$$ −5.57717e11 + 9.65994e11i −0.622142 + 1.07758i 0.366945 + 0.930243i $$0.380404\pi$$
−0.989086 + 0.147338i $$0.952929\pi$$
$$150$$ 0 0
$$151$$ 4.12224e11 + 7.13992e11i 0.427326 + 0.740151i 0.996635 0.0819732i $$-0.0261222\pi$$
−0.569308 + 0.822124i $$0.692789\pi$$
$$152$$ −9.00677e11 −0.900387
$$153$$ 0 0
$$154$$ 2.14837e11 0.199869
$$155$$ −1.27616e11 2.21038e11i −0.114573 0.198446i
$$156$$ 0 0
$$157$$ −6.57558e11 + 1.13892e12i −0.550156 + 0.952899i 0.448106 + 0.893980i $$0.352099\pi$$
−0.998263 + 0.0589187i $$0.981235\pi$$
$$158$$ −4.57402e11 + 7.92244e11i −0.369559 + 0.640096i
$$159$$ 0 0
$$160$$ 4.75046e11 + 8.22803e11i 0.358159 + 0.620349i
$$161$$ 3.12163e11 0.227425
$$162$$ 0 0
$$163$$ −3.57833e11 −0.243584 −0.121792 0.992556i $$-0.538864\pi$$
−0.121792 + 0.992556i $$0.538864\pi$$
$$164$$ −2.26777e11 3.92789e11i −0.149265 0.258534i
$$165$$ 0 0
$$166$$ −3.52021e11 + 6.09719e11i −0.216758 + 0.375435i
$$167$$ 1.37742e12 2.38576e12i 0.820587 1.42130i −0.0846581 0.996410i $$-0.526980\pi$$
0.905245 0.424889i $$-0.139687\pi$$
$$168$$ 0 0
$$169$$ 7.29190e11 + 1.26299e12i 0.406877 + 0.704732i
$$170$$ −8.00536e11 −0.432426
$$171$$ 0 0
$$172$$ 2.52090e10 0.0127688
$$173$$ −4.75194e11 8.23060e11i −0.233140 0.403811i 0.725590 0.688127i $$-0.241567\pi$$
−0.958731 + 0.284316i $$0.908233\pi$$
$$174$$ 0 0
$$175$$ −2.13480e11 + 3.69757e11i −0.0983211 + 0.170297i
$$176$$ 2.63867e11 4.57032e11i 0.117779 0.203998i
$$177$$ 0 0
$$178$$ −2.99915e11 5.19468e11i −0.125802 0.217896i
$$179$$ −1.68138e12 −0.683873 −0.341936 0.939723i $$-0.611083\pi$$
−0.341936 + 0.939723i $$0.611083\pi$$
$$180$$ 0 0
$$181$$ −9.96774e11 −0.381386 −0.190693 0.981650i $$-0.561073\pi$$
−0.190693 + 0.981650i $$0.561073\pi$$
$$182$$ −1.16084e11 2.01063e11i −0.0430902 0.0746345i
$$183$$ 0 0
$$184$$ −7.87492e11 + 1.36398e12i −0.275263 + 0.476770i
$$185$$ −4.40045e11 + 7.62181e11i −0.149298 + 0.258591i
$$186$$ 0 0
$$187$$ 1.84600e12 + 3.19736e12i 0.590340 + 1.02250i
$$188$$ 3.95578e12 1.22847
$$189$$ 0 0
$$190$$ −1.23587e12 −0.362100
$$191$$ 1.38120e12 + 2.39231e12i 0.393164 + 0.680980i 0.992865 0.119244i $$-0.0380472\pi$$
−0.599701 + 0.800224i $$0.704714\pi$$
$$192$$ 0 0
$$193$$ −2.72119e12 + 4.71325e12i −0.731466 + 1.26694i 0.224790 + 0.974407i $$0.427830\pi$$
−0.956256 + 0.292530i $$0.905503\pi$$
$$194$$ −9.00163e11 + 1.55913e12i −0.235186 + 0.407354i
$$195$$ 0 0
$$196$$ −1.24897e12 2.16327e12i −0.308420 0.534199i
$$197$$ 2.87609e12 0.690619 0.345309 0.938489i $$-0.387774\pi$$
0.345309 + 0.938489i $$0.387774\pi$$
$$198$$ 0 0
$$199$$ 7.28391e11 0.165452 0.0827262 0.996572i $$-0.473637\pi$$
0.0827262 + 0.996572i $$0.473637\pi$$
$$200$$ −1.07709e12 1.86557e12i −0.238005 0.412237i
$$201$$ 0 0
$$202$$ 9.80916e11 1.69900e12i 0.205210 0.355435i
$$203$$ −1.07502e12 + 1.86199e12i −0.218871 + 0.379096i
$$204$$ 0 0
$$205$$ −7.44111e11 1.28884e12i −0.143546 0.248629i
$$206$$ −5.41812e12 −1.01760
$$207$$ 0 0
$$208$$ −5.70306e11 −0.101569
$$209$$ 2.84986e12 + 4.93610e12i 0.494333 + 0.856209i
$$210$$ 0 0
$$211$$ 3.39658e12 5.88306e12i 0.559099 0.968388i −0.438473 0.898745i $$-0.644480\pi$$
0.997572 0.0696437i $$-0.0221863\pi$$
$$212$$ 1.17470e12 2.03463e12i 0.188399 0.326317i
$$213$$ 0 0
$$214$$ 1.08290e12 + 1.87563e12i 0.164934 + 0.285674i
$$215$$ 8.27172e10 0.0122796
$$216$$ 0 0
$$217$$ 8.84806e11 0.124830
$$218$$ −8.81792e11 1.52731e12i −0.121299 0.210095i
$$219$$ 0 0
$$220$$ 1.90048e12 3.29173e12i 0.248622 0.430625i
$$221$$ 1.99491e12 3.45529e12i 0.254546 0.440886i
$$222$$ 0 0
$$223$$ −3.66743e12 6.35218e12i −0.445333 0.771340i 0.552742 0.833352i $$-0.313582\pi$$
−0.998075 + 0.0620124i $$0.980248\pi$$
$$224$$ −3.29365e12 −0.390223
$$225$$ 0 0
$$226$$ 2.04352e12 0.230560
$$227$$ −6.79920e11 1.17766e12i −0.0748713 0.129681i 0.826159 0.563437i $$-0.190521\pi$$
−0.901030 + 0.433756i $$0.857188\pi$$
$$228$$ 0 0
$$229$$ 5.91221e12 1.02402e13i 0.620375 1.07452i −0.369041 0.929413i $$-0.620314\pi$$
0.989416 0.145108i $$-0.0463530\pi$$
$$230$$ −1.08056e12 + 1.87159e12i −0.110700 + 0.191738i
$$231$$ 0 0
$$232$$ −5.42390e12 9.39446e12i −0.529819 0.917673i
$$233$$ 1.75634e13 1.67552 0.837761 0.546038i $$-0.183865\pi$$
0.837761 + 0.546038i $$0.183865\pi$$
$$234$$ 0 0
$$235$$ 1.29799e13 1.18140
$$236$$ 3.81925e12 + 6.61514e12i 0.339596 + 0.588197i
$$237$$ 0 0
$$238$$ 1.38760e12 2.40339e12i 0.117785 0.204009i
$$239$$ −3.56979e12 + 6.18306e12i −0.296111 + 0.512879i −0.975243 0.221137i $$-0.929023\pi$$
0.679132 + 0.734016i $$0.262356\pi$$
$$240$$ 0 0
$$241$$ 1.15653e11 + 2.00318e11i 0.00916357 + 0.0158718i 0.870571 0.492043i $$-0.163750\pi$$
−0.861407 + 0.507915i $$0.830416\pi$$
$$242$$ 1.19597e10 0.000926264
$$243$$ 0 0
$$244$$ −1.02399e13 −0.757972
$$245$$ −4.09817e12 7.09824e12i −0.296604 0.513733i
$$246$$ 0 0
$$247$$ 3.07975e12 5.33429e12i 0.213149 0.369184i
$$248$$ −2.23210e12 + 3.86610e12i −0.151087 + 0.261691i
$$249$$ 0 0
$$250$$ −4.30801e12 7.46170e12i −0.279002 0.483245i
$$251$$ −1.29831e13 −0.822567 −0.411284 0.911507i $$-0.634919\pi$$
−0.411284 + 0.911507i $$0.634919\pi$$
$$252$$ 0 0
$$253$$ 9.96692e12 0.604502
$$254$$ 3.15261e12 + 5.46047e12i 0.187105 + 0.324075i
$$255$$ 0 0
$$256$$ 6.82094e12 1.18142e13i 0.387725 0.671560i
$$257$$ 1.19806e13 2.07510e13i 0.666571 1.15453i −0.312286 0.949988i $$-0.601095\pi$$
0.978857 0.204546i $$-0.0655719\pi$$
$$258$$ 0 0
$$259$$ −1.52549e12 2.64223e12i −0.0813318 0.140871i
$$260$$ −4.10758e12 −0.214404
$$261$$ 0 0
$$262$$ −1.51567e13 −0.758485
$$263$$ −1.21369e13 2.10217e13i −0.594771 1.03017i −0.993579 0.113139i $$-0.963909\pi$$
0.398808 0.917034i $$-0.369424\pi$$
$$264$$ 0 0
$$265$$ 3.85447e12 6.67615e12i 0.181181 0.313815i
$$266$$ 2.14218e12 3.71036e12i 0.0986294 0.170831i
$$267$$ 0 0
$$268$$ −1.13946e13 1.97361e13i −0.503453 0.872006i
$$269$$ −2.58377e13 −1.11845 −0.559225 0.829016i $$-0.688901\pi$$
−0.559225 + 0.829016i $$0.688901\pi$$
$$270$$ 0 0
$$271$$ −3.76793e12 −0.156593 −0.0782964 0.996930i $$-0.524948\pi$$
−0.0782964 + 0.996930i $$0.524948\pi$$
$$272$$ −3.40855e12 5.90378e12i −0.138816 0.240437i
$$273$$ 0 0
$$274$$ −3.56638e12 + 6.17716e12i −0.139508 + 0.241636i
$$275$$ −6.81610e12 + 1.18058e13i −0.261340 + 0.452654i
$$276$$ 0 0
$$277$$ 8.20947e12 + 1.42192e13i 0.302466 + 0.523886i 0.976694 0.214637i $$-0.0688569\pi$$
−0.674228 + 0.738523i $$0.735524\pi$$
$$278$$ 1.43230e13 0.517355
$$279$$ 0 0
$$280$$ −6.83219e12 −0.237242
$$281$$ 1.05179e13 + 1.82175e13i 0.358132 + 0.620302i 0.987649 0.156684i $$-0.0500806\pi$$
−0.629517 + 0.776987i $$0.716747\pi$$
$$282$$ 0 0
$$283$$ −8.35659e12 + 1.44740e13i −0.273655 + 0.473985i −0.969795 0.243922i $$-0.921566\pi$$
0.696140 + 0.717906i $$0.254899\pi$$
$$284$$ −7.20653e12 + 1.24821e13i −0.231460 + 0.400900i
$$285$$ 0 0
$$286$$ −3.70639e12 6.41965e12i −0.114535 0.198380i
$$287$$ 5.15917e12 0.156397
$$288$$ 0 0
$$289$$ 1.34200e13 0.391575
$$290$$ −7.44245e12 1.28907e13i −0.213072 0.369052i
$$291$$ 0 0
$$292$$ 1.07735e12 1.86603e12i 0.0296996 0.0514413i
$$293$$ −1.19634e13 + 2.07213e13i −0.323656 + 0.560589i −0.981239 0.192793i $$-0.938245\pi$$
0.657583 + 0.753382i $$0.271579\pi$$
$$294$$ 0 0
$$295$$ 1.25319e13 + 2.17059e13i 0.326585 + 0.565663i
$$296$$ 1.53934e13 0.393758
$$297$$ 0 0
$$298$$ 2.67704e13 0.659881
$$299$$ −5.38546e12 9.32790e12i −0.130326 0.225731i
$$300$$ 0 0
$$301$$ −1.43376e11 + 2.48335e11i −0.00334474 + 0.00579326i
$$302$$ 9.89337e12 1.71358e13i 0.226624 0.392524i
$$303$$ 0 0
$$304$$ −5.26214e12 9.11429e12i −0.116240 0.201334i
$$305$$ −3.35998e13 −0.728933
$$306$$ 0 0
$$307$$ 1.53111e13 0.320439 0.160219 0.987081i $$-0.448780\pi$$
0.160219 + 0.987081i $$0.448780\pi$$
$$308$$ 6.58834e12 + 1.14113e13i 0.135440 + 0.234589i
$$309$$ 0 0
$$310$$ −3.06279e12 + 5.30491e12i −0.0607614 + 0.105242i
$$311$$ 2.49376e13 4.31932e13i 0.486040 0.841846i −0.513831 0.857891i $$-0.671774\pi$$
0.999871 + 0.0160451i $$0.00510753\pi$$
$$312$$ 0 0
$$313$$ 4.97404e13 + 8.61529e13i 0.935870 + 1.62097i 0.773075 + 0.634315i $$0.218718\pi$$
0.162795 + 0.986660i $$0.447949\pi$$
$$314$$ 3.15628e13 0.583529
$$315$$ 0 0
$$316$$ −5.61080e13 −1.00172
$$317$$ 4.16846e13 + 7.21999e13i 0.731392 + 1.26681i 0.956289 + 0.292425i $$0.0944621\pi$$
−0.224897 + 0.974383i $$0.572205\pi$$
$$318$$ 0 0
$$319$$ −3.43239e13 + 5.94507e13i −0.581765 + 1.00765i
$$320$$ 6.51880e12 1.12909e13i 0.108603 0.188106i
$$321$$ 0 0
$$322$$ −3.74596e12 6.48819e12i −0.0603053 0.104452i
$$323$$ 7.36271e13 1.16526
$$324$$ 0 0
$$325$$ 1.47319e13 0.225372
$$326$$ 4.29399e12 + 7.43741e12i 0.0645899 + 0.111873i
$$327$$ 0 0
$$328$$ −1.30150e13 + 2.25427e13i −0.189295 + 0.327868i
$$329$$ −2.24985e13 + 3.89685e13i −0.321792 + 0.557361i
$$330$$ 0 0
$$331$$ 3.17920e13 + 5.50654e13i 0.439809 + 0.761771i 0.997674 0.0681600i $$-0.0217128\pi$$
−0.557865 + 0.829931i $$0.688379\pi$$
$$332$$ −4.31813e13 −0.587538
$$333$$ 0 0
$$334$$ −6.61160e13 −0.870364
$$335$$ −3.73886e13 6.47590e13i −0.484164 0.838597i
$$336$$ 0 0
$$337$$ −6.05007e13 + 1.04790e14i −0.758221 + 1.31328i 0.185535 + 0.982638i $$0.440598\pi$$
−0.943757 + 0.330640i $$0.892735\pi$$
$$338$$ 1.75006e13 3.03118e13i 0.215779 0.373741i
$$339$$ 0 0
$$340$$ −2.45498e13 4.25214e13i −0.293031 0.507544i
$$341$$ 2.82506e13 0.331802
$$342$$ 0 0
$$343$$ 6.15223e13 0.699705
$$344$$ −7.23390e11 1.25295e12i −0.00809657 0.0140237i
$$345$$ 0 0
$$346$$ −1.14046e13 + 1.97534e13i −0.123641 + 0.214153i
$$347$$ −7.78308e13 + 1.34807e14i −0.830499 + 1.43847i 0.0671435 + 0.997743i $$0.478611\pi$$
−0.897643 + 0.440724i $$0.854722\pi$$
$$348$$ 0 0
$$349$$ 1.28215e13 + 2.22075e13i 0.132556 + 0.229594i 0.924661 0.380791i $$-0.124348\pi$$
−0.792105 + 0.610385i $$0.791015\pi$$
$$350$$ 1.02470e13 0.104285
$$351$$ 0 0
$$352$$ −1.05162e14 −1.03722
$$353$$ 1.24549e13 + 2.15725e13i 0.120943 + 0.209479i 0.920140 0.391590i $$-0.128075\pi$$
−0.799197 + 0.601069i $$0.794742\pi$$
$$354$$ 0 0
$$355$$ −2.36464e13 + 4.09568e13i −0.222592 + 0.385541i
$$356$$ 1.83948e13 3.18607e13i 0.170498 0.295312i
$$357$$ 0 0
$$358$$ 2.01766e13 + 3.49469e13i 0.181339 + 0.314089i
$$359$$ −1.57584e14 −1.39474 −0.697370 0.716712i $$-0.745646\pi$$
−0.697370 + 0.716712i $$0.745646\pi$$
$$360$$ 0 0
$$361$$ −2.82438e12 −0.0242457
$$362$$ 1.19613e13 + 2.07176e13i 0.101130 + 0.175163i
$$363$$ 0 0
$$364$$ 7.11980e12 1.23319e13i 0.0583997 0.101151i
$$365$$ 3.53506e12 6.12290e12i 0.0285618 0.0494705i
$$366$$ 0 0
$$367$$ 8.89506e13 + 1.54067e14i 0.697406 + 1.20794i 0.969363 + 0.245633i $$0.0789958\pi$$
−0.271957 + 0.962309i $$0.587671\pi$$
$$368$$ −1.84034e13 −0.142146
$$369$$ 0 0
$$370$$ 2.11222e13 0.158354
$$371$$ 1.33622e13 + 2.31440e13i 0.0987008 + 0.170955i
$$372$$ 0 0
$$373$$ 2.75809e13 4.77715e13i 0.197792 0.342586i −0.750020 0.661415i $$-0.769956\pi$$
0.947812 + 0.318829i $$0.103290\pi$$
$$374$$ 4.43039e13 7.67367e13i 0.313075 0.542262i
$$375$$ 0 0
$$376$$ −1.13514e14 1.96611e14i −0.778959 1.34920i
$$377$$ 7.41854e13 0.501696
$$378$$ 0 0
$$379$$ 1.46463e14 0.962083 0.481042 0.876698i $$-0.340259\pi$$
0.481042 + 0.876698i $$0.340259\pi$$
$$380$$ −3.79001e13 6.56448e13i −0.245375 0.425002i
$$381$$ 0 0
$$382$$ 3.31488e13 5.74155e13i 0.208507 0.361144i
$$383$$ 1.15725e14 2.00441e14i 0.717519 1.24278i −0.244462 0.969659i $$-0.578611\pi$$
0.961980 0.273120i $$-0.0880555\pi$$
$$384$$ 0 0
$$385$$ 2.16180e13 + 3.74434e13i 0.130251 + 0.225601i
$$386$$ 1.30617e14 0.775837
$$387$$ 0 0
$$388$$ −1.10420e14 −0.637490
$$389$$ −7.49358e13 1.29793e14i −0.426547 0.738800i 0.570017 0.821633i $$-0.306937\pi$$
−0.996563 + 0.0828326i $$0.973603\pi$$
$$390$$ 0 0
$$391$$ 6.43746e13 1.11500e14i 0.356240 0.617025i
$$392$$ −7.16798e13 + 1.24153e14i −0.391132 + 0.677461i
$$393$$ 0 0
$$394$$ −3.45131e13 5.97784e13i −0.183128 0.317187i
$$395$$ −1.84104e14 −0.963341
$$396$$ 0 0
$$397$$ 2.08111e14 1.05912 0.529562 0.848271i $$-0.322356\pi$$
0.529562 + 0.848271i $$0.322356\pi$$
$$398$$ −8.74070e12 1.51393e13i −0.0438722 0.0759888i
$$399$$ 0 0
$$400$$ 1.25856e13 2.17989e13i 0.0614531 0.106440i
$$401$$ −6.67040e13 + 1.15535e14i −0.321261 + 0.556440i −0.980748 0.195275i $$-0.937440\pi$$
0.659488 + 0.751715i $$0.270773\pi$$
$$402$$ 0 0
$$403$$ −1.52648e13 2.64393e13i −0.0715339 0.123900i
$$404$$ 1.20326e14 0.556238
$$405$$ 0 0
$$406$$ 5.16010e13 0.232148
$$407$$ −4.87067e13 8.43625e13i −0.216182 0.374438i
$$408$$ 0 0
$$409$$ 1.03084e14 1.78546e14i 0.445361 0.771388i −0.552716 0.833369i $$-0.686409\pi$$
0.998077 + 0.0619816i $$0.0197420\pi$$
$$410$$ −1.78587e13 + 3.09321e13i −0.0761268 + 0.131856i
$$411$$ 0 0
$$412$$ −1.66156e14 2.87790e14i −0.689574 1.19438i
$$413$$ −8.68880e13 −0.355824
$$414$$ 0 0
$$415$$ −1.41689e14 −0.565028
$$416$$ 5.68224e13 + 9.84192e13i 0.223618 + 0.387317i
$$417$$ 0 0
$$418$$ 6.83967e13 1.18467e14i 0.262159 0.454073i
$$419$$ 3.67018e13 6.35693e13i 0.138838 0.240475i −0.788219 0.615395i $$-0.788996\pi$$
0.927057 + 0.374920i $$0.122330\pi$$
$$420$$ 0 0
$$421$$ −8.55560e13 1.48187e14i −0.315282 0.546084i 0.664216 0.747541i $$-0.268766\pi$$
−0.979497 + 0.201457i $$0.935432\pi$$
$$422$$ −1.63036e14 −0.593014
$$423$$ 0 0
$$424$$ −1.34835e14 −0.477848
$$425$$ 8.80480e13 + 1.52504e14i 0.308021 + 0.533508i
$$426$$ 0 0
$$427$$ 5.82396e13 1.00874e14i 0.198548 0.343895i
$$428$$ −6.64176e13 + 1.15039e14i −0.223533 + 0.387171i
$$429$$ 0 0
$$430$$ −9.92606e11 1.71924e12i −0.00325612 0.00563977i
$$431$$ 7.17758e13 0.232463 0.116231 0.993222i $$-0.462919\pi$$
0.116231 + 0.993222i $$0.462919\pi$$
$$432$$ 0 0
$$433$$ 9.98812e13 0.315356 0.157678 0.987491i $$-0.449599\pi$$
0.157678 + 0.987491i $$0.449599\pi$$
$$434$$ −1.06177e13 1.83903e13i −0.0331006 0.0573319i
$$435$$ 0 0
$$436$$ 5.40832e13 9.36749e13i 0.164394 0.284739i
$$437$$ 9.93819e13 1.72134e14i 0.298304 0.516678i
$$438$$ 0 0
$$439$$ 1.45156e13 + 2.51418e13i 0.0424894 + 0.0735938i 0.886488 0.462752i $$-0.153138\pi$$
−0.843999 + 0.536345i $$0.819804\pi$$
$$440$$ −2.18142e14 −0.630594
$$441$$ 0 0
$$442$$ −9.57557e13 −0.269987
$$443$$ 1.64185e14 + 2.84377e14i 0.457207 + 0.791906i 0.998812 0.0487274i $$-0.0155166\pi$$
−0.541605 + 0.840633i $$0.682183\pi$$
$$444$$ 0 0
$$445$$ 6.03579e13 1.04543e14i 0.163966 0.283998i
$$446$$ −8.80184e13 + 1.52452e14i −0.236174 + 0.409065i
$$447$$ 0 0
$$448$$ 2.25985e13 + 3.91418e13i 0.0591631 + 0.102473i
$$449$$ 6.12368e14 1.58364 0.791822 0.610752i $$-0.209133\pi$$
0.791822 + 0.610752i $$0.209133\pi$$
$$450$$ 0 0
$$451$$ 1.64725e14 0.415708
$$452$$ 6.26681e13 + 1.08544e14i 0.156237 + 0.270611i
$$453$$ 0 0
$$454$$ −1.63181e13 + 2.82637e13i −0.0397065 + 0.0687737i
$$455$$ 2.33619e13 4.04639e13i 0.0561623 0.0972759i
$$456$$ 0 0
$$457$$ −1.51742e14 2.62824e14i −0.356095 0.616774i 0.631210 0.775612i $$-0.282559\pi$$
−0.987305 + 0.158838i $$0.949225\pi$$
$$458$$ −2.83786e14 −0.658007
$$459$$ 0 0
$$460$$ −1.32549e14 −0.300061
$$461$$ −3.64654e14 6.31599e14i −0.815691 1.41282i −0.908830 0.417166i $$-0.863023\pi$$
0.0931391 0.995653i $$-0.470310\pi$$
$$462$$ 0 0
$$463$$ −6.10941e13 + 1.05818e14i −0.133445 + 0.231134i −0.925003 0.379961i $$-0.875937\pi$$
0.791557 + 0.611095i $$0.209271\pi$$
$$464$$ 6.33774e13 1.09773e14i 0.136800 0.236944i
$$465$$ 0 0
$$466$$ −2.10760e14 3.65047e14i −0.444290 0.769532i
$$467$$ 6.17381e14 1.28621 0.643103 0.765780i $$-0.277647\pi$$
0.643103 + 0.765780i $$0.277647\pi$$
$$468$$ 0 0
$$469$$ 2.59228e14 0.527510
$$470$$ −1.55759e14 2.69782e14i −0.313267 0.542594i
$$471$$ 0 0
$$472$$ 2.19192e14 3.79652e14i 0.430669 0.745941i
$$473$$ −4.57780e12 + 7.92899e12i −0.00889039 + 0.0153986i
$$474$$ 0 0
$$475$$ 1.35929e14 + 2.35436e14i 0.257927 + 0.446743i
$$476$$ 1.70212e14 0.319265
$$477$$ 0 0
$$478$$ 1.71350e14 0.314073
$$479$$ 5.25419e14 + 9.10052e14i 0.952052 + 1.64900i 0.740976 + 0.671532i $$0.234363\pi$$
0.211076 + 0.977470i $$0.432303\pi$$
$$480$$ 0 0
$$481$$ −5.26358e13 + 9.11678e13i −0.0932144 + 0.161452i
$$482$$ 2.77568e12 4.80762e12i 0.00485972 0.00841728i
$$483$$ 0 0
$$484$$ 3.66763e11 + 6.35253e11i 0.000627678 + 0.00108717i
$$485$$ −3.62316e14 −0.613066
$$486$$ 0 0
$$487$$ −2.19910e14 −0.363777 −0.181889 0.983319i $$-0.558221\pi$$
−0.181889 + 0.983319i $$0.558221\pi$$
$$488$$ 2.93842e14 + 5.08949e14i 0.480623 + 0.832463i
$$489$$ 0 0
$$490$$ −9.83561e13 + 1.70358e14i −0.157298 + 0.272448i
$$491$$ −2.41932e14 + 4.19038e14i −0.382599 + 0.662682i −0.991433 0.130616i $$-0.958304\pi$$
0.608834 + 0.793298i $$0.291638\pi$$
$$492$$ 0 0
$$493$$ 4.43384e14 + 7.67963e14i 0.685681 + 1.18763i
$$494$$ −1.47828e14 −0.226078
$$495$$ 0 0
$$496$$ −5.21634e13 −0.0780219
$$497$$ −8.19743e13 1.41984e14i −0.121260 0.210029i
$$498$$ 0 0
$$499$$ 5.44389e13 9.42909e13i 0.0787691 0.136432i −0.823950 0.566663i $$-0.808234\pi$$
0.902719 + 0.430230i $$0.141568\pi$$
$$500$$ 2.64225e14 4.57651e14i 0.378128 0.654937i
$$501$$ 0 0
$$502$$ 1.55797e14 + 2.69848e14i 0.218116 + 0.377788i
$$503$$ −5.06588e14 −0.701506 −0.350753 0.936468i $$-0.614074\pi$$
−0.350753 + 0.936468i $$0.614074\pi$$
$$504$$ 0 0
$$505$$ 3.94818e14 0.534927
$$506$$ −1.19603e14 2.07158e14i −0.160293 0.277635i
$$507$$ 0 0
$$508$$ −1.93360e14 + 3.34909e14i −0.253581 + 0.439214i
$$509$$ 4.28767e13 7.42646e13i 0.0556254 0.0963461i −0.836872 0.547399i $$-0.815618\pi$$
0.892497 + 0.451053i $$0.148951\pi$$
$$510$$ 0 0
$$511$$ 1.22549e13 + 2.12260e13i 0.0155594 + 0.0269497i
$$512$$ 3.64965e14 0.458423
$$513$$ 0 0
$$514$$ −5.75069e14 −0.707005
$$515$$ −5.45199e14 9.44312e14i −0.663155 1.14862i
$$516$$ 0 0
$$517$$ −7.18344e14 + 1.24421e15i −0.855332 + 1.48148i
$$518$$ −3.66118e13 + 6.34134e13i −0.0431327 + 0.0747081i
$$519$$ 0 0
$$520$$ 1.17870e14 + 2.04156e14i 0.135951 + 0.235475i
$$521$$ −9.27575e14 −1.05862 −0.529312 0.848428i $$-0.677550\pi$$
−0.529312 + 0.848428i $$0.677550\pi$$
$$522$$ 0 0
$$523$$ −2.18187e13 −0.0243820 −0.0121910 0.999926i $$-0.503881\pi$$
−0.0121910 + 0.999926i $$0.503881\pi$$
$$524$$ −4.64805e14 8.05066e14i −0.513983 0.890245i
$$525$$ 0 0
$$526$$ −2.91285e14 + 5.04520e14i −0.315425 + 0.546332i
$$527$$ 1.82466e14 3.16040e14i 0.195534 0.338675i
$$528$$ 0 0
$$529$$ 3.02619e14 + 5.24152e14i 0.317607 + 0.550112i
$$530$$ −1.85015e14 −0.192172
$$531$$ 0 0
$$532$$ 2.62774e14 0.267343
$$533$$ −8.90064e13 1.54164e14i −0.0896235 0.155232i
$$534$$ 0 0
$$535$$ −2.17933e14 + 3.77470e14i −0.214969 + 0.372338i
$$536$$ −6.53952e14 + 1.13268e15i −0.638469 + 1.10586i
$$537$$ 0 0
$$538$$ 3.10052e14 + 5.37027e14i 0.296574 + 0.513681i
$$539$$ 9.07218e14 0.858961
$$540$$ 0 0
$$541$$ −1.69527e15 −1.57273 −0.786363 0.617765i $$-0.788038\pi$$
−0.786363 + 0.617765i $$0.788038\pi$$
$$542$$ 4.52152e13 + 7.83150e13i 0.0415230 + 0.0719199i
$$543$$ 0 0
$$544$$ −6.79220e14 + 1.17644e15i −0.611247 + 1.05871i
$$545$$ 1.77461e14 3.07371e14i 0.158096 0.273831i
$$546$$ 0 0
$$547$$ −3.76072e14 6.51376e14i −0.328353 0.568724i 0.653832 0.756640i $$-0.273160\pi$$
−0.982185 + 0.187915i $$0.939827\pi$$
$$548$$ −4.37477e14 −0.378148
$$549$$ 0 0
$$550$$ 3.27173e14 0.277193
$$551$$ 6.84499e14 + 1.18559e15i 0.574168 + 0.994488i
$$552$$ 0 0
$$553$$ 3.19114e14 5.52722e14i 0.262396 0.454484i
$$554$$ 1.97027e14 3.41261e14i 0.160407 0.277833i
$$555$$ 0 0
$$556$$ 4.39240e14 + 7.60786e14i 0.350583 + 0.607227i
$$557$$ −1.87489e14 −0.148174 −0.0740870 0.997252i $$-0.523604\pi$$
−0.0740870 + 0.997252i $$0.523604\pi$$
$$558$$ 0 0
$$559$$ 9.89417e12 0.00766681
$$560$$ −3.99166e13 6.91375e13i −0.0306280 0.0530493i
$$561$$ 0 0
$$562$$ 2.52429e14 4.37219e14i 0.189928 0.328965i
$$563$$ 1.22486e14 2.12151e14i 0.0912618 0.158070i −0.816781 0.576949i $$-0.804243\pi$$
0.908042 + 0.418878i $$0.137577\pi$$
$$564$$ 0 0
$$565$$ 2.05630e14 + 3.56161e14i 0.150252 + 0.260244i
$$566$$ 4.01116e14 0.290255
$$567$$ 0 0
$$568$$ 8.27185e14 0.587066
$$569$$ 6.76213e14 + 1.17124e15i 0.475298 + 0.823240i 0.999600 0.0282923i $$-0.00900691\pi$$
−0.524302 + 0.851533i $$0.675674\pi$$
$$570$$ 0 0
$$571$$ −7.16114e14 + 1.24035e15i −0.493723 + 0.855154i −0.999974 0.00723249i $$-0.997698\pi$$
0.506250 + 0.862387i $$0.331031\pi$$
$$572$$ 2.27325e14 3.93739e14i 0.155228 0.268862i
$$573$$ 0 0
$$574$$ −6.19100e13 1.07231e14i −0.0414711 0.0718301i
$$575$$ 4.75389e14 0.315410
$$576$$ 0 0
$$577$$ −8.77659e14 −0.571293 −0.285647 0.958335i $$-0.592208\pi$$
−0.285647 + 0.958335i $$0.592208\pi$$
$$578$$ −1.61040e14 2.78930e14i −0.103832 0.179842i
$$579$$ 0 0
$$580$$ 4.56470e14 7.90630e14i 0.288774 0.500172i
$$581$$ 2.45593e14 4.25380e14i 0.153903 0.266568i
$$582$$ 0 0
$$583$$ 4.26635e14 + 7.38954e14i 0.262349 + 0.454402i
$$584$$ −1.23661e14 −0.0753290
$$585$$ 0 0
$$586$$ 5.74245e14 0.343289
$$587$$ −1.21713e15 2.10812e15i −0.720818 1.24849i −0.960672 0.277685i $$-0.910433\pi$$
0.239854 0.970809i $$-0.422900\pi$$
$$588$$ 0 0
$$589$$ 2.81692e14 4.87904e14i 0.163734 0.283596i
$$590$$ 3.00766e14 5.20942e14i 0.173198 0.299988i
$$591$$ 0 0
$$592$$ 8.99347e13 + 1.55771e14i 0.0508344 + 0.0880478i
$$593$$ 3.03318e14 0.169863 0.0849313 0.996387i $$-0.472933\pi$$
0.0849313 + 0.996387i $$0.472933\pi$$
$$594$$ 0 0
$$595$$ 5.58507e14 0.307033
$$596$$ 8.20959e14 + 1.42194e15i 0.447164 + 0.774511i
$$597$$ 0 0
$$598$$ −1.29251e14 + 2.23870e14i −0.0691159 + 0.119712i
$$599$$ −8.50992e14 + 1.47396e15i −0.450898 + 0.780978i −0.998442 0.0557990i $$-0.982229\pi$$
0.547544 + 0.836777i $$0.315563\pi$$
$$600$$ 0 0
$$601$$ −1.16961e15 2.02582e15i −0.608458 1.05388i −0.991495 0.130147i $$-0.958455\pi$$
0.383036 0.923733i $$-0.374878\pi$$
$$602$$ 6.88207e12 0.00354763
$$603$$ 0 0
$$604$$ 1.21359e15 0.614282
$$605$$ 1.20344e12 + 2.08442e12i 0.000603630 + 0.00104552i
$$606$$ 0 0
$$607$$ 1.24804e15 2.16166e15i 0.614737 1.06476i −0.375694 0.926744i $$-0.622595\pi$$
0.990431 0.138012i $$-0.0440712\pi$$
$$608$$ −1.04858e15 + 1.81620e15i −0.511839 + 0.886532i
$$609$$ 0 0
$$610$$ 4.03198e14 + 6.98359e14i 0.193287 + 0.334784i
$$611$$ 1.55258e15 0.737612
$$612$$ 0 0
$$613$$ 2.47301e15 1.15397 0.576983 0.816756i $$-0.304230\pi$$
0.576983 + 0.816756i $$0.304230\pi$$
$$614$$ −1.83733e14 3.18235e14i −0.0849692 0.147171i
$$615$$ 0 0
$$616$$ 3.78113e14 6.54911e14i 0.171762 0.297501i
$$617$$ 1.21684e13 2.10763e13i 0.00547854 0.00948911i −0.863273 0.504737i $$-0.831589\pi$$
0.868752 + 0.495248i $$0.164923\pi$$
$$618$$ 0 0
$$619$$ −2.11273e15 3.65935e15i −0.934425 1.61847i −0.775656 0.631156i $$-0.782581\pi$$
−0.158769 0.987316i $$-0.550753\pi$$
$$620$$ −3.75702e14 −0.164698
$$621$$ 0 0
$$622$$ −1.19700e15 −0.515523
$$623$$ 2.09241e14 + 3.62416e14i 0.0893227 + 0.154711i
$$624$$ 0 0
$$625$$ 2.44448e14 4.23396e14i 0.102529 0.177585i
$$626$$ 1.19377e15 2.06767e15i 0.496320 0.859652i
$$627$$ 0 0
$$628$$ 9.67926e14 + 1.67650e15i 0.395425 + 0.684896i
$$629$$ −1.25835e15 −0.509594
$$630$$ 0 0
$$631$$ −4.26326e15 −1.69660 −0.848302 0.529513i $$-0.822375\pi$$
−0.848302 + 0.529513i $$0.822375\pi$$
$$632$$ 1.61006e15 + 2.78870e15i 0.635180 + 1.10016i
$$633$$ 0 0
$$634$$ 1.00043e15 1.73280e15i 0.387879 0.671826i
$$635$$ −6.34462e14 + 1.09892e15i −0.243865 + 0.422387i
$$636$$ 0 0
$$637$$ −4.90201e14 8.49052e14i −0.185186 0.320751i
$$638$$ 1.64755e15 0.617055
$$639$$ 0 0
$$640$$ 1.63288e15 0.601126
$$641$$ 5.04148e14 + 8.73210e14i 0.184009 + 0.318713i 0.943242 0.332106i $$-0.107759\pi$$
−0.759233 + 0.650819i $$0.774426\pi$$
$$642$$ 0 0
$$643$$ −1.51991e14 + 2.63256e14i −0.0545328 + 0.0944536i −0.892003 0.452029i $$-0.850700\pi$$
0.837470 + 0.546483i $$0.184034\pi$$
$$644$$ 2.29752e14 3.97942e14i 0.0817310 0.141562i
$$645$$ 0 0
$$646$$ −8.83525e14 1.53031e15i −0.308987 0.535181i
$$647$$ −3.43583e15 −1.19140 −0.595700 0.803207i $$-0.703125\pi$$
−0.595700 + 0.803207i $$0.703125\pi$$
$$648$$ 0 0
$$649$$ −2.77421e15 −0.945788
$$650$$ −1.76782e14 3.06196e14i −0.0597607 0.103509i
$$651$$ 0 0
$$652$$ −2.63365e14 + 4.56161e14i −0.0875379 + 0.151620i
$$653$$ −5.92694e14 + 1.02658e15i −0.195347 + 0.338352i −0.947014 0.321191i $$-0.895917\pi$$
0.751667 + 0.659543i $$0.229250\pi$$
$$654$$ 0 0
$$655$$ −1.52514e15 2.64162e15i −0.494291 0.856138i
$$656$$ −3.04157e14 −0.0977522
$$657$$ 0 0
$$658$$ 1.07993e15 0.341312
$$659$$ −1.13255e15 1.96164e15i −0.354967 0.614821i 0.632145 0.774850i $$-0.282175\pi$$
−0.987112 + 0.160029i $$0.948841\pi$$
$$660$$ 0 0
$$661$$ 2.66506e15 4.61602e15i 0.821484 1.42285i −0.0830931 0.996542i $$-0.526480\pi$$
0.904577 0.426310i $$-0.140187\pi$$
$$662$$ 7.63008e14 1.32157e15i 0.233244 0.403990i
$$663$$ 0 0
$$664$$ 1.23911e15 + 2.14621e15i 0.372552 + 0.645279i
$$665$$ 8.62227e14 0.257100
$$666$$ 0 0
$$667$$ 2.39392e15 0.702130
$$668$$ −2.02756e15 3.51183e15i −0.589797 1.02156i
$$669$$ 0 0
$$670$$ −8.97327e14 + 1.55422e15i −0.256767 + 0.444733i
$$671$$ 1.85951e15 3.22076e15i 0.527745 0.914082i
$$672$$ 0 0
$$673$$ −2.37060e15 4.10600e15i −0.661874 1.14640i −0.980123 0.198392i $$-0.936428\pi$$
0.318249 0.948007i $$-0.396905\pi$$
$$674$$ 2.90403e15 0.804215
$$675$$ 0 0
$$676$$ 2.14673e15 0.584886
$$677$$ −7.06536e14 1.22376e15i −0.190940 0.330717i 0.754622 0.656160i $$-0.227820\pi$$
−0.945562 + 0.325442i $$0.894487\pi$$
$$678$$ 0 0
$$679$$ 6.28014e14 1.08775e15i 0.166988 0.289232i
$$680$$ −1.40894e15 + 2.44036e15i −0.371616 + 0.643658i
$$681$$ 0 0
$$682$$ −3.39007e14 5.87178e14i −0.0879822 0.152390i
$$683$$ 3.03116e15 0.780359 0.390180 0.920739i $$-0.372413\pi$$
0.390180 + 0.920739i $$0.372413\pi$$
$$684$$ 0 0
$$685$$ −1.43547e15 −0.363660
$$686$$ −7.38268e14 1.27872e15i −0.185537 0.321360i
$$687$$ 0 0
$$688$$ 8.45270e12 1.46405e13i 0.00209054 0.00362093i
$$689$$ 4.61051e14 7.98564e14i 0.113121 0.195931i
$$690$$ 0 0
$$691$$ 1.37366e15 + 2.37924e15i 0.331703 + 0.574526i 0.982846 0.184429i $$-0.0590436\pi$$
−0.651143 + 0.758955i $$0.725710\pi$$
$$692$$ −1.39897e15 −0.335139
$$693$$ 0 0
$$694$$ 3.73588e15 0.880878
$$695$$ 1.44126e15 + 2.49633e15i 0.337151 + 0.583963i
$$696$$ 0 0
$$697$$ 1.06393e15 1.84278e15i 0.244981 0.424320i
$$698$$ 3.07716e14 5.32980e14i 0.0702984 0.121760i
$$699$$ 0 0
$$700$$ 3.14242e14 + 5.44283e14i 0.0706683 + 0.122401i
$$701$$ −5.72747e15 −1.27795 −0.638974 0.769228i $$-0.720641\pi$$
−0.638974 + 0.769228i $$0.720641\pi$$
$$702$$ 0 0
$$703$$ −1.94265e15 −0.426718
$$704$$ 7.21538e14 + 1.24974e15i 0.157257 + 0.272377i
$$705$$ 0 0
$$706$$ 2.98918e14 5.17741e14i 0.0641395 0.111093i
$$707$$ −6.84352e14 + 1.18533e15i −0.145704 + 0.252368i
$$708$$ 0 0
$$709$$ −3.49163e14 6.04768e14i −0.0731938 0.126775i 0.827106 0.562047i $$-0.189986\pi$$
−0.900299 + 0.435271i $$0.856652\pi$$
$$710$$ 1.13503e15 0.236095
$$711$$ 0 0
$$712$$ −2.11140e15 −0.432445
$$713$$ −4.92585e14 8.53182e14i −0.100113 0.173400i
$$714$$ 0 0
$$715$$ 7.45911e14 1.29196e15i 0.149281 0.258562i
$$716$$ −1.23750e15 + 2.14341e15i −0.245767 + 0.425681i
$$717$$ 0 0
$$718$$ 1.89101e15 + 3.27533e15i 0.369836 + 0.640575i
$$719$$ −9.70979e15 −1.88452 −0.942260 0.334882i $$-0.891304\pi$$
−0.942260 + 0.334882i $$0.891304\pi$$
$$720$$ 0 0
$$721$$ 3.78004e15 0.722525
$$722$$ 3.38926e13 + 5.87037e13i 0.00642910 + 0.0111355i
$$723$$ 0 0
$$724$$ −7.33626e14 + 1.27068e15i −0.137061 + 0.237396i
$$725$$ −1.63713e15 + 2.83560e15i −0.303547 + 0.525758i
$$726$$ 0 0
$$727$$ −1.23234e15 2.13448e15i −0.225057 0.389810i 0.731280 0.682078i $$-0.238923\pi$$
−0.956337 + 0.292268i $$0.905590\pi$$
$$728$$ −8.17230e14 −0.148123
$$729$$ 0 0
$$730$$ −1.69683e14 −0.0302944
$$731$$ 5.91345e13 + 1.02424e14i 0.0104784 + 0.0181491i
$$732$$ 0 0
$$733$$ −3.95643e15 + 6.85273e15i −0.690607 + 1.19617i 0.281032 + 0.959698i $$0.409323\pi$$
−0.971639 + 0.236469i $$0.924010\pi$$
$$734$$ 2.13481e15 3.69761e15i 0.369855 0.640608i
$$735$$ 0 0
$$736$$ 1.83362e15 + 3.17593e15i 0.312955 + 0.542055i
$$737$$ 8.27677e15 1.40213
$$738$$ 0 0
$$739$$ −8.40694e15 −1.40312 −0.701558 0.712613i $$-0.747512\pi$$
−0.701558 + 0.712613i $$0.747512\pi$$
$$740$$ 6.47746e14 + 1.12193e15i 0.107308 + 0.185862i
$$741$$ 0 0
$$742$$ 3.20692e14 5.55455e14i 0.0523440 0.0906625i
$$743$$ 6.81435e14 1.18028e15i 0.110404 0.191226i −0.805529 0.592556i $$-0.798119\pi$$
0.915933 + 0.401330i $$0.131452\pi$$
$$744$$ 0 0
$$745$$ 2.69377e15 + 4.66575e15i 0.430033 + 0.744838i
$$746$$ −1.32388e15 −0.209790
$$747$$ 0 0
$$748$$ 5.43462e15 0.848614
$$749$$ −7.55500e14 1.30856e15i −0.117107 0.202836i
$$750$$ 0 0
$$751$$ −3.40861e15 + 5.90389e15i −0.520664 + 0.901817i 0.479047 + 0.877789i $$0.340982\pi$$
−0.999711 + 0.0240276i $$0.992351\pi$$
$$752$$ 1.32639e15 2.29737e15i 0.201128 0.348364i
$$753$$ 0 0
$$754$$ −8.90225e14 1.54191e15i −0.133032 0.230419i
$$755$$ 3.98208e15 0.590747
$$756$$ 0 0
$$757$$ −6.67049e14 −0.0975282 −0.0487641 0.998810i $$-0.515528\pi$$
−0.0487641 + 0.998810i $$0.515528\pi$$
$$758$$ −1.75756e15 3.04418e15i −0.255111 0.441865i
$$759$$ 0 0
$$760$$ −2.17513e15 + 3.76744e15i −0.311180 + 0.538979i
$$761$$ −3.87204e15 + 6.70657e15i −0.549951 + 0.952544i 0.448326 + 0.893870i $$0.352020\pi$$
−0.998277 + 0.0586734i $$0.981313\pi$$
$$762$$ 0 0
$$763$$ 6.15197e14 + 1.06555e15i 0.0861250 + 0.149173i
$$764$$ 4.06626e15 0.565173
$$765$$ 0 0
$$766$$ −5.55479e15 −0.761043
$$767$$ 1.49900e15 + 2.59634e15i 0.203905 + 0.353173i
$$768$$ 0 0
$$769$$ −1.26206e15 + 2.18594e15i −0.169232 + 0.293119i −0.938150 0.346228i $$-0.887462\pi$$
0.768918 + 0.639348i $$0.220796\pi$$
$$770$$ 5.18831e14 8.98642e14i 0.0690760 0.119643i
$$771$$ 0 0
$$772$$ 4.00560e15 + 6.93790e15i 0.525741 + 0.910611i
$$773$$ 1.11453e16 1.45246 0.726229 0.687453i $$-0.241271\pi$$
0.726229 + 0.687453i $$0.241271\pi$$