# Properties

 Label 2760.3.g.a.2161.17 Level $2760$ Weight $3$ Character 2760.2161 Analytic conductor $75.205$ Analytic rank $0$ Dimension $96$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2760,3,Mod(2161,2760)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2760, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2760.2161");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2760.g (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$75.2045529634$$ Analytic rank: $$0$$ Dimension: $$96$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 2161.17 Character $$\chi$$ $$=$$ 2760.2161 Dual form 2760.3.g.a.2161.32

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.73205 q^{3} -2.23607i q^{5} +5.23512i q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-1.73205 q^{3} -2.23607i q^{5} +5.23512i q^{7} +3.00000 q^{9} -0.200771i q^{11} -23.8661 q^{13} +3.87298i q^{15} -1.11718i q^{17} -19.7042i q^{19} -9.06750i q^{21} +(-18.8058 - 13.2416i) q^{23} -5.00000 q^{25} -5.19615 q^{27} +2.39590 q^{29} +38.2118 q^{31} +0.347746i q^{33} +11.7061 q^{35} -38.0912i q^{37} +41.3372 q^{39} +26.9899 q^{41} +35.3606i q^{43} -6.70820i q^{45} -9.80621 q^{47} +21.5935 q^{49} +1.93501i q^{51} +78.2168i q^{53} -0.448939 q^{55} +34.1286i q^{57} -63.9063 q^{59} -0.253327i q^{61} +15.7054i q^{63} +53.3661i q^{65} -17.8439i q^{67} +(32.5727 + 22.9352i) q^{69} +76.3329 q^{71} -77.6479 q^{73} +8.66025 q^{75} +1.05106 q^{77} -25.9565i q^{79} +9.00000 q^{81} -18.6692i q^{83} -2.49809 q^{85} -4.14982 q^{87} +28.6300i q^{89} -124.942i q^{91} -66.1847 q^{93} -44.0598 q^{95} -47.1436i q^{97} -0.602314i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$96 q + 288 q^{9}+O(q^{10})$$ 96 * q + 288 * q^9 $$96 q + 288 q^{9} - 16 q^{23} - 480 q^{25} - 80 q^{31} + 80 q^{35} + 48 q^{39} + 112 q^{41} + 32 q^{47} - 688 q^{49} - 80 q^{55} - 496 q^{59} - 96 q^{69} - 416 q^{71} - 320 q^{73} + 864 q^{81} + 192 q^{93}+O(q^{100})$$ 96 * q + 288 * q^9 - 16 * q^23 - 480 * q^25 - 80 * q^31 + 80 * q^35 + 48 * q^39 + 112 * q^41 + 32 * q^47 - 688 * q^49 - 80 * q^55 - 496 * q^59 - 96 * q^69 - 416 * q^71 - 320 * q^73 + 864 * q^81 + 192 * q^93

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2760\mathbb{Z}\right)^\times$$.

 $$n$$ $$1201$$ $$1381$$ $$1657$$ $$1841$$ $$2071$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$

## 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
$$3$$ −1.73205 −0.577350
$$4$$ 0 0
$$5$$ 2.23607i 0.447214i
$$6$$ 0 0
$$7$$ 5.23512i 0.747875i 0.927454 + 0.373937i $$0.121992\pi$$
−0.927454 + 0.373937i $$0.878008\pi$$
$$8$$ 0 0
$$9$$ 3.00000 0.333333
$$10$$ 0 0
$$11$$ 0.200771i 0.0182519i −0.999958 0.00912597i $$-0.997095\pi$$
0.999958 0.00912597i $$-0.00290493\pi$$
$$12$$ 0 0
$$13$$ −23.8661 −1.83585 −0.917925 0.396754i $$-0.870137\pi$$
−0.917925 + 0.396754i $$0.870137\pi$$
$$14$$ 0 0
$$15$$ 3.87298i 0.258199i
$$16$$ 0 0
$$17$$ 1.11718i 0.0657164i −0.999460 0.0328582i $$-0.989539\pi$$
0.999460 0.0328582i $$-0.0104610\pi$$
$$18$$ 0 0
$$19$$ 19.7042i 1.03706i −0.855059 0.518531i $$-0.826479\pi$$
0.855059 0.518531i $$-0.173521\pi$$
$$20$$ 0 0
$$21$$ 9.06750i 0.431786i
$$22$$ 0 0
$$23$$ −18.8058 13.2416i −0.817645 0.575723i
$$24$$ 0 0
$$25$$ −5.00000 −0.200000
$$26$$ 0 0
$$27$$ −5.19615 −0.192450
$$28$$ 0 0
$$29$$ 2.39590 0.0826173 0.0413086 0.999146i $$-0.486847\pi$$
0.0413086 + 0.999146i $$0.486847\pi$$
$$30$$ 0 0
$$31$$ 38.2118 1.23264 0.616319 0.787497i $$-0.288623\pi$$
0.616319 + 0.787497i $$0.288623\pi$$
$$32$$ 0 0
$$33$$ 0.347746i 0.0105378i
$$34$$ 0 0
$$35$$ 11.7061 0.334460
$$36$$ 0 0
$$37$$ 38.0912i 1.02949i −0.857343 0.514745i $$-0.827886\pi$$
0.857343 0.514745i $$-0.172114\pi$$
$$38$$ 0 0
$$39$$ 41.3372 1.05993
$$40$$ 0 0
$$41$$ 26.9899 0.658291 0.329145 0.944279i $$-0.393239\pi$$
0.329145 + 0.944279i $$0.393239\pi$$
$$42$$ 0 0
$$43$$ 35.3606i 0.822338i 0.911559 + 0.411169i $$0.134879\pi$$
−0.911559 + 0.411169i $$0.865121\pi$$
$$44$$ 0 0
$$45$$ 6.70820i 0.149071i
$$46$$ 0 0
$$47$$ −9.80621 −0.208643 −0.104321 0.994544i $$-0.533267\pi$$
−0.104321 + 0.994544i $$0.533267\pi$$
$$48$$ 0 0
$$49$$ 21.5935 0.440684
$$50$$ 0 0
$$51$$ 1.93501i 0.0379414i
$$52$$ 0 0
$$53$$ 78.2168i 1.47579i 0.674916 + 0.737895i $$0.264180\pi$$
−0.674916 + 0.737895i $$0.735820\pi$$
$$54$$ 0 0
$$55$$ −0.448939 −0.00816252
$$56$$ 0 0
$$57$$ 34.1286i 0.598748i
$$58$$ 0 0
$$59$$ −63.9063 −1.08316 −0.541579 0.840650i $$-0.682173\pi$$
−0.541579 + 0.840650i $$0.682173\pi$$
$$60$$ 0 0
$$61$$ 0.253327i 0.00415290i −0.999998 0.00207645i $$-0.999339\pi$$
0.999998 0.00207645i $$-0.000660955\pi$$
$$62$$ 0 0
$$63$$ 15.7054i 0.249292i
$$64$$ 0 0
$$65$$ 53.3661i 0.821017i
$$66$$ 0 0
$$67$$ 17.8439i 0.266326i −0.991094 0.133163i $$-0.957487\pi$$
0.991094 0.133163i $$-0.0425134\pi$$
$$68$$ 0 0
$$69$$ 32.5727 + 22.9352i 0.472067 + 0.332394i
$$70$$ 0 0
$$71$$ 76.3329 1.07511 0.537555 0.843228i $$-0.319348\pi$$
0.537555 + 0.843228i $$0.319348\pi$$
$$72$$ 0 0
$$73$$ −77.6479 −1.06367 −0.531835 0.846848i $$-0.678497\pi$$
−0.531835 + 0.846848i $$0.678497\pi$$
$$74$$ 0 0
$$75$$ 8.66025 0.115470
$$76$$ 0 0
$$77$$ 1.05106 0.0136502
$$78$$ 0 0
$$79$$ 25.9565i 0.328563i −0.986413 0.164282i $$-0.947469\pi$$
0.986413 0.164282i $$-0.0525306\pi$$
$$80$$ 0 0
$$81$$ 9.00000 0.111111
$$82$$ 0 0
$$83$$ 18.6692i 0.224930i −0.993656 0.112465i $$-0.964125\pi$$
0.993656 0.112465i $$-0.0358746\pi$$
$$84$$ 0 0
$$85$$ −2.49809 −0.0293893
$$86$$ 0 0
$$87$$ −4.14982 −0.0476991
$$88$$ 0 0
$$89$$ 28.6300i 0.321686i 0.986980 + 0.160843i $$0.0514212\pi$$
−0.986980 + 0.160843i $$0.948579\pi$$
$$90$$ 0 0
$$91$$ 124.942i 1.37299i
$$92$$ 0 0
$$93$$ −66.1847 −0.711663
$$94$$ 0 0
$$95$$ −44.0598 −0.463788
$$96$$ 0 0
$$97$$ 47.1436i 0.486017i −0.970024 0.243008i $$-0.921866\pi$$
0.970024 0.243008i $$-0.0781342\pi$$
$$98$$ 0 0
$$99$$ 0.602314i 0.00608398i
$$100$$ 0 0
$$101$$ −69.8248 −0.691334 −0.345667 0.938357i $$-0.612347\pi$$
−0.345667 + 0.938357i $$0.612347\pi$$
$$102$$ 0 0
$$103$$ 50.4967i 0.490260i 0.969490 + 0.245130i $$0.0788306\pi$$
−0.969490 + 0.245130i $$0.921169\pi$$
$$104$$ 0 0
$$105$$ −20.2755 −0.193100
$$106$$ 0 0
$$107$$ 119.697i 1.11866i −0.828945 0.559330i $$-0.811059\pi$$
0.828945 0.559330i $$-0.188941\pi$$
$$108$$ 0 0
$$109$$ 137.224i 1.25894i 0.777026 + 0.629469i $$0.216728\pi$$
−0.777026 + 0.629469i $$0.783272\pi$$
$$110$$ 0 0
$$111$$ 65.9758i 0.594377i
$$112$$ 0 0
$$113$$ 197.504i 1.74783i 0.486083 + 0.873913i $$0.338425\pi$$
−0.486083 + 0.873913i $$0.661575\pi$$
$$114$$ 0 0
$$115$$ −29.6092 + 42.0511i −0.257471 + 0.365662i
$$116$$ 0 0
$$117$$ −71.5982 −0.611950
$$118$$ 0 0
$$119$$ 5.84856 0.0491476
$$120$$ 0 0
$$121$$ 120.960 0.999667
$$122$$ 0 0
$$123$$ −46.7479 −0.380064
$$124$$ 0 0
$$125$$ 11.1803i 0.0894427i
$$126$$ 0 0
$$127$$ 126.780 0.998267 0.499133 0.866525i $$-0.333652\pi$$
0.499133 + 0.866525i $$0.333652\pi$$
$$128$$ 0 0
$$129$$ 61.2463i 0.474777i
$$130$$ 0 0
$$131$$ −8.63807 −0.0659395 −0.0329697 0.999456i $$-0.510496\pi$$
−0.0329697 + 0.999456i $$0.510496\pi$$
$$132$$ 0 0
$$133$$ 103.154 0.775592
$$134$$ 0 0
$$135$$ 11.6190i 0.0860663i
$$136$$ 0 0
$$137$$ 77.8979i 0.568598i −0.958736 0.284299i $$-0.908239\pi$$
0.958736 0.284299i $$-0.0917608\pi$$
$$138$$ 0 0
$$139$$ −0.316859 −0.00227956 −0.00113978 0.999999i $$-0.500363\pi$$
−0.00113978 + 0.999999i $$0.500363\pi$$
$$140$$ 0 0
$$141$$ 16.9849 0.120460
$$142$$ 0 0
$$143$$ 4.79162i 0.0335078i
$$144$$ 0 0
$$145$$ 5.35740i 0.0369476i
$$146$$ 0 0
$$147$$ −37.4010 −0.254429
$$148$$ 0 0
$$149$$ 253.992i 1.70465i 0.523015 + 0.852323i $$0.324807\pi$$
−0.523015 + 0.852323i $$0.675193\pi$$
$$150$$ 0 0
$$151$$ 106.476 0.705140 0.352570 0.935785i $$-0.385308\pi$$
0.352570 + 0.935785i $$0.385308\pi$$
$$152$$ 0 0
$$153$$ 3.35153i 0.0219055i
$$154$$ 0 0
$$155$$ 85.4441i 0.551252i
$$156$$ 0 0
$$157$$ 54.7747i 0.348883i 0.984668 + 0.174442i $$0.0558120\pi$$
−0.984668 + 0.174442i $$0.944188\pi$$
$$158$$ 0 0
$$159$$ 135.476i 0.852047i
$$160$$ 0 0
$$161$$ 69.3215 98.4508i 0.430569 0.611496i
$$162$$ 0 0
$$163$$ −217.561 −1.33473 −0.667365 0.744731i $$-0.732578\pi$$
−0.667365 + 0.744731i $$0.732578\pi$$
$$164$$ 0 0
$$165$$ 0.777584 0.00471263
$$166$$ 0 0
$$167$$ −153.009 −0.916222 −0.458111 0.888895i $$-0.651474\pi$$
−0.458111 + 0.888895i $$0.651474\pi$$
$$168$$ 0 0
$$169$$ 400.589 2.37035
$$170$$ 0 0
$$171$$ 59.1125i 0.345687i
$$172$$ 0 0
$$173$$ 105.144 0.607769 0.303884 0.952709i $$-0.401716\pi$$
0.303884 + 0.952709i $$0.401716\pi$$
$$174$$ 0 0
$$175$$ 26.1756i 0.149575i
$$176$$ 0 0
$$177$$ 110.689 0.625362
$$178$$ 0 0
$$179$$ −109.111 −0.609558 −0.304779 0.952423i $$-0.598583\pi$$
−0.304779 + 0.952423i $$0.598583\pi$$
$$180$$ 0 0
$$181$$ 283.290i 1.56514i 0.622562 + 0.782570i $$0.286092\pi$$
−0.622562 + 0.782570i $$0.713908\pi$$
$$182$$ 0 0
$$183$$ 0.438775i 0.00239768i
$$184$$ 0 0
$$185$$ −85.1744 −0.460402
$$186$$ 0 0
$$187$$ −0.224297 −0.00119945
$$188$$ 0 0
$$189$$ 27.2025i 0.143929i
$$190$$ 0 0
$$191$$ 66.8202i 0.349844i 0.984582 + 0.174922i $$0.0559673\pi$$
−0.984582 + 0.174922i $$0.944033\pi$$
$$192$$ 0 0
$$193$$ 179.398 0.929525 0.464763 0.885435i $$-0.346140\pi$$
0.464763 + 0.885435i $$0.346140\pi$$
$$194$$ 0 0
$$195$$ 92.4328i 0.474015i
$$196$$ 0 0
$$197$$ 294.073 1.49276 0.746378 0.665522i $$-0.231791\pi$$
0.746378 + 0.665522i $$0.231791\pi$$
$$198$$ 0 0
$$199$$ 106.727i 0.536316i 0.963375 + 0.268158i $$0.0864149\pi$$
−0.963375 + 0.268158i $$0.913585\pi$$
$$200$$ 0 0
$$201$$ 30.9065i 0.153764i
$$202$$ 0 0
$$203$$ 12.5428i 0.0617874i
$$204$$ 0 0
$$205$$ 60.3513i 0.294397i
$$206$$ 0 0
$$207$$ −56.4175 39.7249i −0.272548 0.191908i
$$208$$ 0 0
$$209$$ −3.95603 −0.0189284
$$210$$ 0 0
$$211$$ 87.6103 0.415215 0.207607 0.978212i $$-0.433432\pi$$
0.207607 + 0.978212i $$0.433432\pi$$
$$212$$ 0 0
$$213$$ −132.212 −0.620716
$$214$$ 0 0
$$215$$ 79.0686 0.367761
$$216$$ 0 0
$$217$$ 200.043i 0.921858i
$$218$$ 0 0
$$219$$ 134.490 0.614110
$$220$$ 0 0
$$221$$ 26.6626i 0.120645i
$$222$$ 0 0
$$223$$ 226.958 1.01775 0.508874 0.860841i $$-0.330062\pi$$
0.508874 + 0.860841i $$0.330062\pi$$
$$224$$ 0 0
$$225$$ −15.0000 −0.0666667
$$226$$ 0 0
$$227$$ 269.830i 1.18868i 0.804214 + 0.594340i $$0.202587\pi$$
−0.804214 + 0.594340i $$0.797413\pi$$
$$228$$ 0 0
$$229$$ 193.430i 0.844673i 0.906439 + 0.422337i $$0.138790\pi$$
−0.906439 + 0.422337i $$0.861210\pi$$
$$230$$ 0 0
$$231$$ −1.82049 −0.00788093
$$232$$ 0 0
$$233$$ −27.9090 −0.119781 −0.0598906 0.998205i $$-0.519075\pi$$
−0.0598906 + 0.998205i $$0.519075\pi$$
$$234$$ 0 0
$$235$$ 21.9274i 0.0933079i
$$236$$ 0 0
$$237$$ 44.9580i 0.189696i
$$238$$ 0 0
$$239$$ −203.637 −0.852039 −0.426020 0.904714i $$-0.640085\pi$$
−0.426020 + 0.904714i $$0.640085\pi$$
$$240$$ 0 0
$$241$$ 466.175i 1.93434i 0.254134 + 0.967169i $$0.418210\pi$$
−0.254134 + 0.967169i $$0.581790\pi$$
$$242$$ 0 0
$$243$$ −15.5885 −0.0641500
$$244$$ 0 0
$$245$$ 48.2845i 0.197080i
$$246$$ 0 0
$$247$$ 470.261i 1.90389i
$$248$$ 0 0
$$249$$ 32.3360i 0.129863i
$$250$$ 0 0
$$251$$ 167.843i 0.668696i −0.942450 0.334348i $$-0.891484\pi$$
0.942450 0.334348i $$-0.108516\pi$$
$$252$$ 0 0
$$253$$ −2.65854 + 3.77567i −0.0105081 + 0.0149236i
$$254$$ 0 0
$$255$$ 4.32681 0.0169679
$$256$$ 0 0
$$257$$ 82.9455 0.322745 0.161373 0.986894i $$-0.448408\pi$$
0.161373 + 0.986894i $$0.448408\pi$$
$$258$$ 0 0
$$259$$ 199.412 0.769930
$$260$$ 0 0
$$261$$ 7.18770 0.0275391
$$262$$ 0 0
$$263$$ 231.115i 0.878765i 0.898300 + 0.439383i $$0.144803\pi$$
−0.898300 + 0.439383i $$0.855197\pi$$
$$264$$ 0 0
$$265$$ 174.898 0.659993
$$266$$ 0 0
$$267$$ 49.5887i 0.185725i
$$268$$ 0 0
$$269$$ 10.6727 0.0396756 0.0198378 0.999803i $$-0.493685\pi$$
0.0198378 + 0.999803i $$0.493685\pi$$
$$270$$ 0 0
$$271$$ 323.563 1.19396 0.596980 0.802256i $$-0.296367\pi$$
0.596980 + 0.802256i $$0.296367\pi$$
$$272$$ 0 0
$$273$$ 216.405i 0.792694i
$$274$$ 0 0
$$275$$ 1.00386i 0.00365039i
$$276$$ 0 0
$$277$$ 71.4145 0.257814 0.128907 0.991657i $$-0.458853\pi$$
0.128907 + 0.991657i $$0.458853\pi$$
$$278$$ 0 0
$$279$$ 114.635 0.410879
$$280$$ 0 0
$$281$$ 393.137i 1.39906i −0.714601 0.699532i $$-0.753392\pi$$
0.714601 0.699532i $$-0.246608\pi$$
$$282$$ 0 0
$$283$$ 96.7722i 0.341951i 0.985275 + 0.170976i $$0.0546919\pi$$
−0.985275 + 0.170976i $$0.945308\pi$$
$$284$$ 0 0
$$285$$ 76.3139 0.267768
$$286$$ 0 0
$$287$$ 141.296i 0.492319i
$$288$$ 0 0
$$289$$ 287.752 0.995681
$$290$$ 0 0
$$291$$ 81.6551i 0.280602i
$$292$$ 0 0
$$293$$ 43.7569i 0.149341i −0.997208 0.0746704i $$-0.976210\pi$$
0.997208 0.0746704i $$-0.0237905\pi$$
$$294$$ 0 0
$$295$$ 142.899i 0.484403i
$$296$$ 0 0
$$297$$ 1.04324i 0.00351259i
$$298$$ 0 0
$$299$$ 448.821 + 316.025i 1.50107 + 1.05694i
$$300$$ 0 0
$$301$$ −185.117 −0.615006
$$302$$ 0 0
$$303$$ 120.940 0.399142
$$304$$ 0 0
$$305$$ −0.566456 −0.00185723
$$306$$ 0 0
$$307$$ −338.800 −1.10358 −0.551791 0.833982i $$-0.686056\pi$$
−0.551791 + 0.833982i $$0.686056\pi$$
$$308$$ 0 0
$$309$$ 87.4629i 0.283052i
$$310$$ 0 0
$$311$$ 15.6524 0.0503293 0.0251646 0.999683i $$-0.491989\pi$$
0.0251646 + 0.999683i $$0.491989\pi$$
$$312$$ 0 0
$$313$$ 495.024i 1.58155i 0.612110 + 0.790773i $$0.290321\pi$$
−0.612110 + 0.790773i $$0.709679\pi$$
$$314$$ 0 0
$$315$$ 35.1183 0.111487
$$316$$ 0 0
$$317$$ 209.614 0.661244 0.330622 0.943763i $$-0.392741\pi$$
0.330622 + 0.943763i $$0.392741\pi$$
$$318$$ 0 0
$$319$$ 0.481028i 0.00150793i
$$320$$ 0 0
$$321$$ 207.320i 0.645858i
$$322$$ 0 0
$$323$$ −22.0131 −0.0681519
$$324$$ 0 0
$$325$$ 119.330 0.367170
$$326$$ 0 0
$$327$$ 237.679i 0.726848i
$$328$$ 0 0
$$329$$ 51.3367i 0.156039i
$$330$$ 0 0
$$331$$ −341.668 −1.03223 −0.516115 0.856520i $$-0.672622\pi$$
−0.516115 + 0.856520i $$0.672622\pi$$
$$332$$ 0 0
$$333$$ 114.273i 0.343164i
$$334$$ 0 0
$$335$$ −39.9001 −0.119105
$$336$$ 0 0
$$337$$ 67.5483i 0.200440i −0.994965 0.100220i $$-0.968045\pi$$
0.994965 0.100220i $$-0.0319547\pi$$
$$338$$ 0 0
$$339$$ 342.087i 1.00911i
$$340$$ 0 0
$$341$$ 7.67183i 0.0224980i
$$342$$ 0 0
$$343$$ 369.566i 1.07745i
$$344$$ 0 0
$$345$$ 51.2846 72.8347i 0.148651 0.211115i
$$346$$ 0 0
$$347$$ 156.348 0.450572 0.225286 0.974293i $$-0.427668\pi$$
0.225286 + 0.974293i $$0.427668\pi$$
$$348$$ 0 0
$$349$$ 231.064 0.662074 0.331037 0.943618i $$-0.392602\pi$$
0.331037 + 0.943618i $$0.392602\pi$$
$$350$$ 0 0
$$351$$ 124.012 0.353310
$$352$$ 0 0
$$353$$ 396.420 1.12300 0.561501 0.827476i $$-0.310224\pi$$
0.561501 + 0.827476i $$0.310224\pi$$
$$354$$ 0 0
$$355$$ 170.686i 0.480804i
$$356$$ 0 0
$$357$$ −10.1300 −0.0283754
$$358$$ 0 0
$$359$$ 302.034i 0.841320i −0.907218 0.420660i $$-0.861799\pi$$
0.907218 0.420660i $$-0.138201\pi$$
$$360$$ 0 0
$$361$$ −27.2540 −0.0754957
$$362$$ 0 0
$$363$$ −209.508 −0.577158
$$364$$ 0 0
$$365$$ 173.626i 0.475688i
$$366$$ 0 0
$$367$$ 402.123i 1.09570i −0.836576 0.547851i $$-0.815446\pi$$
0.836576 0.547851i $$-0.184554\pi$$
$$368$$ 0 0
$$369$$ 80.9698 0.219430
$$370$$ 0 0
$$371$$ −409.475 −1.10371
$$372$$ 0 0
$$373$$ 203.213i 0.544806i −0.962183 0.272403i $$-0.912182\pi$$
0.962183 0.272403i $$-0.0878185\pi$$
$$374$$ 0 0
$$375$$ 19.3649i 0.0516398i
$$376$$ 0 0
$$377$$ −57.1807 −0.151673
$$378$$ 0 0
$$379$$ 223.194i 0.588903i −0.955666 0.294451i $$-0.904863\pi$$
0.955666 0.294451i $$-0.0951369\pi$$
$$380$$ 0 0
$$381$$ −219.589 −0.576350
$$382$$ 0 0
$$383$$ 154.120i 0.402403i 0.979550 + 0.201202i $$0.0644847\pi$$
−0.979550 + 0.201202i $$0.935515\pi$$
$$384$$ 0 0
$$385$$ 2.35025i 0.00610454i
$$386$$ 0 0
$$387$$ 106.082i 0.274113i
$$388$$ 0 0
$$389$$ 344.101i 0.884578i 0.896873 + 0.442289i $$0.145833\pi$$
−0.896873 + 0.442289i $$0.854167\pi$$
$$390$$ 0 0
$$391$$ −14.7933 + 21.0095i −0.0378344 + 0.0537327i
$$392$$ 0 0
$$393$$ 14.9616 0.0380702
$$394$$ 0 0
$$395$$ −58.0405 −0.146938
$$396$$ 0 0
$$397$$ 62.7088 0.157957 0.0789783 0.996876i $$-0.474834\pi$$
0.0789783 + 0.996876i $$0.474834\pi$$
$$398$$ 0 0
$$399$$ −178.667 −0.447788
$$400$$ 0 0
$$401$$ 151.037i 0.376650i 0.982107 + 0.188325i $$0.0603058\pi$$
−0.982107 + 0.188325i $$0.939694\pi$$
$$402$$ 0 0
$$403$$ −911.964 −2.26294
$$404$$ 0 0
$$405$$ 20.1246i 0.0496904i
$$406$$ 0 0
$$407$$ −7.64762 −0.0187902
$$408$$ 0 0
$$409$$ −173.909 −0.425206 −0.212603 0.977139i $$-0.568194\pi$$
−0.212603 + 0.977139i $$0.568194\pi$$
$$410$$ 0 0
$$411$$ 134.923i 0.328280i
$$412$$ 0 0
$$413$$ 334.557i 0.810066i
$$414$$ 0 0
$$415$$ −41.7456 −0.100592
$$416$$ 0 0
$$417$$ 0.548816 0.00131611
$$418$$ 0 0
$$419$$ 182.183i 0.434805i −0.976082 0.217402i $$-0.930242\pi$$
0.976082 0.217402i $$-0.0697584\pi$$
$$420$$ 0 0
$$421$$ 365.856i 0.869017i 0.900668 + 0.434508i $$0.143078\pi$$
−0.900668 + 0.434508i $$0.856922\pi$$
$$422$$ 0 0
$$423$$ −29.4186 −0.0695476
$$424$$ 0 0
$$425$$ 5.58589i 0.0131433i
$$426$$ 0 0
$$427$$ 1.32620 0.00310585
$$428$$ 0 0
$$429$$ 8.29933i 0.0193458i
$$430$$ 0 0
$$431$$ 114.799i 0.266355i 0.991092 + 0.133177i $$0.0425180\pi$$
−0.991092 + 0.133177i $$0.957482\pi$$
$$432$$ 0 0
$$433$$ 268.115i 0.619202i 0.950867 + 0.309601i $$0.100196\pi$$
−0.950867 + 0.309601i $$0.899804\pi$$
$$434$$ 0 0
$$435$$ 9.27928i 0.0213317i
$$436$$ 0 0
$$437$$ −260.915 + 370.553i −0.597060 + 0.847948i
$$438$$ 0 0
$$439$$ −44.3726 −0.101077 −0.0505383 0.998722i $$-0.516094\pi$$
−0.0505383 + 0.998722i $$0.516094\pi$$
$$440$$ 0 0
$$441$$ 64.7805 0.146895
$$442$$ 0 0
$$443$$ 630.841 1.42402 0.712010 0.702169i $$-0.247785\pi$$
0.712010 + 0.702169i $$0.247785\pi$$
$$444$$ 0 0
$$445$$ 64.0187 0.143862
$$446$$ 0 0
$$447$$ 439.928i 0.984178i
$$448$$ 0 0
$$449$$ −67.6896 −0.150756 −0.0753781 0.997155i $$-0.524016\pi$$
−0.0753781 + 0.997155i $$0.524016\pi$$
$$450$$ 0 0
$$451$$ 5.41881i 0.0120151i
$$452$$ 0 0
$$453$$ −184.422 −0.407113
$$454$$ 0 0
$$455$$ −279.378 −0.614018
$$456$$ 0 0
$$457$$ 379.024i 0.829373i 0.909964 + 0.414687i $$0.136109\pi$$
−0.909964 + 0.414687i $$0.863891\pi$$
$$458$$ 0 0
$$459$$ 5.80503i 0.0126471i
$$460$$ 0 0
$$461$$ 58.6697 0.127266 0.0636330 0.997973i $$-0.479731\pi$$
0.0636330 + 0.997973i $$0.479731\pi$$
$$462$$ 0 0
$$463$$ −422.962 −0.913525 −0.456762 0.889589i $$-0.650991\pi$$
−0.456762 + 0.889589i $$0.650991\pi$$
$$464$$ 0 0
$$465$$ 147.993i 0.318266i
$$466$$ 0 0
$$467$$ 600.100i 1.28501i −0.766281 0.642506i $$-0.777895\pi$$
0.766281 0.642506i $$-0.222105\pi$$
$$468$$ 0 0
$$469$$ 93.4148 0.199179
$$470$$ 0 0
$$471$$ 94.8725i 0.201428i
$$472$$ 0 0
$$473$$ 7.09939 0.0150093
$$474$$ 0 0
$$475$$ 98.5208i 0.207412i
$$476$$ 0 0
$$477$$ 234.650i 0.491930i
$$478$$ 0 0
$$479$$ 491.467i 1.02603i 0.858381 + 0.513013i $$0.171471\pi$$
−0.858381 + 0.513013i $$0.828529\pi$$
$$480$$ 0 0
$$481$$ 909.086i 1.88999i
$$482$$ 0 0
$$483$$ −120.068 + 170.522i −0.248589 + 0.353047i
$$484$$ 0 0
$$485$$ −105.416 −0.217353
$$486$$ 0 0
$$487$$ 409.006 0.839849 0.419925 0.907559i $$-0.362057\pi$$
0.419925 + 0.907559i $$0.362057\pi$$
$$488$$ 0 0
$$489$$ 376.827 0.770607
$$490$$ 0 0
$$491$$ −109.571 −0.223159 −0.111580 0.993756i $$-0.535591\pi$$
−0.111580 + 0.993756i $$0.535591\pi$$
$$492$$ 0 0
$$493$$ 2.67665i 0.00542931i
$$494$$ 0 0
$$495$$ −1.34682 −0.00272084
$$496$$ 0 0
$$497$$ 399.612i 0.804048i
$$498$$ 0 0
$$499$$ 185.334 0.371412 0.185706 0.982605i $$-0.440543\pi$$
0.185706 + 0.982605i $$0.440543\pi$$
$$500$$ 0 0
$$501$$ 265.019 0.528981
$$502$$ 0 0
$$503$$ 582.863i 1.15877i −0.815053 0.579387i $$-0.803292\pi$$
0.815053 0.579387i $$-0.196708\pi$$
$$504$$ 0 0
$$505$$ 156.133i 0.309174i
$$506$$ 0 0
$$507$$ −693.840 −1.36852
$$508$$ 0 0
$$509$$ 148.389 0.291530 0.145765 0.989319i $$-0.453436\pi$$
0.145765 + 0.989319i $$0.453436\pi$$
$$510$$ 0 0
$$511$$ 406.496i 0.795492i
$$512$$ 0 0
$$513$$ 102.386i 0.199583i
$$514$$ 0 0
$$515$$ 112.914 0.219251
$$516$$ 0 0
$$517$$ 1.96881i 0.00380814i
$$518$$ 0 0
$$519$$ −182.115 −0.350895
$$520$$ 0 0
$$521$$ 862.617i 1.65569i −0.560954 0.827847i $$-0.689565\pi$$
0.560954 0.827847i $$-0.310435\pi$$
$$522$$ 0 0
$$523$$ 874.917i 1.67288i 0.548057 + 0.836441i $$0.315368\pi$$
−0.548057 + 0.836441i $$0.684632\pi$$
$$524$$ 0 0
$$525$$ 45.3375i 0.0863571i
$$526$$ 0 0
$$527$$ 42.6893i 0.0810044i
$$528$$ 0 0
$$529$$ 178.319 + 498.040i 0.337086 + 0.941474i
$$530$$ 0 0
$$531$$ −191.719 −0.361053
$$532$$ 0 0
$$533$$ −644.143 −1.20852
$$534$$ 0 0
$$535$$ −267.650 −0.500280
$$536$$ 0 0
$$537$$ 188.986 0.351928
$$538$$ 0 0
$$539$$ 4.33536i 0.00804333i
$$540$$ 0 0
$$541$$ 528.756 0.977368 0.488684 0.872461i $$-0.337477\pi$$
0.488684 + 0.872461i $$0.337477\pi$$
$$542$$ 0 0
$$543$$ 490.673i 0.903634i
$$544$$ 0 0
$$545$$ 306.843 0.563014
$$546$$ 0 0
$$547$$ 746.212 1.36419 0.682095 0.731264i $$-0.261069\pi$$
0.682095 + 0.731264i $$0.261069\pi$$
$$548$$ 0 0
$$549$$ 0.759980i 0.00138430i
$$550$$ 0 0
$$551$$ 47.2092i 0.0856792i
$$552$$ 0 0
$$553$$ 135.885 0.245724
$$554$$ 0 0
$$555$$ 147.526 0.265813
$$556$$ 0 0
$$557$$ 225.174i 0.404262i −0.979358 0.202131i $$-0.935213\pi$$
0.979358 0.202131i $$-0.0647867\pi$$
$$558$$ 0 0
$$559$$ 843.917i 1.50969i
$$560$$ 0 0
$$561$$ 0.388495 0.000692504
$$562$$ 0 0
$$563$$ 274.306i 0.487222i 0.969873 + 0.243611i $$0.0783320\pi$$
−0.969873 + 0.243611i $$0.921668\pi$$
$$564$$ 0 0
$$565$$ 441.633 0.781651
$$566$$ 0 0
$$567$$ 47.1161i 0.0830972i
$$568$$ 0 0
$$569$$ 100.058i 0.175848i −0.996127 0.0879241i $$-0.971977\pi$$
0.996127 0.0879241i $$-0.0280233\pi$$
$$570$$ 0 0
$$571$$ 951.356i 1.66612i 0.553180 + 0.833061i $$0.313414\pi$$
−0.553180 + 0.833061i $$0.686586\pi$$
$$572$$ 0 0
$$573$$ 115.736i 0.201983i
$$574$$ 0 0
$$575$$ 94.0292 + 66.2081i 0.163529 + 0.115145i
$$576$$ 0 0
$$577$$ −585.207 −1.01422 −0.507112 0.861880i $$-0.669287\pi$$
−0.507112 + 0.861880i $$0.669287\pi$$
$$578$$ 0 0
$$579$$ −310.727 −0.536662
$$580$$ 0 0
$$581$$ 97.7355 0.168219
$$582$$ 0 0
$$583$$ 15.7037 0.0269360
$$584$$ 0 0
$$585$$ 160.098i 0.273672i
$$586$$ 0 0
$$587$$ 555.851 0.946936 0.473468 0.880811i $$-0.343002\pi$$
0.473468 + 0.880811i $$0.343002\pi$$
$$588$$ 0 0
$$589$$ 752.930i 1.27832i
$$590$$ 0 0
$$591$$ −509.349 −0.861843
$$592$$ 0 0
$$593$$ −995.087 −1.67806 −0.839028 0.544089i $$-0.816875\pi$$
−0.839028 + 0.544089i $$0.816875\pi$$
$$594$$ 0 0
$$595$$ 13.0778i 0.0219795i
$$596$$ 0 0
$$597$$ 184.856i 0.309642i
$$598$$ 0 0
$$599$$ 249.063 0.415797 0.207899 0.978150i $$-0.433338\pi$$
0.207899 + 0.978150i $$0.433338\pi$$
$$600$$ 0 0
$$601$$ 678.462 1.12889 0.564445 0.825471i $$-0.309090\pi$$
0.564445 + 0.825471i $$0.309090\pi$$
$$602$$ 0 0
$$603$$ 53.5316i 0.0887754i
$$604$$ 0 0
$$605$$ 270.474i 0.447065i
$$606$$ 0 0
$$607$$ 484.630 0.798403 0.399201 0.916863i $$-0.369287\pi$$
0.399201 + 0.916863i $$0.369287\pi$$
$$608$$ 0 0
$$609$$ 21.7248i 0.0356729i
$$610$$ 0 0
$$611$$ 234.036 0.383037
$$612$$ 0 0
$$613$$ 56.3353i 0.0919009i 0.998944 + 0.0459505i $$0.0146316\pi$$
−0.998944 + 0.0459505i $$0.985368\pi$$
$$614$$ 0 0
$$615$$ 104.532i 0.169970i
$$616$$ 0 0
$$617$$ 259.103i 0.419940i −0.977708 0.209970i $$-0.932663\pi$$
0.977708 0.209970i $$-0.0673367\pi$$
$$618$$ 0 0
$$619$$ 1067.70i 1.72488i −0.506163 0.862438i $$-0.668937\pi$$
0.506163 0.862438i $$-0.331063\pi$$
$$620$$ 0 0
$$621$$ 97.7180 + 68.8055i 0.157356 + 0.110798i
$$622$$ 0 0
$$623$$ −149.882 −0.240581
$$624$$ 0 0
$$625$$ 25.0000 0.0400000
$$626$$ 0 0
$$627$$ 6.85205 0.0109283
$$628$$ 0 0
$$629$$ −42.5546 −0.0676544
$$630$$ 0 0
$$631$$ 999.923i 1.58466i −0.610091 0.792332i $$-0.708867\pi$$
0.610091 0.792332i $$-0.291133\pi$$
$$632$$ 0 0
$$633$$ −151.745 −0.239724
$$634$$ 0 0
$$635$$ 283.488i 0.446438i
$$636$$ 0 0
$$637$$ −515.352 −0.809029
$$638$$ 0 0
$$639$$ 228.999 0.358370
$$640$$ 0 0
$$641$$ 568.784i 0.887338i 0.896191 + 0.443669i $$0.146323\pi$$
−0.896191 + 0.443669i $$0.853677\pi$$
$$642$$ 0 0
$$643$$ 748.876i 1.16466i 0.812953 + 0.582330i $$0.197859\pi$$
−0.812953 + 0.582330i $$0.802141\pi$$
$$644$$ 0 0
$$645$$ −136.951 −0.212327
$$646$$ 0 0
$$647$$ −67.0944 −0.103701 −0.0518504 0.998655i $$-0.516512\pi$$
−0.0518504 + 0.998655i $$0.516512\pi$$
$$648$$ 0 0
$$649$$ 12.8306i 0.0197697i
$$650$$ 0 0
$$651$$ 346.485i 0.532235i
$$652$$ 0 0
$$653$$ −1250.62 −1.91519 −0.957593 0.288125i $$-0.906968\pi$$
−0.957593 + 0.288125i $$0.906968\pi$$
$$654$$ 0 0
$$655$$ 19.3153i 0.0294890i
$$656$$ 0 0
$$657$$ −232.944 −0.354557
$$658$$ 0 0
$$659$$ 1297.90i 1.96950i −0.173980 0.984749i $$-0.555663\pi$$
0.173980 0.984749i $$-0.444337\pi$$
$$660$$ 0 0
$$661$$ 939.253i 1.42096i −0.703719 0.710479i $$-0.748478\pi$$
0.703719 0.710479i $$-0.251522\pi$$
$$662$$ 0 0
$$663$$ 46.1810i 0.0696547i
$$664$$ 0 0
$$665$$ 230.659i 0.346855i
$$666$$ 0 0
$$667$$ −45.0569 31.7256i −0.0675516 0.0475647i
$$668$$ 0 0
$$669$$ −393.103 −0.587597
$$670$$ 0 0
$$671$$ −0.0508608 −7.57985e−5
$$672$$ 0 0
$$673$$ 772.694 1.14813 0.574067 0.818808i $$-0.305365\pi$$
0.574067 + 0.818808i $$0.305365\pi$$
$$674$$ 0 0
$$675$$ 25.9808 0.0384900
$$676$$ 0 0
$$677$$ 766.136i 1.13166i 0.824521 + 0.565832i $$0.191445\pi$$
−0.824521 + 0.565832i $$0.808555\pi$$
$$678$$ 0 0
$$679$$ 246.803 0.363479
$$680$$ 0 0
$$681$$ 467.360i 0.686285i
$$682$$ 0 0
$$683$$ −1010.44 −1.47942 −0.739709 0.672926i $$-0.765037\pi$$
−0.739709 + 0.672926i $$0.765037\pi$$
$$684$$ 0 0
$$685$$ −174.185 −0.254285
$$686$$ 0 0
$$687$$ 335.031i 0.487672i
$$688$$ 0 0
$$689$$ 1866.73i 2.70933i
$$690$$ 0 0
$$691$$ −53.5977 −0.0775654 −0.0387827 0.999248i $$-0.512348\pi$$
−0.0387827 + 0.999248i $$0.512348\pi$$
$$692$$ 0 0
$$693$$ 3.15319 0.00455006
$$694$$ 0 0
$$695$$ 0.708519i 0.00101945i
$$696$$ 0 0
$$697$$ 30.1526i 0.0432605i
$$698$$ 0 0
$$699$$ 48.3398 0.0691557
$$700$$ 0 0
$$701$$ 943.325i 1.34568i −0.739786 0.672842i $$-0.765073\pi$$
0.739786 0.672842i $$-0.234927\pi$$
$$702$$ 0 0
$$703$$ −750.554 −1.06765
$$704$$ 0 0
$$705$$ 37.9793i 0.0538713i
$$706$$ 0 0
$$707$$ 365.541i 0.517031i
$$708$$ 0 0
$$709$$ 304.039i 0.428828i 0.976743 + 0.214414i $$0.0687842\pi$$
−0.976743 + 0.214414i $$0.931216\pi$$
$$710$$ 0 0
$$711$$ 77.8695i 0.109521i
$$712$$ 0 0
$$713$$ −718.604 505.986i −1.00786 0.709657i
$$714$$ 0 0
$$715$$ 10.7144 0.0149852
$$716$$ 0 0
$$717$$ 352.710 0.491925
$$718$$ 0 0
$$719$$ 89.2663 0.124153 0.0620767 0.998071i $$-0.480228\pi$$
0.0620767 + 0.998071i $$0.480228\pi$$
$$720$$ 0 0
$$721$$ −264.357 −0.366653
$$722$$ 0 0
$$723$$ 807.440i 1.11679i
$$724$$ 0 0
$$725$$ −11.9795 −0.0165235
$$726$$ 0 0
$$727$$ 172.629i 0.237454i 0.992927 + 0.118727i $$0.0378813\pi$$
−0.992927 + 0.118727i $$0.962119\pi$$
$$728$$ 0 0
$$729$$ 27.0000 0.0370370
$$730$$ 0 0
$$731$$ 39.5040 0.0540411
$$732$$ 0 0
$$733$$ 382.885i 0.522353i 0.965291 + 0.261176i $$0.0841104\pi$$
−0.965291 + 0.261176i $$0.915890\pi$$
$$734$$ 0 0
$$735$$ 83.6312i 0.113784i
$$736$$ 0 0
$$737$$ −3.58254 −0.00486097
$$738$$ 0 0
$$739$$ 1099.12 1.48730 0.743652 0.668567i $$-0.233092\pi$$
0.743652 + 0.668567i $$0.233092\pi$$
$$740$$ 0 0
$$741$$ 814.515i 1.09921i
$$742$$ 0 0
$$743$$ 647.782i 0.871846i −0.899984 0.435923i $$-0.856422\pi$$
0.899984 0.435923i $$-0.143578\pi$$
$$744$$ 0 0
$$745$$ 567.944 0.762341
$$746$$ 0 0
$$747$$ 56.0076i 0.0749767i
$$748$$ 0 0
$$749$$ 626.626 0.836617
$$750$$ 0 0
$$751$$ 848.139i 1.12935i 0.825315 + 0.564673i $$0.190998\pi$$
−0.825315 + 0.564673i $$0.809002\pi$$
$$752$$ 0 0
$$753$$ 290.712i 0.386072i
$$754$$ 0 0
$$755$$ 238.088i 0.315348i
$$756$$ 0 0
$$757$$ 1499.22i 1.98048i 0.139388 + 0.990238i $$0.455487\pi$$
−0.139388 + 0.990238i $$0.544513\pi$$
$$758$$ 0 0
$$759$$ 4.60473 6.53966i 0.00606683 0.00861615i
$$760$$ 0 0
$$761$$ −625.715 −0.822228 −0.411114 0.911584i $$-0.634860\pi$$
−0.411114 + 0.911584i $$0.634860\pi$$
$$762$$ 0 0
$$763$$ −718.386 −0.941528
$$764$$ 0 0
$$765$$ −7.49426 −0.00979642
$$766$$ 0 0
$$767$$ 1525.19 1.98852
$$768$$ 0 0
$$769$$ 10.9625i 0.0142555i −0.999975 0.00712774i $$-0.997731\pi$$
0.999975 0.00712774i $$-0.00226885\pi$$
$$770$$ 0 0
$$771$$ −143.666 −0.186337
$$772$$ 0 0
$$773$$ 948.455i 1.22698i 0.789703 + 0.613490i $$0.210235\pi$$
−0.789703 + 0.613490i $$0.789765\pi$$
$$774$$ 0 0
$$775$$ −191.059 −0.246527
$$776$$ 0 0
$$777$$ −345.392 −0.444519
$$778$$ 0 0
$$779$$ 531.814i 0.682688i
$$780$$ 0 0
$$781$$ 15.3255i 0.0196229i
$$782$$ 0 0
$$783$$ −12.4495 −0.0158997
$$784$$ 0 0
$$785$$ 122.480 0.156025
$$786$$ 0 0
$$787$$ 846.711i 1.07587i −0.842986 0.537936i $$-0.819204\pi$$
0.842986 0.537936i $$-0.180796\pi$$
$$788$$ 0 0
$$789$$ 400.303i 0.507355i
$$790$$ 0 0
$$791$$ −1033.96 −1.30715
$$792$$ 0 0
$$793$$ 6.04591i 0.00762410i
$$794$$ 0 0
$$795$$ −302.932 −0.381047
$$796$$ 0 0
$$797$$ 1107.68i 1.38981i −0.719102 0.694905i $$-0.755447\pi$$
0.719102 0.694905i $$-0.244553\pi$$
$$798$$ 0 0