# Properties

 Label 2592.2.i.v.865.1 Level $2592$ Weight $2$ Character 2592.865 Analytic conductor $20.697$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2592 = 2^{5} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2592.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$20.6972242039$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 864) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2592.865 Dual form 2592.2.i.v.1729.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{5} +(1.50000 - 2.59808i) q^{7} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{5} +(1.50000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{11} +(1.50000 + 2.59808i) q^{13} +2.00000 q^{17} +3.00000 q^{19} +(-3.00000 - 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-4.00000 + 6.92820i) q^{29} +6.00000 q^{35} +7.00000 q^{37} +(4.00000 + 6.92820i) q^{41} +(-6.00000 + 10.3923i) q^{43} +(-3.00000 + 5.19615i) q^{47} +(-1.00000 - 1.73205i) q^{49} -4.00000 q^{53} -12.0000 q^{55} +(-3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-3.00000 + 5.19615i) q^{65} +(-1.50000 - 2.59808i) q^{67} +12.0000 q^{71} -15.0000 q^{73} +(9.00000 + 15.5885i) q^{77} +(4.50000 - 7.79423i) q^{79} +(6.00000 - 10.3923i) q^{83} +(2.00000 + 3.46410i) q^{85} +10.0000 q^{89} +9.00000 q^{91} +(3.00000 + 5.19615i) q^{95} +(-4.50000 + 7.79423i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{5} + 3 q^{7} + O(q^{10})$$ $$2 q + 2 q^{5} + 3 q^{7} - 6 q^{11} + 3 q^{13} + 4 q^{17} + 6 q^{19} - 6 q^{23} + q^{25} - 8 q^{29} + 12 q^{35} + 14 q^{37} + 8 q^{41} - 12 q^{43} - 6 q^{47} - 2 q^{49} - 8 q^{53} - 24 q^{55} - 6 q^{59} + q^{61} - 6 q^{65} - 3 q^{67} + 24 q^{71} - 30 q^{73} + 18 q^{77} + 9 q^{79} + 12 q^{83} + 4 q^{85} + 20 q^{89} + 18 q^{91} + 6 q^{95} - 9 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1217$$ $$2431$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$5$$ 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i $$-0.0190830\pi$$
−0.550990 + 0.834512i $$0.685750\pi$$
$$6$$ 0 0
$$7$$ 1.50000 2.59808i 0.566947 0.981981i −0.429919 0.902867i $$-0.641458\pi$$
0.996866 0.0791130i $$-0.0252088\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i $$0.526448\pi$$
−0.821541 + 0.570149i $$0.806886\pi$$
$$12$$ 0 0
$$13$$ 1.50000 + 2.59808i 0.416025 + 0.720577i 0.995535 0.0943882i $$-0.0300895\pi$$
−0.579510 + 0.814965i $$0.696756\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ 3.00000 0.688247 0.344124 0.938924i $$-0.388176\pi$$
0.344124 + 0.938924i $$0.388176\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.00000 + 6.92820i −0.742781 + 1.28654i 0.208443 + 0.978035i $$0.433160\pi$$
−0.951224 + 0.308500i $$0.900173\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 6.00000 1.01419
$$36$$ 0 0
$$37$$ 7.00000 1.15079 0.575396 0.817875i $$-0.304848\pi$$
0.575396 + 0.817875i $$0.304848\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.00000 + 6.92820i 0.624695 + 1.08200i 0.988600 + 0.150567i $$0.0481100\pi$$
−0.363905 + 0.931436i $$0.618557\pi$$
$$42$$ 0 0
$$43$$ −6.00000 + 10.3923i −0.914991 + 1.58481i −0.108078 + 0.994142i $$0.534469\pi$$
−0.806914 + 0.590669i $$0.798864\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i $$-0.977503\pi$$
0.559908 + 0.828554i $$0.310836\pi$$
$$48$$ 0 0
$$49$$ −1.00000 1.73205i −0.142857 0.247436i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −4.00000 −0.549442 −0.274721 0.961524i $$-0.588586\pi$$
−0.274721 + 0.961524i $$0.588586\pi$$
$$54$$ 0 0
$$55$$ −12.0000 −1.61808
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i $$-0.294388\pi$$
−0.992524 + 0.122047i $$0.961054\pi$$
$$60$$ 0 0
$$61$$ 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i $$-0.812942\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −3.00000 + 5.19615i −0.372104 + 0.644503i
$$66$$ 0 0
$$67$$ −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i $$-0.225330\pi$$
−0.942987 + 0.332830i $$0.891996\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ −15.0000 −1.75562 −0.877809 0.479012i $$-0.840995\pi$$
−0.877809 + 0.479012i $$0.840995\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 9.00000 + 15.5885i 1.02565 + 1.77647i
$$78$$ 0 0
$$79$$ 4.50000 7.79423i 0.506290 0.876919i −0.493684 0.869641i $$-0.664350\pi$$
0.999974 0.00727784i $$-0.00231663\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i $$-0.604488\pi$$
0.980982 0.194099i $$-0.0621783\pi$$
$$84$$ 0 0
$$85$$ 2.00000 + 3.46410i 0.216930 + 0.375735i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 9.00000 0.943456
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 3.00000 + 5.19615i 0.307794 + 0.533114i
$$96$$ 0 0
$$97$$ −4.50000 + 7.79423i −0.456906 + 0.791384i −0.998796 0.0490655i $$-0.984376\pi$$
0.541890 + 0.840450i $$0.317709\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −8.00000 + 13.8564i −0.796030 + 1.37876i 0.126153 + 0.992011i $$0.459737\pi$$
−0.922183 + 0.386753i $$0.873597\pi$$
$$102$$ 0 0
$$103$$ 7.50000 + 12.9904i 0.738997 + 1.27998i 0.952947 + 0.303136i $$0.0980336\pi$$
−0.213950 + 0.976845i $$0.568633\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.00000 −0.580042 −0.290021 0.957020i $$-0.593662\pi$$
−0.290021 + 0.957020i $$0.593662\pi$$
$$108$$ 0 0
$$109$$ 6.00000 0.574696 0.287348 0.957826i $$-0.407226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 7.00000 + 12.1244i 0.658505 + 1.14056i 0.981003 + 0.193993i $$0.0621440\pi$$
−0.322498 + 0.946570i $$0.604523\pi$$
$$114$$ 0 0
$$115$$ 6.00000 10.3923i 0.559503 0.969087i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 3.00000 5.19615i 0.275010 0.476331i
$$120$$ 0 0
$$121$$ −12.5000 21.6506i −1.13636 1.96824i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 12.0000 1.06483 0.532414 0.846484i $$-0.321285\pi$$
0.532414 + 0.846484i $$0.321285\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$132$$ 0 0
$$133$$ 4.50000 7.79423i 0.390199 0.675845i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −7.00000 + 12.1244i −0.598050 + 1.03585i 0.395058 + 0.918656i $$0.370724\pi$$
−0.993109 + 0.117198i $$0.962609\pi$$
$$138$$ 0 0
$$139$$ −10.5000 18.1865i −0.890598 1.54256i −0.839159 0.543885i $$-0.816953\pi$$
−0.0514389 0.998676i $$-0.516381\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −18.0000 −1.50524
$$144$$ 0 0
$$145$$ −16.0000 −1.32873
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2.00000 + 3.46410i 0.163846 + 0.283790i 0.936245 0.351348i $$-0.114277\pi$$
−0.772399 + 0.635138i $$0.780943\pi$$
$$150$$ 0 0
$$151$$ −1.50000 + 2.59808i −0.122068 + 0.211428i −0.920583 0.390547i $$-0.872286\pi$$
0.798515 + 0.601975i $$0.205619\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i $$0.0220180\pi$$
−0.438948 + 0.898513i $$0.644649\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −18.0000 −1.41860
$$162$$ 0 0
$$163$$ −3.00000 −0.234978 −0.117489 0.993074i $$-0.537485\pi$$
−0.117489 + 0.993074i $$0.537485\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 9.00000 + 15.5885i 0.696441 + 1.20627i 0.969693 + 0.244328i $$0.0785675\pi$$
−0.273252 + 0.961943i $$0.588099\pi$$
$$168$$ 0 0
$$169$$ 2.00000 3.46410i 0.153846 0.266469i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 4.00000 6.92820i 0.304114 0.526742i −0.672949 0.739689i $$-0.734973\pi$$
0.977064 + 0.212947i $$0.0683062\pi$$
$$174$$ 0 0
$$175$$ −1.50000 2.59808i −0.113389 0.196396i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ 9.00000 0.668965 0.334482 0.942402i $$-0.391439\pi$$
0.334482 + 0.942402i $$0.391439\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 7.00000 + 12.1244i 0.514650 + 0.891400i
$$186$$ 0 0
$$187$$ −6.00000 + 10.3923i −0.438763 + 0.759961i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i $$-0.763683\pi$$
0.953912 + 0.300088i $$0.0970159\pi$$
$$192$$ 0 0
$$193$$ 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i $$-0.109072\pi$$
−0.761911 + 0.647682i $$0.775738\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ −15.0000 −1.06332 −0.531661 0.846957i $$-0.678432\pi$$
−0.531661 + 0.846957i $$0.678432\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 12.0000 + 20.7846i 0.842235 + 1.45879i
$$204$$ 0 0
$$205$$ −8.00000 + 13.8564i −0.558744 + 0.967773i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −9.00000 + 15.5885i −0.622543 + 1.07828i
$$210$$ 0 0
$$211$$ 7.50000 + 12.9904i 0.516321 + 0.894295i 0.999820 + 0.0189499i $$0.00603229\pi$$
−0.483499 + 0.875345i $$0.660634\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −24.0000 −1.63679
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 3.00000 + 5.19615i 0.201802 + 0.349531i
$$222$$ 0 0
$$223$$ −12.0000 + 20.7846i −0.803579 + 1.39184i 0.113666 + 0.993519i $$0.463740\pi$$
−0.917246 + 0.398321i $$0.869593\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i $$-0.963710\pi$$
0.595274 + 0.803523i $$0.297043\pi$$
$$228$$ 0 0
$$229$$ 3.00000 + 5.19615i 0.198246 + 0.343371i 0.947960 0.318390i $$-0.103142\pi$$
−0.749714 + 0.661762i $$0.769809\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 8.00000 0.524097 0.262049 0.965055i $$-0.415602\pi$$
0.262049 + 0.965055i $$0.415602\pi$$
$$234$$ 0 0
$$235$$ −12.0000 −0.782794
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −6.00000 10.3923i −0.388108 0.672222i 0.604087 0.796918i $$-0.293538\pi$$
−0.992195 + 0.124696i $$0.960204\pi$$
$$240$$ 0 0
$$241$$ 1.50000 2.59808i 0.0966235 0.167357i −0.813662 0.581339i $$-0.802529\pi$$
0.910285 + 0.413982i $$0.135862\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2.00000 3.46410i 0.127775 0.221313i
$$246$$ 0 0
$$247$$ 4.50000 + 7.79423i 0.286328 + 0.495935i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 36.0000 2.26330
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −10.0000 17.3205i −0.623783 1.08042i −0.988775 0.149413i $$-0.952262\pi$$
0.364992 0.931011i $$-0.381072\pi$$
$$258$$ 0 0
$$259$$ 10.5000 18.1865i 0.652438 1.13006i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i $$-0.712699\pi$$
0.989561 + 0.144112i $$0.0460326\pi$$
$$264$$ 0 0
$$265$$ −4.00000 6.92820i −0.245718 0.425596i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ 0 0
$$271$$ 15.0000 0.911185 0.455593 0.890188i $$-0.349427\pi$$
0.455593 + 0.890188i $$0.349427\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 3.00000 + 5.19615i 0.180907 + 0.313340i
$$276$$ 0 0
$$277$$ 9.00000 15.5885i 0.540758 0.936620i −0.458103 0.888899i $$-0.651471\pi$$
0.998861 0.0477206i $$-0.0151957\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 4.00000 6.92820i 0.238620 0.413302i −0.721699 0.692207i $$-0.756638\pi$$
0.960319 + 0.278906i $$0.0899716\pi$$
$$282$$ 0 0
$$283$$ 6.00000 + 10.3923i 0.356663 + 0.617758i 0.987401 0.158237i $$-0.0505811\pi$$
−0.630738 + 0.775996i $$0.717248\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 24.0000 1.41668
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.00000 1.73205i −0.0584206 0.101187i 0.835336 0.549740i $$-0.185273\pi$$
−0.893757 + 0.448552i $$0.851940\pi$$
$$294$$ 0 0
$$295$$ 6.00000 10.3923i 0.349334 0.605063i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 9.00000 15.5885i 0.520483 0.901504i
$$300$$ 0 0
$$301$$ 18.0000 + 31.1769i 1.03750 + 1.79701i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 2.00000 0.114520
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −9.00000 15.5885i −0.510343 0.883940i −0.999928 0.0119847i $$-0.996185\pi$$
0.489585 0.871956i $$-0.337148\pi$$
$$312$$ 0 0
$$313$$ 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i $$-0.824336\pi$$
0.879810 + 0.475325i $$0.157669\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.00000 + 3.46410i −0.112331 + 0.194563i −0.916710 0.399554i $$-0.869165\pi$$
0.804379 + 0.594117i $$0.202498\pi$$
$$318$$ 0 0
$$319$$ −24.0000 41.5692i −1.34374 2.32743i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 6.00000 0.333849
$$324$$ 0 0
$$325$$ 3.00000 0.166410
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 9.00000 + 15.5885i 0.496186 + 0.859419i
$$330$$ 0 0
$$331$$ 1.50000 2.59808i 0.0824475 0.142803i −0.821853 0.569699i $$-0.807060\pi$$
0.904301 + 0.426896i $$0.140393\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 3.00000 5.19615i 0.163908 0.283896i
$$336$$ 0 0
$$337$$ −4.50000 7.79423i −0.245131 0.424579i 0.717038 0.697034i $$-0.245498\pi$$
−0.962168 + 0.272456i $$0.912164\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 15.0000 0.809924
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i $$-0.271054\pi$$
−0.980921 + 0.194409i $$0.937721\pi$$
$$348$$ 0 0
$$349$$ 0.500000 0.866025i 0.0267644 0.0463573i −0.852333 0.523000i $$-0.824813\pi$$
0.879097 + 0.476642i $$0.158146\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 10.0000 17.3205i 0.532246 0.921878i −0.467045 0.884234i $$-0.654681\pi$$
0.999291 0.0376440i $$-0.0119853\pi$$
$$354$$ 0 0
$$355$$ 12.0000 + 20.7846i 0.636894 + 1.10313i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 18.0000 0.950004 0.475002 0.879985i $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −15.0000 25.9808i −0.785136 1.35990i
$$366$$ 0 0
$$367$$ 1.50000 2.59808i 0.0782994 0.135618i −0.824217 0.566274i $$-0.808384\pi$$
0.902516 + 0.430656i $$0.141718\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −6.00000 + 10.3923i −0.311504 + 0.539542i
$$372$$ 0 0
$$373$$ −11.5000 19.9186i −0.595447 1.03135i −0.993484 0.113975i $$-0.963641\pi$$
0.398036 0.917370i $$-0.369692\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ 27.0000 1.38690 0.693448 0.720506i $$-0.256091\pi$$
0.693448 + 0.720506i $$0.256091\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ 0 0
$$385$$ −18.0000 + 31.1769i −0.917365 + 1.58892i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 17.0000 29.4449i 0.861934 1.49291i −0.00812520 0.999967i $$-0.502586\pi$$
0.870059 0.492947i $$-0.164080\pi$$
$$390$$ 0 0
$$391$$ −6.00000 10.3923i −0.303433 0.525561i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 18.0000 0.905678
$$396$$ 0 0
$$397$$ 2.00000 0.100377 0.0501886 0.998740i $$-0.484018\pi$$
0.0501886 + 0.998740i $$0.484018\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −10.0000 17.3205i −0.499376 0.864945i 0.500624 0.865665i $$-0.333104\pi$$
−1.00000 0.000720188i $$0.999771\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −21.0000 + 36.3731i −1.04093 + 1.80295i
$$408$$ 0 0
$$409$$ −10.5000 18.1865i −0.519192 0.899266i −0.999751 0.0223042i $$-0.992900\pi$$
0.480560 0.876962i $$-0.340434\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −18.0000 −0.885722
$$414$$ 0 0
$$415$$ 24.0000 1.17811
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −15.0000 25.9808i −0.732798 1.26924i −0.955683 0.294398i $$-0.904881\pi$$
0.222885 0.974845i $$-0.428453\pi$$
$$420$$ 0 0
$$421$$ 7.50000 12.9904i 0.365528 0.633112i −0.623333 0.781956i $$-0.714222\pi$$
0.988861 + 0.148844i $$0.0475552\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.00000 1.73205i 0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ −1.50000 2.59808i −0.0725901 0.125730i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 30.0000 1.44505 0.722525 0.691345i $$-0.242982\pi$$
0.722525 + 0.691345i $$0.242982\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −9.00000 15.5885i −0.430528 0.745697i
$$438$$ 0 0
$$439$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i $$-0.741317\pi$$
0.972626 + 0.232377i $$0.0746503\pi$$
$$444$$ 0 0
$$445$$ 10.0000 + 17.3205i 0.474045 + 0.821071i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ −48.0000 −2.26023
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 9.00000 + 15.5885i 0.421927 + 0.730798i
$$456$$ 0 0
$$457$$ 15.0000 25.9808i 0.701670 1.21533i −0.266209 0.963915i $$-0.585771\pi$$
0.967880 0.251414i $$-0.0808954\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −1.00000 + 1.73205i −0.0465746 + 0.0806696i −0.888373 0.459123i $$-0.848164\pi$$
0.841798 + 0.539792i $$0.181497\pi$$
$$462$$ 0 0
$$463$$ 7.50000 + 12.9904i 0.348555 + 0.603714i 0.985993 0.166787i $$-0.0533393\pi$$
−0.637438 + 0.770501i $$0.720006\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6.00000 0.277647 0.138823 0.990317i $$-0.455668\pi$$
0.138823 + 0.990317i $$0.455668\pi$$
$$468$$ 0 0
$$469$$ −9.00000 −0.415581
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −36.0000 62.3538i −1.65528 2.86703i
$$474$$ 0 0
$$475$$ 1.50000 2.59808i 0.0688247 0.119208i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i $$-0.921729\pi$$
0.695773 + 0.718262i $$0.255062\pi$$
$$480$$ 0 0
$$481$$ 10.5000 + 18.1865i 0.478759 + 0.829235i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −18.0000 −0.817338
$$486$$ 0 0
$$487$$ −15.0000 −0.679715 −0.339857 0.940477i $$-0.610379\pi$$
−0.339857 + 0.940477i $$0.610379\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −21.0000 36.3731i −0.947717 1.64149i −0.750218 0.661190i $$-0.770052\pi$$
−0.197499 0.980303i $$-0.563282\pi$$
$$492$$ 0 0
$$493$$ −8.00000 + 13.8564i −0.360302 + 0.624061i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 18.0000 31.1769i 0.807410 1.39848i
$$498$$ 0 0
$$499$$ 12.0000 + 20.7846i 0.537194 + 0.930447i 0.999054 + 0.0434940i $$0.0138489\pi$$
−0.461860 + 0.886953i $$0.652818\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −42.0000 −1.87269 −0.936344 0.351085i $$-0.885813\pi$$
−0.936344 + 0.351085i $$0.885813\pi$$
$$504$$ 0 0
$$505$$ −32.0000 −1.42398
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 5.00000 + 8.66025i 0.221621 + 0.383859i 0.955300 0.295637i $$-0.0955319\pi$$
−0.733679 + 0.679496i $$0.762199\pi$$
$$510$$ 0 0
$$511$$ −22.5000 + 38.9711i −0.995341 + 1.72398i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −15.0000 + 25.9808i −0.660979 + 1.14485i
$$516$$ 0 0
$$517$$ −18.0000 31.1769i −0.791639 1.37116i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 14.0000 0.613351 0.306676 0.951814i $$-0.400783\pi$$
0.306676 + 0.951814i $$0.400783\pi$$
$$522$$ 0 0
$$523$$ −9.00000 −0.393543 −0.196771 0.980449i $$-0.563046\pi$$
−0.196771 + 0.980449i $$0.563046\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −12.0000 + 20.7846i −0.519778 + 0.900281i
$$534$$ 0 0
$$535$$ −6.00000 10.3923i −0.259403 0.449299i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 12.0000 0.516877
$$540$$ 0 0
$$541$$ −15.0000 −0.644900 −0.322450 0.946586i $$-0.604506\pi$$
−0.322450 + 0.946586i $$0.604506\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 6.00000 + 10.3923i 0.257012 + 0.445157i
$$546$$ 0 0
$$547$$ −4.50000 + 7.79423i −0.192406 + 0.333257i −0.946047 0.324029i $$-0.894962\pi$$
0.753641 + 0.657286i $$0.228296\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −12.0000 + 20.7846i −0.511217 + 0.885454i
$$552$$ 0 0
$$553$$ −13.5000 23.3827i −0.574078 0.994333i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 2.00000 0.0847427 0.0423714 0.999102i $$-0.486509\pi$$
0.0423714 + 0.999102i $$0.486509\pi$$
$$558$$ 0 0
$$559$$ −36.0000 −1.52264
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i $$0.00211371\pi$$
−0.494238 + 0.869326i $$0.664553\pi$$
$$564$$ 0 0
$$565$$ −14.0000 + 24.2487i −0.588984 + 1.02015i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 23.0000 39.8372i 0.964210 1.67006i 0.252488 0.967600i $$-0.418751\pi$$
0.711722 0.702461i $$-0.247915\pi$$
$$570$$ 0 0
$$571$$ −1.50000 2.59808i −0.0627730 0.108726i 0.832931 0.553377i $$-0.186661\pi$$
−0.895704 + 0.444651i $$0.853328\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −6.00000 −0.250217
$$576$$ 0 0
$$577$$ 11.0000 0.457936 0.228968 0.973434i $$-0.426465\pi$$
0.228968 + 0.973434i $$0.426465\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −18.0000 31.1769i −0.746766 1.29344i
$$582$$ 0 0
$$583$$ 12.0000 20.7846i 0.496989 0.860811i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i $$-0.954479\pi$$
0.618322 + 0.785925i $$0.287813\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −28.0000 −1.14982 −0.574911 0.818216i $$-0.694963\pi$$
−0.574911 + 0.818216i $$0.694963\pi$$
$$594$$ 0 0
$$595$$ 12.0000 0.491952
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i $$-0.329782\pi$$
−0.999938 + 0.0111569i $$0.996449\pi$$
$$600$$ 0 0
$$601$$ 13.0000 22.5167i 0.530281 0.918474i −0.469095 0.883148i $$-0.655420\pi$$
0.999376 0.0353259i $$-0.0112469\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 25.0000 43.3013i 1.01639 1.76045i
$$606$$ 0 0
$$607$$ 1.50000 + 2.59808i 0.0608831 + 0.105453i 0.894860 0.446346i $$-0.147275\pi$$
−0.833977 + 0.551799i $$0.813942\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −18.0000 −0.728202
$$612$$ 0 0
$$613$$ 11.0000 0.444286 0.222143 0.975014i $$-0.428695\pi$$
0.222143 + 0.975014i $$0.428695\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.00000 + 1.73205i 0.0402585 + 0.0697297i 0.885453 0.464730i $$-0.153849\pi$$
−0.845194 + 0.534460i $$0.820515\pi$$
$$618$$ 0 0
$$619$$ 4.50000 7.79423i 0.180870 0.313276i −0.761307 0.648392i $$-0.775442\pi$$
0.942177 + 0.335115i $$0.108775\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 15.0000 25.9808i 0.600962 1.04090i
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 14.0000 0.558217
$$630$$ 0 0
$$631$$ 27.0000 1.07485 0.537427 0.843311i $$-0.319397\pi$$
0.537427 + 0.843311i $$0.319397\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 12.0000 + 20.7846i 0.476205 + 0.824812i
$$636$$ 0 0
$$637$$ 3.00000 5.19615i 0.118864 0.205879i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.00000 3.46410i 0.0789953 0.136824i −0.823821 0.566849i $$-0.808162\pi$$
0.902817 + 0.430026i $$0.141495\pi$$
$$642$$ 0 0
$$643$$ −18.0000 31.1769i −0.709851 1.22950i −0.964912 0.262573i $$-0.915429\pi$$
0.255062 0.966925i $$-0.417904\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 24.0000 0.943537 0.471769 0.881722i $$-0.343616\pi$$
0.471769 + 0.881722i $$0.343616\pi$$
$$648$$ 0 0
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −14.0000 24.2487i −0.547862 0.948925i −0.998421 0.0561784i $$-0.982108\pi$$
0.450558 0.892747i $$-0.351225\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i $$-0.758241\pi$$
0.958902 + 0.283738i $$0.0915745\pi$$
$$660$$ 0 0
$$661$$ 2.50000 + 4.33013i 0.0972387 + 0.168422i 0.910541 0.413419i $$-0.135666\pi$$
−0.813302 + 0.581842i $$0.802332\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 18.0000 0.698010
$$666$$ 0 0
$$667$$ 48.0000 1.85857
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 3.00000 + 5.19615i 0.115814 + 0.200595i
$$672$$ 0 0
$$673$$ 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i $$-0.827198\pi$$
0.875501 + 0.483216i $$0.160531\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.00000 1.73205i 0.0384331 0.0665681i −0.846169 0.532915i $$-0.821097\pi$$
0.884602 + 0.466347i $$0.154430\pi$$
$$678$$ 0 0
$$679$$ 13.5000 + 23.3827i 0.518082 + 0.897345i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −24.0000 −0.918334 −0.459167 0.888350i $$-0.651852\pi$$
−0.459167 + 0.888350i $$0.651852\pi$$
$$684$$ 0 0
$$685$$ −28.0000 −1.06983
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −6.00000 10.3923i −0.228582 0.395915i
$$690$$ 0 0
$$691$$ 6.00000 10.3923i 0.228251 0.395342i −0.729039 0.684472i $$-0.760033\pi$$
0.957290 + 0.289130i $$0.0933661\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 21.0000 36.3731i 0.796575 1.37971i
$$696$$ 0 0
$$697$$ 8.00000 + 13.8564i 0.303022 + 0.524849i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −46.0000 −1.73740 −0.868698 0.495342i $$-0.835043\pi$$
−0.868698 + 0.495342i $$0.835043\pi$$
$$702$$ 0 0
$$703$$ 21.0000 0.792030
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 24.0000 + 41.5692i 0.902613 + 1.56337i
$$708$$ 0 0
$$709$$ 25.5000 44.1673i 0.957673 1.65874i 0.229543 0.973299i $$-0.426277\pi$$
0.728130 0.685439i $$-0.240390\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −18.0000 31.1769i −0.673162 1.16595i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 0 0
$$721$$ 45.0000 1.67589
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 4.00000 + 6.92820i 0.148556 + 0.257307i
$$726$$ 0 0
$$727$$ 12.0000 20.7846i 0.445055 0.770859i −0.553001 0.833181i $$-0.686517\pi$$
0.998056 + 0.0623223i $$0.0198507\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −12.0000 + 20.7846i −0.443836 + 0.768747i
$$732$$ 0 0
$$733$$ 9.00000 + 15.5885i 0.332423 + 0.575773i 0.982986 0.183679i $$-0.0588007\pi$$
−0.650564 + 0.759452i $$0.725467\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 18.0000 0.663039
$$738$$ 0 0
$$739$$ 12.0000 0.441427 0.220714 0.975339i $$-0.429161\pi$$
0.220714 + 0.975339i $$0.429161\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i $$-0.201771\pi$$
−0.915794 + 0.401648i $$0.868437\pi$$
$$744$$ 0 0
$$745$$ −4.00000 + 6.92820i −0.146549 + 0.253830i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −9.00000 + 15.5885i −0.328853 + 0.569590i
$$750$$ 0 0
$$751$$ 22.5000 + 38.9711i 0.821037 + 1.42208i 0.904911 + 0.425601i $$0.139937\pi$$
−0.0838743 + 0.996476i $$0.526729\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −6.00000 −0.218362
$$756$$ 0 0
$$757$$ −27.0000 −0.981332 −0.490666 0.871348i $$-0.663246\pi$$
−0.490666 + 0.871348i $$0.663246\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −17.0000 29.4449i −0.616250 1.06738i −0.990164 0.139912i $$-0.955318\pi$$
0.373914 0.927463i $$-0.378015\pi$$
$$762$$ 0 0
$$763$$ 9.00000 15.5885i 0.325822 0.564340i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 9.00000 15.5885i 0.324971 0.562867i
$$768$$ 0 0
$$769$$ 24.5000 + 42.4352i 0.883493 + 1.53025i 0.847432 + 0.530904i $$0.178148\pi$$
0.0360609 + 0.999350i $$0.488519\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 20.0000 0.719350 0.359675 0.933078i $$-0.382888\pi$$
0.359675 + 0.933078i $$0.382888\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 12.0000 + 20.7846i 0.429945 + 0.744686i
$$780$$ 0 0
$$781$$ −36.0000 + 62.3538i −1.28818 + 2.23120i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −14.0000 + 24.2487i −0.499681 + 0.865474i
$$786$$ 0 0
$$787$$ −13.5000 23.3827i −0.481223 0.833503i 0.518545 0.855050i $$-0.326474\pi$$
−0.999768 + 0.0215477i $$0.993141\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 42.0000 1.49335
$$792$$ 0 0
$$793$$ 3.00000 0.106533
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −20.0000 34.6410i −0.708436 1.22705i −0.965437 0.260637i $$-0.916068\pi$$
0.257001 0.966411i $$-0.417266\pi$$
$$798$$ 0 0
$$799$$ −6.00000 + 10.3923i −0.212265 + 0.367653i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 45.0000 77.9423i 1.58802 2.75052i