# Properties

 Label 1440.2.bi.d.847.7 Level $1440$ Weight $2$ Character 1440.847 Analytic conductor $11.498$ Analytic rank $0$ Dimension $16$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1440.bi (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.4984578911$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 5 x^{12} + 28 x^{8} + 80 x^{4} + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{49}]$$ Coefficient ring index: $$2^{18}$$ Twist minimal: no (minimal twist has level 360) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 847.7 Root $$0.512386 + 1.31813i$$ of defining polynomial Character $$\chi$$ $$=$$ 1440.847 Dual form 1440.2.bi.d.1423.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.83051 - 1.28422i) q^{5} +(-2.94984 + 2.94984i) q^{7} +O(q^{10})$$ $$q+(1.83051 - 1.28422i) q^{5} +(-2.94984 + 2.94984i) q^{7} +1.61148 q^{11} +(-2.50967 - 2.50967i) q^{13} +(-4.59398 - 4.59398i) q^{17} -4.00000i q^{19} +(-1.09259 - 1.09259i) q^{23} +(1.70156 - 4.70156i) q^{25} +4.75362 q^{29} -5.01934i q^{31} +(-1.61148 + 9.18797i) q^{35} +(2.50967 - 2.50967i) q^{37} +9.18797 q^{41} +(7.40312 - 7.40312i) q^{43} +(-7.32206 + 7.32206i) q^{47} -10.4031i q^{49} +(-3.11473 - 3.11473i) q^{53} +(2.94984 - 2.06950i) q^{55} -1.61148i q^{59} +6.78003i q^{61} +(-7.81695 - 1.37102i) q^{65} +(-7.40312 - 7.40312i) q^{67} +(5.00000 - 5.00000i) q^{73} +(-4.75362 + 4.75362i) q^{77} -5.01934 q^{79} +(7.57648 - 7.57648i) q^{83} +(-14.3090 - 2.50967i) q^{85} +2.74204i q^{89} +14.8062 q^{91} +(-5.13688 - 7.32206i) q^{95} +(2.40312 + 2.40312i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + O(q^{10})$$ $$16q - 24q^{25} + 16q^{43} - 16q^{67} + 80q^{73} + 32q^{91} - 64q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$$.

 $$n$$ $$577$$ $$641$$ $$901$$ $$991$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$ $$-1$$ $$-1$$

## 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
$$5$$ 1.83051 1.28422i 0.818631 0.574320i
$$6$$ 0 0
$$7$$ −2.94984 + 2.94984i −1.11494 + 1.11494i −0.122462 + 0.992473i $$0.539079\pi$$
−0.992473 + 0.122462i $$0.960921\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.61148 0.485880 0.242940 0.970041i $$-0.421888\pi$$
0.242940 + 0.970041i $$0.421888\pi$$
$$12$$ 0 0
$$13$$ −2.50967 2.50967i −0.696057 0.696057i 0.267501 0.963558i $$-0.413802\pi$$
−0.963558 + 0.267501i $$0.913802\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −4.59398 4.59398i −1.11420 1.11420i −0.992576 0.121629i $$-0.961188\pi$$
−0.121629 0.992576i $$-0.538812\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i −0.888523 0.458831i $$-0.848268\pi$$
0.888523 0.458831i $$-0.151732\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1.09259 1.09259i −0.227821 0.227821i 0.583961 0.811782i $$-0.301502\pi$$
−0.811782 + 0.583961i $$0.801502\pi$$
$$24$$ 0 0
$$25$$ 1.70156 4.70156i 0.340312 0.940312i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.75362 0.882725 0.441362 0.897329i $$-0.354495\pi$$
0.441362 + 0.897329i $$0.354495\pi$$
$$30$$ 0 0
$$31$$ 5.01934i 0.901500i −0.892650 0.450750i $$-0.851157\pi$$
0.892650 0.450750i $$-0.148843\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1.61148 + 9.18797i −0.272390 + 1.55305i
$$36$$ 0 0
$$37$$ 2.50967 2.50967i 0.412587 0.412587i −0.470052 0.882639i $$-0.655765\pi$$
0.882639 + 0.470052i $$0.155765\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 9.18797 1.43492 0.717460 0.696600i $$-0.245305\pi$$
0.717460 + 0.696600i $$0.245305\pi$$
$$42$$ 0 0
$$43$$ 7.40312 7.40312i 1.12897 1.12897i 0.138620 0.990346i $$-0.455733\pi$$
0.990346 0.138620i $$-0.0442667\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −7.32206 + 7.32206i −1.06803 + 1.06803i −0.0705213 + 0.997510i $$0.522466\pi$$
−0.997510 + 0.0705213i $$0.977534\pi$$
$$48$$ 0 0
$$49$$ 10.4031i 1.48616i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −3.11473 3.11473i −0.427841 0.427841i 0.460051 0.887892i $$-0.347831\pi$$
−0.887892 + 0.460051i $$0.847831\pi$$
$$54$$ 0 0
$$55$$ 2.94984 2.06950i 0.397756 0.279051i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 1.61148i 0.209797i −0.994483 0.104899i $$-0.966548\pi$$
0.994483 0.104899i $$-0.0334518\pi$$
$$60$$ 0 0
$$61$$ 6.78003i 0.868093i 0.900890 + 0.434047i $$0.142915\pi$$
−0.900890 + 0.434047i $$0.857085\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −7.81695 1.37102i −0.969573 0.170054i
$$66$$ 0 0
$$67$$ −7.40312 7.40312i −0.904436 0.904436i 0.0913805 0.995816i $$-0.470872\pi$$
−0.995816 + 0.0913805i $$0.970872\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 5.00000 5.00000i 0.585206 0.585206i −0.351123 0.936329i $$-0.614200\pi$$
0.936329 + 0.351123i $$0.114200\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −4.75362 + 4.75362i −0.541725 + 0.541725i
$$78$$ 0 0
$$79$$ −5.01934 −0.564720 −0.282360 0.959309i $$-0.591117\pi$$
−0.282360 + 0.959309i $$0.591117\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 7.57648 7.57648i 0.831627 0.831627i −0.156112 0.987739i $$-0.549896\pi$$
0.987739 + 0.156112i $$0.0498961\pi$$
$$84$$ 0 0
$$85$$ −14.3090 2.50967i −1.55203 0.272212i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.74204i 0.290655i 0.989384 + 0.145328i $$0.0464236\pi$$
−0.989384 + 0.145328i $$0.953576\pi$$
$$90$$ 0 0
$$91$$ 14.8062 1.55212
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −5.13688 7.32206i −0.527032 0.751227i
$$96$$ 0 0
$$97$$ 2.40312 + 2.40312i 0.244000 + 0.244000i 0.818503 0.574503i $$-0.194804\pi$$
−0.574503 + 0.818503i $$0.694804\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.79790i 0.875424i 0.899115 + 0.437712i $$0.144211\pi$$
−0.899115 + 0.437712i $$0.855789\pi$$
$$102$$ 0 0
$$103$$ −7.96918 7.96918i −0.785227 0.785227i 0.195481 0.980707i $$-0.437373\pi$$
−0.980707 + 0.195481i $$0.937373\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1.61148 + 1.61148i 0.155788 + 0.155788i 0.780697 0.624909i $$-0.214864\pi$$
−0.624909 + 0.780697i $$0.714864\pi$$
$$108$$ 0 0
$$109$$ −11.7994 −1.13017 −0.565087 0.825031i $$-0.691157\pi$$
−0.565087 + 0.825031i $$0.691157\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −4.59398 + 4.59398i −0.432166 + 0.432166i −0.889364 0.457199i $$-0.848853\pi$$
0.457199 + 0.889364i $$0.348853\pi$$
$$114$$ 0 0
$$115$$ −3.40312 0.596876i −0.317343 0.0556590i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 27.1030 2.48453
$$120$$ 0 0
$$121$$ −8.40312 −0.763920
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −2.92310 10.7915i −0.261450 0.965217i
$$126$$ 0 0
$$127$$ −3.83019 + 3.83019i −0.339874 + 0.339874i −0.856320 0.516446i $$-0.827255\pi$$
0.516446 + 0.856320i $$0.327255\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −13.5415 −1.18313 −0.591563 0.806259i $$-0.701489\pi$$
−0.591563 + 0.806259i $$0.701489\pi$$
$$132$$ 0 0
$$133$$ 11.7994 + 11.7994i 1.02313 + 1.02313i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 11.0399 + 11.0399i 0.943203 + 0.943203i 0.998472 0.0552681i $$-0.0176013\pi$$
−0.0552681 + 0.998472i $$0.517601\pi$$
$$138$$ 0 0
$$139$$ 4.00000i 0.339276i 0.985506 + 0.169638i $$0.0542598\pi$$
−0.985506 + 0.169638i $$0.945740\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −4.04429 4.04429i −0.338200 0.338200i
$$144$$ 0 0
$$145$$ 8.70156 6.10469i 0.722625 0.506967i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 8.79790 0.720752 0.360376 0.932807i $$-0.382648\pi$$
0.360376 + 0.932807i $$0.382648\pi$$
$$150$$ 0 0
$$151$$ 0.880344i 0.0716414i −0.999358 0.0358207i $$-0.988595\pi$$
0.999358 0.0358207i $$-0.0114045\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −6.44593 9.18797i −0.517750 0.737995i
$$156$$ 0 0
$$157$$ 9.28970 9.28970i 0.741398 0.741398i −0.231449 0.972847i $$-0.574347\pi$$
0.972847 + 0.231449i $$0.0743465\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 6.44593 0.508010
$$162$$ 0 0
$$163$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 7.32206 7.32206i 0.566598 0.566598i −0.364576 0.931174i $$-0.618786\pi$$
0.931174 + 0.364576i $$0.118786\pi$$
$$168$$ 0 0
$$169$$ 0.403124i 0.0310096i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −7.86835 7.86835i −0.598220 0.598220i 0.341619 0.939839i $$-0.389025\pi$$
−0.939839 + 0.341619i $$0.889025\pi$$
$$174$$ 0 0
$$175$$ 8.84952 + 18.8882i 0.668961 + 1.42781i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 26.4333i 1.97572i −0.155343 0.987861i $$-0.549648\pi$$
0.155343 0.987861i $$-0.450352\pi$$
$$180$$ 0 0
$$181$$ 11.7994i 0.877040i −0.898721 0.438520i $$-0.855503\pi$$
0.898721 0.438520i $$-0.144497\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.37102 7.81695i 0.100799 0.574713i
$$186$$ 0 0
$$187$$ −7.40312 7.40312i −0.541370 0.541370i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 19.0145i 1.37584i 0.725787 + 0.687919i $$0.241476\pi$$
−0.725787 + 0.687919i $$0.758524\pi$$
$$192$$ 0 0
$$193$$ −12.4031 + 12.4031i −0.892796 + 0.892796i −0.994786 0.101989i $$-0.967479\pi$$
0.101989 + 0.994786i $$0.467479\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −9.34420 + 9.34420i −0.665747 + 0.665747i −0.956729 0.290982i $$-0.906018\pi$$
0.290982 + 0.956729i $$0.406018\pi$$
$$198$$ 0 0
$$199$$ 20.9577 1.48565 0.742826 0.669485i $$-0.233485\pi$$
0.742826 + 0.669485i $$0.233485\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −14.0224 + 14.0224i −0.984181 + 0.984181i
$$204$$ 0 0
$$205$$ 16.8187 11.7994i 1.17467 0.824103i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 6.44593i 0.445874i
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 4.04429 23.0588i 0.275818 1.57259i
$$216$$ 0 0
$$217$$ 14.8062 + 14.8062i 1.00511 + 1.00511i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 23.0588i 1.55110i
$$222$$ 0 0
$$223$$ −3.83019 3.83019i −0.256488 0.256488i 0.567136 0.823624i $$-0.308051\pi$$
−0.823624 + 0.567136i $$0.808051\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 15.6339 + 15.6339i 1.03766 + 1.03766i 0.999263 + 0.0383956i $$0.0122247\pi$$
0.0383956 + 0.999263i $$0.487775\pi$$
$$228$$ 0 0
$$229$$ 6.78003 0.448037 0.224018 0.974585i $$-0.428082\pi$$
0.224018 + 0.974585i $$0.428082\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −11.0399 + 11.0399i −0.723249 + 0.723249i −0.969266 0.246017i $$-0.920878\pi$$
0.246017 + 0.969266i $$0.420878\pi$$
$$234$$ 0 0
$$235$$ −4.00000 + 22.8062i −0.260931 + 1.48772i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −8.08857 −0.523206 −0.261603 0.965176i $$-0.584251\pi$$
−0.261603 + 0.965176i $$0.584251\pi$$
$$240$$ 0 0
$$241$$ −6.80625 −0.438429 −0.219215 0.975677i $$-0.570349\pi$$
−0.219215 + 0.975677i $$0.570349\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −13.3599 19.0431i −0.853532 1.21662i
$$246$$ 0 0
$$247$$ −10.0387 + 10.0387i −0.638746 + 0.638746i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 19.9874 1.26159 0.630797 0.775948i $$-0.282728\pi$$
0.630797 + 0.775948i $$0.282728\pi$$
$$252$$ 0 0
$$253$$ −1.76069 1.76069i −0.110694 0.110694i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 13.7820 + 13.7820i 0.859694 + 0.859694i 0.991302 0.131607i $$-0.0420138\pi$$
−0.131607 + 0.991302i $$0.542014\pi$$
$$258$$ 0 0
$$259$$ 14.8062i 0.920016i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2.95170 + 2.95170i 0.182009 + 0.182009i 0.792231 0.610221i $$-0.208920\pi$$
−0.610221 + 0.792231i $$0.708920\pi$$
$$264$$ 0 0
$$265$$ −9.70156 1.70156i −0.595962 0.104526i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 18.3051 1.11608 0.558042 0.829813i $$-0.311553\pi$$
0.558042 + 0.829813i $$0.311553\pi$$
$$270$$ 0 0
$$271$$ 12.6797i 0.770237i −0.922867 0.385119i $$-0.874160\pi$$
0.922867 0.385119i $$-0.125840\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2.74204 7.57648i 0.165351 0.456879i
$$276$$ 0 0
$$277$$ −7.52901 + 7.52901i −0.452374 + 0.452374i −0.896142 0.443768i $$-0.853642\pi$$
0.443768 + 0.896142i $$0.353642\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −27.5639 −1.64432 −0.822162 0.569253i $$-0.807232\pi$$
−0.822162 + 0.569253i $$0.807232\pi$$
$$282$$ 0 0
$$283$$ −7.40312 + 7.40312i −0.440070 + 0.440070i −0.892035 0.451965i $$-0.850723\pi$$
0.451965 + 0.892035i $$0.350723\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −27.1030 + 27.1030i −1.59984 + 1.59984i
$$288$$ 0 0
$$289$$ 25.2094i 1.48290i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 3.11473 + 3.11473i 0.181965 + 0.181965i 0.792211 0.610247i $$-0.208930\pi$$
−0.610247 + 0.792211i $$0.708930\pi$$
$$294$$ 0 0
$$295$$ −2.06950 2.94984i −0.120491 0.171746i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 5.48408i 0.317152i
$$300$$ 0 0
$$301$$ 43.6761i 2.51745i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 8.70704 + 12.4109i 0.498564 + 0.710648i
$$306$$ 0 0
$$307$$ 20.0000 + 20.0000i 1.14146 + 1.14146i 0.988183 + 0.153277i $$0.0489827\pi$$
0.153277 + 0.988183i $$0.451017\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 8.08857i 0.458661i 0.973349 + 0.229330i $$0.0736537\pi$$
−0.973349 + 0.229330i $$0.926346\pi$$
$$312$$ 0 0
$$313$$ −19.8062 + 19.8062i −1.11952 + 1.11952i −0.127703 + 0.991812i $$0.540760\pi$$
−0.991812 + 0.127703i $$0.959240\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −4.59058 + 4.59058i −0.257833 + 0.257833i −0.824172 0.566339i $$-0.808359\pi$$
0.566339 + 0.824172i $$0.308359\pi$$
$$318$$ 0 0
$$319$$ 7.66037 0.428898
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −18.3759 + 18.3759i −1.02246 + 1.02246i
$$324$$ 0 0
$$325$$ −16.0697 + 7.52901i −0.891388 + 0.417634i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 43.1978i 2.38157i
$$330$$ 0 0
$$331$$ −2.80625 −0.154245 −0.0771227 0.997022i $$-0.524573\pi$$
−0.0771227 + 0.997022i $$0.524573\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −23.0588 4.04429i −1.25983 0.220963i
$$336$$ 0 0
$$337$$ −2.40312 2.40312i −0.130907 0.130907i 0.638618 0.769524i $$-0.279507\pi$$
−0.769524 + 0.638618i $$0.779507\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.08857i 0.438021i
$$342$$ 0 0
$$343$$ 10.0387 + 10.0387i 0.542038 + 0.542038i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −2.74204 2.74204i −0.147200 0.147200i 0.629666 0.776866i $$-0.283192\pi$$
−0.776866 + 0.629666i $$0.783192\pi$$
$$348$$ 0 0
$$349$$ −6.78003 −0.362926 −0.181463 0.983398i $$-0.558083\pi$$
−0.181463 + 0.983398i $$0.558083\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 13.7820 13.7820i 0.733539 0.733539i −0.237780 0.971319i $$-0.576420\pi$$
0.971319 + 0.237780i $$0.0764197\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 35.1916 1.85734 0.928671 0.370904i $$-0.120952\pi$$
0.928671 + 0.370904i $$0.120952\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.73147 15.5737i 0.142972 0.815163i
$$366$$ 0 0
$$367$$ 14.7492 14.7492i 0.769902 0.769902i −0.208187 0.978089i $$-0.566756\pi$$
0.978089 + 0.208187i $$0.0667562\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 18.3759 0.954031
$$372$$ 0 0
$$373$$ 14.3090 + 14.3090i 0.740894 + 0.740894i 0.972750 0.231856i $$-0.0744799\pi$$
−0.231856 + 0.972750i $$0.574480\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −11.9300 11.9300i −0.614427 0.614427i
$$378$$ 0 0
$$379$$ 18.8062i 0.966012i 0.875617 + 0.483006i $$0.160455\pi$$
−0.875617 + 0.483006i $$0.839545\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −26.0105 26.0105i −1.32907 1.32907i −0.906180 0.422892i $$-0.861015\pi$$
−0.422892 0.906180i $$-0.638985\pi$$
$$384$$ 0 0
$$385$$ −2.59688 + 14.8062i −0.132349 + 0.754596i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 37.3196 1.89218 0.946090 0.323905i $$-0.104996\pi$$
0.946090 + 0.323905i $$0.104996\pi$$
$$390$$ 0 0
$$391$$ 10.0387i 0.507678i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −9.18797 + 6.44593i −0.462297 + 0.324330i
$$396$$ 0 0
$$397$$ 19.3284 19.3284i 0.970063 0.970063i −0.0295016 0.999565i $$-0.509392\pi$$
0.999565 + 0.0295016i $$0.00939202\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 12.8919 0.643789 0.321894 0.946776i $$-0.395680\pi$$
0.321894 + 0.946776i $$0.395680\pi$$
$$402$$ 0 0
$$403$$ −12.5969 + 12.5969i −0.627495 + 0.627495i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 4.04429 4.04429i 0.200468 0.200468i
$$408$$ 0 0
$$409$$ 3.40312i 0.168274i 0.996454 + 0.0841368i $$0.0268133\pi$$
−0.996454 + 0.0841368i $$0.973187\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 4.75362 + 4.75362i 0.233910 + 0.233910i
$$414$$ 0 0
$$415$$ 4.13899 23.5987i 0.203175 1.15842i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 31.9174i 1.55927i 0.626235 + 0.779634i $$0.284595\pi$$
−0.626235 + 0.779634i $$0.715405\pi$$
$$420$$ 0 0
$$421$$ 30.3788i 1.48057i −0.672293 0.740285i $$-0.734691\pi$$
0.672293 0.740285i $$-0.265309\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −29.4158 + 13.7820i −1.42688 + 0.668523i
$$426$$ 0 0
$$427$$ −20.0000 20.0000i −0.967868 0.967868i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 27.1030i 1.30551i 0.757570 + 0.652754i $$0.226386\pi$$
−0.757570 + 0.652754i $$0.773614\pi$$
$$432$$ 0 0
$$433$$ 12.4031 12.4031i 0.596056 0.596056i −0.343205 0.939261i $$-0.611512\pi$$
0.939261 + 0.343205i $$0.111512\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −4.37036 + 4.37036i −0.209063 + 0.209063i
$$438$$ 0 0
$$439$$ −10.9190 −0.521136 −0.260568 0.965455i $$-0.583910\pi$$
−0.260568 + 0.965455i $$0.583910\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 15.6339 15.6339i 0.742789 0.742789i −0.230325 0.973114i $$-0.573979\pi$$
0.973114 + 0.230325i $$0.0739789\pi$$
$$444$$ 0 0
$$445$$ 3.52138 + 5.01934i 0.166929 + 0.237939i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 6.44593i 0.304202i −0.988365 0.152101i $$-0.951396\pi$$
0.988365 0.152101i $$-0.0486039\pi$$
$$450$$ 0 0
$$451$$ 14.8062 0.697199
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 27.1030 19.0145i 1.27061 0.891412i
$$456$$ 0 0
$$457$$ −9.80625 9.80625i −0.458717 0.458717i 0.439517 0.898234i $$-0.355150\pi$$
−0.898234 + 0.439517i $$0.855150\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 18.3051i 0.852555i −0.904592 0.426278i $$-0.859825\pi$$
0.904592 0.426278i $$-0.140175\pi$$
$$462$$ 0 0
$$463$$ 14.7492 + 14.7492i 0.685454 + 0.685454i 0.961224 0.275770i $$-0.0889328\pi$$
−0.275770 + 0.961224i $$0.588933\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −10.7994 10.7994i −0.499739 0.499739i 0.411618 0.911357i $$-0.364964\pi$$
−0.911357 + 0.411618i $$0.864964\pi$$
$$468$$ 0 0
$$469$$ 43.6761 2.01677
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 11.9300 11.9300i 0.548542 0.548542i
$$474$$ 0 0
$$475$$ −18.8062 6.80625i −0.862890 0.312292i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −8.08857 −0.369576 −0.184788 0.982778i $$-0.559160\pi$$
−0.184788 + 0.982778i $$0.559160\pi$$
$$480$$ 0 0
$$481$$ −12.5969 −0.574368
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 7.48509 + 1.31281i 0.339880 + 0.0596118i
$$486$$ 0 0
$$487$$ 2.06950 2.06950i 0.0937778 0.0937778i −0.658662 0.752439i $$-0.728877\pi$$
0.752439 + 0.658662i $$0.228877\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 11.2804 0.509076 0.254538 0.967063i $$-0.418077\pi$$
0.254538 + 0.967063i $$0.418077\pi$$
$$492$$ 0 0
$$493$$ −21.8380 21.8380i −0.983536 0.983536i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 18.8062i 0.841883i −0.907088 0.420942i $$-0.861700\pi$$
0.907088 0.420942i $$-0.138300\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 5.13688 + 5.13688i 0.229042 + 0.229042i 0.812292 0.583250i $$-0.198219\pi$$
−0.583250 + 0.812292i $$0.698219\pi$$
$$504$$ 0 0
$$505$$ 11.2984 + 16.1047i 0.502774 + 0.716649i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 12.8422 0.569220 0.284610 0.958643i $$-0.408136\pi$$
0.284610 + 0.958643i $$0.408136\pi$$
$$510$$ 0 0
$$511$$ 29.4984i 1.30493i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −24.8219 4.35352i −1.09378 0.191839i
$$516$$ 0 0
$$517$$ −11.7994 + 11.7994i −0.518935 + 0.518935i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 6.44593 0.282401 0.141201 0.989981i $$-0.454904\pi$$
0.141201 + 0.989981i $$0.454904\pi$$
$$522$$ 0 0
$$523$$ 5.19375 5.19375i 0.227107 0.227107i −0.584376 0.811483i $$-0.698661\pi$$
0.811483 + 0.584376i $$0.198661\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −23.0588 + 23.0588i −1.00446 + 1.00446i
$$528$$ 0 0
$$529$$ 20.6125i 0.896196i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −23.0588 23.0588i −0.998786 0.998786i
$$534$$ 0 0
$$535$$ 5.01934 + 0.880344i 0.217005 + 0.0380606i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 16.7645i 0.722096i
$$540$$ 0 0
$$541$$ 8.27799i 0.355898i −0.984040 0.177949i $$-0.943054\pi$$
0.984040 0.177949i $$-0.0569463\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −21.5989 + 15.1530i −0.925195 + 0.649082i
$$546$$ 0 0
$$547$$ 22.2094 + 22.2094i 0.949604 + 0.949604i 0.998790 0.0491855i $$-0.0156625\pi$$
−0.0491855 + 0.998790i $$0.515663\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 19.0145i 0.810044i
$$552$$ 0 0
$$553$$ 14.8062 14.8062i 0.629626 0.629626i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −13.7146 + 13.7146i −0.581104 + 0.581104i −0.935207 0.354102i $$-0.884786\pi$$
0.354102 + 0.935207i $$0.384786\pi$$
$$558$$ 0 0
$$559$$ −37.1588 −1.57165
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2.74204 2.74204i 0.115563 0.115563i −0.646960 0.762524i $$-0.723960\pi$$
0.762524 + 0.646960i $$0.223960\pi$$
$$564$$ 0 0
$$565$$ −2.50967 + 14.3090i −0.105583 + 0.601986i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 36.7519i 1.54072i 0.637610 + 0.770359i $$0.279923\pi$$
−0.637610 + 0.770359i $$0.720077\pi$$
$$570$$ 0 0
$$571$$ −17.6125 −0.737060 −0.368530 0.929616i $$-0.620139\pi$$
−0.368530 + 0.929616i $$0.620139\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −6.99599 + 3.27777i −0.291753 + 0.136692i
$$576$$ 0 0
$$577$$ 12.4031 + 12.4031i 0.516349 + 0.516349i 0.916465 0.400116i $$-0.131030\pi$$
−0.400116 + 0.916465i $$0.631030\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 44.6989i 1.85442i
$$582$$ 0 0
$$583$$ −5.01934 5.01934i −0.207880 0.207880i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.61148 1.61148i −0.0665130 0.0665130i 0.673068 0.739581i $$-0.264976\pi$$
−0.739581 + 0.673068i $$0.764976\pi$$
$$588$$ 0 0
$$589$$ −20.0774 −0.827273
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 4.59398 4.59398i 0.188652 0.188652i −0.606461 0.795113i $$-0.707411\pi$$
0.795113 + 0.606461i $$0.207411\pi$$
$$594$$ 0 0
$$595$$ 49.6125 34.8062i 2.03391 1.42692i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 27.1030 1.10740 0.553700 0.832716i $$-0.313215\pi$$
0.553700 + 0.832716i $$0.313215\pi$$
$$600$$ 0 0
$$601$$ 20.2094 0.824358 0.412179 0.911103i $$-0.364768\pi$$
0.412179 + 0.911103i $$0.364768\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −15.3820 + 10.7915i −0.625369 + 0.438735i
$$606$$ 0 0
$$607$$ −18.8882 + 18.8882i −0.766648 + 0.766648i −0.977515 0.210867i $$-0.932371\pi$$
0.210867 + 0.977515i $$0.432371\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 36.7519 1.48682
$$612$$ 0 0
$$613$$ −19.3284 19.3284i −0.780666 0.780666i 0.199278 0.979943i $$-0.436140\pi$$
−0.979943 + 0.199278i $$0.936140\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 7.33602 + 7.33602i 0.295337 + 0.295337i 0.839184 0.543847i $$-0.183033\pi$$
−0.543847 + 0.839184i $$0.683033\pi$$
$$618$$ 0 0
$$619$$ 10.8062i 0.434340i −0.976134 0.217170i $$-0.930317\pi$$
0.976134 0.217170i $$-0.0696826\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −8.08857 8.08857i −0.324062 0.324062i
$$624$$ 0 0
$$625$$ −19.2094 16.0000i −0.768375 0.640000i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −23.0588 −0.919413
$$630$$ 0 0
$$631$$ 25.0967i 0.999083i −0.866290 0.499542i $$-0.833502\pi$$
0.866290 0.499542i $$-0.166498\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −2.09241 + 11.9300i −0.0830348 + 0.473428i
$$636$$ 0 0
$$637$$ −26.1084 + 26.1084i −1.03445 + 1.03445i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.74204 0.108304 0.0541520 0.998533i $$-0.482754\pi$$
0.0541520 + 0.998533i $$0.482754\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 19.7810 19.7810i 0.777671 0.777671i −0.201763 0.979434i $$-0.564667\pi$$
0.979434 + 0.201763i $$0.0646672\pi$$
$$648$$ 0 0
$$649$$ 2.59688i 0.101936i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −15.1904 15.1904i −0.594447 0.594447i 0.344383 0.938829i $$-0.388088\pi$$
−0.938829 + 0.344383i $$0.888088\pi$$
$$654$$ 0 0
$$655$$ −24.7879 + 17.3902i −0.968543 + 0.679493i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 4.83445i 0.188323i −0.995557 0.0941617i $$-0.969983\pi$$
0.995557 0.0941617i $$-0.0300171\pi$$
$$660$$ 0 0
$$661$$ 26.8574i 1.04463i −0.852752 0.522315i $$-0.825068\pi$$
0.852752 0.522315i $$-0.174932\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 36.7519 + 6.44593i 1.42518 + 0.249962i
$$666$$ 0 0
$$667$$ −5.19375 5.19375i −0.201103 0.201103i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 10.9259i 0.421789i
$$672$$ 0 0
$$673$$ 15.0000 15.0000i 0.578208 0.578208i −0.356202 0.934409i $$-0.615928\pi$$
0.934409 + 0.356202i $$0.115928\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −18.1421 + 18.1421i −0.697258 + 0.697258i −0.963818 0.266560i $$-0.914113\pi$$
0.266560 + 0.963818i $$0.414113\pi$$
$$678$$ 0 0
$$679$$ −14.1777 −0.544089
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.13056 1.13056i 0.0432595 0.0432595i −0.685146 0.728406i $$-0.740262\pi$$
0.728406 + 0.685146i $$0.240262\pi$$
$$684$$ 0 0
$$685$$ 34.3864 + 6.03105i 1.31384 + 0.230434i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 15.6339i 0.595604i
$$690$$ 0 0
$$691$$ −28.0000 −1.06517 −0.532585 0.846376i $$-0.678779\pi$$
−0.532585 + 0.846376i $$0.678779\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 5.13688 + 7.32206i 0.194853 + 0.277741i
$$696$$ 0 0
$$697$$ −42.2094 42.2094i −1.59879 1.59879i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 3.33496i 0.125960i 0.998015 + 0.0629798i $$0.0200604\pi$$
−0.998015 + 0.0629798i $$0.979940\pi$$
$$702$$ 0 0
$$703$$ −10.0387 10.0387i −0.378616 0.378616i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −25.9524 25.9524i −0.976041 0.976041i
$$708$$ 0 0
$$709$$ −26.8574 −1.00865 −0.504325 0.863514i $$-0.668259\pi$$
−0.504325 + 0.863514i $$0.668259\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −5.48408 + 5.48408i −0.205380 + 0.205380i
$$714$$ 0 0
$$715$$ −12.5969 2.20937i −0.471096 0.0826259i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −8.08857 −0.301653 −0.150826 0.988560i $$-0.548193\pi$$
−0.150826 + 0.988560i $$0.548193\pi$$
$$720$$ 0 0
$$721$$ 47.0156 1.75095
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 8.08857 22.3494i 0.300402 0.830037i
$$726$$ 0 0
$$727$$ 35.7069 35.7069i 1.32430 1.32430i 0.414034 0.910261i $$-0.364119\pi$$
0.910261 0.414034i $$-0.135881\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −68.0197 −2.51580
$$732$$ 0 0
$$733$$ −2.50967 2.50967i −0.0926967 0.0926967i 0.659238 0.751935i $$-0.270879\pi$$
−0.751935 + 0.659238i $$0.770879\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −11.9300 11.9300i −0.439447 0.439447i
$$738$$ 0 0
$$739$$ 48.4187i 1.78111i −0.454873 0.890556i $$-0.650315\pi$$
0.454873 0.890556i $$-0.349685\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 9.18116 + 9.18116i 0.336824 + 0.336824i 0.855171 0.518346i $$-0.173452\pi$$
−0.518346 + 0.855171i $$0.673452\pi$$
$$744$$ 0 0
$$745$$ 16.1047 11.2984i 0.590030 0.413943i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −9.50723 −0.347387
$$750$$ 0 0
$$751$$ 15.0580i 0.549475i −0.961519 0.274737i $$-0.911409\pi$$
0.961519 0.274737i $$-0.0885909\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −1.13056 1.61148i −0.0411451 0.0586479i
$$756$$ 0 0
$$757$$ −11.0504 + 11.0504i −0.401633 + 0.401633i −0.878808 0.477175i $$-0.841661\pi$$
0.477175 + 0.878808i $$0.341661\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 43.1978 1.56592 0.782960 0.622073i $$-0.213709\pi$$
0.782960 + 0.622073i $$0.213709\pi$$
$$762$$ 0 0
$$763$$ 34.8062 34.8062i 1.26007 1.26007i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −4.04429 + 4.04429i −0.146031 + 0.146031i
$$768$$ 0 0
$$769$$ 1.40312i 0.0505980i 0.999680 + 0.0252990i $$0.00805377\pi$$
−0.999680 + 0.0252990i $$0.991946\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 25.4642 + 25.4642i 0.915882 + 0.915882i 0.996727 0.0808446i $$-0.0257617\pi$$
−0.0808446 + 0.996727i $$0.525762\pi$$
$$774$$ 0 0
$$775$$ −23.5987 8.54071i −0.847691 0.306792i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 36.7519i 1.31677i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 5.07491 28.9349i 0.181131 1.03273i
$$786$$ 0 0
$$787$$ 20.0000 + 20.0000i 0.712923 + 0.712923i 0.967146 0.254223i $$-0.0818196\pi$$
−0.254223 + 0.967146i $$0.581820\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 27.1030i 0.963673i
$$792$$ 0 0
$$793$$ 17.0156 17.0156i 0.604242 0.604242i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 6.00924 6.00924i 0.212858 0.212858i −0.592622 0.805481i $$-0.701907\pi$$
0.805481 + 0.592622i $$0.201907\pi$$
$$798$$ 0 0
$$799$$ 67.2748 2.38001
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 8.05741 8.05741i 0.284340 0.284340i
$$804$$ 0 0
$$805$$ 11.7994 8.27799i 0.415873 0.291761i