# Properties

 Label 684.3.y.e.145.1 Level $684$ Weight $3$ Character 684.145 Analytic conductor $18.638$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$684 = 2^{2} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 684.y (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.6376500822$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 228) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 145.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 684.145 Dual form 684.3.y.e.217.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(3.00000 + 5.19615i) q^{5} -5.00000 q^{7} +O(q^{10})$$ $$q+(3.00000 + 5.19615i) q^{5} -5.00000 q^{7} +(-16.5000 - 9.52628i) q^{13} +(3.00000 + 5.19615i) q^{17} +(-13.0000 + 13.8564i) q^{19} +(-12.0000 + 20.7846i) q^{23} +(-5.50000 + 9.52628i) q^{25} +(-27.0000 - 15.5885i) q^{29} -29.4449i q^{31} +(-15.0000 - 25.9808i) q^{35} -60.6218i q^{37} +(36.0000 - 20.7846i) q^{41} +(12.5000 + 21.6506i) q^{43} +(-21.0000 + 36.3731i) q^{47} -24.0000 q^{49} +(-54.0000 - 31.1769i) q^{53} +(-63.0000 + 36.3731i) q^{59} +(-21.5000 + 37.2391i) q^{61} -114.315i q^{65} +(49.5000 + 28.5788i) q^{67} +(-54.0000 + 31.1769i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(1.50000 - 0.866025i) q^{79} -126.000 q^{83} +(-18.0000 + 31.1769i) q^{85} +(9.00000 + 5.19615i) q^{89} +(82.5000 + 47.6314i) q^{91} +(-111.000 - 25.9808i) q^{95} +(-114.000 + 65.8179i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 6 q^{5} - 10 q^{7}+O(q^{10})$$ 2 * q + 6 * q^5 - 10 * q^7 $$2 q + 6 q^{5} - 10 q^{7} - 33 q^{13} + 6 q^{17} - 26 q^{19} - 24 q^{23} - 11 q^{25} - 54 q^{29} - 30 q^{35} + 72 q^{41} + 25 q^{43} - 42 q^{47} - 48 q^{49} - 108 q^{53} - 126 q^{59} - 43 q^{61} + 99 q^{67} - 108 q^{71} - 11 q^{73} + 3 q^{79} - 252 q^{83} - 36 q^{85} + 18 q^{89} + 165 q^{91} - 222 q^{95} - 228 q^{97}+O(q^{100})$$ 2 * q + 6 * q^5 - 10 * q^7 - 33 * q^13 + 6 * q^17 - 26 * q^19 - 24 * q^23 - 11 * q^25 - 54 * q^29 - 30 * q^35 + 72 * q^41 + 25 * q^43 - 42 * q^47 - 48 * q^49 - 108 * q^53 - 126 * q^59 - 43 * q^61 + 99 * q^67 - 108 * q^71 - 11 * q^73 + 3 * q^79 - 252 * q^83 - 36 * q^85 + 18 * q^89 + 165 * q^91 - 222 * q^95 - 228 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$343$$ $$533$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 3.00000 + 5.19615i 0.600000 + 1.03923i 0.992820 + 0.119615i $$0.0381661\pi$$
−0.392820 + 0.919615i $$0.628501\pi$$
$$6$$ 0 0
$$7$$ −5.00000 −0.714286 −0.357143 0.934050i $$-0.616249\pi$$
−0.357143 + 0.934050i $$0.616249\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ −16.5000 9.52628i −1.26923 0.732791i −0.294388 0.955686i $$-0.595116\pi$$
−0.974842 + 0.222895i $$0.928449\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.00000 + 5.19615i 0.176471 + 0.305656i 0.940669 0.339325i $$-0.110199\pi$$
−0.764199 + 0.644981i $$0.776865\pi$$
$$18$$ 0 0
$$19$$ −13.0000 + 13.8564i −0.684211 + 0.729285i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −12.0000 + 20.7846i −0.521739 + 0.903679i 0.477941 + 0.878392i $$0.341383\pi$$
−0.999680 + 0.0252868i $$0.991950\pi$$
$$24$$ 0 0
$$25$$ −5.50000 + 9.52628i −0.220000 + 0.381051i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −27.0000 15.5885i −0.931034 0.537533i −0.0438959 0.999036i $$-0.513977\pi$$
−0.887139 + 0.461503i $$0.847310\pi$$
$$30$$ 0 0
$$31$$ 29.4449i 0.949834i −0.880031 0.474917i $$-0.842478\pi$$
0.880031 0.474917i $$-0.157522\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −15.0000 25.9808i −0.428571 0.742307i
$$36$$ 0 0
$$37$$ 60.6218i 1.63843i −0.573489 0.819213i $$-0.694410\pi$$
0.573489 0.819213i $$-0.305590\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 36.0000 20.7846i 0.878049 0.506942i 0.00803422 0.999968i $$-0.497443\pi$$
0.870015 + 0.493026i $$0.164109\pi$$
$$42$$ 0 0
$$43$$ 12.5000 + 21.6506i 0.290698 + 0.503503i 0.973975 0.226656i $$-0.0727793\pi$$
−0.683277 + 0.730159i $$0.739446\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −21.0000 + 36.3731i −0.446809 + 0.773895i −0.998176 0.0603673i $$-0.980773\pi$$
0.551368 + 0.834262i $$0.314106\pi$$
$$48$$ 0 0
$$49$$ −24.0000 −0.489796
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −54.0000 31.1769i −1.01887 0.588244i −0.105092 0.994462i $$-0.533514\pi$$
−0.913776 + 0.406219i $$0.866847\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −63.0000 + 36.3731i −1.06780 + 0.616493i −0.927579 0.373628i $$-0.878114\pi$$
−0.140218 + 0.990121i $$0.544780\pi$$
$$60$$ 0 0
$$61$$ −21.5000 + 37.2391i −0.352459 + 0.610477i −0.986680 0.162675i $$-0.947988\pi$$
0.634221 + 0.773152i $$0.281321\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 114.315i 1.75870i
$$66$$ 0 0
$$67$$ 49.5000 + 28.5788i 0.738806 + 0.426550i 0.821635 0.570014i $$-0.193062\pi$$
−0.0828290 + 0.996564i $$0.526396\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −54.0000 + 31.1769i −0.760563 + 0.439111i −0.829498 0.558510i $$-0.811373\pi$$
0.0689346 + 0.997621i $$0.478040\pi$$
$$72$$ 0 0
$$73$$ −5.50000 9.52628i −0.0753425 0.130497i 0.825893 0.563827i $$-0.190672\pi$$
−0.901235 + 0.433330i $$0.857338\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1.50000 0.866025i 0.0189873 0.0109623i −0.490476 0.871455i $$-0.663177\pi$$
0.509464 + 0.860492i $$0.329844\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −126.000 −1.51807 −0.759036 0.651048i $$-0.774329\pi$$
−0.759036 + 0.651048i $$0.774329\pi$$
$$84$$ 0 0
$$85$$ −18.0000 + 31.1769i −0.211765 + 0.366787i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 9.00000 + 5.19615i 0.101124 + 0.0583837i 0.549709 0.835356i $$-0.314739\pi$$
−0.448585 + 0.893740i $$0.648072\pi$$
$$90$$ 0 0
$$91$$ 82.5000 + 47.6314i 0.906593 + 0.523422i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −111.000 25.9808i −1.16842 0.273482i
$$96$$ 0 0
$$97$$ −114.000 + 65.8179i −1.17526 + 0.678535i −0.954913 0.296887i $$-0.904052\pi$$
−0.220345 + 0.975422i $$0.570718\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 78.0000 135.100i 0.772277 1.33762i −0.164035 0.986455i $$-0.552451\pi$$
0.936312 0.351169i $$-0.114216\pi$$
$$102$$ 0 0
$$103$$ 36.3731i 0.353137i 0.984288 + 0.176568i $$0.0564996\pi$$
−0.984288 + 0.176568i $$0.943500\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 90.0000 51.9615i 0.825688 0.476711i −0.0266859 0.999644i $$-0.508495\pi$$
0.852374 + 0.522933i $$0.175162\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 155.885i 1.37951i 0.724043 + 0.689755i $$0.242282\pi$$
−0.724043 + 0.689755i $$0.757718\pi$$
$$114$$ 0 0
$$115$$ −144.000 −1.25217
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −15.0000 25.9808i −0.126050 0.218326i
$$120$$ 0 0
$$121$$ −121.000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 84.0000 0.672000
$$126$$ 0 0
$$127$$ −36.0000 20.7846i −0.283465 0.163658i 0.351526 0.936178i $$-0.385663\pi$$
−0.634991 + 0.772520i $$0.718996\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 24.0000 + 41.5692i 0.183206 + 0.317322i 0.942971 0.332876i $$-0.108019\pi$$
−0.759764 + 0.650198i $$0.774686\pi$$
$$132$$ 0 0
$$133$$ 65.0000 69.2820i 0.488722 0.520918i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −66.0000 + 114.315i −0.481752 + 0.834419i −0.999781 0.0209445i $$-0.993333\pi$$
0.518029 + 0.855363i $$0.326666\pi$$
$$138$$ 0 0
$$139$$ −0.500000 + 0.866025i −0.00359712 + 0.00623040i −0.867818 0.496882i $$-0.834478\pi$$
0.864221 + 0.503112i $$0.167812\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 187.061i 1.29008i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 90.0000 + 155.885i 0.604027 + 1.04621i 0.992204 + 0.124621i $$0.0397714\pi$$
−0.388178 + 0.921585i $$0.626895\pi$$
$$150$$ 0 0
$$151$$ 235.559i 1.55999i −0.625784 0.779996i $$-0.715221\pi$$
0.625784 0.779996i $$-0.284779\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 153.000 88.3346i 0.987097 0.569901i
$$156$$ 0 0
$$157$$ 38.5000 + 66.6840i 0.245223 + 0.424739i 0.962194 0.272364i $$-0.0878055\pi$$
−0.716971 + 0.697103i $$0.754472\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 60.0000 103.923i 0.372671 0.645485i
$$162$$ 0 0
$$163$$ 145.000 0.889571 0.444785 0.895637i $$-0.353280\pi$$
0.444785 + 0.895637i $$0.353280\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 261.000 + 150.688i 1.56287 + 0.902326i 0.996964 + 0.0778587i $$0.0248083\pi$$
0.565910 + 0.824467i $$0.308525\pi$$
$$168$$ 0 0
$$169$$ 97.0000 + 168.009i 0.573964 + 0.994136i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 9.00000 5.19615i 0.0520231 0.0300356i −0.473763 0.880652i $$-0.657105\pi$$
0.525786 + 0.850617i $$0.323771\pi$$
$$174$$ 0 0
$$175$$ 27.5000 47.6314i 0.157143 0.272179i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ −66.0000 38.1051i −0.364641 0.210526i 0.306474 0.951879i $$-0.400851\pi$$
−0.671115 + 0.741354i $$0.734184\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 315.000 181.865i 1.70270 0.983056i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 18.0000 0.0942408 0.0471204 0.998889i $$-0.484996\pi$$
0.0471204 + 0.998889i $$0.484996\pi$$
$$192$$ 0 0
$$193$$ 49.5000 28.5788i 0.256477 0.148077i −0.366250 0.930517i $$-0.619358\pi$$
0.622726 + 0.782440i $$0.286025\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 90.0000 0.456853 0.228426 0.973561i $$-0.426642\pi$$
0.228426 + 0.973561i $$0.426642\pi$$
$$198$$ 0 0
$$199$$ 111.500 193.124i 0.560302 0.970471i −0.437168 0.899380i $$-0.644019\pi$$
0.997470 0.0710910i $$-0.0226481\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 135.000 + 77.9423i 0.665025 + 0.383952i
$$204$$ 0 0
$$205$$ 216.000 + 124.708i 1.05366 + 0.608330i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −292.500 + 168.875i −1.38626 + 0.800355i −0.992891 0.119027i $$-0.962022\pi$$
−0.393365 + 0.919382i $$0.628689\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −75.0000 + 129.904i −0.348837 + 0.604204i
$$216$$ 0 0
$$217$$ 147.224i 0.678453i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 114.315i 0.517264i
$$222$$ 0 0
$$223$$ −370.500 + 213.908i −1.66143 + 0.959230i −0.689404 + 0.724377i $$0.742128\pi$$
−0.972031 + 0.234853i $$0.924539\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 176.669i 0.778278i 0.921179 + 0.389139i $$0.127227\pi$$
−0.921179 + 0.389139i $$0.872773\pi$$
$$228$$ 0 0
$$229$$ 391.000 1.70742 0.853712 0.520746i $$-0.174346\pi$$
0.853712 + 0.520746i $$0.174346\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 72.0000 + 124.708i 0.309013 + 0.535226i 0.978147 0.207916i $$-0.0666680\pi$$
−0.669134 + 0.743142i $$0.733335\pi$$
$$234$$ 0 0
$$235$$ −252.000 −1.07234
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −450.000 −1.88285 −0.941423 0.337229i $$-0.890510\pi$$
−0.941423 + 0.337229i $$0.890510\pi$$
$$240$$ 0 0
$$241$$ 67.5000 + 38.9711i 0.280083 + 0.161706i 0.633461 0.773775i $$-0.281634\pi$$
−0.353378 + 0.935481i $$0.614967\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −72.0000 124.708i −0.293878 0.509011i
$$246$$ 0 0
$$247$$ 346.500 104.789i 1.40283 0.424247i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −21.0000 + 36.3731i −0.0836653 + 0.144913i −0.904822 0.425791i $$-0.859996\pi$$
0.821156 + 0.570703i $$0.193329\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −414.000 239.023i −1.61089 0.930051i −0.989163 0.146820i $$-0.953096\pi$$
−0.621732 0.783230i $$-0.713571\pi$$
$$258$$ 0 0
$$259$$ 303.109i 1.17030i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 78.0000 + 135.100i 0.296578 + 0.513688i 0.975351 0.220660i $$-0.0708212\pi$$
−0.678773 + 0.734348i $$0.737488\pi$$
$$264$$ 0 0
$$265$$ 374.123i 1.41178i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 459.000 265.004i 1.70632 0.985144i 0.767295 0.641294i $$-0.221602\pi$$
0.939025 0.343850i $$-0.111731\pi$$
$$270$$ 0 0
$$271$$ 257.000 + 445.137i 0.948339 + 1.64257i 0.748923 + 0.662657i $$0.230571\pi$$
0.199417 + 0.979915i $$0.436095\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 238.000 0.859206 0.429603 0.903018i $$-0.358654\pi$$
0.429603 + 0.903018i $$0.358654\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 225.000 + 129.904i 0.800712 + 0.462291i 0.843720 0.536784i $$-0.180361\pi$$
−0.0430082 + 0.999075i $$0.513694\pi$$
$$282$$ 0 0
$$283$$ 113.000 + 195.722i 0.399293 + 0.691596i 0.993639 0.112613i $$-0.0359222\pi$$
−0.594346 + 0.804210i $$0.702589\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −180.000 + 103.923i −0.627178 + 0.362101i
$$288$$ 0 0
$$289$$ 126.500 219.104i 0.437716 0.758147i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 31.1769i 0.106406i 0.998584 + 0.0532029i $$0.0169430\pi$$
−0.998584 + 0.0532029i $$0.983057\pi$$
$$294$$ 0 0
$$295$$ −378.000 218.238i −1.28136 0.739791i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 396.000 228.631i 1.32441 0.764651i
$$300$$ 0 0
$$301$$ −62.5000 108.253i −0.207641 0.359645i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −258.000 −0.845902
$$306$$ 0 0
$$307$$ 54.0000 31.1769i 0.175896 0.101553i −0.409467 0.912325i $$-0.634285\pi$$
0.585363 + 0.810771i $$0.300952\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 534.000 1.71704 0.858521 0.512779i $$-0.171384\pi$$
0.858521 + 0.512779i $$0.171384\pi$$
$$312$$ 0 0
$$313$$ −269.000 + 465.922i −0.859425 + 1.48857i 0.0130534 + 0.999915i $$0.495845\pi$$
−0.872478 + 0.488653i $$0.837488\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −81.0000 46.7654i −0.255521 0.147525i 0.366769 0.930312i $$-0.380464\pi$$
−0.622289 + 0.782787i $$0.713797\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −111.000 25.9808i −0.343653 0.0804358i
$$324$$ 0 0
$$325$$ 181.500 104.789i 0.558462 0.322428i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 105.000 181.865i 0.319149 0.552782i
$$330$$ 0 0
$$331$$ 278.860i 0.842478i 0.906950 + 0.421239i $$0.138405\pi$$
−0.906950 + 0.421239i $$0.861595\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 342.946i 1.02372i
$$336$$ 0 0
$$337$$ 418.500 241.621i 1.24184 0.716977i 0.272371 0.962192i $$-0.412192\pi$$
0.969469 + 0.245216i $$0.0788588\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 365.000 1.06414
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −267.000 462.458i −0.769452 1.33273i −0.937860 0.347013i $$-0.887196\pi$$
0.168408 0.985717i $$-0.446137\pi$$
$$348$$ 0 0
$$349$$ −187.000 −0.535817 −0.267908 0.963444i $$-0.586332\pi$$
−0.267908 + 0.963444i $$0.586332\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −438.000 −1.24079 −0.620397 0.784288i $$-0.713028\pi$$
−0.620397 + 0.784288i $$0.713028\pi$$
$$354$$ 0 0
$$355$$ −324.000 187.061i −0.912676 0.526934i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −168.000 290.985i −0.467967 0.810542i 0.531363 0.847144i $$-0.321680\pi$$
−0.999330 + 0.0366021i $$0.988347\pi$$
$$360$$ 0 0
$$361$$ −23.0000 360.267i −0.0637119 0.997968i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 33.0000 57.1577i 0.0904110 0.156596i
$$366$$ 0 0
$$367$$ −50.5000 + 87.4686i −0.137602 + 0.238334i −0.926588 0.376077i $$-0.877273\pi$$
0.788986 + 0.614411i $$0.210606\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 270.000 + 155.885i 0.727763 + 0.420174i
$$372$$ 0 0
$$373$$ 547.328i 1.46737i −0.679491 0.733684i $$-0.737799\pi$$
0.679491 0.733684i $$-0.262201\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 297.000 + 514.419i 0.787798 + 1.36451i
$$378$$ 0 0
$$379$$ 46.7654i 0.123391i −0.998095 0.0616957i $$-0.980349\pi$$
0.998095 0.0616957i $$-0.0196508\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −342.000 + 197.454i −0.892950 + 0.515545i −0.874906 0.484292i $$-0.839077\pi$$
−0.0180440 + 0.999837i $$0.505744\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −228.000 + 394.908i −0.586118 + 1.01519i 0.408617 + 0.912706i $$0.366011\pi$$
−0.994735 + 0.102481i $$0.967322\pi$$
$$390$$ 0 0
$$391$$ −144.000 −0.368286
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 9.00000 + 5.19615i 0.0227848 + 0.0131548i
$$396$$ 0 0
$$397$$ −116.500 201.784i −0.293451 0.508272i 0.681172 0.732123i $$-0.261470\pi$$
−0.974623 + 0.223851i $$0.928137\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −63.0000 + 36.3731i −0.157107 + 0.0907059i −0.576492 0.817102i $$-0.695579\pi$$
0.419385 + 0.907808i $$0.362246\pi$$
$$402$$ 0 0
$$403$$ −280.500 + 485.840i −0.696030 + 1.20556i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −210.000 121.244i −0.513447 0.296439i 0.220802 0.975319i $$-0.429132\pi$$
−0.734250 + 0.678880i $$0.762466\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 315.000 181.865i 0.762712 0.440352i
$$414$$ 0 0
$$415$$ −378.000 654.715i −0.910843 1.57763i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −84.0000 −0.200477 −0.100239 0.994963i $$-0.531961\pi$$
−0.100239 + 0.994963i $$0.531961\pi$$
$$420$$ 0 0
$$421$$ −678.000 + 391.443i −1.61045 + 0.929794i −0.621186 + 0.783663i $$0.713349\pi$$
−0.989265 + 0.146131i $$0.953318\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −66.0000 −0.155294
$$426$$ 0 0
$$427$$ 107.500 186.195i 0.251756 0.436055i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 333.000 + 192.258i 0.772622 + 0.446073i 0.833809 0.552053i $$-0.186155\pi$$
−0.0611873 + 0.998126i $$0.519489\pi$$
$$432$$ 0 0
$$433$$ 253.500 + 146.358i 0.585450 + 0.338010i 0.763296 0.646048i $$-0.223580\pi$$
−0.177846 + 0.984058i $$0.556913\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −132.000 436.477i −0.302059 0.998803i
$$438$$ 0 0
$$439$$ −97.5000 + 56.2917i −0.222096 + 0.128227i −0.606920 0.794763i $$-0.707595\pi$$
0.384825 + 0.922990i $$0.374262\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 93.0000 161.081i 0.209932 0.363613i −0.741761 0.670665i $$-0.766009\pi$$
0.951693 + 0.307051i $$0.0993423\pi$$
$$444$$ 0 0
$$445$$ 62.3538i 0.140121i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 135.100i 0.300891i 0.988618 + 0.150445i $$0.0480708\pi$$
−0.988618 + 0.150445i $$0.951929\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 571.577i 1.25621i
$$456$$ 0 0
$$457$$ −565.000 −1.23632 −0.618162 0.786051i $$-0.712122\pi$$
−0.618162 + 0.786051i $$0.712122\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −69.0000 119.512i −0.149675 0.259244i 0.781433 0.623990i $$-0.214489\pi$$
−0.931107 + 0.364746i $$0.881156\pi$$
$$462$$ 0 0
$$463$$ −139.000 −0.300216 −0.150108 0.988670i $$-0.547962\pi$$
−0.150108 + 0.988670i $$0.547962\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −888.000 −1.90150 −0.950749 0.309960i $$-0.899684\pi$$
−0.950749 + 0.309960i $$0.899684\pi$$
$$468$$ 0 0
$$469$$ −247.500 142.894i −0.527719 0.304678i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −60.5000 200.052i −0.127368 0.421162i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −348.000 + 602.754i −0.726514 + 1.25836i 0.231834 + 0.972755i $$0.425527\pi$$
−0.958348 + 0.285603i $$0.907806\pi$$
$$480$$ 0 0
$$481$$ −577.500 + 1000.26i −1.20062 + 2.07954i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −684.000 394.908i −1.41031 0.814242i
$$486$$ 0 0
$$487$$ 214.774i 0.441015i −0.975385 0.220507i $$-0.929229\pi$$
0.975385 0.220507i $$-0.0707713\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −468.000 810.600i −0.953157 1.65092i −0.738531 0.674220i $$-0.764480\pi$$
−0.214626 0.976696i $$-0.568853\pi$$
$$492$$ 0 0
$$493$$ 187.061i 0.379435i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 270.000 155.885i 0.543260 0.313651i
$$498$$ 0 0
$$499$$ 263.500 + 456.395i 0.528056 + 0.914620i 0.999465 + 0.0327053i $$0.0104123\pi$$
−0.471409 + 0.881915i $$0.656254\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −195.000 + 337.750i −0.387674 + 0.671471i −0.992136 0.125163i $$-0.960055\pi$$
0.604462 + 0.796634i $$0.293388\pi$$
$$504$$ 0 0
$$505$$ 936.000 1.85347
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −513.000 296.181i −1.00786 0.581887i −0.0972946 0.995256i $$-0.531019\pi$$
−0.910564 + 0.413368i $$0.864352\pi$$
$$510$$ 0 0
$$511$$ 27.5000 + 47.6314i 0.0538160 + 0.0932121i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −189.000 + 109.119i −0.366990 + 0.211882i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 103.923i 0.199468i 0.995014 + 0.0997342i $$0.0317993\pi$$
−0.995014 + 0.0997342i $$0.968201\pi$$
$$522$$ 0 0
$$523$$ 118.500 + 68.4160i 0.226577 + 0.130815i 0.608992 0.793176i $$-0.291574\pi$$
−0.382415 + 0.923991i $$0.624907\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 153.000 88.3346i 0.290323 0.167618i
$$528$$ 0 0
$$529$$ −23.5000 40.7032i −0.0444234 0.0769437i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −792.000 −1.48593
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 99.5000 172.339i 0.183919 0.318556i −0.759293 0.650749i $$-0.774455\pi$$
0.943212 + 0.332192i $$0.107788\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 540.000 + 311.769i 0.990826 + 0.572053i
$$546$$ 0 0
$$547$$ 532.500 + 307.439i 0.973492 + 0.562046i 0.900299 0.435272i $$-0.143348\pi$$
0.0731928 + 0.997318i $$0.476681\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 567.000 171.473i 1.02904 0.311203i
$$552$$ 0 0
$$553$$ −7.50000 + 4.33013i −0.0135624 + 0.00783025i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 360.000 623.538i 0.646320 1.11946i −0.337675 0.941263i $$-0.609641\pi$$
0.983995 0.178196i $$-0.0570260\pi$$
$$558$$ 0 0
$$559$$ 476.314i 0.852082i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 374.123i 0.664517i −0.943188 0.332258i $$-0.892189\pi$$
0.943188 0.332258i $$-0.107811\pi$$
$$564$$ 0 0
$$565$$ −810.000 + 467.654i −1.43363 + 0.827706i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 290.985i 0.511396i 0.966757 + 0.255698i $$0.0823053\pi$$
−0.966757 + 0.255698i $$0.917695\pi$$
$$570$$ 0 0
$$571$$ 95.0000 0.166375 0.0831874 0.996534i $$-0.473490\pi$$
0.0831874 + 0.996534i $$0.473490\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −132.000 228.631i −0.229565 0.397619i
$$576$$ 0 0
$$577$$ 874.000 1.51473 0.757366 0.652991i $$-0.226486\pi$$
0.757366 + 0.652991i $$0.226486\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 630.000 1.08434
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −327.000 566.381i −0.557070 0.964873i −0.997739 0.0672038i $$-0.978592\pi$$
0.440669 0.897669i $$-0.354741\pi$$
$$588$$ 0 0
$$589$$ 408.000 + 382.783i 0.692699 + 0.649887i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −471.000 + 815.796i −0.794266 + 1.37571i 0.129037 + 0.991640i $$0.458811\pi$$
−0.923304 + 0.384070i $$0.874522\pi$$
$$594$$ 0 0
$$595$$ 90.0000 155.885i 0.151261 0.261991i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −324.000 187.061i −0.540902 0.312290i 0.204543 0.978858i $$-0.434429\pi$$
−0.745444 + 0.666568i $$0.767763\pi$$
$$600$$ 0 0
$$601$$ 646.055i 1.07497i −0.843274 0.537483i $$-0.819375\pi$$
0.843274 0.537483i $$-0.180625\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −363.000 628.734i −0.600000 1.03923i
$$606$$ 0 0
$$607$$ 358.535i 0.590666i 0.955394 + 0.295333i $$0.0954307\pi$$
−0.955394 + 0.295333i $$0.904569\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 693.000 400.104i 1.13421 0.654834i
$$612$$ 0 0
$$613$$ −383.000 663.375i −0.624796 1.08218i −0.988580 0.150695i $$-0.951849\pi$$
0.363784 0.931483i $$-0.381485\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −270.000 + 467.654i −0.437601 + 0.757948i −0.997504 0.0706107i $$-0.977505\pi$$
0.559903 + 0.828558i $$0.310839\pi$$
$$618$$ 0 0
$$619$$ 97.0000 0.156704 0.0783522 0.996926i $$-0.475034\pi$$
0.0783522 + 0.996926i $$0.475034\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −45.0000 25.9808i −0.0722311 0.0417027i
$$624$$ 0 0
$$625$$ 389.500 + 674.634i 0.623200 + 1.07941i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 315.000 181.865i 0.500795 0.289134i
$$630$$ 0 0
$$631$$ 224.500 388.845i 0.355784 0.616237i −0.631467 0.775402i $$-0.717547\pi$$
0.987252 + 0.159166i $$0.0508804\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 249.415i 0.392780i
$$636$$ 0 0
$$637$$ 396.000 + 228.631i 0.621664 + 0.358918i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 513.000 296.181i 0.800312 0.462060i −0.0432682 0.999063i $$-0.513777\pi$$
0.843580 + 0.537003i $$0.180444\pi$$
$$642$$ 0 0
$$643$$ −461.500 799.341i −0.717729 1.24314i −0.961897 0.273411i $$-0.911848\pi$$
0.244168 0.969733i $$-0.421485\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −594.000 −0.918083 −0.459042 0.888415i $$-0.651807\pi$$
−0.459042 + 0.888415i $$0.651807\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −936.000 −1.43338 −0.716692 0.697390i $$-0.754345\pi$$
−0.716692 + 0.697390i $$0.754345\pi$$
$$654$$ 0 0
$$655$$ −144.000 + 249.415i −0.219847 + 0.380787i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 252.000 + 145.492i 0.382398 + 0.220777i 0.678861 0.734267i $$-0.262474\pi$$
−0.296463 + 0.955044i $$0.595807\pi$$
$$660$$ 0 0
$$661$$ −672.000 387.979i −1.01664 0.586958i −0.103512 0.994628i $$-0.533008\pi$$
−0.913129 + 0.407670i $$0.866341\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 555.000 + 129.904i 0.834586 + 0.195344i
$$666$$ 0 0
$$667$$ 648.000 374.123i 0.971514 0.560904i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 961.288i 1.42836i 0.699961 + 0.714181i $$0.253201\pi$$
−0.699961 + 0.714181i $$0.746799\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 259.808i 0.383763i 0.981418 + 0.191882i $$0.0614589\pi$$
−0.981418 + 0.191882i $$0.938541\pi$$
$$678$$ 0 0
$$679$$ 570.000 329.090i 0.839470 0.484668i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1132.76i 1.65851i 0.558872 + 0.829254i $$0.311234\pi$$
−0.558872 + 0.829254i $$0.688766\pi$$
$$684$$ 0 0
$$685$$ −792.000 −1.15620
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 594.000 + 1028.84i 0.862119 + 1.49323i
$$690$$ 0 0
$$691$$ −58.0000 −0.0839363 −0.0419682 0.999119i $$-0.513363\pi$$
−0.0419682 + 0.999119i $$0.513363\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −6.00000 −0.00863309
$$696$$ 0 0
$$697$$ 216.000 + 124.708i 0.309900 + 0.178921i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −171.000 296.181i −0.243937 0.422512i 0.717895 0.696151i $$-0.245106\pi$$
−0.961832 + 0.273640i $$0.911772\pi$$
$$702$$ 0 0
$$703$$ 840.000 + 788.083i 1.19488 + 1.12103i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −390.000 + 675.500i −0.551627 + 0.955445i
$$708$$ 0 0
$$709$$ −272.500 + 471.984i −0.384344 + 0.665704i −0.991678 0.128743i $$-0.958906\pi$$
0.607334 + 0.794447i $$0.292239\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 612.000 + 353.338i 0.858345 + 0.495566i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −534.000 924.915i −0.742698 1.28639i −0.951262 0.308382i $$-0.900212\pi$$
0.208564 0.978009i $$-0.433121\pi$$
$$720$$ 0 0
$$721$$ 181.865i 0.252240i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 297.000 171.473i 0.409655 0.236515i
$$726$$ 0 0
$$727$$ 57.5000 + 99.5929i 0.0790922 + 0.136992i 0.902858 0.429938i $$-0.141465\pi$$
−0.823766 + 0.566929i $$0.808131\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −75.0000 + 129.904i −0.102599 + 0.177707i
$$732$$ 0 0
$$733$$ −298.000 −0.406548 −0.203274 0.979122i $$-0.565158\pi$$
−0.203274 + 0.979122i $$0.565158\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −666.500 1154.41i −0.901894 1.56213i −0.825033 0.565085i $$-0.808843\pi$$
−0.0768619 0.997042i $$-0.524490\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 738.000 426.084i 0.993271 0.573465i 0.0870202 0.996207i $$-0.472266\pi$$
0.906250 + 0.422742i $$0.138932\pi$$
$$744$$ 0 0
$$745$$ −540.000 + 935.307i −0.724832 + 1.25545i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −343.500 198.320i −0.457390 0.264074i 0.253556 0.967321i $$-0.418400\pi$$
−0.710946 + 0.703246i $$0.751733\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 1224.00 706.677i 1.62119 0.935996i
$$756$$ 0 0
$$757$$ −117.500 203.516i −0.155218 0.268845i 0.777920 0.628363i $$-0.216275\pi$$
−0.933138 + 0.359517i $$0.882941\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1158.00 1.52168 0.760841 0.648938i $$-0.224787\pi$$
0.760841 + 0.648938i $$0.224787\pi$$
$$762$$ 0 0
$$763$$ −450.000 + 259.808i −0.589777 + 0.340508i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1386.00 1.80704
$$768$$ 0 0
$$769$$ −492.500 + 853.035i −0.640442 + 1.10928i 0.344892 + 0.938642i $$0.387916\pi$$
−0.985334 + 0.170636i $$0.945418\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 873.000 + 504.027i 1.12937 + 0.652040i 0.943775 0.330587i $$-0.107247\pi$$
0.185591 + 0.982627i $$0.440580\pi$$
$$774$$ 0 0
$$775$$ 280.500 + 161.947i 0.361935 + 0.208964i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −180.000 + 769.031i −0.231065 + 0.987202i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −231.000 + 400.104i −0.294268 + 0.509686i
$$786$$ 0 0
$$787$$ 1404.69i 1.78487i −0.451175 0.892435i $$-0.648995\pi$$
0.451175 0.892435i $$-0.351005\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 779.423i 0.985364i
$$792$$ 0 0
$$793$$ 709.500 409.630i 0.894704 0.516557i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1267.86i 1.59079i 0.606090 + 0.795396i $$0.292737\pi$$
−0.606090 + 0.795396i $$0.707263\pi$$
$$798$$ 0 0
$$799$$ −252.000 −0.315394
$$800$$ 0