# Properties

 Label 1296.2.i.c.865.1 Level $1296$ Weight $2$ Character 1296.865 Analytic conductor $10.349$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1296 = 2^{4} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1296.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.3486121020$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 54) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1296.865 Dual form 1296.2.i.c.433.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})$$ $$q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.50000 + 2.59808i) q^{11} +(2.00000 + 3.46410i) q^{13} -2.00000 q^{19} +(-3.00000 - 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-3.00000 + 5.19615i) q^{29} +(2.50000 + 4.33013i) q^{31} +3.00000 q^{35} +2.00000 q^{37} +(3.00000 + 5.19615i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(3.00000 - 5.19615i) q^{47} +(3.00000 + 5.19615i) q^{49} +9.00000 q^{53} +9.00000 q^{55} +(6.00000 + 10.3923i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(6.00000 - 10.3923i) q^{65} +(7.00000 + 12.1244i) q^{67} -7.00000 q^{73} +(-1.50000 - 2.59808i) q^{77} +(4.00000 - 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{83} -18.0000 q^{89} -4.00000 q^{91} +(3.00000 + 5.19615i) q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 3 q^{5} - q^{7}+O(q^{10})$$ 2 * q - 3 * q^5 - q^7 $$2 q - 3 q^{5} - q^{7} - 3 q^{11} + 4 q^{13} - 4 q^{19} - 6 q^{23} - 4 q^{25} - 6 q^{29} + 5 q^{31} + 6 q^{35} + 4 q^{37} + 6 q^{41} - 10 q^{43} + 6 q^{47} + 6 q^{49} + 18 q^{53} + 18 q^{55} + 12 q^{59} - 8 q^{61} + 12 q^{65} + 14 q^{67} - 14 q^{73} - 3 q^{77} + 8 q^{79} - 3 q^{83} - 36 q^{89} - 8 q^{91} + 6 q^{95} + q^{97}+O(q^{100})$$ 2 * q - 3 * q^5 - q^7 - 3 * q^11 + 4 * q^13 - 4 * q^19 - 6 * q^23 - 4 * q^25 - 6 * q^29 + 5 * q^31 + 6 * q^35 + 4 * q^37 + 6 * q^41 - 10 * q^43 + 6 * q^47 + 6 * q^49 + 18 * q^53 + 18 * q^55 + 12 * q^59 - 8 * q^61 + 12 * q^65 + 14 * q^67 - 14 * q^73 - 3 * q^77 + 8 * q^79 - 3 * q^83 - 36 * q^89 - 8 * q^91 + 6 * q^95 + q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1217$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$5$$ −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i $$-0.932609\pi$$
0.306851 0.951757i $$-0.400725\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 0.866025i −0.188982 + 0.327327i −0.944911 0.327327i $$-0.893852\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ 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
$$13$$ 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i $$0.0205004\pi$$
−0.443227 + 0.896410i $$0.646166\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 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
$$25$$ −2.00000 + 3.46410i −0.400000 + 0.692820i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i $$0.354747\pi$$
−0.997738 + 0.0672232i $$0.978586\pi$$
$$30$$ 0 0
$$31$$ 2.50000 + 4.33013i 0.449013 + 0.777714i 0.998322 0.0579057i $$-0.0184423\pi$$
−0.549309 + 0.835619i $$0.685109\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 3.00000 0.507093
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i $$-0.0114536\pi$$
−0.530831 + 0.847477i $$0.678120\pi$$
$$42$$ 0 0
$$43$$ −5.00000 + 8.66025i −0.762493 + 1.32068i 0.179069 + 0.983836i $$0.442691\pi$$
−0.941562 + 0.336840i $$0.890642\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 0 0
$$49$$ 3.00000 + 5.19615i 0.428571 + 0.742307i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ 0 0
$$55$$ 9.00000 1.21356
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i $$0.118692\pi$$
−0.150148 + 0.988663i $$0.547975\pi$$
$$60$$ 0 0
$$61$$ −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i $$0.337817\pi$$
−0.999901 + 0.0140840i $$0.995517\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 6.00000 10.3923i 0.744208 1.28901i
$$66$$ 0 0
$$67$$ 7.00000 + 12.1244i 0.855186 + 1.48123i 0.876472 + 0.481452i $$0.159891\pi$$
−0.0212861 + 0.999773i $$0.506776\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −7.00000 −0.819288 −0.409644 0.912245i $$-0.634347\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −1.50000 2.59808i −0.170941 0.296078i
$$78$$ 0 0
$$79$$ 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i $$-0.684745\pi$$
0.998388 + 0.0567635i $$0.0180781\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1.50000 + 2.59808i −0.164646 + 0.285176i −0.936530 0.350588i $$-0.885982\pi$$
0.771883 + 0.635764i $$0.219315\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −18.0000 −1.90800 −0.953998 0.299813i $$-0.903076\pi$$
−0.953998 + 0.299813i $$0.903076\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 3.00000 + 5.19615i 0.307794 + 0.533114i
$$96$$ 0 0
$$97$$ 0.500000 0.866025i 0.0507673 0.0879316i −0.839525 0.543321i $$-0.817167\pi$$
0.890292 + 0.455389i $$0.150500\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i $$-0.785646\pi$$
0.930953 + 0.365140i $$0.118979\pi$$
$$102$$ 0 0
$$103$$ −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i $$-0.229808\pi$$
−0.947576 + 0.319531i $$0.896475\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −9.00000 −0.870063 −0.435031 0.900415i $$-0.643263\pi$$
−0.435031 + 0.900415i $$0.643263\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i $$-0.0755971\pi$$
−0.689714 + 0.724082i $$0.742264\pi$$
$$114$$ 0 0
$$115$$ −9.00000 + 15.5885i −0.839254 + 1.45363i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 7.00000 0.621150 0.310575 0.950549i $$-0.399478\pi$$
0.310575 + 0.950549i $$0.399478\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i $$-0.939218\pi$$
0.326546 0.945181i $$-0.394115\pi$$
$$132$$ 0 0
$$133$$ 1.00000 1.73205i 0.0867110 0.150188i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i $$-0.915839\pi$$
0.708942 + 0.705266i $$0.249173\pi$$
$$138$$ 0 0
$$139$$ −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i $$-0.220926\pi$$
−0.938293 + 0.345843i $$0.887593\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −12.0000 −1.00349
$$144$$ 0 0
$$145$$ 18.0000 1.49482
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i $$-0.205881\pi$$
−0.920904 + 0.389789i $$0.872548\pi$$
$$150$$ 0 0
$$151$$ 8.50000 14.7224i 0.691720 1.19809i −0.279554 0.960130i $$-0.590186\pi$$
0.971274 0.237964i $$-0.0764802\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 7.50000 12.9904i 0.602414 1.04341i
$$156$$ 0 0
$$157$$ 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i $$-0.115641\pi$$
−0.775113 + 0.631822i $$0.782307\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 6.00000 0.472866
$$162$$ 0 0
$$163$$ −20.0000 −1.56652 −0.783260 0.621694i $$-0.786445\pi$$
−0.783260 + 0.621694i $$0.786445\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i $$-0.241242\pi$$
−0.958440 + 0.285295i $$0.907908\pi$$
$$168$$ 0 0
$$169$$ −1.50000 + 2.59808i −0.115385 + 0.199852i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i $$0.359807\pi$$
−0.996544 + 0.0830722i $$0.973527\pi$$
$$174$$ 0 0
$$175$$ −2.00000 3.46410i −0.151186 0.261861i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 9.00000 0.672692 0.336346 0.941739i $$-0.390809\pi$$
0.336346 + 0.941739i $$0.390809\pi$$
$$180$$ 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
$$185$$ −3.00000 5.19615i −0.220564 0.382029i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i $$-0.976283\pi$$
0.563081 + 0.826402i $$0.309616\pi$$
$$192$$ 0 0
$$193$$ −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i $$-0.224262\pi$$
−0.941865 + 0.335993i $$0.890928\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 9.00000 0.641223 0.320612 0.947211i $$-0.396112\pi$$
0.320612 + 0.947211i $$0.396112\pi$$
$$198$$ 0 0
$$199$$ 7.00000 0.496217 0.248108 0.968732i $$-0.420191\pi$$
0.248108 + 0.968732i $$0.420191\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −3.00000 5.19615i −0.210559 0.364698i
$$204$$ 0 0
$$205$$ 9.00000 15.5885i 0.628587 1.08875i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 3.00000 5.19615i 0.207514 0.359425i
$$210$$ 0 0
$$211$$ −11.0000 19.0526i −0.757271 1.31163i −0.944237 0.329266i $$-0.893199\pi$$
0.186966 0.982366i $$-0.440135\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 30.0000 2.04598
$$216$$ 0 0
$$217$$ −5.00000 −0.339422
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i $$-0.747017\pi$$
0.968309 + 0.249756i $$0.0803503\pi$$
$$224$$ 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
$$229$$ −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i $$-0.319740\pi$$
−0.999088 + 0.0426906i $$0.986407\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ 0 0
$$235$$ −18.0000 −1.17419
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 15.0000 + 25.9808i 0.970269 + 1.68056i 0.694737 + 0.719264i $$0.255521\pi$$
0.275533 + 0.961292i $$0.411146\pi$$
$$240$$ 0 0
$$241$$ 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i $$-0.728952\pi$$
0.980917 + 0.194429i $$0.0622852\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 9.00000 15.5885i 0.574989 0.995910i
$$246$$ 0 0
$$247$$ −4.00000 6.92820i −0.254514 0.440831i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 18.0000 1.13165
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i $$-0.288773\pi$$
−0.990217 + 0.139533i $$0.955440\pi$$
$$258$$ 0 0
$$259$$ −1.00000 + 1.73205i −0.0621370 + 0.107624i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −15.0000 + 25.9808i −0.924940 + 1.60204i −0.133281 + 0.991078i $$0.542551\pi$$
−0.791658 + 0.610964i $$0.790782\pi$$
$$264$$ 0 0
$$265$$ −13.5000 23.3827i −0.829298 1.43639i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ 25.0000 1.51864 0.759321 0.650716i $$-0.225531\pi$$
0.759321 + 0.650716i $$0.225531\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −6.00000 10.3923i −0.361814 0.626680i
$$276$$ 0 0
$$277$$ −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i $$-0.910591\pi$$
0.720473 + 0.693482i $$0.243925\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −12.0000 + 20.7846i −0.715860 + 1.23991i 0.246767 + 0.969075i $$0.420632\pi$$
−0.962627 + 0.270831i $$0.912702\pi$$
$$282$$ 0 0
$$283$$ 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i $$-0.0300609\pi$$
−0.579437 + 0.815017i $$0.696728\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −6.00000 −0.354169
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i $$-0.110589\pi$$
−0.764990 + 0.644042i $$0.777256\pi$$
$$294$$ 0 0
$$295$$ 18.0000 31.1769i 1.04800 1.81519i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 12.0000 20.7846i 0.693978 1.20201i
$$300$$ 0 0
$$301$$ −5.00000 8.66025i −0.288195 0.499169i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 24.0000 1.37424
$$306$$ 0 0
$$307$$ 16.0000 0.913168 0.456584 0.889680i $$-0.349073\pi$$
0.456584 + 0.889680i $$0.349073\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i $$-0.221080\pi$$
−0.938460 + 0.345389i $$0.887747\pi$$
$$312$$ 0 0
$$313$$ 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i $$-0.652902\pi$$
0.999065 0.0432311i $$-0.0137652\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i $$-0.806484\pi$$
0.905071 + 0.425261i $$0.139818\pi$$
$$318$$ 0 0
$$319$$ −9.00000 15.5885i −0.503903 0.872786i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −16.0000 −0.887520
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 3.00000 + 5.19615i 0.165395 + 0.286473i
$$330$$ 0 0
$$331$$ −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i $$-0.921953\pi$$
0.695266 + 0.718752i $$0.255287\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 21.0000 36.3731i 1.14735 1.98727i
$$336$$ 0 0
$$337$$ 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i $$0.0378512\pi$$
−0.393730 + 0.919226i $$0.628816\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −15.0000 −0.812296
$$342$$ 0 0
$$343$$ −13.0000 −0.701934
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i $$-0.141007\pi$$
−0.822951 + 0.568112i $$0.807674\pi$$
$$348$$ 0 0
$$349$$ 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i $$-0.747088\pi$$
0.968253 + 0.249973i $$0.0804216\pi$$
$$350$$ 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
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −18.0000 −0.950004 −0.475002 0.879985i $$-0.657553\pi$$
−0.475002 + 0.879985i $$0.657553\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 10.5000 + 18.1865i 0.549595 + 0.951927i
$$366$$ 0 0
$$367$$ 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i $$-0.687000\pi$$
0.997960 + 0.0638362i $$0.0203335\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −4.50000 + 7.79423i −0.233628 + 0.404656i
$$372$$ 0 0
$$373$$ −16.0000 27.7128i −0.828449 1.43492i −0.899255 0.437425i $$-0.855891\pi$$
0.0708063 0.997490i $$-0.477443\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i $$-0.956560\pi$$
0.377531 0.925997i $$-0.376773\pi$$
$$384$$ 0 0
$$385$$ −4.50000 + 7.79423i −0.229341 + 0.397231i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 10.5000 18.1865i 0.532371 0.922094i −0.466915 0.884302i $$-0.654634\pi$$
0.999286 0.0377914i $$-0.0120322\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −24.0000 −1.20757
$$396$$ 0 0
$$397$$ 20.0000 1.00377 0.501886 0.864934i $$-0.332640\pi$$
0.501886 + 0.864934i $$0.332640\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i $$-0.263528\pi$$
−0.976050 + 0.217545i $$0.930195\pi$$
$$402$$ 0 0
$$403$$ −10.0000 + 17.3205i −0.498135 + 0.862796i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −3.00000 + 5.19615i −0.148704 + 0.257564i
$$408$$ 0 0
$$409$$ −11.5000 19.9186i −0.568638 0.984911i −0.996701 0.0811615i $$-0.974137\pi$$
0.428063 0.903749i $$-0.359196\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −12.0000 −0.590481
$$414$$ 0 0
$$415$$ 9.00000 0.441793
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i $$-0.0719734\pi$$
−0.681426 + 0.731887i $$0.738640\pi$$
$$420$$ 0 0
$$421$$ −4.00000 + 6.92820i −0.194948 + 0.337660i −0.946883 0.321577i $$-0.895787\pi$$
0.751935 + 0.659237i $$0.229121\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −4.00000 6.92820i −0.193574 0.335279i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −18.0000 −0.867029 −0.433515 0.901146i $$-0.642727\pi$$
−0.433515 + 0.901146i $$0.642727\pi$$
$$432$$ 0 0
$$433$$ 29.0000 1.39365 0.696826 0.717241i $$-0.254595\pi$$
0.696826 + 0.717241i $$0.254595\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 6.00000 + 10.3923i 0.287019 + 0.497131i
$$438$$ 0 0
$$439$$ −9.50000 + 16.4545i −0.453410 + 0.785330i −0.998595 0.0529862i $$-0.983126\pi$$
0.545185 + 0.838316i $$0.316459\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i $$-0.925350\pi$$
0.687557 + 0.726130i $$0.258683\pi$$
$$444$$ 0 0
$$445$$ 27.0000 + 46.7654i 1.27992 + 2.21689i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ −18.0000 −0.847587
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 6.00000 + 10.3923i 0.281284 + 0.487199i
$$456$$ 0 0
$$457$$ 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i $$-0.825888\pi$$
0.877483 + 0.479608i $$0.159221\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 10.5000 18.1865i 0.489034 0.847031i −0.510887 0.859648i $$-0.670683\pi$$
0.999920 + 0.0126168i $$0.00401615\pi$$
$$462$$ 0 0
$$463$$ −6.50000 11.2583i −0.302081 0.523219i 0.674526 0.738251i $$-0.264348\pi$$
−0.976607 + 0.215032i $$0.931015\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 27.0000 1.24941 0.624705 0.780860i $$-0.285219\pi$$
0.624705 + 0.780860i $$0.285219\pi$$
$$468$$ 0 0
$$469$$ −14.0000 −0.646460
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −15.0000 25.9808i −0.689701 1.19460i
$$474$$ 0 0
$$475$$ 4.00000 6.92820i 0.183533 0.317888i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 3.00000 5.19615i 0.137073 0.237418i −0.789314 0.613990i $$-0.789564\pi$$
0.926388 + 0.376571i $$0.122897\pi$$
$$480$$ 0 0
$$481$$ 4.00000 + 6.92820i 0.182384 + 0.315899i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −3.00000 −0.136223
$$486$$ 0 0
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 19.5000 + 33.7750i 0.880023 + 1.52424i 0.851314 + 0.524656i $$0.175806\pi$$
0.0287085 + 0.999588i $$0.490861\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 7.00000 + 12.1244i 0.313363 + 0.542761i 0.979088 0.203436i $$-0.0652110\pi$$
−0.665725 + 0.746197i $$0.731878\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 18.0000 0.802580 0.401290 0.915951i $$-0.368562\pi$$
0.401290 + 0.915951i $$0.368562\pi$$
$$504$$ 0 0
$$505$$ −9.00000 −0.400495
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i $$-0.0587976\pi$$
−0.650556 + 0.759458i $$0.725464\pi$$
$$510$$ 0 0
$$511$$ 3.50000 6.06218i 0.154831 0.268175i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −6.00000 + 10.3923i −0.264392 + 0.457940i
$$516$$ 0 0
$$517$$ 9.00000 + 15.5885i 0.395820 + 0.685580i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 36.0000 1.57719 0.788594 0.614914i $$-0.210809\pi$$
0.788594 + 0.614914i $$0.210809\pi$$
$$522$$ 0 0
$$523$$ 16.0000 0.699631 0.349816 0.936819i $$-0.386244\pi$$
0.349816 + 0.936819i $$0.386244\pi$$
$$524$$ 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
$$535$$ 13.5000 + 23.3827i 0.583656 + 1.01092i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −18.0000 −0.775315
$$540$$ 0 0
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −3.00000 5.19615i −0.128506 0.222579i
$$546$$ 0 0
$$547$$ 4.00000 6.92820i 0.171028 0.296229i −0.767752 0.640747i $$-0.778625\pi$$
0.938779 + 0.344519i $$0.111958\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 6.00000 10.3923i 0.255609 0.442727i
$$552$$ 0 0
$$553$$ 4.00000 + 6.92820i 0.170097 + 0.294617i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 27.0000 1.14403 0.572013 0.820244i $$-0.306163\pi$$
0.572013 + 0.820244i $$0.306163\pi$$
$$558$$ 0 0
$$559$$ −40.0000 −1.69182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.50000 + 2.59808i 0.0632175 + 0.109496i 0.895902 0.444252i $$-0.146530\pi$$
−0.832684 + 0.553748i $$0.813197\pi$$
$$564$$ 0 0
$$565$$ 9.00000 15.5885i 0.378633 0.655811i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 6.00000 10.3923i 0.251533 0.435668i −0.712415 0.701758i $$-0.752399\pi$$
0.963948 + 0.266090i $$0.0857319\pi$$
$$570$$ 0 0
$$571$$ −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i $$-0.193340\pi$$
−0.904835 + 0.425762i $$0.860006\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 24.0000 1.00087
$$576$$ 0 0
$$577$$ 38.0000 1.58196 0.790980 0.611842i $$-0.209571\pi$$
0.790980 + 0.611842i $$0.209571\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1.50000 2.59808i −0.0622305 0.107786i
$$582$$ 0 0
$$583$$ −13.5000 + 23.3827i −0.559113 + 0.968412i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i $$-0.853053\pi$$
0.833408 + 0.552658i $$0.186386\pi$$
$$588$$ 0 0
$$589$$ −5.00000 8.66025i −0.206021 0.356840i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −21.0000 36.3731i −0.858037 1.48616i −0.873799 0.486287i $$-0.838351\pi$$
0.0157622 0.999876i $$-0.494983\pi$$
$$600$$ 0 0
$$601$$ −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i $$0.419712\pi$$
−0.963405 + 0.268049i $$0.913621\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 3.00000 5.19615i 0.121967 0.211254i
$$606$$ 0 0
$$607$$ 16.0000 + 27.7128i 0.649420 + 1.12483i 0.983262 + 0.182199i $$0.0583216\pi$$
−0.333842 + 0.942629i $$0.608345\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 24.0000 0.970936
$$612$$ 0 0
$$613$$ −34.0000 −1.37325 −0.686624 0.727013i $$-0.740908\pi$$
−0.686624 + 0.727013i $$0.740908\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i $$0.153988\pi$$
−0.0398207 + 0.999207i $$0.512679\pi$$
$$618$$ 0 0
$$619$$ −14.0000 + 24.2487i −0.562708 + 0.974638i 0.434551 + 0.900647i $$0.356907\pi$$
−0.997259 + 0.0739910i $$0.976426\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 9.00000 15.5885i 0.360577 0.624538i
$$624$$ 0 0
$$625$$ 14.5000 + 25.1147i 0.580000 + 1.00459i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 25.0000 0.995234 0.497617 0.867397i $$-0.334208\pi$$
0.497617 + 0.867397i $$0.334208\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −10.5000 18.1865i −0.416680 0.721711i
$$636$$ 0 0
$$637$$ −12.0000 + 20.7846i −0.475457 + 0.823516i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −21.0000 + 36.3731i −0.829450 + 1.43665i 0.0690201 + 0.997615i $$0.478013\pi$$
−0.898470 + 0.439034i $$0.855321\pi$$
$$642$$ 0 0
$$643$$ −2.00000 3.46410i −0.0788723 0.136611i 0.823891 0.566748i $$-0.191799\pi$$
−0.902764 + 0.430137i $$0.858465\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ −36.0000 −1.41312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −19.5000 33.7750i −0.763094 1.32172i −0.941248 0.337715i $$-0.890346\pi$$
0.178154 0.984003i $$-0.442987\pi$$
$$654$$ 0 0
$$655$$ −22.5000 + 38.9711i −0.879148 + 1.52273i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −10.5000 + 18.1865i −0.409022 + 0.708447i −0.994780 0.102039i $$-0.967463\pi$$
0.585758 + 0.810486i $$0.300797\pi$$
$$660$$ 0 0
$$661$$ −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i $$-0.254441\pi$$
−0.969442 + 0.245319i $$0.921107\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −6.00000 −0.232670
$$666$$ 0 0
$$667$$ 36.0000 1.39393
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −12.0000 20.7846i −0.463255 0.802381i
$$672$$ 0 0
$$673$$ 9.50000 16.4545i 0.366198 0.634274i −0.622770 0.782405i $$-0.713993\pi$$
0.988968 + 0.148132i $$0.0473259\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −21.0000 + 36.3731i −0.807096 + 1.39793i 0.107772 + 0.994176i $$0.465628\pi$$
−0.914867 + 0.403755i $$0.867705\pi$$
$$678$$ 0 0
$$679$$ 0.500000 + 0.866025i 0.0191882 + 0.0332350i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ 18.0000 0.687745
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 18.0000 + 31.1769i 0.685745 + 1.18775i
$$690$$ 0 0
$$691$$ 22.0000 38.1051i 0.836919 1.44959i −0.0555386 0.998457i $$-0.517688\pi$$
0.892458 0.451130i $$-0.148979\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −6.00000 + 10.3923i −0.227593 + 0.394203i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 9.00000 0.339925 0.169963 0.985451i $$-0.445635\pi$$
0.169963 + 0.985451i $$0.445635\pi$$
$$702$$ 0 0
$$703$$ −4.00000 −0.150863
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.50000 + 2.59808i 0.0564133 + 0.0977107i
$$708$$ 0 0
$$709$$ −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i $$0.476184\pi$$
−0.900978 + 0.433865i $$0.857149\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 15.0000 25.9808i 0.561754 0.972987i
$$714$$ 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
$$721$$ 4.00000 0.148968
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −12.0000 20.7846i −0.445669 0.771921i
$$726$$ 0 0
$$727$$ −0.500000 + 0.866025i −0.0185440 + 0.0321191i −0.875148 0.483854i $$-0.839236\pi$$
0.856605 + 0.515974i $$0.172570\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i $$-0.0334875\pi$$
−0.588177 + 0.808732i $$0.700154\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −42.0000 −1.54709
$$738$$ 0 0
$$739$$ 16.0000 0.588570 0.294285 0.955718i $$-0.404919\pi$$
0.294285 + 0.955718i $$0.404919\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 6.00000 + 10.3923i 0.220119 + 0.381257i 0.954844 0.297108i $$-0.0960222\pi$$
−0.734725 + 0.678365i $$0.762689\pi$$
$$744$$ 0 0
$$745$$ −4.50000 + 7.79423i −0.164867 + 0.285558i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 4.50000 7.79423i 0.164426 0.284795i
$$750$$ 0 0
$$751$$ 20.5000 + 35.5070i 0.748056 + 1.29567i 0.948753 + 0.316017i $$0.102346\pi$$
−0.200698 + 0.979653i $$0.564321\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −51.0000 −1.85608
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −24.0000 41.5692i −0.869999 1.50688i −0.861996 0.506915i $$-0.830786\pi$$
−0.00800331 0.999968i $$-0.502548\pi$$
$$762$$ 0 0
$$763$$ −1.00000 + 1.73205i −0.0362024 + 0.0627044i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −24.0000 + 41.5692i −0.866590 + 1.50098i
$$768$$ 0 0
$$769$$ 15.5000 + 26.8468i 0.558944 + 0.968120i 0.997585 + 0.0694574i $$0.0221268\pi$$
−0.438641 + 0.898663i $$0.644540\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ 0 0
$$775$$ −20.0000 −0.718421
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −6.00000 10.3923i −0.214972 0.372343i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 6.00000 10.3923i 0.214149 0.370917i
$$786$$ 0 0
$$787$$ 16.0000 + 27.7128i 0.570338 + 0.987855i 0.996531 + 0.0832226i $$0.0265213\pi$$
−0.426193 + 0.904632i $$0.640145\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −6.00000 −0.213335
$$792$$ 0 0
$$793$$ −32.0000 −1.13635
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −19.5000 33.7750i −0.690725 1.19637i −0.971601 0.236627i $$-0.923958\pi$$
0.280875 0.959744i $$-0.409375\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0