# Properties

 Label 585.2.j.a.451.1 Level $585$ Weight $2$ Character 585.451 Analytic conductor $4.671$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.j (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.67124851824$$ 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 195) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 451.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 585.451 Dual form 585.2.j.a.406.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{4} +1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{4} +1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(3.00000 - 5.19615i) q^{11} +(2.50000 - 2.59808i) q^{13} +(-2.00000 + 3.46410i) q^{16} +(2.00000 + 3.46410i) q^{19} +(1.00000 + 1.73205i) q^{20} +(-3.00000 + 5.19615i) q^{23} +1.00000 q^{25} +(-1.00000 + 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(-5.50000 - 9.52628i) q^{43} +12.0000 q^{44} -6.00000 q^{47} +(3.00000 - 5.19615i) q^{49} +(7.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{55} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} -8.00000 q^{64} +(2.50000 - 2.59808i) q^{65} +(-5.50000 + 9.52628i) q^{67} +(-3.00000 - 5.19615i) q^{71} +5.00000 q^{73} +(-4.00000 + 6.92820i) q^{76} +6.00000 q^{77} +11.0000 q^{79} +(-2.00000 + 3.46410i) q^{80} -12.0000 q^{83} +(6.00000 - 10.3923i) q^{89} +(3.50000 + 0.866025i) q^{91} -12.0000 q^{92} +(2.00000 + 3.46410i) q^{95} +(-8.50000 - 14.7224i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{4} + 2 q^{5} + q^{7}+O(q^{10})$$ 2 * q + 2 * q^4 + 2 * q^5 + q^7 $$2 q + 2 q^{4} + 2 q^{5} + q^{7} + 6 q^{11} + 5 q^{13} - 4 q^{16} + 4 q^{19} + 2 q^{20} - 6 q^{23} + 2 q^{25} - 2 q^{28} - 6 q^{29} + 10 q^{31} + q^{35} - 2 q^{37} - 11 q^{43} + 24 q^{44} - 12 q^{47} + 6 q^{49} + 14 q^{52} + 6 q^{55} + 6 q^{59} + q^{61} - 16 q^{64} + 5 q^{65} - 11 q^{67} - 6 q^{71} + 10 q^{73} - 8 q^{76} + 12 q^{77} + 22 q^{79} - 4 q^{80} - 24 q^{83} + 12 q^{89} + 7 q^{91} - 24 q^{92} + 4 q^{95} - 17 q^{97}+O(q^{100})$$ 2 * q + 2 * q^4 + 2 * q^5 + q^7 + 6 * q^11 + 5 * q^13 - 4 * q^16 + 4 * q^19 + 2 * q^20 - 6 * q^23 + 2 * q^25 - 2 * q^28 - 6 * q^29 + 10 * q^31 + q^35 - 2 * q^37 - 11 * q^43 + 24 * q^44 - 12 * q^47 + 6 * q^49 + 14 * q^52 + 6 * q^55 + 6 * q^59 + q^61 - 16 * q^64 + 5 * q^65 - 11 * q^67 - 6 * q^71 + 10 * q^73 - 8 * q^76 + 12 * q^77 + 22 * q^79 - 4 * q^80 - 24 * q^83 + 12 * q^89 + 7 * q^91 - 24 * q^92 + 4 * q^95 - 17 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$496$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$3$$ 0 0
$$4$$ 1.00000 + 1.73205i 0.500000 + 0.866025i
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i $$-0.106148\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i $$-0.473552\pi$$
0.821541 0.570149i $$-0.193114\pi$$
$$12$$ 0 0
$$13$$ 2.50000 2.59808i 0.693375 0.720577i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −2.00000 + 3.46410i −0.500000 + 0.866025i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 0 0
$$19$$ 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i $$-0.0149348\pi$$
−0.540068 + 0.841621i $$0.681602\pi$$
$$20$$ 1.00000 + 1.73205i 0.223607 + 0.387298i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i $$0.381789\pi$$
−0.988436 + 0.151642i $$0.951544\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ −1.00000 + 1.73205i −0.188982 + 0.327327i
$$29$$ −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
$$31$$ 5.00000 0.898027 0.449013 0.893525i $$-0.351776\pi$$
0.449013 + 0.893525i $$0.351776\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0.500000 + 0.866025i 0.0845154 + 0.146385i
$$36$$ 0 0
$$37$$ −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i $$-0.885902\pi$$
0.772043 + 0.635571i $$0.219235\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$42$$ 0 0
$$43$$ −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i $$-0.849958\pi$$
0.0522047 0.998636i $$-0.483375\pi$$
$$44$$ 12.0000 1.80907
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 0 0
$$49$$ 3.00000 5.19615i 0.428571 0.742307i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 7.00000 + 1.73205i 0.970725 + 0.240192i
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 3.00000 5.19615i 0.404520 0.700649i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i $$-0.0389457\pi$$
−0.601958 + 0.798528i $$0.705612\pi$$
$$60$$ 0 0
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 2.50000 2.59808i 0.310087 0.322252i
$$66$$ 0 0
$$67$$ −5.50000 + 9.52628i −0.671932 + 1.16382i 0.305424 + 0.952217i $$0.401202\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i $$-0.282538\pi$$
−0.987294 + 0.158901i $$0.949205\pi$$
$$72$$ 0 0
$$73$$ 5.00000 0.585206 0.292603 0.956234i $$-0.405479\pi$$
0.292603 + 0.956234i $$0.405479\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −4.00000 + 6.92820i −0.458831 + 0.794719i
$$77$$ 6.00000 0.683763
$$78$$ 0 0
$$79$$ 11.0000 1.23760 0.618798 0.785550i $$-0.287620\pi$$
0.618798 + 0.785550i $$0.287620\pi$$
$$80$$ −2.00000 + 3.46410i −0.223607 + 0.387298i
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i $$-0.613922\pi$$
0.986303 0.164946i $$-0.0527450\pi$$
$$90$$ 0 0
$$91$$ 3.50000 + 0.866025i 0.366900 + 0.0907841i
$$92$$ −12.0000 −1.25109
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 2.00000 + 3.46410i 0.205196 + 0.355409i
$$96$$ 0 0
$$97$$ −8.50000 14.7224i −0.863044 1.49484i −0.868976 0.494854i $$-0.835222\pi$$
0.00593185 0.999982i $$-0.498112\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1.00000 + 1.73205i 0.100000 + 0.173205i
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ 0 0
$$103$$ −13.0000 −1.28093 −0.640464 0.767988i $$-0.721258\pi$$
−0.640464 + 0.767988i $$0.721258\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i $$-0.497411\pi$$
0.861931 0.507026i $$-0.169255\pi$$
$$108$$ 0 0
$$109$$ −7.00000 −0.670478 −0.335239 0.942133i $$-0.608817\pi$$
−0.335239 + 0.942133i $$0.608817\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −4.00000 −0.377964
$$113$$ −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i $$-0.257736\pi$$
−0.971930 + 0.235269i $$0.924403\pi$$
$$114$$ 0 0
$$115$$ −3.00000 + 5.19615i −0.279751 + 0.484544i
$$116$$ −12.0000 −1.11417
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −12.5000 21.6506i −1.13636 1.96824i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 5.00000 + 8.66025i 0.449013 + 0.777714i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 0.500000 0.866025i 0.0443678 0.0768473i −0.842989 0.537931i $$-0.819206\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −18.0000 −1.57267 −0.786334 0.617802i $$-0.788023\pi$$
−0.786334 + 0.617802i $$0.788023\pi$$
$$132$$ 0 0
$$133$$ −2.00000 + 3.46410i −0.173422 + 0.300376i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i $$0.00465636\pi$$
−0.487278 + 0.873247i $$0.662010\pi$$
$$138$$ 0 0
$$139$$ 9.50000 + 16.4545i 0.805779 + 1.39565i 0.915764 + 0.401718i $$0.131587\pi$$
−0.109984 + 0.993933i $$0.535080\pi$$
$$140$$ −1.00000 + 1.73205i −0.0845154 + 0.146385i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −6.00000 20.7846i −0.501745 1.73810i
$$144$$ 0 0
$$145$$ −3.00000 + 5.19615i −0.249136 + 0.431517i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ −4.00000 −0.328798
$$149$$ 12.0000 + 20.7846i 0.983078 + 1.70274i 0.650183 + 0.759778i $$0.274692\pi$$
0.332896 + 0.942964i $$0.391974\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 5.00000 0.401610
$$156$$ 0 0
$$157$$ −1.00000 −0.0798087 −0.0399043 0.999204i $$-0.512705\pi$$
−0.0399043 + 0.999204i $$0.512705\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −6.00000 −0.472866
$$162$$ 0 0
$$163$$ −5.50000 9.52628i −0.430793 0.746156i 0.566149 0.824303i $$-0.308433\pi$$
−0.996942 + 0.0781474i $$0.975100\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i $$-0.987025\pi$$
0.534875 + 0.844931i $$0.320359\pi$$
$$168$$ 0 0
$$169$$ −0.500000 12.9904i −0.0384615 0.999260i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 11.0000 19.0526i 0.838742 1.45274i
$$173$$ −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i $$-0.239913\pi$$
−0.957241 + 0.289292i $$0.906580\pi$$
$$174$$ 0 0
$$175$$ 0.500000 + 0.866025i 0.0377964 + 0.0654654i
$$176$$ 12.0000 + 20.7846i 0.904534 + 1.56670i
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i $$-0.981361\pi$$
0.549825 + 0.835280i $$0.314694\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1.00000 + 1.73205i −0.0735215 + 0.127343i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −6.00000 10.3923i −0.437595 0.757937i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i $$-0.0970159\pi$$
−0.736839 + 0.676068i $$0.763683\pi$$
$$192$$ 0 0
$$193$$ 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i $$-0.678351\pi$$
0.999326 + 0.0366998i $$0.0116845\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 12.0000 0.857143
$$197$$ 6.00000 10.3923i 0.427482 0.740421i −0.569166 0.822222i $$-0.692734\pi$$
0.996649 + 0.0818013i $$0.0260673\pi$$
$$198$$ 0 0
$$199$$ −8.50000 14.7224i −0.602549 1.04365i −0.992434 0.122782i $$-0.960818\pi$$
0.389885 0.920864i $$-0.372515\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −6.00000 −0.421117
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 4.00000 + 13.8564i 0.277350 + 0.960769i
$$209$$ 24.0000 1.66011
$$210$$ 0 0
$$211$$ 6.50000 11.2583i 0.447478 0.775055i −0.550743 0.834675i $$-0.685655\pi$$
0.998221 + 0.0596196i $$0.0189888\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −5.50000 9.52628i −0.375097 0.649687i
$$216$$ 0 0
$$217$$ 2.50000 + 4.33013i 0.169711 + 0.293948i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 12.0000 0.809040
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i $$-0.919650\pi$$
0.700449 + 0.713702i $$0.252983\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ −6.00000 −0.391397
$$236$$ −6.00000 + 10.3923i −0.390567 + 0.676481i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i $$0.0839937\pi$$
−0.256814 + 0.966461i $$0.582673\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ −1.00000 + 1.73205i −0.0640184 + 0.110883i
$$245$$ 3.00000 5.19615i 0.191663 0.331970i
$$246$$ 0 0
$$247$$ 14.0000 + 3.46410i 0.890799 + 0.220416i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$252$$ 0 0
$$253$$ 18.0000 + 31.1769i 1.13165 + 1.96008i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i $$-0.955440\pi$$
0.615948 + 0.787787i $$0.288773\pi$$
$$258$$ 0 0
$$259$$ −2.00000 −0.124274
$$260$$ 7.00000 + 1.73205i 0.434122 + 0.107417i
$$261$$ 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
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −22.0000 −1.34386
$$269$$ −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i $$-0.905416\pi$$
0.224523 0.974469i $$-0.427917\pi$$
$$270$$ 0 0
$$271$$ 3.50000 6.06218i 0.212610 0.368251i −0.739921 0.672694i $$-0.765137\pi$$
0.952531 + 0.304443i $$0.0984703\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 3.00000 5.19615i 0.180907 0.313340i
$$276$$ 0 0
$$277$$ 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i $$-0.0695395\pi$$
−0.675810 + 0.737075i $$0.736206\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ −11.5000 + 19.9186i −0.683604 + 1.18404i 0.290269 + 0.956945i $$0.406255\pi$$
−0.973873 + 0.227092i $$0.927078\pi$$
$$284$$ 6.00000 10.3923i 0.356034 0.616670i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 5.00000 + 8.66025i 0.292603 + 0.506803i
$$293$$ 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
$$295$$ 3.00000 + 5.19615i 0.174667 + 0.302532i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 6.00000 + 20.7846i 0.346989 + 1.20201i
$$300$$ 0 0
$$301$$ 5.50000 9.52628i 0.317015 0.549086i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −16.0000 −0.917663
$$305$$ 0.500000 + 0.866025i 0.0286299 + 0.0495885i
$$306$$ 0 0
$$307$$ −25.0000 −1.42683 −0.713413 0.700744i $$-0.752851\pi$$
−0.713413 + 0.700744i $$0.752851\pi$$
$$308$$ 6.00000 + 10.3923i 0.341882 + 0.592157i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ 23.0000 1.30004 0.650018 0.759918i $$-0.274761\pi$$
0.650018 + 0.759918i $$0.274761\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 11.0000 + 19.0526i 0.618798 + 1.07179i
$$317$$ 12.0000 0.673987 0.336994 0.941507i $$-0.390590\pi$$
0.336994 + 0.941507i $$0.390590\pi$$
$$318$$ 0 0
$$319$$ 18.0000 + 31.1769i 1.00781 + 1.74557i
$$320$$ −8.00000 −0.447214
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 2.50000 2.59808i 0.138675 0.144115i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −3.00000 5.19615i −0.165395 0.286473i
$$330$$ 0 0
$$331$$ 3.50000 + 6.06218i 0.192377 + 0.333207i 0.946038 0.324057i $$-0.105047\pi$$
−0.753660 + 0.657264i $$0.771714\pi$$
$$332$$ −12.0000 20.7846i −0.658586 1.14070i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −5.50000 + 9.52628i −0.300497 + 0.520476i
$$336$$ 0 0
$$337$$ −7.00000 −0.381314 −0.190657 0.981657i $$-0.561062\pi$$
−0.190657 + 0.981657i $$0.561062\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 15.0000 25.9808i 0.812296 1.40694i
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i $$-0.0622790\pi$$
−0.658824 + 0.752297i $$0.728946\pi$$
$$348$$ 0 0
$$349$$ −5.50000 + 9.52628i −0.294408 + 0.509930i −0.974847 0.222875i $$-0.928456\pi$$
0.680439 + 0.732805i $$0.261789\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i $$-0.992342\pi$$
0.520689 + 0.853746i $$0.325675\pi$$
$$354$$ 0 0
$$355$$ −3.00000 5.19615i −0.159223 0.275783i
$$356$$ 24.0000 1.27200
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −12.0000 −0.633336 −0.316668 0.948536i $$-0.602564\pi$$
−0.316668 + 0.948536i $$0.602564\pi$$
$$360$$ 0 0
$$361$$ 1.50000 2.59808i 0.0789474 0.136741i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 2.00000 + 6.92820i 0.104828 + 0.363137i
$$365$$ 5.00000 0.261712
$$366$$ 0 0
$$367$$ −2.50000 + 4.33013i −0.130499 + 0.226031i −0.923869 0.382709i $$-0.874991\pi$$
0.793370 + 0.608740i $$0.208325\pi$$
$$368$$ −12.0000 20.7846i −0.625543 1.08347i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 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
$$377$$ 6.00000 + 20.7846i 0.309016 + 1.07046i
$$378$$ 0 0
$$379$$ 0.500000 0.866025i 0.0256833 0.0444847i −0.852898 0.522077i $$-0.825157\pi$$
0.878581 + 0.477593i $$0.158491\pi$$
$$380$$ −4.00000 + 6.92820i −0.205196 + 0.355409i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i $$0.0434398\pi$$
−0.377531 + 0.925997i $$0.623227\pi$$
$$384$$ 0 0
$$385$$ 6.00000 0.305788
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 17.0000 29.4449i 0.863044 1.49484i
$$389$$ −24.0000 −1.21685 −0.608424 0.793612i $$-0.708198\pi$$
−0.608424 + 0.793612i $$0.708198\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 11.0000 0.553470
$$396$$ 0 0
$$397$$ 6.50000 + 11.2583i 0.326226 + 0.565039i 0.981760 0.190126i $$-0.0608897\pi$$
−0.655534 + 0.755166i $$0.727556\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −2.00000 + 3.46410i −0.100000 + 0.173205i
$$401$$ −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i $$-0.930195\pi$$
0.676425 + 0.736512i $$0.263528\pi$$
$$402$$ 0 0
$$403$$ 12.5000 12.9904i 0.622669 0.647097i
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 6.00000 + 10.3923i 0.297409 + 0.515127i
$$408$$ 0 0
$$409$$ −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i $$-0.206116\pi$$
−0.921192 + 0.389109i $$0.872783\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −13.0000 22.5167i −0.640464 1.10932i
$$413$$ −3.00000 + 5.19615i −0.147620 + 0.255686i
$$414$$ 0 0
$$415$$ −12.0000 −0.589057
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −12.0000 + 20.7846i −0.586238 + 1.01539i 0.408481 + 0.912767i $$0.366058\pi$$
−0.994720 + 0.102628i $$0.967275\pi$$
$$420$$ 0 0
$$421$$ 17.0000 0.828529 0.414265 0.910156i $$-0.364039\pi$$
0.414265 + 0.910156i $$0.364039\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −0.500000 + 0.866025i −0.0241967 + 0.0419099i
$$428$$ 36.0000 1.74013
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 20.7846i 0.578020 1.00116i −0.417687 0.908591i $$-0.637159\pi$$
0.995706 0.0925683i $$-0.0295076\pi$$
$$432$$ 0 0
$$433$$ −5.50000 9.52628i −0.264313 0.457804i 0.703070 0.711120i $$-0.251812\pi$$
−0.967383 + 0.253317i $$0.918479\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −7.00000 12.1244i −0.335239 0.580651i
$$437$$ −24.0000 −1.14808
$$438$$ 0 0
$$439$$ −5.50000 + 9.52628i −0.262501 + 0.454665i −0.966906 0.255134i $$-0.917881\pi$$
0.704405 + 0.709798i $$0.251214\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 0 0
$$445$$ 6.00000 10.3923i 0.284427 0.492642i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ −4.00000 6.92820i −0.188982 0.327327i
$$449$$ 3.00000 + 5.19615i 0.141579 + 0.245222i 0.928091 0.372353i $$-0.121449\pi$$
−0.786513 + 0.617574i $$0.788115\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 6.00000 10.3923i 0.282216 0.488813i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 3.50000 + 0.866025i 0.164083 + 0.0405999i
$$456$$ 0 0
$$457$$ 15.5000 26.8468i 0.725059 1.25584i −0.233890 0.972263i $$-0.575146\pi$$
0.958950 0.283577i $$-0.0915211\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −12.0000 −0.559503
$$461$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$462$$ 0 0
$$463$$ −19.0000 −0.883005 −0.441502 0.897260i $$-0.645554\pi$$
−0.441502 + 0.897260i $$0.645554\pi$$
$$464$$ −12.0000 20.7846i −0.557086 0.964901i
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −42.0000 −1.94353 −0.971764 0.235954i $$-0.924178\pi$$
−0.971764 + 0.235954i $$0.924178\pi$$
$$468$$ 0 0
$$469$$ −11.0000 −0.507933
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −66.0000 −3.03468
$$474$$ 0 0
$$475$$ 2.00000 + 3.46410i 0.0917663 + 0.158944i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$480$$ 0 0
$$481$$ 2.00000 + 6.92820i 0.0911922 + 0.315899i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 25.0000 43.3013i 1.13636 1.96824i
$$485$$ −8.50000 14.7224i −0.385965 0.668511i
$$486$$ 0 0
$$487$$ 14.0000 + 24.2487i 0.634401 + 1.09881i 0.986642 + 0.162905i $$0.0520863\pi$$
−0.352241 + 0.935909i $$0.614580\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 15.0000 25.9808i 0.676941 1.17250i −0.298957 0.954267i $$-0.596639\pi$$
0.975898 0.218229i $$-0.0700279\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −10.0000 + 17.3205i −0.449013 + 0.777714i
$$497$$ 3.00000 5.19615i 0.134568 0.233079i
$$498$$ 0 0
$$499$$ −40.0000 −1.79065 −0.895323 0.445418i $$-0.853055\pi$$
−0.895323 + 0.445418i $$0.853055\pi$$
$$500$$ 1.00000 + 1.73205i 0.0447214 + 0.0774597i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 21.0000 + 36.3731i 0.936344 + 1.62179i 0.772220 + 0.635355i $$0.219146\pi$$
0.164124 + 0.986440i $$0.447520\pi$$
$$504$$ 0 0
$$505$$ 3.00000 5.19615i 0.133498 0.231226i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 2.00000 0.0887357
$$509$$ −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i $$-0.963948\pi$$
0.594675 + 0.803966i $$0.297281\pi$$
$$510$$ 0 0
$$511$$ 2.50000 + 4.33013i 0.110593 + 0.191554i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −13.0000 −0.572848
$$516$$ 0 0
$$517$$ −18.0000 + 31.1769i −0.791639 + 1.37116i
$$518$$ 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
$$523$$ 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i $$-0.805460\pi$$
0.906434 + 0.422347i $$0.138794\pi$$
$$524$$ −18.0000 31.1769i −0.786334 1.36197i
$$525$$ 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
$$532$$ −8.00000 −0.346844
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 9.00000 15.5885i 0.389104 0.673948i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −18.0000 31.1769i −0.775315 1.34288i
$$540$$ 0 0
$$541$$ −7.00000 −0.300954 −0.150477 0.988614i $$-0.548081\pi$$
−0.150477 + 0.988614i $$0.548081\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −7.00000 −0.299847
$$546$$ 0 0
$$547$$ −7.00000 −0.299298 −0.149649 0.988739i $$-0.547814\pi$$
−0.149649 + 0.988739i $$0.547814\pi$$
$$548$$ −12.0000 + 20.7846i −0.512615 + 0.887875i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −24.0000 −1.02243
$$552$$ 0 0
$$553$$ 5.50000 + 9.52628i 0.233884 + 0.405099i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −19.0000 + 32.9090i −0.805779 + 1.39565i
$$557$$ −6.00000 + 10.3923i −0.254228 + 0.440336i −0.964686 0.263404i $$-0.915155\pi$$
0.710457 + 0.703740i $$0.248488\pi$$
$$558$$ 0 0
$$559$$ −38.5000 9.52628i −1.62838 0.402919i
$$560$$ −4.00000 −0.169031
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 21.0000 + 36.3731i 0.885044 + 1.53294i 0.845663 + 0.533718i $$0.179206\pi$$
0.0393818 + 0.999224i $$0.487461\pi$$
$$564$$ 0 0
$$565$$ −3.00000 5.19615i −0.126211 0.218604i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 15.0000 25.9808i 0.628833 1.08917i −0.358954 0.933355i $$-0.616866\pi$$
0.987786 0.155815i $$-0.0498003\pi$$
$$570$$ 0 0
$$571$$ −28.0000 −1.17176 −0.585882 0.810397i $$-0.699252\pi$$
−0.585882 + 0.810397i $$0.699252\pi$$
$$572$$ 30.0000 31.1769i 1.25436 1.30357i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −3.00000 + 5.19615i −0.125109 + 0.216695i
$$576$$ 0 0
$$577$$ 14.0000 0.582828 0.291414 0.956597i $$-0.405874\pi$$
0.291414 + 0.956597i $$0.405874\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ −12.0000 −0.498273
$$581$$ −6.00000 10.3923i −0.248922 0.431145i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 21.0000 36.3731i 0.866763 1.50128i 0.00147660 0.999999i $$-0.499530\pi$$
0.865286 0.501278i $$-0.167137\pi$$
$$588$$ 0 0
$$589$$ 10.0000 + 17.3205i 0.412043 + 0.713679i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −4.00000 6.92820i −0.164399 0.284747i
$$593$$ 30.0000 1.23195 0.615976 0.787765i $$-0.288762\pi$$
0.615976 + 0.787765i $$0.288762\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −24.0000 + 41.5692i −0.983078 + 1.70274i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −18.0000 −0.735460 −0.367730 0.929933i $$-0.619865\pi$$
−0.367730 + 0.929933i $$0.619865\pi$$
$$600$$ 0 0
$$601$$ −13.0000 + 22.5167i −0.530281 + 0.918474i 0.469095 + 0.883148i $$0.344580\pi$$
−0.999376 + 0.0353259i $$0.988753\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −16.0000 27.7128i −0.651031 1.12762i
$$605$$ −12.5000 21.6506i −0.508197 0.880223i
$$606$$ 0 0
$$607$$ 20.0000 + 34.6410i 0.811775 + 1.40604i 0.911621 + 0.411033i $$0.134832\pi$$
−0.0998457 + 0.995003i $$0.531835\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −15.0000 + 15.5885i −0.606835 + 0.630641i
$$612$$ 0 0
$$613$$ −11.5000 + 19.9186i −0.464481 + 0.804504i −0.999178 0.0405396i $$-0.987092\pi$$
0.534697 + 0.845044i $$0.320426\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i $$-0.128129\pi$$
−0.799298 + 0.600935i $$0.794795\pi$$
$$618$$ 0 0
$$619$$ −19.0000 −0.763674 −0.381837 0.924230i $$-0.624709\pi$$
−0.381837 + 0.924230i $$0.624709\pi$$
$$620$$ 5.00000 + 8.66025i 0.200805 + 0.347804i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 12.0000 0.480770
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −1.00000 1.73205i −0.0399043 0.0691164i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 18.5000 + 32.0429i 0.736473 + 1.27561i 0.954074 + 0.299571i $$0.0968437\pi$$
−0.217601 + 0.976038i $$0.569823\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.500000 0.866025i 0.0198419 0.0343672i
$$636$$ 0 0
$$637$$ −6.00000 20.7846i −0.237729 0.823516i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i $$-0.964822\pi$$
0.401435 0.915888i $$-0.368512\pi$$
$$642$$ 0 0
$$643$$ −5.50000 9.52628i −0.216899 0.375680i 0.736959 0.675937i $$-0.236261\pi$$
−0.953858 + 0.300257i $$0.902928\pi$$
$$644$$ −6.00000 10.3923i −0.236433 0.409514i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −3.00000 + 5.19615i −0.117942 + 0.204282i −0.918952 0.394369i $$-0.870963\pi$$
0.801010 + 0.598651i $$0.204296\pi$$
$$648$$ 0 0
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 11.0000 19.0526i 0.430793 0.746156i
$$653$$ 24.0000 41.5692i 0.939193 1.62673i 0.172211 0.985060i $$-0.444909\pi$$
0.766982 0.641669i $$-0.221758\pi$$
$$654$$ 0 0
$$655$$ −18.0000 −0.703318
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i $$-0.919323\pi$$
0.266872 0.963732i $$-0.414010\pi$$
$$660$$ 0 0
$$661$$ 24.5000 42.4352i 0.952940 1.65054i 0.213925 0.976850i $$-0.431375\pi$$
0.739014 0.673690i $$-0.235292\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −2.00000 + 3.46410i −0.0775567 + 0.134332i
$$666$$ 0 0
$$667$$ −18.0000 31.1769i −0.696963 1.20717i
$$668$$ −24.0000 −0.928588
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 6.00000 0.231627
$$672$$ 0 0
$$673$$ −5.50000 + 9.52628i −0.212009 + 0.367211i −0.952343 0.305028i $$-0.901334\pi$$
0.740334 + 0.672239i $$0.234667\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 22.0000 13.8564i 0.846154 0.532939i
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 8.50000 14.7224i 0.326200 0.564995i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 9.00000 + 15.5885i 0.344375 + 0.596476i 0.985240 0.171178i $$-0.0547574\pi$$
−0.640865 + 0.767654i $$0.721424\pi$$
$$684$$ 0 0
$$685$$ 6.00000 + 10.3923i 0.229248 + 0.397070i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 44.0000 1.67748
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −2.50000 + 4.33013i −0.0951045 + 0.164726i −0.909652 0.415371i $$-0.863652\pi$$
0.814548 + 0.580097i $$0.196985\pi$$
$$692$$ 6.00000 10.3923i 0.228086 0.395056i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 9.50000 + 16.4545i 0.360356 + 0.624154i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −1.00000 + 1.73205i −0.0377964 + 0.0654654i
$$701$$ 12.0000 0.453234 0.226617 0.973984i $$-0.427233\pi$$
0.226617 + 0.973984i $$0.427233\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ −24.0000 + 41.5692i −0.904534 + 1.56670i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 6.00000 0.225653
$$708$$ 0 0
$$709$$ 9.50000 + 16.4545i 0.356780 + 0.617961i 0.987421 0.158114i $$-0.0505412\pi$$
−0.630641 + 0.776075i $$0.717208\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −15.0000 + 25.9808i −0.561754 + 0.972987i
$$714$$ 0 0
$$715$$ −6.00000 20.7846i −0.224387 0.777300i
$$716$$ −24.0000 −0.896922
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i $$-0.130979\pi$$
−0.804648 + 0.593753i $$0.797646\pi$$
$$720$$ 0 0
$$721$$ −6.50000 11.2583i −0.242073 0.419282i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ −10.0000 17.3205i −0.371647 0.643712i
$$725$$ −3.00000 + 5.19615i −0.111417 + 0.192980i
$$726$$ 0 0
$$727$$ −25.0000 −0.927199 −0.463599 0.886045i $$-0.653442\pi$$
−0.463599 + 0.886045i $$0.653442\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 29.0000 1.07114 0.535570 0.844491i $$-0.320097\pi$$
0.535570 + 0.844491i $$0.320097\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 33.0000 + 57.1577i 1.21557 + 2.10543i
$$738$$ 0 0
$$739$$ −10.0000 + 17.3205i −0.367856 + 0.637145i −0.989230 0.146369i $$-0.953241\pi$$
0.621374 + 0.783514i $$0.286575\pi$$
$$740$$ −4.00000 −0.147043
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i $$-0.798229\pi$$
0.915794 + 0.401648i $$0.131563\pi$$
$$744$$ 0 0
$$745$$ 12.0000 + 20.7846i 0.439646 + 0.761489i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 18.0000 0.657706
$$750$$ 0 0
$$751$$ 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i $$-0.572942\pi$$
0.956963 0.290209i $$-0.0937250\pi$$
$$752$$ 12.0000 20.7846i 0.437595 0.757937i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ −7.00000 + 12.1244i −0.254419 + 0.440667i −0.964738 0.263213i $$-0.915218\pi$$
0.710318 + 0.703881i $$0.248551\pi$$
$$758$$ 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
$$763$$ −3.50000 6.06218i −0.126709 0.219466i
$$764$$ −6.00000 + 10.3923i −0.217072 + 0.375980i
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 21.0000 + 5.19615i 0.758266 + 0.187622i
$$768$$ 0 0
$$769$$ −19.0000 + 32.9090i −0.685158 + 1.18673i 0.288230 + 0.957561i $$0.406933\pi$$
−0.973387 + 0.229166i $$0.926400\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 26.0000 0.935760
$$773$$ −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i $$-0.271596\pi$$
−0.981250 + 0.192740i $$0.938263\pi$$
$$774$$ 0 0
$$775$$ 5.00000 0.179605
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −36.0000 −1.28818
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 12.0000 + 20.7846i 0.428571 + 0.742307i
$$785$$ −1.00000 −0.0356915
$$786$$ 0 0
$$787$$ 6.50000 + 11.2583i 0.231700 + 0.401316i 0.958308 0.285736i $$-0.0922379\pi$$
−0.726609 + 0.687052i $$0.758905\pi$$
$$788$$ 24.0000 0.854965
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 3.00000 5.19615i 0.106668 0.184754i
$$792$$ 0 0
$$793$$ 3.50000 + 0.866025i 0.124289 + 0.0307535i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 17.0000 29.4449i 0.602549 1.04365i
$$797$$ 6.00000 + 10.3923i 0.212531 + 0.368114i 0.952506 0.304520i $$-0.0984960\pi$$
−0.739975 + 0.672634i $$0.765163\pi$$
$$798$$ 0 0
$$799$$