# Properties

 Label 2268.2.i.n.2053.7 Level $2268$ Weight $2$ Character 2268.2053 Analytic conductor $18.110$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2268.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.1100711784$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 9 x^{14} + 31 x^{12} - 282 x^{10} + 1695 x^{8} - 3318 x^{6} + 4606 x^{4} - 4116 x^{2} + 2401$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$3^{7}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 2053.7 Root $$2.40332 + 0.123797i$$ of defining polynomial Character $$\chi$$ $$=$$ 2268.2053 Dual form 2268.2.i.n.865.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +O(q^{10})$$ $$q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +(-2.23145 + 3.86499i) q^{11} +(1.42148 - 2.46208i) q^{13} +(-0.115312 - 0.199726i) q^{17} +(-1.49360 + 2.58700i) q^{19} +(0.400294 + 0.693329i) q^{23} +(-0.149635 + 0.259175i) q^{25} +(3.82751 + 6.62944i) q^{29} +5.28647 q^{31} +(4.93376 + 3.57112i) q^{35} +(-1.69333 + 2.93293i) q^{37} +(-0.899697 + 1.55832i) q^{41} +(4.85860 + 8.41533i) q^{43} +5.77636 q^{47} +(4.66527 - 5.21874i) q^{49} +(-4.31905 - 7.48081i) q^{53} -10.2737 q^{55} -8.35585 q^{59} -13.1735 q^{61} +6.54454 q^{65} -7.53090 q^{67} +8.59672 q^{71} +(-2.29287 - 3.97137i) q^{73} +(-1.21323 + 11.7453i) q^{77} +9.67313 q^{79} +(8.46521 + 14.6622i) q^{83} +(0.265450 - 0.459773i) q^{85} +(0.944450 - 1.63584i) q^{89} +(0.772852 - 7.48196i) q^{91} -6.87659 q^{95} +(7.70796 + 13.3506i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 6 q^{7} + O(q^{10})$$ $$16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1541$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 1.15101 + 1.99360i 0.514746 + 0.891566i 0.999854 + 0.0171118i $$0.00544711\pi$$
−0.485108 + 0.874454i $$0.661220\pi$$
$$6$$ 0 0
$$7$$ 2.41508 1.08045i 0.912816 0.408371i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −2.23145 + 3.86499i −0.672809 + 1.16534i 0.304295 + 0.952578i $$0.401579\pi$$
−0.977104 + 0.212761i $$0.931754\pi$$
$$12$$ 0 0
$$13$$ 1.42148 2.46208i 0.394248 0.682858i −0.598757 0.800931i $$-0.704338\pi$$
0.993005 + 0.118073i $$0.0376717\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −0.115312 0.199726i −0.0279673 0.0484408i 0.851703 0.524025i $$-0.175570\pi$$
−0.879670 + 0.475584i $$0.842237\pi$$
$$18$$ 0 0
$$19$$ −1.49360 + 2.58700i −0.342656 + 0.593498i −0.984925 0.172982i $$-0.944660\pi$$
0.642269 + 0.766479i $$0.277993\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0.400294 + 0.693329i 0.0834670 + 0.144569i 0.904737 0.425971i $$-0.140067\pi$$
−0.821270 + 0.570540i $$0.806734\pi$$
$$24$$ 0 0
$$25$$ −0.149635 + 0.259175i −0.0299269 + 0.0518349i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 3.82751 + 6.62944i 0.710750 + 1.23106i 0.964576 + 0.263806i $$0.0849778\pi$$
−0.253825 + 0.967250i $$0.581689\pi$$
$$30$$ 0 0
$$31$$ 5.28647 0.949479 0.474739 0.880126i $$-0.342542\pi$$
0.474739 + 0.880126i $$0.342542\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 4.93376 + 3.57112i 0.833958 + 0.603629i
$$36$$ 0 0
$$37$$ −1.69333 + 2.93293i −0.278382 + 0.482171i −0.970983 0.239150i $$-0.923131\pi$$
0.692601 + 0.721321i $$0.256465\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.899697 + 1.55832i −0.140509 + 0.243369i −0.927688 0.373355i $$-0.878207\pi$$
0.787179 + 0.616724i $$0.211541\pi$$
$$42$$ 0 0
$$43$$ 4.85860 + 8.41533i 0.740929 + 1.28333i 0.952073 + 0.305871i $$0.0989478\pi$$
−0.211144 + 0.977455i $$0.567719\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 5.77636 0.842569 0.421284 0.906929i $$-0.361579\pi$$
0.421284 + 0.906929i $$0.361579\pi$$
$$48$$ 0 0
$$49$$ 4.66527 5.21874i 0.666467 0.745535i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −4.31905 7.48081i −0.593267 1.02757i −0.993789 0.111281i $$-0.964505\pi$$
0.400522 0.916287i $$-0.368829\pi$$
$$54$$ 0 0
$$55$$ −10.2737 −1.38530
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −8.35585 −1.08784 −0.543920 0.839137i $$-0.683060\pi$$
−0.543920 + 0.839137i $$0.683060\pi$$
$$60$$ 0 0
$$61$$ −13.1735 −1.68669 −0.843347 0.537370i $$-0.819418\pi$$
−0.843347 + 0.537370i $$0.819418\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 6.54454 0.811751
$$66$$ 0 0
$$67$$ −7.53090 −0.920046 −0.460023 0.887907i $$-0.652159\pi$$
−0.460023 + 0.887907i $$0.652159\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.59672 1.02024 0.510122 0.860102i $$-0.329600\pi$$
0.510122 + 0.860102i $$0.329600\pi$$
$$72$$ 0 0
$$73$$ −2.29287 3.97137i −0.268360 0.464814i 0.700078 0.714066i $$-0.253148\pi$$
−0.968439 + 0.249252i $$0.919815\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −1.21323 + 11.7453i −0.138260 + 1.33850i
$$78$$ 0 0
$$79$$ 9.67313 1.08831 0.544156 0.838984i $$-0.316850\pi$$
0.544156 + 0.838984i $$0.316850\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 8.46521 + 14.6622i 0.929177 + 1.60938i 0.784701 + 0.619874i $$0.212816\pi$$
0.144476 + 0.989508i $$0.453850\pi$$
$$84$$ 0 0
$$85$$ 0.265450 0.459773i 0.0287921 0.0498694i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0.944450 1.63584i 0.100111 0.173398i −0.811619 0.584187i $$-0.801413\pi$$
0.911730 + 0.410789i $$0.134747\pi$$
$$90$$ 0 0
$$91$$ 0.772852 7.48196i 0.0810169 0.784323i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −6.87659 −0.705523
$$96$$ 0 0
$$97$$ 7.70796 + 13.3506i 0.782624 + 1.35555i 0.930408 + 0.366525i $$0.119453\pi$$
−0.147784 + 0.989020i $$0.547214\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1.40744 2.43775i 0.140045 0.242566i −0.787468 0.616355i $$-0.788609\pi$$
0.927513 + 0.373790i $$0.121942\pi$$
$$102$$ 0 0
$$103$$ −2.55832 4.43114i −0.252079 0.436614i 0.712019 0.702160i $$-0.247781\pi$$
−0.964098 + 0.265547i $$0.914448\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.29487 + 2.24278i −0.125180 + 0.216818i −0.921803 0.387658i $$-0.873284\pi$$
0.796623 + 0.604476i $$0.206617\pi$$
$$108$$ 0 0
$$109$$ −8.76728 15.1854i −0.839753 1.45450i −0.890101 0.455764i $$-0.849366\pi$$
0.0503474 0.998732i $$-0.483967\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −8.21711 + 14.2325i −0.773001 + 1.33888i 0.162910 + 0.986641i $$0.447912\pi$$
−0.935911 + 0.352236i $$0.885421\pi$$
$$114$$ 0 0
$$115$$ −0.921482 + 1.59605i −0.0859286 + 0.148833i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −0.494282 0.357767i −0.0453108 0.0327965i
$$120$$ 0 0
$$121$$ −4.45878 7.72283i −0.405344 0.702076i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 10.8211 0.967873
$$126$$ 0 0
$$127$$ 8.13145 0.721549 0.360775 0.932653i $$-0.382512\pi$$
0.360775 + 0.932653i $$0.382512\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 6.25591 + 10.8356i 0.546582 + 0.946707i 0.998506 + 0.0546508i $$0.0174046\pi$$
−0.451924 + 0.892057i $$0.649262\pi$$
$$132$$ 0 0
$$133$$ −0.812064 + 7.86157i −0.0704148 + 0.681685i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −8.09668 + 14.0239i −0.691746 + 1.19814i 0.279519 + 0.960140i $$0.409825\pi$$
−0.971265 + 0.237999i $$0.923508\pi$$
$$138$$ 0 0
$$139$$ 3.07212 5.32107i 0.260574 0.451327i −0.705821 0.708391i $$-0.749422\pi$$
0.966395 + 0.257063i $$0.0827549\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 6.34394 + 10.9880i 0.530507 + 0.918866i
$$144$$ 0 0
$$145$$ −8.81098 + 15.2611i −0.731712 + 1.26736i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −3.85927 6.68446i −0.316164 0.547612i 0.663520 0.748158i $$-0.269062\pi$$
−0.979684 + 0.200546i $$0.935728\pi$$
$$150$$ 0 0
$$151$$ 7.45878 12.9190i 0.606987 1.05133i −0.384747 0.923022i $$-0.625711\pi$$
0.991734 0.128310i $$-0.0409553\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.08477 + 10.5391i 0.488740 + 0.846523i
$$156$$ 0 0
$$157$$ −0.257220 −0.0205284 −0.0102642 0.999947i $$-0.503267\pi$$
−0.0102642 + 0.999947i $$0.503267\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1.71585 + 1.24195i 0.135228 + 0.0978795i
$$162$$ 0 0
$$163$$ −6.28748 + 10.8902i −0.492473 + 0.852989i −0.999962 0.00866931i $$-0.997240\pi$$
0.507489 + 0.861658i $$0.330574\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 10.8470 18.7875i 0.839363 1.45382i −0.0510657 0.998695i $$-0.516262\pi$$
0.890428 0.455123i $$-0.150405\pi$$
$$168$$ 0 0
$$169$$ 2.45878 + 4.25873i 0.189137 + 0.327595i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 13.7605 1.04619 0.523095 0.852275i $$-0.324777\pi$$
0.523095 + 0.852275i $$0.324777\pi$$
$$174$$ 0 0
$$175$$ −0.0813555 + 0.787601i −0.00614990 + 0.0595370i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −0.448262 0.776412i −0.0335046 0.0580317i 0.848787 0.528735i $$-0.177334\pi$$
−0.882292 + 0.470703i $$0.844000\pi$$
$$180$$ 0 0
$$181$$ −17.4613 −1.29788 −0.648942 0.760838i $$-0.724788\pi$$
−0.648942 + 0.760838i $$0.724788\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −7.79613 −0.573183
$$186$$ 0 0
$$187$$ 1.02925 0.0752665
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.46902 −0.106295 −0.0531474 0.998587i $$-0.516925\pi$$
−0.0531474 + 0.998587i $$0.516925\pi$$
$$192$$ 0 0
$$193$$ 6.50330 0.468118 0.234059 0.972222i $$-0.424799\pi$$
0.234059 + 0.972222i $$0.424799\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −11.9521 −0.851552 −0.425776 0.904828i $$-0.639999\pi$$
−0.425776 + 0.904828i $$0.639999\pi$$
$$198$$ 0 0
$$199$$ 9.73886 + 16.8682i 0.690369 + 1.19575i 0.971717 + 0.236149i $$0.0758852\pi$$
−0.281348 + 0.959606i $$0.590781\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 16.4065 + 11.8752i 1.15151 + 0.833478i
$$204$$ 0 0
$$205$$ −4.14223 −0.289306
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −6.66581 11.5455i −0.461084 0.798621i
$$210$$ 0 0
$$211$$ 6.43611 11.1477i 0.443080 0.767437i −0.554836 0.831960i $$-0.687219\pi$$
0.997916 + 0.0645225i $$0.0205524\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −11.1846 + 19.3722i −0.762780 + 1.32117i
$$216$$ 0 0
$$217$$ 12.7673 5.71176i 0.866700 0.387739i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −0.655656 −0.0441042
$$222$$ 0 0
$$223$$ −4.92331 8.52743i −0.329690 0.571039i 0.652761 0.757564i $$-0.273611\pi$$
−0.982450 + 0.186525i $$0.940277\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −12.2254 + 21.1750i −0.811426 + 1.40543i 0.100439 + 0.994943i $$0.467975\pi$$
−0.911866 + 0.410489i $$0.865358\pi$$
$$228$$ 0 0
$$229$$ 11.0018 + 19.0557i 0.727022 + 1.25924i 0.958136 + 0.286312i $$0.0924293\pi$$
−0.231115 + 0.972926i $$0.574237\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 10.8179 18.7372i 0.708706 1.22752i −0.256631 0.966510i $$-0.582612\pi$$
0.965337 0.261006i $$-0.0840542\pi$$
$$234$$ 0 0
$$235$$ 6.64863 + 11.5158i 0.433709 + 0.751206i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −8.86360 + 15.3522i −0.573338 + 0.993051i 0.422882 + 0.906185i $$0.361019\pi$$
−0.996220 + 0.0868662i $$0.972315\pi$$
$$240$$ 0 0
$$241$$ −2.15887 + 3.73927i −0.139065 + 0.240868i −0.927143 0.374708i $$-0.877743\pi$$
0.788078 + 0.615575i $$0.211076\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 15.7739 + 3.29388i 1.00775 + 0.210438i
$$246$$ 0 0
$$247$$ 4.24626 + 7.35473i 0.270183 + 0.467971i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 10.2938 0.649741 0.324870 0.945759i $$-0.394679\pi$$
0.324870 + 0.945759i $$0.394679\pi$$
$$252$$ 0 0
$$253$$ −3.57295 −0.224629
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5.89568 10.2116i −0.367763 0.636983i 0.621453 0.783452i $$-0.286543\pi$$
−0.989215 + 0.146468i $$0.953209\pi$$
$$258$$ 0 0
$$259$$ −0.920654 + 8.91283i −0.0572066 + 0.553816i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −2.59359 + 4.49223i −0.159928 + 0.277003i −0.934842 0.355063i $$-0.884459\pi$$
0.774915 + 0.632066i $$0.217793\pi$$
$$264$$ 0 0
$$265$$ 9.94251 17.2209i 0.610763 1.05787i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −14.6103 25.3058i −0.890805 1.54292i −0.838912 0.544268i $$-0.816808\pi$$
−0.0518936 0.998653i $$-0.516526\pi$$
$$270$$ 0 0
$$271$$ 10.2801 17.8056i 0.624470 1.08161i −0.364173 0.931331i $$-0.618648\pi$$
0.988643 0.150283i $$-0.0480184\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −0.667805 1.15667i −0.0402702 0.0697500i
$$276$$ 0 0
$$277$$ 5.97833 10.3548i 0.359203 0.622158i −0.628625 0.777709i $$-0.716382\pi$$
0.987828 + 0.155550i $$0.0497151\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −14.9166 25.8363i −0.889850 1.54126i −0.840052 0.542506i $$-0.817476\pi$$
−0.0497975 0.998759i $$-0.515858\pi$$
$$282$$ 0 0
$$283$$ −9.57094 −0.568933 −0.284467 0.958686i $$-0.591817\pi$$
−0.284467 + 0.958686i $$0.591817\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −0.489161 + 4.73555i −0.0288742 + 0.279531i
$$288$$ 0 0
$$289$$ 8.47341 14.6764i 0.498436 0.863316i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 7.41014 12.8347i 0.432905 0.749813i −0.564217 0.825626i $$-0.690822\pi$$
0.997122 + 0.0758132i $$0.0241553\pi$$
$$294$$ 0 0
$$295$$ −9.61765 16.6583i −0.559961 0.969881i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 2.27604 0.131627
$$300$$ 0 0
$$301$$ 20.8262 + 15.0743i 1.20040 + 0.868867i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −15.1628 26.2627i −0.868219 1.50380i
$$306$$ 0 0
$$307$$ −5.88207 −0.335708 −0.167854 0.985812i $$-0.553684\pi$$
−0.167854 + 0.985812i $$0.553684\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 16.2351 0.920606 0.460303 0.887762i $$-0.347741\pi$$
0.460303 + 0.887762i $$0.347741\pi$$
$$312$$ 0 0
$$313$$ 17.6896 0.999875 0.499937 0.866062i $$-0.333356\pi$$
0.499937 + 0.866062i $$0.333356\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −5.28017 −0.296564 −0.148282 0.988945i $$-0.547374\pi$$
−0.148282 + 0.988945i $$0.547374\pi$$
$$318$$ 0 0
$$319$$ −34.1636 −1.91280
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0.688922 0.0383326
$$324$$ 0 0
$$325$$ 0.425406 + 0.736824i 0.0235973 + 0.0408716i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 13.9504 6.24105i 0.769110 0.344080i
$$330$$ 0 0
$$331$$ −15.6072 −0.857847 −0.428923 0.903341i $$-0.641107\pi$$
−0.428923 + 0.903341i $$0.641107\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −8.66812 15.0136i −0.473590 0.820282i
$$336$$ 0 0
$$337$$ −3.77185 + 6.53303i −0.205466 + 0.355877i −0.950281 0.311394i $$-0.899204\pi$$
0.744815 + 0.667271i $$0.232538\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −11.7965 + 20.4322i −0.638818 + 1.10646i
$$342$$ 0 0
$$343$$ 5.62843 17.6443i 0.303907 0.952702i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −26.9003 −1.44408 −0.722042 0.691849i $$-0.756796\pi$$
−0.722042 + 0.691849i $$0.756796\pi$$
$$348$$ 0 0
$$349$$ 7.00100 + 12.1261i 0.374755 + 0.649095i 0.990290 0.139014i $$-0.0443934\pi$$
−0.615535 + 0.788109i $$0.711060\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 15.1655 26.2675i 0.807180 1.39808i −0.107630 0.994191i $$-0.534326\pi$$
0.914810 0.403885i $$-0.132341\pi$$
$$354$$ 0 0
$$355$$ 9.89489 + 17.1384i 0.525166 + 0.909614i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 6.99876 12.1222i 0.369381 0.639786i −0.620088 0.784532i $$-0.712903\pi$$
0.989469 + 0.144746i $$0.0462366\pi$$
$$360$$ 0 0
$$361$$ 5.03830 + 8.72659i 0.265174 + 0.459294i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 5.27822 9.14215i 0.276275 0.478522i
$$366$$ 0 0
$$367$$ 1.25165 2.16792i 0.0653356 0.113165i −0.831507 0.555514i $$-0.812522\pi$$
0.896843 + 0.442349i $$0.145855\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −18.5135 13.4003i −0.961172 0.695708i
$$372$$ 0 0
$$373$$ −8.80311 15.2474i −0.455808 0.789482i 0.542926 0.839780i $$-0.317316\pi$$
−0.998734 + 0.0502980i $$0.983983\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 21.7629 1.12085
$$378$$ 0 0
$$379$$ 10.5474 0.541781 0.270891 0.962610i $$-0.412682\pi$$
0.270891 + 0.962610i $$0.412682\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 10.8418 + 18.7786i 0.553992 + 0.959542i 0.997981 + 0.0635100i $$0.0202295\pi$$
−0.443989 + 0.896032i $$0.646437\pi$$
$$384$$ 0 0
$$385$$ −24.8118 + 11.1002i −1.26453 + 0.565717i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 6.96652 12.0664i 0.353217 0.611790i −0.633594 0.773665i $$-0.718421\pi$$
0.986811 + 0.161876i $$0.0517545\pi$$
$$390$$ 0 0
$$391$$ 0.0923174 0.159898i 0.00466869 0.00808641i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 11.1338 + 19.2844i 0.560204 + 0.970303i
$$396$$ 0 0
$$397$$ 13.9542 24.1694i 0.700342 1.21303i −0.268004 0.963418i $$-0.586364\pi$$
0.968346 0.249610i $$-0.0803025\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −17.4525 30.2285i −0.871534 1.50954i −0.860410 0.509603i $$-0.829792\pi$$
−0.0111242 0.999938i $$-0.503541\pi$$
$$402$$ 0 0
$$403$$ 7.51463 13.0157i 0.374330 0.648359i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −7.55717 13.0894i −0.374595 0.648818i
$$408$$ 0 0
$$409$$ −20.6739 −1.02226 −0.511128 0.859504i $$-0.670772\pi$$
−0.511128 + 0.859504i $$0.670772\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −20.1801 + 9.02806i −0.992998 + 0.444242i
$$414$$ 0 0
$$415$$ −19.4870 + 33.7525i −0.956581 + 1.65685i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 19.9859 34.6166i 0.976376 1.69113i 0.301061 0.953605i $$-0.402659\pi$$
0.675316 0.737529i $$-0.264007\pi$$
$$420$$ 0 0
$$421$$ −12.5082 21.6649i −0.609614 1.05588i −0.991304 0.131592i $$-0.957991\pi$$
0.381690 0.924290i $$-0.375342\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0.0690187 0.00334790
$$426$$ 0 0
$$427$$ −31.8151 + 14.2333i −1.53964 + 0.688796i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 7.05181 + 12.2141i 0.339674 + 0.588332i 0.984371 0.176106i $$-0.0563500\pi$$
−0.644698 + 0.764438i $$0.723017\pi$$
$$432$$ 0 0
$$433$$ 1.58941 0.0763821 0.0381911 0.999270i $$-0.487840\pi$$
0.0381911 + 0.999270i $$0.487840\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.39152 −0.114402
$$438$$ 0 0
$$439$$ −24.3768 −1.16344 −0.581721 0.813389i $$-0.697620\pi$$
−0.581721 + 0.813389i $$0.697620\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −18.5640 −0.882002 −0.441001 0.897507i $$-0.645376\pi$$
−0.441001 + 0.897507i $$0.645376\pi$$
$$444$$ 0 0
$$445$$ 4.34827 0.206128
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −21.4616 −1.01284 −0.506418 0.862288i $$-0.669031\pi$$
−0.506418 + 0.862288i $$0.669031\pi$$
$$450$$ 0 0
$$451$$ −4.01527 6.95465i −0.189072 0.327482i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 15.8056 7.07103i 0.740979 0.331495i
$$456$$ 0 0
$$457$$ 15.1274 0.707631 0.353816 0.935315i $$-0.384884\pi$$
0.353816 + 0.935315i $$0.384884\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −16.5385 28.6455i −0.770273 1.33415i −0.937413 0.348219i $$-0.886787\pi$$
0.167140 0.985933i $$-0.446547\pi$$
$$462$$ 0 0
$$463$$ −13.4223 + 23.2481i −0.623788 + 1.08043i 0.364986 + 0.931013i $$0.381074\pi$$
−0.988774 + 0.149419i $$0.952260\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −5.93579 + 10.2811i −0.274675 + 0.475752i −0.970053 0.242893i $$-0.921904\pi$$
0.695378 + 0.718644i $$0.255237\pi$$
$$468$$ 0 0
$$469$$ −18.1878 + 8.13674i −0.839833 + 0.375720i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −43.3669 −1.99401
$$474$$ 0 0
$$475$$ −0.446989 0.774208i −0.0205093 0.0355231i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −8.71973 + 15.1030i −0.398415 + 0.690075i −0.993531 0.113565i $$-0.963773\pi$$
0.595116 + 0.803640i $$0.297106\pi$$
$$480$$ 0 0
$$481$$ 4.81407 + 8.33822i 0.219503 + 0.380190i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −17.7438 + 30.7332i −0.805706 + 1.39552i
$$486$$ 0 0
$$487$$ 18.3889 + 31.8504i 0.833279 + 1.44328i 0.895424 + 0.445214i $$0.146872\pi$$
−0.0621458 + 0.998067i $$0.519794\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 4.54050 7.86437i 0.204910 0.354914i −0.745194 0.666847i $$-0.767643\pi$$
0.950104 + 0.311933i $$0.100977\pi$$
$$492$$ 0 0
$$493$$ 0.882716 1.52891i 0.0397555 0.0688586i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 20.7618 9.28831i 0.931294 0.416638i
$$498$$ 0 0
$$499$$ −3.41261 5.91082i −0.152769 0.264604i 0.779475 0.626433i $$-0.215486\pi$$
−0.932245 + 0.361829i $$0.882153\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4.09211 0.182458 0.0912291 0.995830i $$-0.470920\pi$$
0.0912291 + 0.995830i $$0.470920\pi$$
$$504$$ 0 0
$$505$$ 6.47989 0.288351
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 14.3991 + 24.9400i 0.638228 + 1.10544i 0.985821 + 0.167798i $$0.0536658\pi$$
−0.347593 + 0.937646i $$0.613001\pi$$
$$510$$ 0 0
$$511$$ −9.82834 7.11387i −0.434780 0.314699i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 5.88929 10.2006i 0.259513 0.449490i
$$516$$ 0 0
$$517$$ −12.8897 + 22.3256i −0.566888 + 0.981878i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −5.92170 10.2567i −0.259434 0.449353i 0.706656 0.707557i $$-0.250203\pi$$
−0.966090 + 0.258204i $$0.916869\pi$$
$$522$$ 0 0
$$523$$ 6.86664 11.8934i 0.300257 0.520061i −0.675937 0.736959i $$-0.736261\pi$$
0.976194 + 0.216899i $$0.0695942\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −0.609594 1.05585i −0.0265543 0.0459935i
$$528$$ 0 0
$$529$$ 11.1795 19.3635i 0.486067 0.841892i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 2.55781 + 4.43025i 0.110791 + 0.191896i
$$534$$ 0 0
$$535$$ −5.96162 −0.257743
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 9.76008 + 29.6766i 0.420396 + 1.27826i
$$540$$ 0 0
$$541$$ 21.7425 37.6592i 0.934784 1.61909i 0.159765 0.987155i $$-0.448926\pi$$
0.775019 0.631938i $$-0.217740\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 20.1824 34.9570i 0.864519 1.49739i
$$546$$ 0 0
$$547$$ −11.0307 19.1058i −0.471640 0.816904i 0.527834 0.849348i $$-0.323004\pi$$
−0.999474 + 0.0324437i $$0.989671\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −22.8671 −0.974171
$$552$$ 0 0
$$553$$ 23.3614 10.4513i 0.993429 0.444435i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −16.0925 27.8730i −0.681862 1.18102i −0.974412 0.224769i $$-0.927837\pi$$
0.292551 0.956250i $$-0.405496\pi$$
$$558$$ 0 0
$$559$$ 27.6256 1.16844
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 3.38738 0.142761 0.0713804 0.997449i $$-0.477260\pi$$
0.0713804 + 0.997449i $$0.477260\pi$$
$$564$$ 0 0
$$565$$ −37.8318 −1.59160
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −40.3474 −1.69145 −0.845726 0.533618i $$-0.820832\pi$$
−0.845726 + 0.533618i $$0.820832\pi$$
$$570$$ 0 0
$$571$$ −10.4386 −0.436840 −0.218420 0.975855i $$-0.570090\pi$$
−0.218420 + 0.975855i $$0.570090\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −0.239591 −0.00999164
$$576$$ 0 0
$$577$$ 5.55156 + 9.61559i 0.231114 + 0.400302i 0.958136 0.286312i $$-0.0924295\pi$$
−0.727022 + 0.686614i $$0.759096\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 36.2859 + 26.2642i 1.50539 + 1.08962i
$$582$$ 0 0
$$583$$ 38.5510 1.59662
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −20.3875 35.3122i −0.841482 1.45749i −0.888642 0.458602i $$-0.848350\pi$$
0.0471601 0.998887i $$-0.484983\pi$$
$$588$$ 0 0
$$589$$ −7.89589 + 13.6761i −0.325345 + 0.563513i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 14.7930 25.6221i 0.607474 1.05218i −0.384182 0.923258i $$-0.625516\pi$$
0.991655 0.128918i $$-0.0411503\pi$$
$$594$$ 0 0
$$595$$ 0.144324 1.39720i 0.00591669 0.0572794i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −18.3552 −0.749973 −0.374987 0.927030i $$-0.622353\pi$$
−0.374987 + 0.927030i $$0.622353\pi$$
$$600$$ 0 0
$$601$$ 15.9250 + 27.5828i 0.649593 + 1.12513i 0.983220 + 0.182423i $$0.0583939\pi$$
−0.333628 + 0.942705i $$0.608273\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 10.2642 17.7781i 0.417298 0.722781i
$$606$$ 0 0
$$607$$ −11.8452 20.5164i −0.480780 0.832736i 0.518977 0.854788i $$-0.326313\pi$$
−0.999757 + 0.0220527i $$0.992980\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 8.21099 14.2219i 0.332181 0.575354i
$$612$$ 0 0
$$613$$ 13.3159 + 23.0638i 0.537824 + 0.931539i 0.999021 + 0.0442411i $$0.0140870\pi$$
−0.461197 + 0.887298i $$0.652580\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 4.72483 8.18364i 0.190214 0.329461i −0.755107 0.655602i $$-0.772415\pi$$
0.945321 + 0.326141i $$0.105748\pi$$
$$618$$ 0 0
$$619$$ 18.0474 31.2589i 0.725385 1.25640i −0.233431 0.972373i $$-0.574995\pi$$
0.958815 0.284030i $$-0.0916714\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0.513492 4.97111i 0.0205726 0.199163i
$$624$$ 0 0
$$625$$ 13.2034 + 22.8689i 0.528136 + 0.914758i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0.781045 0.0311423
$$630$$ 0 0
$$631$$ 0.0100579 0.000400401 0.000200200 1.00000i $$-0.499936\pi$$
0.000200200 1.00000i $$0.499936\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 9.35935 + 16.2109i 0.371415 + 0.643309i
$$636$$ 0 0
$$637$$ −6.21737 18.9046i −0.246341 0.749028i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.45227 4.24745i 0.0968587 0.167764i −0.813524 0.581531i $$-0.802454\pi$$
0.910383 + 0.413767i $$0.135787\pi$$
$$642$$ 0 0
$$643$$ 22.0655 38.2186i 0.870180 1.50720i 0.00837033 0.999965i $$-0.497336\pi$$
0.861810 0.507231i $$-0.169331\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.8813 43.0957i −0.978186 1.69427i −0.668993 0.743268i $$-0.733275\pi$$
−0.309192 0.950999i $$-0.600059\pi$$
$$648$$ 0 0
$$649$$ 18.6457 32.2953i 0.731908 1.26770i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6.98578 12.0997i −0.273375 0.473499i 0.696349 0.717703i $$-0.254807\pi$$
−0.969724 + 0.244205i $$0.921473\pi$$
$$654$$ 0 0
$$655$$ −14.4012 + 24.9436i −0.562702 + 0.974628i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 12.9827 + 22.4867i 0.505733 + 0.875956i 0.999978 + 0.00663317i $$0.00211142\pi$$
−0.494245 + 0.869323i $$0.664555\pi$$
$$660$$ 0 0
$$661$$ 25.5362 0.993244 0.496622 0.867967i $$-0.334574\pi$$
0.496622 + 0.867967i $$0.334574\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −16.6075 + 7.42979i −0.644013 + 0.288115i
$$666$$ 0 0
$$667$$ −3.06425 + 5.30744i −0.118648 + 0.205505i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 29.3961 50.9155i 1.13482 1.96557i
$$672$$ 0 0
$$673$$ 2.71472 + 4.70203i 0.104645 + 0.181250i 0.913593 0.406630i $$-0.133296\pi$$
−0.808948 + 0.587880i $$0.799963\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −14.1514 −0.543883 −0.271942 0.962314i $$-0.587666\pi$$
−0.271942 + 0.962314i $$0.587666\pi$$
$$678$$ 0 0
$$679$$ 33.0400 + 23.9147i 1.26796 + 0.917763i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −0.553330 0.958397i −0.0211726 0.0366720i 0.855245 0.518224i $$-0.173407\pi$$
−0.876418 + 0.481552i $$0.840073\pi$$
$$684$$ 0 0
$$685$$ −37.2773 −1.42429
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −24.5578 −0.935577
$$690$$ 0 0
$$691$$ 22.9077 0.871450 0.435725 0.900080i $$-0.356492\pi$$
0.435725 + 0.900080i $$0.356492\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 14.1441 0.536517
$$696$$ 0 0
$$697$$ 0.414984 0.0157186
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −11.4056 −0.430782 −0.215391 0.976528i $$-0.569103\pi$$
−0.215391 + 0.976528i $$0.569103\pi$$
$$702$$ 0 0
$$703$$ −5.05832 8.76127i −0.190778 0.330438i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0.765216 7.40805i 0.0287789 0.278608i
$$708$$ 0 0
$$709$$ −37.0671 −1.39208 −0.696042 0.718001i $$-0.745057\pi$$
−0.696042 + 0.718001i $$0.745057\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2.11614 + 3.66527i 0.0792502 + 0.137265i
$$714$$ 0 0
$$715$$ −14.6038 + 25.2946i −0.546153 + 0.945965i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −0.459342 + 0.795604i −0.0171306 + 0.0296710i −0.874464 0.485091i $$-0.838786\pi$$
0.857333 + 0.514762i $$0.172120\pi$$
$$720$$ 0 0
$$721$$ −10.9662 7.93745i −0.408402 0.295606i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.29091 −0.0850822
$$726$$ 0 0
$$727$$ 7.34433 + 12.7208i 0.272386 + 0.471787i 0.969472 0.245201i $$-0.0788538\pi$$
−0.697086 + 0.716987i $$0.745521\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 1.12051 1.94078i 0.0414435 0.0717823i
$$732$$ 0 0
$$733$$ 11.4312 + 19.7994i 0.422220 + 0.731307i 0.996156 0.0875931i $$-0.0279175\pi$$
−0.573936 + 0.818900i $$0.694584\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 16.8049 29.1069i 0.619015 1.07217i
$$738$$ 0 0
$$739$$ 19.6692 + 34.0681i 0.723544 + 1.25321i 0.959571 + 0.281468i $$0.0908212\pi$$
−0.236027 + 0.971746i $$0.575845\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 10.8663 18.8210i 0.398647 0.690477i −0.594912 0.803791i $$-0.702813\pi$$
0.993559 + 0.113314i $$0.0361465\pi$$
$$744$$ 0 0
$$745$$ 8.88410 15.3877i 0.325488 0.563762i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −0.704014 + 6.81554i −0.0257241 + 0.249034i
$$750$$ 0 0
$$751$$ −10.3071 17.8525i −0.376113 0.651446i 0.614380 0.789010i $$-0.289406\pi$$
−0.990493 + 0.137564i $$0.956073\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 34.3404 1.24978
$$756$$ 0 0
$$757$$ 17.8453 0.648600 0.324300 0.945954i $$-0.394871\pi$$
0.324300 + 0.945954i $$0.394871\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 16.9714 + 29.3953i 0.615211 + 1.06558i 0.990347 + 0.138607i $$0.0442626\pi$$
−0.375136 + 0.926970i $$0.622404\pi$$
$$762$$ 0 0
$$763$$ −37.5807 27.2014i −1.36051 0.984756i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −11.8777 + 20.5728i −0.428879 + 0.742840i
$$768$$ 0 0
$$769$$ 20.3452 35.2389i 0.733665 1.27075i −0.221641 0.975128i $$-0.571141\pi$$
0.955306 0.295617i $$-0.0955253\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 2.17562 + 3.76829i 0.0782517 + 0.135536i 0.902496 0.430699i $$-0.141733\pi$$
−0.824244 + 0.566235i $$0.808400\pi$$
$$774$$ 0 0
$$775$$ −0.791039 + 1.37012i −0.0284150 + 0.0492162i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −2.68758 4.65503i −0.0962926 0.166784i
$$780$$ 0 0
$$781$$ −19.1832 + 33.2263i −0.686429 + 1.18893i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −0.296062 0.512795i −0.0105669 0.0183024i
$$786$$ 0 0
$$787$$ 37.6220 1.34108 0.670539 0.741874i $$-0.266063\pi$$
0.670539 + 0.741874i $$0.266063\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −4.46760 + 43.2508i −0.158850 + 1.53782i
$$792$$ 0 0
$$793$$ −18.7259 + 32.4342i −0.664976 + 1.15177i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −22.1570 + 38.3771i −0.784842 + 1.35939i 0.144251 + 0.989541i $$0.453923\pi$$
−0.929093 + 0.369845i $$0.879411\pi$$
$$798$$ 0 0
$$799$$ −0.666084 1.15369i −0.0235644 0.0408147i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 20.4658 0.722221
$$804$$ 0 0