# Properties

 Label 1512.2.s.e.865.1 Level $1512$ Weight $2$ Character 1512.865 Analytic conductor $12.073$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1512 = 2^{3} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1512.s (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.0733807856$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1512.865 Dual form 1512.2.s.e.1297.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})$$ $$q+(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-1.50000 + 2.59808i) q^{11} +6.00000 q^{13} +(-2.00000 + 3.46410i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(-1.00000 - 5.19615i) q^{35} -2.00000 q^{41} +8.00000 q^{43} +(-1.00000 - 1.73205i) q^{47} +(5.50000 + 4.33013i) q^{49} +(5.00000 - 8.66025i) q^{53} +6.00000 q^{55} +(-4.50000 + 7.79423i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-6.00000 - 10.3923i) q^{65} +(3.00000 - 5.19615i) q^{67} +12.0000 q^{71} +(5.50000 - 9.52628i) q^{73} +(-6.00000 + 5.19615i) q^{77} +(-0.500000 - 0.866025i) q^{79} +15.0000 q^{83} +8.00000 q^{85} +(-5.00000 - 8.66025i) q^{89} +(15.0000 + 5.19615i) q^{91} +(-4.00000 + 6.92820i) q^{95} -5.00000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{5} + 5q^{7} + O(q^{10})$$ $$2q - 2q^{5} + 5q^{7} - 3q^{11} + 12q^{13} - 4q^{17} - 4q^{19} + 4q^{23} + q^{25} + 10q^{29} - 7q^{31} - 2q^{35} - 4q^{41} + 16q^{43} - 2q^{47} + 11q^{49} + 10q^{53} + 12q^{55} - 9q^{59} + 8q^{61} - 12q^{65} + 6q^{67} + 24q^{71} + 11q^{73} - 12q^{77} - q^{79} + 30q^{83} + 16q^{85} - 10q^{89} + 30q^{91} - 8q^{95} - 10q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$$.

 $$n$$ $$757$$ $$785$$ $$1081$$ $$1135$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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 0.550990 0.834512i $$-0.314250\pi$$
−0.998203 + 0.0599153i $$0.980917\pi$$
$$6$$ 0 0
$$7$$ 2.50000 + 0.866025i 0.944911 + 0.327327i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ 0 0
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i $$-0.994540\pi$$
0.514782 + 0.857321i $$0.327873\pi$$
$$18$$ 0 0
$$19$$ −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i $$-0.318398\pi$$
−0.998899 + 0.0469020i $$0.985065\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i $$-0.0297381\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 5.00000 0.928477 0.464238 0.885710i $$-0.346328\pi$$
0.464238 + 0.885710i $$0.346328\pi$$
$$30$$ 0 0
$$31$$ −3.50000 + 6.06218i −0.628619 + 1.08880i 0.359211 + 0.933257i $$0.383046\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1.00000 5.19615i −0.169031 0.878310i
$$36$$ 0 0
$$37$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i $$-0.213263\pi$$
−0.929695 + 0.368329i $$0.879930\pi$$
$$48$$ 0 0
$$49$$ 5.50000 + 4.33013i 0.785714 + 0.618590i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 5.00000 8.66025i 0.686803 1.18958i −0.286064 0.958211i $$-0.592347\pi$$
0.972867 0.231367i $$-0.0743197\pi$$
$$54$$ 0 0
$$55$$ 6.00000 0.809040
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i $$0.365906\pi$$
−0.994769 + 0.102151i $$0.967427\pi$$
$$60$$ 0 0
$$61$$ 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i $$0.00448323\pi$$
−0.487753 + 0.872982i $$0.662183\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −6.00000 10.3923i −0.744208 1.28901i
$$66$$ 0 0
$$67$$ 3.00000 5.19615i 0.366508 0.634811i −0.622509 0.782613i $$-0.713886\pi$$
0.989017 + 0.147802i $$0.0472198\pi$$
$$68$$ 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
$$73$$ 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i $$-0.610721\pi$$
0.984594 0.174855i $$-0.0559458\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −6.00000 + 5.19615i −0.683763 + 0.592157i
$$78$$ 0 0
$$79$$ −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i $$-0.184582\pi$$
−0.892781 + 0.450490i $$0.851249\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 15.0000 1.64646 0.823232 0.567705i $$-0.192169\pi$$
0.823232 + 0.567705i $$0.192169\pi$$
$$84$$ 0 0
$$85$$ 8.00000 0.867722
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i $$-0.988859\pi$$
0.469389 0.882992i $$-0.344474\pi$$
$$90$$ 0 0
$$91$$ 15.0000 + 5.19615i 1.57243 + 0.544705i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −4.00000 + 6.92820i −0.410391 + 0.710819i
$$96$$ 0 0
$$97$$ −5.00000 −0.507673 −0.253837 0.967247i $$-0.581693\pi$$
−0.253837 + 0.967247i $$0.581693\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i $$-0.565172\pi$$
0.949595 0.313478i $$-0.101494\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i $$0.0302972\pi$$
−0.415432 + 0.909624i $$0.636370\pi$$
$$108$$ 0 0
$$109$$ −8.00000 + 13.8564i −0.766261 + 1.32720i 0.173316 + 0.984866i $$0.444552\pi$$
−0.939577 + 0.342337i $$0.888782\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ 0 0
$$115$$ 4.00000 6.92820i 0.373002 0.646058i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −8.00000 + 6.92820i −0.733359 + 0.635107i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 6.50000 + 11.2583i 0.567908 + 0.983645i 0.996773 + 0.0802763i $$0.0255803\pi$$
−0.428865 + 0.903369i $$0.641086\pi$$
$$132$$ 0 0
$$133$$ −2.00000 10.3923i −0.173422 0.901127i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i $$-0.593796\pi$$
0.973910 0.226935i $$-0.0728704\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −9.00000 + 15.5885i −0.752618 + 1.30357i
$$144$$ 0 0
$$145$$ −5.00000 8.66025i −0.415227 0.719195i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2.50000 + 4.33013i 0.204808 + 0.354738i 0.950072 0.312032i $$-0.101010\pi$$
−0.745264 + 0.666770i $$0.767676\pi$$
$$150$$ 0 0
$$151$$ −9.50000 + 16.4545i −0.773099 + 1.33905i 0.162758 + 0.986666i $$0.447961\pi$$
−0.935857 + 0.352381i $$0.885372\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 14.0000 1.12451
$$156$$ 0 0
$$157$$ 9.00000 15.5885i 0.718278 1.24409i −0.243403 0.969925i $$-0.578264\pi$$
0.961681 0.274169i $$-0.0884028\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 2.00000 + 10.3923i 0.157622 + 0.819028i
$$162$$ 0 0
$$163$$ 7.00000 + 12.1244i 0.548282 + 0.949653i 0.998392 + 0.0566798i $$0.0180514\pi$$
−0.450110 + 0.892973i $$0.648615\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −5.50000 9.52628i −0.418157 0.724270i 0.577597 0.816322i $$-0.303991\pi$$
−0.995754 + 0.0920525i $$0.970657\pi$$
$$174$$ 0 0
$$175$$ 2.00000 1.73205i 0.151186 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0.500000 0.866025i 0.0373718 0.0647298i −0.846735 0.532016i $$-0.821435\pi$$
0.884106 + 0.467286i $$0.154768\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −6.00000 10.3923i −0.438763 0.759961i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i $$-0.284500\pi$$
−0.988255 + 0.152813i $$0.951167\pi$$
$$192$$ 0 0
$$193$$ −10.5000 + 18.1865i −0.755807 + 1.30910i 0.189166 + 0.981945i $$0.439422\pi$$
−0.944972 + 0.327150i $$0.893912\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −3.00000 −0.213741 −0.106871 0.994273i $$-0.534083\pi$$
−0.106871 + 0.994273i $$0.534083\pi$$
$$198$$ 0 0
$$199$$ 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i $$-0.753524\pi$$
0.963001 + 0.269498i $$0.0868577\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 12.5000 + 4.33013i 0.877328 + 0.303915i
$$204$$ 0 0
$$205$$ 2.00000 + 3.46410i 0.139686 + 0.241943i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ −22.0000 −1.51454 −0.757271 0.653101i $$-0.773468\pi$$
−0.757271 + 0.653101i $$0.773468\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −8.00000 13.8564i −0.545595 0.944999i
$$216$$ 0 0
$$217$$ −14.0000 + 12.1244i −0.950382 + 0.823055i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −12.0000 + 20.7846i −0.807207 + 1.39812i
$$222$$ 0 0
$$223$$ −21.0000 −1.40626 −0.703132 0.711059i $$-0.748216\pi$$
−0.703132 + 0.711059i $$0.748216\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 6.50000 11.2583i 0.431420 0.747242i −0.565576 0.824696i $$-0.691346\pi$$
0.996996 + 0.0774548i $$0.0246793\pi$$
$$228$$ 0 0
$$229$$ −10.0000 17.3205i −0.660819 1.14457i −0.980401 0.197013i $$-0.936876\pi$$
0.319582 0.947559i $$-0.396457\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5.00000 + 8.66025i 0.327561 + 0.567352i 0.982027 0.188739i $$-0.0604400\pi$$
−0.654466 + 0.756091i $$0.727107\pi$$
$$234$$ 0 0
$$235$$ −2.00000 + 3.46410i −0.130466 + 0.225973i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −16.0000 −1.03495 −0.517477 0.855697i $$-0.673129\pi$$
−0.517477 + 0.855697i $$0.673129\pi$$
$$240$$ 0 0
$$241$$ −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i $$-0.905720\pi$$
0.731001 + 0.682376i $$0.239053\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2.00000 13.8564i 0.127775 0.885253i
$$246$$ 0 0
$$247$$ −12.0000 20.7846i −0.763542 1.32249i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 13.0000 0.820553 0.410276 0.911961i $$-0.365432\pi$$
0.410276 + 0.911961i $$0.365432\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 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
$$265$$ −20.0000 −1.22859
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 13.5000 23.3827i 0.823110 1.42567i −0.0802460 0.996775i $$-0.525571\pi$$
0.903356 0.428892i $$-0.141096\pi$$
$$270$$ 0 0
$$271$$ −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i $$-0.244792\pi$$
−0.961563 + 0.274586i $$0.911459\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.50000 + 2.59808i 0.0904534 + 0.156670i
$$276$$ 0 0
$$277$$ −5.00000 + 8.66025i −0.300421 + 0.520344i −0.976231 0.216731i $$-0.930460\pi$$
0.675810 + 0.737075i $$0.263794\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ −4.00000 + 6.92820i −0.237775 + 0.411839i −0.960076 0.279741i $$-0.909752\pi$$
0.722300 + 0.691580i $$0.243085\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −5.00000 1.73205i −0.295141 0.102240i
$$288$$ 0 0
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 9.00000 0.525786 0.262893 0.964825i $$-0.415323\pi$$
0.262893 + 0.964825i $$0.415323\pi$$
$$294$$ 0 0
$$295$$ 18.0000 1.04800
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 12.0000 + 20.7846i 0.693978 + 1.20201i
$$300$$ 0 0
$$301$$ 20.0000 + 6.92820i 1.15278 + 0.399335i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 8.00000 13.8564i 0.458079 0.793416i
$$306$$ 0 0
$$307$$ −2.00000 −0.114146 −0.0570730 0.998370i $$-0.518177\pi$$
−0.0570730 + 0.998370i $$0.518177\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i $$0.337148\pi$$
−0.999928 + 0.0119847i $$0.996185\pi$$
$$312$$ 0 0
$$313$$ −13.0000 22.5167i −0.734803 1.27272i −0.954810 0.297218i $$-0.903941\pi$$
0.220006 0.975499i $$-0.429392\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 13.5000 + 23.3827i 0.758236 + 1.31330i 0.943750 + 0.330661i $$0.107272\pi$$
−0.185514 + 0.982642i $$0.559395\pi$$
$$318$$ 0 0
$$319$$ −7.50000 + 12.9904i −0.419919 + 0.727322i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 16.0000 0.890264
$$324$$ 0 0
$$325$$ 3.00000 5.19615i 0.166410 0.288231i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1.00000 5.19615i −0.0551318 0.286473i
$$330$$ 0 0
$$331$$ −16.0000 27.7128i −0.879440 1.52323i −0.851957 0.523612i $$-0.824584\pi$$
−0.0274825 0.999622i $$-0.508749\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −12.0000 −0.655630
$$336$$ 0 0
$$337$$ 29.0000 1.57973 0.789865 0.613280i $$-0.210150\pi$$
0.789865 + 0.613280i $$0.210150\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −10.5000 18.1865i −0.568607 0.984856i
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i $$-0.858993\pi$$
0.822951 + 0.568112i $$0.192326\pi$$
$$348$$ 0 0
$$349$$ −4.00000 −0.214115 −0.107058 0.994253i $$-0.534143\pi$$
−0.107058 + 0.994253i $$0.534143\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i $$-0.884378\pi$$
0.775077 + 0.631867i $$0.217711\pi$$
$$354$$ 0 0
$$355$$ −12.0000 20.7846i −0.636894 1.10313i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −12.0000 20.7846i −0.633336 1.09697i −0.986865 0.161546i $$-0.948352\pi$$
0.353529 0.935423i $$-0.384981\pi$$
$$360$$ 0 0
$$361$$ 1.50000 2.59808i 0.0789474 0.136741i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −22.0000 −1.15153
$$366$$ 0 0
$$367$$ −10.0000 + 17.3205i −0.521996 + 0.904123i 0.477677 + 0.878536i $$0.341479\pi$$
−0.999673 + 0.0255875i $$0.991854\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 20.0000 17.3205i 1.03835 0.899236i
$$372$$ 0 0
$$373$$ 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i $$-0.133645\pi$$
−0.809591 + 0.586994i $$0.800311\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 30.0000 1.54508
$$378$$ 0 0
$$379$$ −6.00000 −0.308199 −0.154100 0.988055i $$-0.549248\pi$$
−0.154100 + 0.988055i $$0.549248\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 18.0000 + 31.1769i 0.919757 + 1.59307i 0.799783 + 0.600289i $$0.204948\pi$$
0.119974 + 0.992777i $$0.461719\pi$$
$$384$$ 0 0
$$385$$ 15.0000 + 5.19615i 0.764471 + 0.264820i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −9.50000 + 16.4545i −0.481669 + 0.834275i −0.999779 0.0210389i $$-0.993303\pi$$
0.518110 + 0.855314i $$0.326636\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −1.00000 + 1.73205i −0.0503155 + 0.0871489i
$$396$$ 0 0
$$397$$ −11.0000 19.0526i −0.552074 0.956221i −0.998125 0.0612128i $$-0.980503\pi$$
0.446051 0.895008i $$-0.352830\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i $$-0.315043\pi$$
−0.998350 + 0.0574304i $$0.981709\pi$$
$$402$$ 0 0
$$403$$ −21.0000 + 36.3731i −1.04608 + 1.81187i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −3.00000 + 5.19615i −0.148340 + 0.256933i −0.930614 0.366002i $$-0.880726\pi$$
0.782274 + 0.622935i $$0.214060\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −18.0000 + 15.5885i −0.885722 + 0.767058i
$$414$$ 0 0
$$415$$ −15.0000 25.9808i −0.736321 1.27535i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.00000 + 3.46410i 0.0970143 + 0.168034i
$$426$$ 0 0
$$427$$ 4.00000 + 20.7846i 0.193574 + 1.00584i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i $$-0.976060\pi$$
0.563658 + 0.826008i $$0.309393\pi$$
$$432$$ 0 0
$$433$$ −23.0000 −1.10531 −0.552655 0.833410i $$-0.686385\pi$$
−0.552655 + 0.833410i $$0.686385\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 8.00000 13.8564i 0.382692 0.662842i
$$438$$ 0 0
$$439$$ −7.50000 12.9904i −0.357955 0.619997i 0.629664 0.776868i $$-0.283193\pi$$
−0.987619 + 0.156871i $$0.949859\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −14.5000 25.1147i −0.688916 1.19324i −0.972189 0.234198i $$-0.924754\pi$$
0.283273 0.959039i $$-0.408580\pi$$
$$444$$ 0 0
$$445$$ −10.0000 + 17.3205i −0.474045 + 0.821071i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ 0 0
$$451$$ 3.00000 5.19615i 0.141264 0.244677i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −6.00000 31.1769i −0.281284 1.46160i
$$456$$ 0 0
$$457$$ −11.0000 19.0526i −0.514558 0.891241i −0.999857 0.0168929i $$-0.994623\pi$$
0.485299 0.874348i $$-0.338711\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −21.0000 −0.978068 −0.489034 0.872265i $$-0.662651\pi$$
−0.489034 + 0.872265i $$0.662651\pi$$
$$462$$ 0 0
$$463$$ −1.00000 −0.0464739 −0.0232370 0.999730i $$-0.507397\pi$$
−0.0232370 + 0.999730i $$0.507397\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 7.50000 + 12.9904i 0.347059 + 0.601123i 0.985726 0.168360i $$-0.0538472\pi$$
−0.638667 + 0.769483i $$0.720514\pi$$
$$468$$ 0 0
$$469$$ 12.0000 10.3923i 0.554109 0.479872i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −12.0000 + 20.7846i −0.551761 + 0.955677i
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 1.00000 1.73205i 0.0456912 0.0791394i −0.842275 0.539048i $$-0.818784\pi$$
0.887967 + 0.459908i $$0.152118\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 5.00000 + 8.66025i 0.227038 + 0.393242i
$$486$$ 0 0
$$487$$ −3.50000 + 6.06218i −0.158600 + 0.274703i −0.934364 0.356320i $$-0.884031\pi$$
0.775764 + 0.631023i $$0.217365\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ 0 0
$$493$$ −10.0000 + 17.3205i −0.450377 + 0.780076i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 30.0000 + 10.3923i 1.34568 + 0.466159i
$$498$$ 0 0
$$499$$ 4.00000 + 6.92820i 0.179065 + 0.310149i 0.941560 0.336844i $$-0.109360\pi$$
−0.762496 + 0.646993i $$0.776026\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −14.0000 −0.624229 −0.312115 0.950044i $$-0.601037\pi$$
−0.312115 + 0.950044i $$0.601037\pi$$
$$504$$ 0 0
$$505$$ −30.0000 −1.33498
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 19.5000 + 33.7750i 0.864322 + 1.49705i 0.867719 + 0.497056i $$0.165586\pi$$
−0.00339621 + 0.999994i $$0.501081\pi$$
$$510$$ 0 0
$$511$$ 22.0000 19.0526i 0.973223 0.842836i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 6.00000 0.263880
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −12.0000 + 20.7846i −0.525730 + 0.910590i 0.473821 + 0.880621i $$0.342874\pi$$
−0.999551 + 0.0299693i $$0.990459\pi$$
$$522$$ 0 0
$$523$$ −1.00000 1.73205i −0.0437269 0.0757373i 0.843334 0.537390i $$-0.180590\pi$$
−0.887061 + 0.461653i $$0.847256\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −14.0000 24.2487i −0.609850 1.05629i
$$528$$ 0 0
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ 12.0000 20.7846i 0.518805 0.898597i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −19.5000 + 7.79423i −0.839924 + 0.335721i
$$540$$ 0 0
$$541$$ −5.00000 8.66025i −0.214967 0.372333i 0.738296 0.674477i $$-0.235631\pi$$
−0.953262 + 0.302144i $$0.902298\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 32.0000 1.37073
$$546$$ 0 0
$$547$$ 22.0000 0.940652 0.470326 0.882493i $$-0.344136\pi$$
0.470326 + 0.882493i $$0.344136\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −10.0000 17.3205i −0.426014 0.737878i
$$552$$ 0 0
$$553$$ −0.500000 2.59808i −0.0212622 0.110481i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.50000 + 6.06218i −0.148300 + 0.256863i −0.930599 0.366040i $$-0.880713\pi$$
0.782299 + 0.622903i $$0.214047\pi$$
$$558$$ 0 0
$$559$$ 48.0000 2.03018
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 10.0000 17.3205i 0.421450 0.729972i −0.574632 0.818412i $$-0.694855\pi$$
0.996082 + 0.0884397i $$0.0281881\pi$$
$$564$$ 0 0
$$565$$ 12.0000 + 20.7846i 0.504844 + 0.874415i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000 + 31.1769i 0.754599 + 1.30700i 0.945573 + 0.325409i $$0.105502\pi$$
−0.190974 + 0.981595i $$0.561165\pi$$
$$570$$ 0 0
$$571$$ −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i $$0.400192\pi$$
−0.978022 + 0.208502i $$0.933141\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ −1.50000 + 2.59808i −0.0624458 + 0.108159i −0.895558 0.444945i $$-0.853223\pi$$
0.833112 + 0.553104i $$0.186557\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 37.5000 + 12.9904i 1.55576 + 0.538932i
$$582$$ 0 0
$$583$$ 15.0000 + 25.9808i 0.621237 + 1.07601i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −20.0000 −0.825488 −0.412744 0.910847i $$-0.635430\pi$$
−0.412744 + 0.910847i $$0.635430\pi$$
$$588$$ 0 0
$$589$$ 28.0000 1.15372
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 6.00000 + 10.3923i 0.246390 + 0.426761i 0.962522 0.271205i $$-0.0874221\pi$$
−0.716131 + 0.697966i $$0.754089\pi$$
$$594$$ 0 0
$$595$$ 20.0000 + 6.92820i 0.819920 + 0.284029i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 7.00000 12.1244i 0.286012 0.495388i −0.686842 0.726807i $$-0.741004\pi$$
0.972854 + 0.231419i $$0.0743369\pi$$
$$600$$ 0 0
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2.00000 3.46410i 0.0813116 0.140836i
$$606$$ 0 0
$$607$$ −9.50000 16.4545i −0.385593 0.667867i 0.606258 0.795268i $$-0.292670\pi$$
−0.991851 + 0.127401i $$0.959336\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6.00000 10.3923i −0.242734 0.420428i
$$612$$ 0 0
$$613$$ −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i $$0.407575\pi$$
−0.972924 + 0.231127i $$0.925759\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ 0 0
$$619$$ 18.0000 31.1769i 0.723481 1.25311i −0.236115 0.971725i $$-0.575874\pi$$
0.959596 0.281381i $$-0.0907924\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −5.00000 25.9808i −0.200321 1.04090i
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 41.0000 1.63218 0.816092 0.577922i $$-0.196136\pi$$
0.816092 + 0.577922i $$0.196136\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −8.00000 13.8564i −0.317470 0.549875i
$$636$$ 0 0
$$637$$ 33.0000 + 25.9808i 1.30751 + 1.02940i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 19.0000 32.9090i 0.750455 1.29983i −0.197148 0.980374i $$-0.563168\pi$$
0.947602 0.319452i $$-0.103499\pi$$
$$642$$ 0 0
$$643$$ −26.0000 −1.02534 −0.512670 0.858586i $$-0.671344\pi$$
−0.512670 + 0.858586i $$0.671344\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i $$-0.948453\pi$$
0.633090 + 0.774078i $$0.281786\pi$$
$$648$$ 0 0
$$649$$ −13.5000 23.3827i −0.529921 0.917851i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −7.00000 12.1244i −0.273931 0.474463i 0.695934 0.718106i $$-0.254991\pi$$
−0.969865 + 0.243643i $$0.921657\pi$$
$$654$$ 0 0
$$655$$ 13.0000 22.5167i 0.507952 0.879799i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 23.0000 0.895953 0.447976 0.894045i $$-0.352145\pi$$
0.447976 + 0.894045i $$0.352145\pi$$
$$660$$ 0 0
$$661$$ 23.0000 39.8372i 0.894596 1.54949i 0.0602929 0.998181i $$-0.480797\pi$$
0.834303 0.551306i $$-0.185870\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −16.0000 + 13.8564i −0.620453 + 0.537328i
$$666$$ 0 0
$$667$$ 10.0000 + 17.3205i 0.387202 + 0.670653i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −24.0000 −0.926510
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1.50000 2.59808i −0.0576497 0.0998522i 0.835760 0.549095i $$-0.185027\pi$$
−0.893410 + 0.449242i $$0.851694\pi$$
$$678$$ 0 0
$$679$$ −12.5000 4.33013i −0.479706 0.166175i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 22.5000 38.9711i 0.860939 1.49119i −0.0100856 0.999949i $$-0.503210\pi$$
0.871024 0.491240i $$-0.163456\pi$$
$$684$$ 0 0
$$685$$ −32.0000 −1.22266
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 30.0000 51.9615i 1.14291 1.97958i
$$690$$ 0 0
$$691$$ 8.00000 + 13.8564i 0.304334 + 0.527123i 0.977113 0.212721i $$-0.0682327\pi$$
−0.672779 + 0.739844i $$0.734899\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 4.00000 6.92820i 0.151511 0.262424i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 46.0000 1.73740 0.868698 0.495342i $$-0.164957\pi$$
0.868698 + 0.495342i $$0.164957\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 30.0000 25.9808i 1.12827 0.977107i
$$708$$ 0 0
$$709$$ −20.0000 34.6410i −0.751116 1.30097i −0.947282 0.320400i $$-0.896183\pi$$
0.196167 0.980571i $$-0.437151\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −28.0000 −1.04861
$$714$$ 0 0
$$715$$ 36.0000 1.34632
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −21.0000 36.3731i −0.783168 1.35649i −0.930087 0.367338i $$-0.880269\pi$$
0.146920 0.989148i $$-0.453064\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.50000 4.33013i 0.0928477 0.160817i
$$726$$ 0 0
$$727$$ −40.0000 −1.48352 −0.741759 0.670667i $$-0.766008\pi$$
−0.741759 + 0.670667i $$0.766008\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −16.0000 + 27.7128i −0.591781 + 1.02500i
$$732$$ 0 0
$$733$$ 10.0000 + 17.3205i 0.369358 + 0.639748i 0.989465 0.144770i $$-0.0462441\pi$$
−0.620107 + 0.784517i $$0.712911\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 9.00000 + 15.5885i 0.331519 + 0.574208i
$$738$$ 0 0
$$739$$ 7.00000 12.1244i 0.257499 0.446002i −0.708072 0.706140i $$-0.750435\pi$$
0.965571 + 0.260138i $$0.0837682\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −34.0000 −1.24734 −0.623670 0.781688i $$-0.714359\pi$$
−0.623670 + 0.781688i $$0.714359\pi$$
$$744$$ 0 0
$$745$$ 5.00000 8.66025i 0.183186 0.317287i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 6.00000 + 31.1769i 0.219235 + 1.13918i
$$750$$ 0 0
$$751$$ 14.0000 + 24.2487i 0.510867 + 0.884848i 0.999921 + 0.0125942i $$0.00400897\pi$$
−0.489053 + 0.872254i $$0.662658\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 38.0000 1.38296
$$756$$ 0 0
$$757$$ 46.0000 1.67190 0.835949 0.548807i $$-0.184918\pi$$
0.835949 + 0.548807i $$0.184918\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 24.0000 + 41.5692i 0.869999 + 1.50688i 0.861996 + 0.506915i $$0.169214\pi$$
0.00800331 + 0.999968i $$0.497452\pi$$
$$762$$ 0 0
$$763$$ −32.0000 + 27.7128i −1.15848 + 1.00327i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −27.0000 + 46.7654i −0.974913 + 1.68860i
$$768$$ 0 0
$$769$$ 25.0000 0.901523 0.450762 0.892644i $$-0.351152\pi$$
0.450762 + 0.892644i $$0.351152\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −11.0000 + 19.0526i −0.395643 + 0.685273i −0.993183 0.116566i $$-0.962811\pi$$
0.597540 + 0.801839i $$0.296145\pi$$
$$774$$ 0 0
$$775$$ 3.50000 + 6.06218i 0.125724 + 0.217760i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 4.00000 + 6.92820i 0.143315 + 0.248229i
$$780$$ 0 0
$$781$$ −18.0000 + 31.1769i −0.644091 + 1.11560i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −36.0000 −1.28490
$$786$$ 0 0
$$787$$ 7.00000 12.1244i 0.249523 0.432187i −0.713871 0.700278i $$-0.753059\pi$$
0.963394 + 0.268091i $$0.0863928\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −30.0000 10.3923i −1.06668 0.369508i
$$792$$ 0 0
$$793$$ 24.0000 + 41.5692i 0.852265 + 1.47617i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 3.00000 0.106265 0.0531327 0.998587i $$-0.483079\pi$$
0.0531327 + 0.998587i $$0.483079\pi$$
$$798$$ 0 0
$$799$$ 8.00000 0.283020
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 16.5000 + 28.5788i 0.582272 + 1.00853i