# Properties

 Label 252.9.z.d.73.4 Level $252$ Weight $9$ Character 252.73 Analytic conductor $102.659$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 252.z (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$102.659409735$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96$$ x^12 - 3*x^11 + 148097*x^10 + 46071824*x^9 + 21578502553*x^8 + 3561445462121*x^7 + 576413321817541*x^6 + 47217566733462528*x^5 + 5214056955297543333*x^4 + 358752845334081085965*x^3 + 30962072851910211245661*x^2 + 1221542968331193193318500*x + 45396580558961892385326096 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{20}\cdot 3^{10}\cdot 7^{4}$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 73.4 Root $$-28.8366 + 49.9465i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.73 Dual form 252.9.z.d.145.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +O(q^{10})$$ $$q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +(7474.44 - 12946.1i) q^{11} -39673.5i q^{13} +(-84679.4 - 48889.7i) q^{17} +(-177843. + 102678. i) q^{19} +(185312. + 320970. i) q^{23} +(-167741. + 290535. i) q^{25} -117048. q^{29} +(437915. + 252830. i) q^{31} +(478588. + 298070. i) q^{35} +(-986447. - 1.70858e6i) q^{37} -3.25966e6i q^{41} -4.13332e6 q^{43} +(4.79532e6 - 2.76858e6i) q^{47} +(-3.20947e6 + 4.78876e6i) q^{49} +(3.39093e6 - 5.87326e6i) q^{53} -3.51040e6i q^{55} +(1.91904e7 + 1.10796e7i) q^{59} +(-3.97144e6 + 2.29291e6i) q^{61} +(-4.65820e6 - 8.06823e6i) q^{65} +(-1.86385e7 + 3.22828e7i) q^{67} -4.19870e7 q^{71} +(1.08607e7 + 6.27044e6i) q^{73} +(3.58722e7 + 1.19951e6i) q^{77} +(-2.01064e7 - 3.48253e7i) q^{79} -5.31441e6i q^{83} -2.29612e7 q^{85} +(-6.45415e7 + 3.72630e7i) q^{89} +(8.40397e7 - 4.48445e7i) q^{91} +(-2.41115e7 + 4.17623e7i) q^{95} -3.76415e7i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 285 q^{5} + 198 q^{7}+O(q^{10})$$ 12 * q - 285 * q^5 + 198 * q^7 $$12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100})$$ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 203.366 117.413i 0.325386 0.187862i −0.328405 0.944537i $$-0.606511\pi$$
0.653791 + 0.756676i $$0.273178\pi$$
$$6$$ 0 0
$$7$$ 1130.34 + 2118.29i 0.470778 + 0.882251i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 7474.44 12946.1i 0.510514 0.884237i −0.489411 0.872053i $$-0.662788\pi$$
0.999926 0.0121839i $$-0.00387834\pi$$
$$12$$ 0 0
$$13$$ 39673.5i 1.38908i −0.719455 0.694539i $$-0.755608\pi$$
0.719455 0.694539i $$-0.244392\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −84679.4 48889.7i −1.01387 0.585358i −0.101547 0.994831i $$-0.532379\pi$$
−0.912322 + 0.409473i $$0.865713\pi$$
$$18$$ 0 0
$$19$$ −177843. + 102678.i −1.36465 + 0.787882i −0.990239 0.139380i $$-0.955489\pi$$
−0.374413 + 0.927262i $$0.622156\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 185312. + 320970.i 0.662205 + 1.14697i 0.980035 + 0.198825i $$0.0637124\pi$$
−0.317830 + 0.948148i $$0.602954\pi$$
$$24$$ 0 0
$$25$$ −167741. + 290535.i −0.429416 + 0.743771i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −117048. −0.165490 −0.0827448 0.996571i $$-0.526369\pi$$
−0.0827448 + 0.996571i $$0.526369\pi$$
$$30$$ 0 0
$$31$$ 437915. + 252830.i 0.474180 + 0.273768i 0.717988 0.696056i $$-0.245063\pi$$
−0.243808 + 0.969823i $$0.578397\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 478588. + 298070.i 0.318926 + 0.198631i
$$36$$ 0 0
$$37$$ −986447. 1.70858e6i −0.526341 0.911649i −0.999529 0.0306877i $$-0.990230\pi$$
0.473188 0.880961i $$-0.343103\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.25966e6i 1.15355i −0.816903 0.576776i $$-0.804311\pi$$
0.816903 0.576776i $$-0.195689\pi$$
$$42$$ 0 0
$$43$$ −4.13332e6 −1.20900 −0.604498 0.796607i $$-0.706626\pi$$
−0.604498 + 0.796607i $$0.706626\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 4.79532e6 2.76858e6i 0.982711 0.567369i 0.0796238 0.996825i $$-0.474628\pi$$
0.903088 + 0.429456i $$0.141295\pi$$
$$48$$ 0 0
$$49$$ −3.20947e6 + 4.78876e6i −0.556735 + 0.830690i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 3.39093e6 5.87326e6i 0.429749 0.744347i −0.567102 0.823648i $$-0.691935\pi$$
0.996851 + 0.0793006i $$0.0252687\pi$$
$$54$$ 0 0
$$55$$ 3.51040e6i 0.383624i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 1.91904e7 + 1.10796e7i 1.58371 + 0.914355i 0.994312 + 0.106511i $$0.0339680\pi$$
0.589397 + 0.807843i $$0.299365\pi$$
$$60$$ 0 0
$$61$$ −3.97144e6 + 2.29291e6i −0.286833 + 0.165603i −0.636513 0.771266i $$-0.719624\pi$$
0.349680 + 0.936869i $$0.386290\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −4.65820e6 8.06823e6i −0.260954 0.451986i
$$66$$ 0 0
$$67$$ −1.86385e7 + 3.22828e7i −0.924934 + 1.60203i −0.133267 + 0.991080i $$0.542547\pi$$
−0.791667 + 0.610952i $$0.790787\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −4.19870e7 −1.65227 −0.826135 0.563472i $$-0.809465\pi$$
−0.826135 + 0.563472i $$0.809465\pi$$
$$72$$ 0 0
$$73$$ 1.08607e7 + 6.27044e6i 0.382443 + 0.220804i 0.678881 0.734249i $$-0.262465\pi$$
−0.296438 + 0.955052i $$0.595799\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 3.58722e7 + 1.19951e6i 1.02046 + 0.0341224i
$$78$$ 0 0
$$79$$ −2.01064e7 3.48253e7i −0.516209 0.894100i −0.999823 0.0188184i $$-0.994010\pi$$
0.483614 0.875281i $$-0.339324\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 5.31441e6i 0.111981i −0.998431 0.0559903i $$-0.982168\pi$$
0.998431 0.0559903i $$-0.0178316\pi$$
$$84$$ 0 0
$$85$$ −2.29612e7 −0.439865
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −6.45415e7 + 3.72630e7i −1.02868 + 0.593907i −0.916605 0.399793i $$-0.869082\pi$$
−0.112072 + 0.993700i $$0.535749\pi$$
$$90$$ 0 0
$$91$$ 8.40397e7 4.48445e7i 1.22552 0.653948i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −2.41115e7 + 4.17623e7i −0.296026 + 0.512731i
$$96$$ 0 0
$$97$$ 3.76415e7i 0.425187i −0.977141 0.212593i $$-0.931809\pi$$
0.977141 0.212593i $$-0.0681909\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1.57943e8 9.11884e7i −1.51780 0.876303i −0.999781 0.0209346i $$-0.993336\pi$$
−0.518020 0.855368i $$-0.673331\pi$$
$$102$$ 0 0
$$103$$ −9.37340e7 + 5.41173e7i −0.832814 + 0.480826i −0.854815 0.518932i $$-0.826330\pi$$
0.0220010 + 0.999758i $$0.492996\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 9.48762e6 + 1.64330e7i 0.0723806 + 0.125367i 0.899944 0.436005i $$-0.143607\pi$$
−0.827564 + 0.561372i $$0.810274\pi$$
$$108$$ 0 0
$$109$$ 3.98197e7 6.89697e7i 0.282093 0.488599i −0.689807 0.723993i $$-0.742305\pi$$
0.971900 + 0.235394i $$0.0756381\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −2.14140e8 −1.31336 −0.656680 0.754169i $$-0.728040\pi$$
−0.656680 + 0.754169i $$0.728040\pi$$
$$114$$ 0 0
$$115$$ 7.53723e7 + 4.35162e7i 0.430944 + 0.248806i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 7.84586e6 2.34637e8i 0.0391249 1.17006i
$$120$$ 0 0
$$121$$ −4.55511e6 7.88969e6i −0.0212499 0.0368060i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.70509e8i 0.698406i
$$126$$ 0 0
$$127$$ 2.22002e8 0.853381 0.426690 0.904398i $$-0.359679\pi$$
0.426690 + 0.904398i $$0.359679\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −4.38205e8 + 2.52998e8i −1.48796 + 0.859075i −0.999906 0.0137373i $$-0.995627\pi$$
−0.488056 + 0.872812i $$0.662294\pi$$
$$132$$ 0 0
$$133$$ −4.18523e8 2.60661e8i −1.33756 0.833048i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1.73086e8 + 2.99795e8i −0.491339 + 0.851023i −0.999950 0.00997260i $$-0.996826\pi$$
0.508612 + 0.860996i $$0.330159\pi$$
$$138$$ 0 0
$$139$$ 1.04014e8i 0.278632i −0.990248 0.139316i $$-0.955510\pi$$
0.990248 0.139316i $$-0.0444904\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −5.13617e8 2.96537e8i −1.22827 0.709144i
$$144$$ 0 0
$$145$$ −2.38035e7 + 1.37430e7i −0.0538480 + 0.0310891i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.71762e8 2.97501e8i −0.348483 0.603591i 0.637497 0.770453i $$-0.279970\pi$$
−0.985980 + 0.166862i $$0.946637\pi$$
$$150$$ 0 0
$$151$$ −4.21266e8 + 7.29654e8i −0.810305 + 1.40349i 0.102346 + 0.994749i $$0.467365\pi$$
−0.912651 + 0.408740i $$0.865968\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1.18743e8 0.205722
$$156$$ 0 0
$$157$$ −3.00370e8 1.73419e8i −0.494377 0.285429i 0.232011 0.972713i $$-0.425469\pi$$
−0.726388 + 0.687284i $$0.758803\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −4.70440e8 + 7.55349e8i −0.700166 + 1.12420i
$$162$$ 0 0
$$163$$ 6.38287e7 + 1.10555e8i 0.0904203 + 0.156612i 0.907688 0.419646i $$-0.137846\pi$$
−0.817268 + 0.576258i $$0.804512\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 4.84232e8i 0.622569i −0.950317 0.311284i $$-0.899241\pi$$
0.950317 0.311284i $$-0.100759\pi$$
$$168$$ 0 0
$$169$$ −7.58252e8 −0.929537
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 7.57674e8 4.37444e8i 0.845860 0.488357i −0.0133921 0.999910i $$-0.504263\pi$$
0.859252 + 0.511553i $$0.170930\pi$$
$$174$$ 0 0
$$175$$ −8.05041e8 2.69192e7i −0.858352 0.0287019i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 6.06371e8 1.05027e9i 0.590645 1.02303i −0.403501 0.914979i $$-0.632207\pi$$
0.994146 0.108048i $$-0.0344599\pi$$
$$180$$ 0 0
$$181$$ 2.75613e8i 0.256794i 0.991723 + 0.128397i $$0.0409832\pi$$
−0.991723 + 0.128397i $$0.959017\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −4.01220e8 2.31644e8i −0.342528 0.197758i
$$186$$ 0 0
$$187$$ −1.26586e9 + 7.30846e8i −1.03519 + 0.597667i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −9.56485e8 1.65668e9i −0.718695 1.24482i −0.961517 0.274746i $$-0.911406\pi$$
0.242821 0.970071i $$-0.421927\pi$$
$$192$$ 0 0
$$193$$ 4.90016e8 8.48733e8i 0.353168 0.611705i −0.633635 0.773632i $$-0.718438\pi$$
0.986803 + 0.161928i $$0.0517711\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1.49081e9 −0.989824 −0.494912 0.868943i $$-0.664800\pi$$
−0.494912 + 0.868943i $$0.664800\pi$$
$$198$$ 0 0
$$199$$ −8.60781e8 4.96972e8i −0.548884 0.316898i 0.199788 0.979839i $$-0.435975\pi$$
−0.748672 + 0.662941i $$0.769308\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −1.32304e8 2.47940e8i −0.0779090 0.146004i
$$204$$ 0 0
$$205$$ −3.82728e8 6.62904e8i −0.216708 0.375349i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 3.06983e9i 1.60890i
$$210$$ 0 0
$$211$$ −4.64537e8 −0.234364 −0.117182 0.993110i $$-0.537386\pi$$
−0.117182 + 0.993110i $$0.537386\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −8.40576e8 + 4.85307e8i −0.393390 + 0.227124i
$$216$$ 0 0
$$217$$ −4.05745e7 + 1.21341e9i −0.0182984 + 0.547229i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.93962e9 + 3.35952e9i −0.813107 + 1.40834i
$$222$$ 0 0
$$223$$ 6.58116e7i 0.0266123i −0.999911 0.0133062i $$-0.995764\pi$$
0.999911 0.0133062i $$-0.00423561\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1.98442e9 1.14570e9i −0.747360 0.431489i 0.0773791 0.997002i $$-0.475345\pi$$
−0.824739 + 0.565513i $$0.808678\pi$$
$$228$$ 0 0
$$229$$ 2.77398e9 1.60156e9i 1.00870 0.582373i 0.0978887 0.995197i $$-0.468791\pi$$
0.910811 + 0.412825i $$0.135458\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −7.43830e8 1.28835e9i −0.252377 0.437130i 0.711803 0.702380i $$-0.247879\pi$$
−0.964180 + 0.265249i $$0.914546\pi$$
$$234$$ 0 0
$$235$$ 6.50137e8 1.12607e9i 0.213173 0.369227i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −9.50233e8 −0.291232 −0.145616 0.989341i $$-0.546516\pi$$
−0.145616 + 0.989341i $$0.546516\pi$$
$$240$$ 0 0
$$241$$ −3.55088e9 2.05010e9i −1.05261 0.607725i −0.129232 0.991614i $$-0.541251\pi$$
−0.923379 + 0.383889i $$0.874584\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −9.04318e7 + 1.35071e9i −0.0250990 + 0.374884i
$$246$$ 0 0
$$247$$ 4.07358e9 + 7.05564e9i 1.09443 + 1.89561i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 4.77515e9i 1.20307i −0.798845 0.601537i $$-0.794555\pi$$
0.798845 0.601537i $$-0.205445\pi$$
$$252$$ 0 0
$$253$$ 5.54042e9 1.35226
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.28158e9 2.47197e9i 0.981457 0.566645i 0.0787473 0.996895i $$-0.474908\pi$$
0.902710 + 0.430250i $$0.141575\pi$$
$$258$$ 0 0
$$259$$ 2.50423e9 4.02085e9i 0.556514 0.893550i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3.41497e9 + 5.91490e9i −0.713779 + 1.23630i 0.249650 + 0.968336i $$0.419685\pi$$
−0.963429 + 0.267965i $$0.913649\pi$$
$$264$$ 0 0
$$265$$ 1.59256e9i 0.322933i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 3.01169e9 + 1.73880e9i 0.575176 + 0.332078i 0.759214 0.650841i $$-0.225584\pi$$
−0.184038 + 0.982919i $$0.558917\pi$$
$$270$$ 0 0
$$271$$ −5.59984e9 + 3.23307e9i −1.03824 + 0.599429i −0.919335 0.393477i $$-0.871272\pi$$
−0.118907 + 0.992905i $$0.537939\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2.50754e9 + 4.34318e9i 0.438446 + 0.759411i
$$276$$ 0 0
$$277$$ 2.15914e9 3.73973e9i 0.366742 0.635216i −0.622312 0.782769i $$-0.713806\pi$$
0.989054 + 0.147553i $$0.0471397\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −5.64214e9 −0.904938 −0.452469 0.891780i $$-0.649457\pi$$
−0.452469 + 0.891780i $$0.649457\pi$$
$$282$$ 0 0
$$283$$ 3.51708e9 + 2.03059e9i 0.548323 + 0.316574i 0.748445 0.663197i $$-0.230801\pi$$
−0.200122 + 0.979771i $$0.564134\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 6.90489e9 3.68452e9i 1.01772 0.543067i
$$288$$ 0 0
$$289$$ 1.29252e9 + 2.23871e9i 0.185287 + 0.320927i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 8.43223e7i 0.0114412i −0.999984 0.00572061i $$-0.998179\pi$$
0.999984 0.00572061i $$-0.00182094\pi$$
$$294$$ 0 0
$$295$$ 5.20356e9 0.687088
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1.27340e10 7.35197e9i 1.59323 0.919854i
$$300$$ 0 0
$$301$$ −4.67205e9 8.75554e9i −0.569169 1.06664i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −5.38438e8 + 9.32601e8i −0.0622209 + 0.107770i
$$306$$ 0 0
$$307$$ 6.10423e9i 0.687191i −0.939118 0.343596i $$-0.888355\pi$$
0.939118 0.343596i $$-0.111645\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1.74096e9 + 1.00514e9i 0.186100 + 0.107445i 0.590156 0.807289i $$-0.299066\pi$$
−0.404055 + 0.914735i $$0.632400\pi$$
$$312$$ 0 0
$$313$$ −1.10102e10 + 6.35672e9i −1.14714 + 0.662302i −0.948189 0.317708i $$-0.897087\pi$$
−0.198951 + 0.980009i $$0.563754\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.98773e9 5.17489e9i −0.295872 0.512465i 0.679315 0.733846i $$-0.262277\pi$$
−0.975187 + 0.221381i $$0.928943\pi$$
$$318$$ 0 0
$$319$$ −8.74866e8 + 1.51531e9i −0.0844849 + 0.146332i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2.00795e10 1.84477
$$324$$ 0 0
$$325$$ 1.15265e10 + 6.65485e9i 1.03316 + 0.596492i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1.12850e10 + 7.02842e9i 0.963201 + 0.599894i
$$330$$ 0 0
$$331$$ 6.42439e9 + 1.11274e10i 0.535205 + 0.927002i 0.999153 + 0.0411400i $$0.0130990\pi$$
−0.463948 + 0.885862i $$0.653568\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 8.75362e9i 0.695038i
$$336$$ 0 0
$$337$$ −9.70137e9 −0.752166 −0.376083 0.926586i $$-0.622729\pi$$
−0.376083 + 0.926586i $$0.622729\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 6.54634e9 3.77953e9i 0.484151 0.279525i
$$342$$ 0 0
$$343$$ −1.37718e10 1.38565e9i −0.994976 0.100110i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6.48892e8 1.12391e9i 0.0447563 0.0775203i −0.842779 0.538259i $$-0.819082\pi$$
0.887536 + 0.460739i $$0.152416\pi$$
$$348$$ 0 0
$$349$$ 2.01643e10i 1.35919i 0.733587 + 0.679596i $$0.237845\pi$$
−0.733587 + 0.679596i $$0.762155\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.27487e10 + 1.31340e10i 1.46507 + 0.845857i 0.999238 0.0390186i $$-0.0124232\pi$$
0.465828 + 0.884875i $$0.345756\pi$$
$$354$$ 0 0
$$355$$ −8.53872e9 + 4.92983e9i −0.537625 + 0.310398i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1.13441e10 1.96486e10i −0.682958 1.18292i −0.974074 0.226230i $$-0.927360\pi$$
0.291116 0.956688i $$-0.405973\pi$$
$$360$$ 0 0
$$361$$ 1.25936e10 2.18128e10i 0.741517 1.28435i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.94493e9 0.165922
$$366$$ 0 0
$$367$$ 9.38693e8 + 5.41955e8i 0.0517439 + 0.0298744i 0.525649 0.850702i $$-0.323823\pi$$
−0.473905 + 0.880576i $$0.657156\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1.62741e10 + 5.44179e8i 0.859018 + 0.0287241i
$$372$$ 0 0
$$373$$ 1.91674e9 + 3.31989e9i 0.0990211 + 0.171510i 0.911280 0.411788i $$-0.135096\pi$$
−0.812259 + 0.583297i $$0.801762\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 4.64369e9i 0.229878i
$$378$$ 0 0
$$379$$ 3.26734e10 1.58357 0.791785 0.610800i $$-0.209152\pi$$
0.791785 + 0.610800i $$0.209152\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 1.54251e10 8.90569e9i 0.716858 0.413878i −0.0967371 0.995310i $$-0.530841\pi$$
0.813595 + 0.581432i $$0.197507\pi$$
$$384$$ 0 0
$$385$$ 7.43603e9 3.96794e9i 0.338453 0.180602i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 6.92749e9 1.19988e10i 0.302536 0.524008i −0.674173 0.738573i $$-0.735500\pi$$
0.976710 + 0.214565i $$0.0688333\pi$$
$$390$$ 0 0
$$391$$ 3.62394e10i 1.55051i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −8.17791e9 4.72152e9i −0.335934 0.193951i
$$396$$ 0 0
$$397$$ −1.66863e10 + 9.63385e9i −0.671735 + 0.387827i −0.796734 0.604330i $$-0.793441\pi$$
0.124998 + 0.992157i $$0.460107\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −9.58138e9 1.65954e10i −0.370553 0.641817i 0.619097 0.785314i $$-0.287499\pi$$
−0.989651 + 0.143497i $$0.954165\pi$$
$$402$$ 0 0
$$403$$ 1.00306e10 1.73736e10i 0.380285 0.658672i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −2.94926e10 −1.07482
$$408$$ 0 0
$$409$$ 3.45544e10 + 1.99500e10i 1.23484 + 0.712935i 0.968035 0.250815i $$-0.0806987\pi$$
0.266805 + 0.963751i $$0.414032\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −1.77806e9 + 5.31744e10i −0.0611148 + 1.82769i
$$414$$ 0 0
$$415$$ −6.23984e8 1.08077e9i −0.0210369 0.0364369i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 5.17883e10i 1.68026i 0.542387 + 0.840129i $$0.317521\pi$$
−0.542387 + 0.840129i $$0.682479\pi$$
$$420$$ 0 0
$$421$$ 5.78196e9 0.184055 0.0920273 0.995756i $$-0.470665\pi$$
0.0920273 + 0.995756i $$0.470665\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.84083e10 1.64016e10i 0.870743 0.502724i
$$426$$ 0 0
$$427$$ −9.34612e9 5.82088e9i −0.281138 0.175096i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.29999e10 + 2.25165e10i −0.376730 + 0.652516i −0.990584 0.136903i $$-0.956285\pi$$
0.613854 + 0.789420i $$0.289618\pi$$
$$432$$ 0 0
$$433$$ 3.85244e10i 1.09593i 0.836500 + 0.547967i $$0.184598\pi$$
−0.836500 + 0.547967i $$0.815402\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −6.59128e10 3.80548e10i −1.80736 1.04348i
$$438$$ 0 0
$$439$$ 5.36255e10 3.09607e10i 1.44382 0.833591i 0.445720 0.895172i $$-0.352948\pi$$
0.998102 + 0.0615814i $$0.0196144\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.82777e9 1.18260e10i −0.177282 0.307061i 0.763667 0.645611i $$-0.223397\pi$$
−0.940949 + 0.338550i $$0.890064\pi$$
$$444$$ 0 0
$$445$$ −8.75037e9 + 1.51561e10i −0.223144 + 0.386498i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −6.45335e10 −1.58782 −0.793908 0.608038i $$-0.791957\pi$$
−0.793908 + 0.608038i $$0.791957\pi$$
$$450$$ 0 0
$$451$$ −4.21999e10 2.43641e10i −1.02001 0.588904i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 1.18255e10 1.89872e10i 0.275914 0.443013i
$$456$$ 0 0
$$457$$ 2.13781e10 + 3.70279e10i 0.490122 + 0.848916i 0.999935 0.0113692i $$-0.00361901\pi$$
−0.509814 + 0.860285i $$0.670286\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 3.19885e10i 0.708256i 0.935197 + 0.354128i $$0.115222\pi$$
−0.935197 + 0.354128i $$0.884778\pi$$
$$462$$ 0 0
$$463$$ −6.84419e9 −0.148935 −0.0744677 0.997223i $$-0.523726\pi$$
−0.0744677 + 0.997223i $$0.523726\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 1.83350e10 1.05857e10i 0.385490 0.222563i −0.294714 0.955585i $$-0.595224\pi$$
0.680204 + 0.733023i $$0.261891\pi$$
$$468$$ 0 0
$$469$$ −8.94519e10 2.99112e9i −1.84883 0.0618219i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −3.08942e10 + 5.35104e10i −0.617210 + 1.06904i
$$474$$ 0 0
$$475$$ 6.88928e10i 1.35332i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −9.99972e9 5.77334e9i −0.189953 0.109669i 0.402008 0.915636i $$-0.368313\pi$$
−0.591960 + 0.805967i $$0.701646\pi$$
$$480$$ 0 0
$$481$$ −6.77852e10 + 3.91358e10i −1.26635 + 0.731128i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −4.41961e9 7.65500e9i −0.0798762 0.138350i
$$486$$ 0 0
$$487$$ 3.40949e10 5.90541e10i 0.606141 1.04987i −0.385729 0.922612i $$-0.626050\pi$$
0.991870 0.127255i $$-0.0406165\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 3.71885e10 0.639857 0.319929 0.947442i $$-0.396341\pi$$
0.319929 + 0.947442i $$0.396341\pi$$
$$492$$ 0 0
$$493$$ 9.91152e9 + 5.72242e9i 0.167785 + 0.0968706i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −4.74595e10 8.89404e10i −0.777853 1.45772i
$$498$$ 0 0
$$499$$ 2.66255e10 + 4.61166e10i 0.429432 + 0.743799i 0.996823 0.0796501i $$-0.0253803\pi$$
−0.567390 + 0.823449i $$0.692047\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 9.10881e10i 1.42295i −0.702711 0.711475i $$-0.748027\pi$$
0.702711 0.711475i $$-0.251973\pi$$
$$504$$ 0 0
$$505$$ −4.28270e10 −0.658494
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −5.02031e9 + 2.89848e9i −0.0747927 + 0.0431816i −0.536930 0.843627i $$-0.680416\pi$$
0.462137 + 0.886808i $$0.347083\pi$$
$$510$$ 0 0
$$511$$ −1.00629e9 + 3.00938e10i −0.0147584 + 0.441361i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.27082e10 + 2.20113e10i −0.180657 + 0.312907i
$$516$$ 0 0
$$517$$ 8.27743e10i 1.15860i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 6.38767e10 + 3.68792e10i 0.866945 + 0.500531i 0.866332 0.499469i $$-0.166471\pi$$
0.000613137 1.00000i $$0.499805\pi$$
$$522$$ 0 0
$$523$$ −8.49467e10 + 4.90440e10i −1.13538 + 0.655510i −0.945281 0.326256i $$-0.894213\pi$$
−0.190095 + 0.981766i $$0.560880\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.47216e10 4.28190e10i −0.320504 0.555129i
$$528$$ 0 0
$$529$$ −2.95256e10 + 5.11398e10i −0.377030 + 0.653035i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −1.29322e11 −1.60237
$$534$$ 0 0
$$535$$ 3.85892e9 + 2.22795e9i 0.0471032 + 0.0271950i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3.80069e10 + 7.73435e10i 0.450305 + 0.916365i
$$540$$ 0 0
$$541$$ 1.61177e10 + 2.79168e10i 0.188155 + 0.325894i 0.944635 0.328123i $$-0.106416\pi$$
−0.756480 + 0.654017i $$0.773083\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 1.87015e10i 0.211978i
$$546$$ 0 0
$$547$$ −9.97958e10 −1.11471 −0.557356 0.830273i $$-0.688184\pi$$
−0.557356 + 0.830273i $$0.688184\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 2.08161e10 1.20182e10i 0.225836 0.130386i
$$552$$ 0 0
$$553$$ 5.10428e10 8.19554e10i 0.545801 0.876349i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 3.01561e10 5.22319e10i 0.313295 0.542644i −0.665778 0.746150i $$-0.731900\pi$$
0.979074 + 0.203506i $$0.0652337\pi$$
$$558$$ 0 0
$$559$$ 1.63983e11i 1.67939i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.10263e8 + 6.36604e7i 0.00109748 + 0.000633630i 0.500549 0.865708i $$-0.333132\pi$$
−0.499451 + 0.866342i $$0.666465\pi$$
$$564$$ 0 0
$$565$$ −4.35488e10 + 2.51429e10i −0.427349 + 0.246730i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 5.12713e10 + 8.88046e10i 0.489132 + 0.847201i 0.999922 0.0125047i $$-0.00398046\pi$$
−0.510790 + 0.859705i $$0.670647\pi$$
$$570$$ 0 0
$$571$$ 3.04428e10 5.27285e10i 0.286378 0.496022i −0.686564 0.727069i $$-0.740882\pi$$
0.972943 + 0.231047i $$0.0742152\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.24337e11 −1.13745
$$576$$ 0 0
$$577$$ −2.41312e10 1.39322e10i −0.217709 0.125694i 0.387180 0.922004i $$-0.373449\pi$$
−0.604889 + 0.796310i $$0.706783\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1.12574e10 6.00709e9i 0.0987951 0.0527181i
$$582$$ 0 0
$$583$$ −5.06906e10 8.77986e10i −0.438786 0.760000i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 4.01355e9i 0.0338047i −0.999857 0.0169023i $$-0.994620\pi$$
0.999857 0.0169023i $$-0.00538043\pi$$
$$588$$ 0 0
$$589$$ −1.03840e11 −0.862787
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.32222e11 + 7.63384e10i −1.06926 + 0.617340i −0.927980 0.372630i $$-0.878456\pi$$
−0.141283 + 0.989969i $$0.545123\pi$$
$$594$$ 0 0
$$595$$ −2.59540e10 4.86384e10i −0.207079 0.388071i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 5.45784e10 9.45325e10i 0.423949 0.734301i −0.572373 0.819993i $$-0.693977\pi$$
0.996322 + 0.0856928i $$0.0273104\pi$$
$$600$$ 0 0
$$601$$ 1.79228e11i 1.37375i 0.726776 + 0.686875i $$0.241018\pi$$
−0.726776 + 0.686875i $$0.758982\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1.85271e9 1.06966e9i −0.0138289 0.00798409i
$$606$$ 0 0
$$607$$ 3.96127e10 2.28704e10i 0.291796 0.168469i −0.346955 0.937882i $$-0.612784\pi$$
0.638752 + 0.769413i $$0.279451\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.09839e11 1.90247e11i −0.788119 1.36506i
$$612$$ 0 0
$$613$$ 6.70156e10 1.16074e11i 0.474607 0.822044i −0.524970 0.851121i $$-0.675924\pi$$
0.999577 + 0.0290771i $$0.00925685\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.21594e11 −0.839015 −0.419508 0.907752i $$-0.637797\pi$$
−0.419508 + 0.907752i $$0.637797\pi$$
$$618$$ 0 0
$$619$$ −3.51231e10 2.02783e10i −0.239238 0.138124i 0.375589 0.926787i $$-0.377441\pi$$
−0.614826 + 0.788662i $$0.710774\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −1.51888e11 9.45974e10i −1.00825 0.627953i
$$624$$ 0 0
$$625$$ −4.55036e10 7.88146e10i −0.298212 0.516519i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1.92908e11i 1.23239i
$$630$$ 0 0
$$631$$ 2.35096e11 1.48296 0.741478 0.670978i $$-0.234125\pi$$
0.741478 + 0.670978i $$0.234125\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 4.51478e10 2.60661e10i 0.277678 0.160317i
$$636$$ 0 0
$$637$$ 1.89987e11 + 1.27331e11i 1.15389 + 0.773349i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1.51414e11 + 2.62257e11i −0.896881 + 1.55344i −0.0654207 + 0.997858i $$0.520839\pi$$
−0.831460 + 0.555585i $$0.812494\pi$$
$$642$$ 0 0
$$643$$ 1.17949e11i 0.690001i −0.938603 0.345000i $$-0.887879\pi$$
0.938603 0.345000i $$-0.112121\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.55386e11 + 8.97120e10i 0.886735 + 0.511957i 0.872873 0.487947i $$-0.162254\pi$$
0.0138619 + 0.999904i $$0.495587\pi$$
$$648$$ 0 0
$$649$$ 2.86875e11 1.65627e11i 1.61701 0.933582i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.14200e11 + 1.97801e11i 0.628079 + 1.08786i 0.987937 + 0.154858i $$0.0494918\pi$$
−0.359858 + 0.933007i $$0.617175\pi$$
$$654$$ 0 0
$$655$$ −5.94106e10 + 1.02902e11i −0.322774 + 0.559061i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 2.80179e11 1.48557 0.742785 0.669530i $$-0.233504\pi$$
0.742785 + 0.669530i $$0.233504\pi$$
$$660$$ 0 0
$$661$$ −8.31508e9 4.80071e9i −0.0435573 0.0251478i 0.478063 0.878325i $$-0.341339\pi$$
−0.521621 + 0.853178i $$0.674672\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −1.15719e11 3.86943e9i −0.591720 0.0197861i
$$666$$ 0 0
$$667$$ −2.16903e10 3.75688e10i −0.109588 0.189812i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 6.85530e10i 0.338171i
$$672$$ 0 0
$$673$$ −1.19348e11 −0.581776 −0.290888 0.956757i $$-0.593951\pi$$
−0.290888 + 0.956757i $$0.593951\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 8.44704e10 4.87690e10i 0.402115 0.232161i −0.285281 0.958444i $$-0.592087\pi$$
0.687396 + 0.726283i $$0.258754\pi$$
$$678$$ 0 0
$$679$$ 7.97354e10 4.25476e10i 0.375121 0.200169i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.69347e11 2.93317e11i 0.778204 1.34789i −0.154772 0.987950i $$-0.549464\pi$$
0.932976 0.359939i $$-0.117203\pi$$
$$684$$ 0 0
$$685$$ 8.12907e10i 0.369214i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −2.33012e11 1.34530e11i −1.03396 0.596955i
$$690$$ 0 0
$$691$$ 2.57158e11 1.48470e11i 1.12794 0.651219i 0.184527 0.982827i $$-0.440925\pi$$
0.943417 + 0.331608i $$0.107591\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1.22126e10 2.11529e10i −0.0523443 0.0906630i
$$696$$ 0 0
$$697$$ −1.59364e11 + 2.76026e11i −0.675240 + 1.16955i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.94718e11 0.806370 0.403185 0.915118i $$-0.367903\pi$$
0.403185 + 0.915118i $$0.367903\pi$$
$$702$$ 0 0
$$703$$ 3.50865e11 + 2.02572e11i 1.43654 + 0.829389i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.46340e10 4.37642e11i 0.0585714 1.75163i
$$708$$ 0 0
$$709$$ −2.00882e11 3.47938e11i −0.794979 1.37694i −0.922852 0.385154i $$-0.874148\pi$$
0.127873 0.991791i $$-0.459185\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.87410e11i 0.725161i
$$714$$ 0 0
$$715$$ −1.39270e11 −0.532884
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.54791e11 8.93684e10i 0.579201 0.334402i −0.181615 0.983370i $$-0.558132\pi$$
0.760816 + 0.648968i $$0.224799\pi$$
$$720$$ 0 0
$$721$$ −2.20587e11 1.37384e11i −0.816280 0.508389i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 1.96337e10 3.40065e10i 0.0710639 0.123086i
$$726$$ 0 0
$$727$$ 1.97437e11i 0.706790i 0.935474 + 0.353395i $$0.114973\pi$$
−0.935474 + 0.353395i $$0.885027\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 3.50006e11 + 2.02076e11i 1.22576 + 0.707695i
$$732$$ 0 0
$$733$$ 1.01144e11 5.83958e10i 0.350370 0.202286i −0.314478 0.949265i $$-0.601830\pi$$
0.664848 + 0.746979i $$0.268496\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2.78624e11 + 4.82591e11i 0.944384 + 1.63572i
$$738$$ 0 0
$$739$$ −8.45542e10 + 1.46452e11i −0.283503 + 0.491042i −0.972245 0.233965i $$-0.924830\pi$$
0.688742 + 0.725006i $$0.258163\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1.84466e11 0.605287 0.302644 0.953104i $$-0.402131\pi$$
0.302644 + 0.953104i $$0.402131\pi$$
$$744$$ 0 0
$$745$$ −6.98611e10 4.03343e10i −0.226783 0.130933i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −2.40856e10 + 3.86724e10i −0.0765298 + 0.122878i
$$750$$ 0 0
$$751$$ 1.50650e11 + 2.60933e11i 0.473596 + 0.820293i 0.999543 0.0302244i $$-0.00962218\pi$$
−0.525947 + 0.850518i $$0.676289\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 1.97849e11i 0.608900i
$$756$$ 0 0
$$757$$ 4.94329e11 1.50533 0.752666 0.658403i $$-0.228768\pi$$
0.752666 + 0.658403i $$0.228768\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 5.78956e10 3.34260e10i 0.172626 0.0996658i −0.411197 0.911546i $$-0.634889\pi$$
0.583824 + 0.811881i $$0.301556\pi$$
$$762$$ 0 0
$$763$$ 1.91107e11 + 6.39031e9i 0.563870 + 0.0188549i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 4.39565e11 7.61348e11i 1.27011 2.19989i
$$768$$ 0 0
$$769$$ 1.20153e11i 0.343581i 0.985134 + 0.171790i $$0.0549552\pi$$
−0.985134 + 0.171790i $$0.945045\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 3.05856e11 + 1.76586e11i 0.856640 + 0.494582i 0.862886 0.505399i $$-0.168655\pi$$
−0.00624545 + 0.999980i $$0.501988\pi$$
$$774$$ 0 0
$$775$$ −1.46912e11 + 8.48198e10i −0.407241 + 0.235120i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 3.34694e11 + 5.79707e11i 0.908862 + 1.57420i
$$780$$ 0 0
$$781$$ −3.13829e11 + 5.43568e11i −0.843508 + 1.46100i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −8.14468e10 −0.214484
$$786$$ 0 0
$$787$$ −4.79863e11 2.77049e11i −1.25089 0.722201i −0.279602 0.960116i $$-0.590203\pi$$
−0.971286 + 0.237915i $$0.923536\pi$$
$$788$$ 0 0