# Properties

 Label 1800.2.k.m.901.4 Level $1800$ Weight $2$ Character 1800.901 Analytic conductor $14.373$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1800.k (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.3730723638$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} - 2x^{2} + 4$$ x^4 - 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 40) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 901.4 Root $$-1.22474 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1800.901 Dual form 1800.2.k.m.901.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +2.44949 q^{7} +2.82843i q^{8} +O(q^{10})$$ $$q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +2.44949 q^{7} +2.82843i q^{8} +3.46410i q^{11} +(3.00000 + 1.73205i) q^{14} +(-2.00000 + 3.46410i) q^{16} +4.89898 q^{17} -3.46410i q^{19} +(-2.44949 + 4.24264i) q^{22} -2.44949 q^{23} +(2.44949 + 4.24264i) q^{28} +4.00000 q^{31} +(-4.89898 + 2.82843i) q^{32} +(6.00000 + 3.46410i) q^{34} +8.48528i q^{37} +(2.44949 - 4.24264i) q^{38} +4.24264i q^{43} +(-6.00000 + 3.46410i) q^{44} +(-3.00000 - 1.73205i) q^{46} -7.34847 q^{47} -1.00000 q^{49} -5.65685i q^{53} +6.92820i q^{56} -10.3923i q^{59} +3.46410i q^{61} +(4.89898 + 2.82843i) q^{62} -8.00000 q^{64} +4.24264i q^{67} +(4.89898 + 8.48528i) q^{68} +12.0000 q^{71} +4.89898 q^{73} +(-6.00000 + 10.3923i) q^{74} +(6.00000 - 3.46410i) q^{76} +8.48528i q^{77} +4.00000 q^{79} +9.89949i q^{83} +(-3.00000 + 5.19615i) q^{86} -9.79796 q^{88} +6.00000 q^{89} +(-2.44949 - 4.24264i) q^{92} +(-9.00000 - 5.19615i) q^{94} +4.89898 q^{97} +(-1.22474 - 0.707107i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{4}+O(q^{10})$$ 4 * q + 4 * q^4 $$4 q + 4 q^{4} + 12 q^{14} - 8 q^{16} + 16 q^{31} + 24 q^{34} - 24 q^{44} - 12 q^{46} - 4 q^{49} - 32 q^{64} + 48 q^{71} - 24 q^{74} + 24 q^{76} + 16 q^{79} - 12 q^{86} + 24 q^{89} - 36 q^{94}+O(q^{100})$$ 4 * q + 4 * q^4 + 12 * q^14 - 8 * q^16 + 16 * q^31 + 24 * q^34 - 24 * q^44 - 12 * q^46 - 4 * q^49 - 32 * q^64 + 48 * q^71 - 24 * q^74 + 24 * q^76 + 16 * q^79 - 12 * q^86 + 24 * q^89 - 36 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$$.

 $$n$$ $$577$$ $$901$$ $$1001$$ $$1351$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.22474 + 0.707107i 0.866025 + 0.500000i
$$3$$ 0 0
$$4$$ 1.00000 + 1.73205i 0.500000 + 0.866025i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.44949 0.925820 0.462910 0.886405i $$-0.346805\pi$$
0.462910 + 0.886405i $$0.346805\pi$$
$$8$$ 2.82843i 1.00000i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.46410i 1.04447i 0.852803 + 0.522233i $$0.174901\pi$$
−0.852803 + 0.522233i $$0.825099\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 3.00000 + 1.73205i 0.801784 + 0.462910i
$$15$$ 0 0
$$16$$ −2.00000 + 3.46410i −0.500000 + 0.866025i
$$17$$ 4.89898 1.18818 0.594089 0.804400i $$-0.297513\pi$$
0.594089 + 0.804400i $$0.297513\pi$$
$$18$$ 0 0
$$19$$ 3.46410i 0.794719i −0.917663 0.397360i $$-0.869927\pi$$
0.917663 0.397360i $$-0.130073\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.44949 + 4.24264i −0.522233 + 0.904534i
$$23$$ −2.44949 −0.510754 −0.255377 0.966842i $$-0.582200\pi$$
−0.255377 + 0.966842i $$0.582200\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 2.44949 + 4.24264i 0.462910 + 0.801784i
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ −4.89898 + 2.82843i −0.866025 + 0.500000i
$$33$$ 0 0
$$34$$ 6.00000 + 3.46410i 1.02899 + 0.594089i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 8.48528i 1.39497i 0.716599 + 0.697486i $$0.245698\pi$$
−0.716599 + 0.697486i $$0.754302\pi$$
$$38$$ 2.44949 4.24264i 0.397360 0.688247i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 4.24264i 0.646997i 0.946229 + 0.323498i $$0.104859\pi$$
−0.946229 + 0.323498i $$0.895141\pi$$
$$44$$ −6.00000 + 3.46410i −0.904534 + 0.522233i
$$45$$ 0 0
$$46$$ −3.00000 1.73205i −0.442326 0.255377i
$$47$$ −7.34847 −1.07188 −0.535942 0.844255i $$-0.680044\pi$$
−0.535942 + 0.844255i $$0.680044\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 5.65685i 0.777029i −0.921443 0.388514i $$-0.872988\pi$$
0.921443 0.388514i $$-0.127012\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 6.92820i 0.925820i
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 10.3923i 1.35296i −0.736460 0.676481i $$-0.763504\pi$$
0.736460 0.676481i $$-0.236496\pi$$
$$60$$ 0 0
$$61$$ 3.46410i 0.443533i 0.975100 + 0.221766i $$0.0711822\pi$$
−0.975100 + 0.221766i $$0.928818\pi$$
$$62$$ 4.89898 + 2.82843i 0.622171 + 0.359211i
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.24264i 0.518321i 0.965834 + 0.259161i $$0.0834459\pi$$
−0.965834 + 0.259161i $$0.916554\pi$$
$$68$$ 4.89898 + 8.48528i 0.594089 + 1.02899i
$$69$$ 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
$$73$$ 4.89898 0.573382 0.286691 0.958023i $$-0.407445\pi$$
0.286691 + 0.958023i $$0.407445\pi$$
$$74$$ −6.00000 + 10.3923i −0.697486 + 1.20808i
$$75$$ 0 0
$$76$$ 6.00000 3.46410i 0.688247 0.397360i
$$77$$ 8.48528i 0.966988i
$$78$$ 0 0
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 9.89949i 1.08661i 0.839535 + 0.543305i $$0.182827\pi$$
−0.839535 + 0.543305i $$0.817173\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −3.00000 + 5.19615i −0.323498 + 0.560316i
$$87$$ 0 0
$$88$$ −9.79796 −1.04447
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −2.44949 4.24264i −0.255377 0.442326i
$$93$$ 0 0
$$94$$ −9.00000 5.19615i −0.928279 0.535942i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 4.89898 0.497416 0.248708 0.968579i $$-0.419994\pi$$
0.248708 + 0.968579i $$0.419994\pi$$
$$98$$ −1.22474 0.707107i −0.123718 0.0714286i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 13.8564i 1.37876i −0.724398 0.689382i $$-0.757882\pi$$
0.724398 0.689382i $$-0.242118\pi$$
$$102$$ 0 0
$$103$$ −7.34847 −0.724066 −0.362033 0.932165i $$-0.617917\pi$$
−0.362033 + 0.932165i $$0.617917\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 4.00000 6.92820i 0.388514 0.672927i
$$107$$ 1.41421i 0.136717i 0.997661 + 0.0683586i $$0.0217762\pi$$
−0.997661 + 0.0683586i $$0.978224\pi$$
$$108$$ 0 0
$$109$$ 3.46410i 0.331801i 0.986143 + 0.165900i $$0.0530530\pi$$
−0.986143 + 0.165900i $$0.946947\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −4.89898 + 8.48528i −0.462910 + 0.801784i
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 7.34847 12.7279i 0.676481 1.17170i
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ −1.00000 −0.0909091
$$122$$ −2.44949 + 4.24264i −0.221766 + 0.384111i
$$123$$ 0 0
$$124$$ 4.00000 + 6.92820i 0.359211 + 0.622171i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −17.1464 −1.52150 −0.760750 0.649045i $$-0.775169\pi$$
−0.760750 + 0.649045i $$0.775169\pi$$
$$128$$ −9.79796 5.65685i −0.866025 0.500000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 3.46410i 0.302660i −0.988483 0.151330i $$-0.951644\pi$$
0.988483 0.151330i $$-0.0483556\pi$$
$$132$$ 0 0
$$133$$ 8.48528i 0.735767i
$$134$$ −3.00000 + 5.19615i −0.259161 + 0.448879i
$$135$$ 0 0
$$136$$ 13.8564i 1.18818i
$$137$$ −9.79796 −0.837096 −0.418548 0.908195i $$-0.637461\pi$$
−0.418548 + 0.908195i $$0.637461\pi$$
$$138$$ 0 0
$$139$$ 10.3923i 0.881464i −0.897639 0.440732i $$-0.854719\pi$$
0.897639 0.440732i $$-0.145281\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 14.6969 + 8.48528i 1.23334 + 0.712069i
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 6.00000 + 3.46410i 0.496564 + 0.286691i
$$147$$ 0 0
$$148$$ −14.6969 + 8.48528i −1.20808 + 0.697486i
$$149$$ 17.3205i 1.41895i −0.704730 0.709476i $$-0.748932\pi$$
0.704730 0.709476i $$-0.251068\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 9.79796 0.794719
$$153$$ 0 0
$$154$$ −6.00000 + 10.3923i −0.483494 + 0.837436i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 8.48528i 0.677199i −0.940931 0.338600i $$-0.890047\pi$$
0.940931 0.338600i $$-0.109953\pi$$
$$158$$ 4.89898 + 2.82843i 0.389742 + 0.225018i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −6.00000 −0.472866
$$162$$ 0 0
$$163$$ 21.2132i 1.66155i 0.556611 + 0.830773i $$0.312101\pi$$
−0.556611 + 0.830773i $$0.687899\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −7.00000 + 12.1244i −0.543305 + 0.941033i
$$167$$ 12.2474 0.947736 0.473868 0.880596i $$-0.342857\pi$$
0.473868 + 0.880596i $$0.342857\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −7.34847 + 4.24264i −0.560316 + 0.323498i
$$173$$ 2.82843i 0.215041i −0.994203 0.107521i $$-0.965709\pi$$
0.994203 0.107521i $$-0.0342912\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −12.0000 6.92820i −0.904534 0.522233i
$$177$$ 0 0
$$178$$ 7.34847 + 4.24264i 0.550791 + 0.317999i
$$179$$ 3.46410i 0.258919i −0.991585 0.129460i $$-0.958676\pi$$
0.991585 0.129460i $$-0.0413242\pi$$
$$180$$ 0 0
$$181$$ 13.8564i 1.02994i −0.857209 0.514969i $$-0.827803\pi$$
0.857209 0.514969i $$-0.172197\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 6.92820i 0.510754i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 16.9706i 1.24101i
$$188$$ −7.34847 12.7279i −0.535942 0.928279i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −24.0000 −1.73658 −0.868290 0.496058i $$-0.834780\pi$$
−0.868290 + 0.496058i $$0.834780\pi$$
$$192$$ 0 0
$$193$$ 24.4949 1.76318 0.881591 0.472015i $$-0.156473\pi$$
0.881591 + 0.472015i $$0.156473\pi$$
$$194$$ 6.00000 + 3.46410i 0.430775 + 0.248708i
$$195$$ 0 0
$$196$$ −1.00000 1.73205i −0.0714286 0.123718i
$$197$$ 5.65685i 0.403034i −0.979485 0.201517i $$-0.935413\pi$$
0.979485 0.201517i $$-0.0645872\pi$$
$$198$$ 0 0
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 9.79796 16.9706i 0.689382 1.19404i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −9.00000 5.19615i −0.627060 0.362033i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ 24.2487i 1.66935i −0.550743 0.834675i $$-0.685655\pi$$
0.550743 0.834675i $$-0.314345\pi$$
$$212$$ 9.79796 5.65685i 0.672927 0.388514i
$$213$$ 0 0
$$214$$ −1.00000 + 1.73205i −0.0683586 + 0.118401i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 9.79796 0.665129
$$218$$ −2.44949 + 4.24264i −0.165900 + 0.287348i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −22.0454 −1.47627 −0.738135 0.674653i $$-0.764293\pi$$
−0.738135 + 0.674653i $$0.764293\pi$$
$$224$$ −12.0000 + 6.92820i −0.801784 + 0.462910i
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.41421i 0.0938647i −0.998898 0.0469323i $$-0.985055\pi$$
0.998898 0.0469323i $$-0.0149445\pi$$
$$228$$ 0 0
$$229$$ 27.7128i 1.83131i −0.401960 0.915657i $$-0.631671\pi$$
0.401960 0.915657i $$-0.368329\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 14.6969 0.962828 0.481414 0.876493i $$-0.340123\pi$$
0.481414 + 0.876493i $$0.340123\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 18.0000 10.3923i 1.17170 0.676481i
$$237$$ 0 0
$$238$$ 14.6969 + 8.48528i 0.952661 + 0.550019i
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ 4.00000 0.257663 0.128831 0.991667i $$-0.458877\pi$$
0.128831 + 0.991667i $$0.458877\pi$$
$$242$$ −1.22474 0.707107i −0.0787296 0.0454545i
$$243$$ 0 0
$$244$$ −6.00000 + 3.46410i −0.384111 + 0.221766i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 11.3137i 0.718421i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 10.3923i 0.655956i −0.944685 0.327978i $$-0.893633\pi$$
0.944685 0.327978i $$-0.106367\pi$$
$$252$$ 0 0
$$253$$ 8.48528i 0.533465i
$$254$$ −21.0000 12.1244i −1.31766 0.760750i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 9.79796 0.611180 0.305590 0.952163i $$-0.401146\pi$$
0.305590 + 0.952163i $$0.401146\pi$$
$$258$$ 0 0
$$259$$ 20.7846i 1.29149i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 2.44949 4.24264i 0.151330 0.262111i
$$263$$ −7.34847 −0.453126 −0.226563 0.973997i $$-0.572749\pi$$
−0.226563 + 0.973997i $$0.572749\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 6.00000 10.3923i 0.367884 0.637193i
$$267$$ 0 0
$$268$$ −7.34847 + 4.24264i −0.448879 + 0.259161i
$$269$$ 10.3923i 0.633630i −0.948487 0.316815i $$-0.897387\pi$$
0.948487 0.316815i $$-0.102613\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ −9.79796 + 16.9706i −0.594089 + 1.02899i
$$273$$ 0 0
$$274$$ −12.0000 6.92820i −0.724947 0.418548i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 25.4558i 1.52949i −0.644331 0.764747i $$-0.722864\pi$$
0.644331 0.764747i $$-0.277136\pi$$
$$278$$ 7.34847 12.7279i 0.440732 0.763370i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 12.0000 0.715860 0.357930 0.933748i $$-0.383483\pi$$
0.357930 + 0.933748i $$0.383483\pi$$
$$282$$ 0 0
$$283$$ 21.2132i 1.26099i −0.776192 0.630497i $$-0.782851\pi$$
0.776192 0.630497i $$-0.217149\pi$$
$$284$$ 12.0000 + 20.7846i 0.712069 + 1.23334i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 7.00000 0.411765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 4.89898 + 8.48528i 0.286691 + 0.496564i
$$293$$ 19.7990i 1.15667i 0.815800 + 0.578335i $$0.196297\pi$$
−0.815800 + 0.578335i $$0.803703\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −24.0000 −1.39497
$$297$$ 0 0
$$298$$ 12.2474 21.2132i 0.709476 1.22885i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 10.3923i 0.599002i
$$302$$ −19.5959 11.3137i −1.12762 0.651031i
$$303$$ 0 0
$$304$$ 12.0000 + 6.92820i 0.688247 + 0.397360i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 29.6985i 1.69498i −0.530810 0.847491i $$-0.678112\pi$$
0.530810 0.847491i $$-0.321888\pi$$
$$308$$ −14.6969 + 8.48528i −0.837436 + 0.483494i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 0 0
$$313$$ 9.79796 0.553813 0.276907 0.960897i $$-0.410691\pi$$
0.276907 + 0.960897i $$0.410691\pi$$
$$314$$ 6.00000 10.3923i 0.338600 0.586472i
$$315$$ 0 0
$$316$$ 4.00000 + 6.92820i 0.225018 + 0.389742i
$$317$$ 28.2843i 1.58860i −0.607524 0.794301i $$-0.707837\pi$$
0.607524 0.794301i $$-0.292163\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −7.34847 4.24264i −0.409514 0.236433i
$$323$$ 16.9706i 0.944267i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −15.0000 + 25.9808i −0.830773 + 1.43894i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −18.0000 −0.992372
$$330$$ 0 0
$$331$$ 31.1769i 1.71364i 0.515617 + 0.856819i $$0.327563\pi$$
−0.515617 + 0.856819i $$0.672437\pi$$
$$332$$ −17.1464 + 9.89949i −0.941033 + 0.543305i
$$333$$ 0 0
$$334$$ 15.0000 + 8.66025i 0.820763 + 0.473868i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 15.9217 + 9.19239i 0.866025 + 0.500000i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 13.8564i 0.750366i
$$342$$ 0 0
$$343$$ −19.5959 −1.05808
$$344$$ −12.0000 −0.646997
$$345$$ 0 0
$$346$$ 2.00000 3.46410i 0.107521 0.186231i
$$347$$ 15.5563i 0.835109i 0.908652 + 0.417554i $$0.137113\pi$$
−0.908652 + 0.417554i $$0.862887\pi$$
$$348$$ 0 0
$$349$$ 13.8564i 0.741716i 0.928689 + 0.370858i $$0.120936\pi$$
−0.928689 + 0.370858i $$0.879064\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −9.79796 16.9706i −0.522233 0.904534i
$$353$$ 29.3939 1.56448 0.782239 0.622978i $$-0.214078\pi$$
0.782239 + 0.622978i $$0.214078\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 6.00000 + 10.3923i 0.317999 + 0.550791i
$$357$$ 0 0
$$358$$ 2.44949 4.24264i 0.129460 0.224231i
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ 7.00000 0.368421
$$362$$ 9.79796 16.9706i 0.514969 0.891953i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 12.2474 0.639312 0.319656 0.947534i $$-0.396433\pi$$
0.319656 + 0.947534i $$0.396433\pi$$
$$368$$ 4.89898 8.48528i 0.255377 0.442326i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 13.8564i 0.719389i
$$372$$ 0 0
$$373$$ 8.48528i 0.439351i −0.975573 0.219676i $$-0.929500\pi$$
0.975573 0.219676i $$-0.0704999\pi$$
$$374$$ −12.0000 + 20.7846i −0.620505 + 1.07475i
$$375$$ 0 0
$$376$$ 20.7846i 1.07188i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 24.2487i 1.24557i −0.782392 0.622786i $$-0.786001\pi$$
0.782392 0.622786i $$-0.213999\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −29.3939 16.9706i −1.50392 0.868290i
$$383$$ −26.9444 −1.37679 −0.688397 0.725334i $$-0.741685\pi$$
−0.688397 + 0.725334i $$0.741685\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 30.0000 + 17.3205i 1.52696 + 0.881591i
$$387$$ 0 0
$$388$$ 4.89898 + 8.48528i 0.248708 + 0.430775i
$$389$$ 3.46410i 0.175637i −0.996136 0.0878185i $$-0.972010\pi$$
0.996136 0.0878185i $$-0.0279895\pi$$
$$390$$ 0 0
$$391$$ −12.0000 −0.606866
$$392$$ 2.82843i 0.142857i
$$393$$ 0 0
$$394$$ 4.00000 6.92820i 0.201517 0.349038i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 16.9706i 0.851728i 0.904787 + 0.425864i $$0.140030\pi$$
−0.904787 + 0.425864i $$0.859970\pi$$
$$398$$ −4.89898 2.82843i −0.245564 0.141776i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 24.0000 13.8564i 1.19404 0.689382i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −29.3939 −1.45700
$$408$$ 0 0
$$409$$ −32.0000 −1.58230 −0.791149 0.611623i $$-0.790517\pi$$
−0.791149 + 0.611623i $$0.790517\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −7.34847 12.7279i −0.362033 0.627060i
$$413$$ 25.4558i 1.25260i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 14.6969 + 8.48528i 0.718851 + 0.415029i
$$419$$ 10.3923i 0.507697i 0.967244 + 0.253849i $$0.0816965\pi$$
−0.967244 + 0.253849i $$0.918303\pi$$
$$420$$ 0 0
$$421$$ 24.2487i 1.18181i 0.806741 + 0.590905i $$0.201229\pi$$
−0.806741 + 0.590905i $$0.798771\pi$$
$$422$$ 17.1464 29.6985i 0.834675 1.44570i
$$423$$ 0 0
$$424$$ 16.0000 0.777029
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 8.48528i 0.410632i
$$428$$ −2.44949 + 1.41421i −0.118401 + 0.0683586i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ −4.89898 −0.235430 −0.117715 0.993047i $$-0.537557\pi$$
−0.117715 + 0.993047i $$0.537557\pi$$
$$434$$ 12.0000 + 6.92820i 0.576018 + 0.332564i
$$435$$ 0 0
$$436$$ −6.00000 + 3.46410i −0.287348 + 0.165900i
$$437$$ 8.48528i 0.405906i
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 1.41421i 0.0671913i −0.999436 0.0335957i $$-0.989304\pi$$
0.999436 0.0335957i $$-0.0106958\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −27.0000 15.5885i −1.27849 0.738135i
$$447$$ 0 0
$$448$$ −19.5959 −0.925820
$$449$$ −12.0000 −0.566315 −0.283158 0.959073i $$-0.591382\pi$$
−0.283158 + 0.959073i $$0.591382\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 1.00000 1.73205i 0.0469323 0.0812892i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −19.5959 −0.916658 −0.458329 0.888783i $$-0.651552\pi$$
−0.458329 + 0.888783i $$0.651552\pi$$
$$458$$ 19.5959 33.9411i 0.915657 1.58596i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 13.8564i 0.645357i 0.946509 + 0.322679i $$0.104583\pi$$
−0.946509 + 0.322679i $$0.895417\pi$$
$$462$$ 0 0
$$463$$ −17.1464 −0.796862 −0.398431 0.917198i $$-0.630445\pi$$
−0.398431 + 0.917198i $$0.630445\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 18.0000 + 10.3923i 0.833834 + 0.481414i
$$467$$ 7.07107i 0.327210i −0.986526 0.163605i $$-0.947688\pi$$
0.986526 0.163605i $$-0.0523123\pi$$
$$468$$ 0 0
$$469$$ 10.3923i 0.479872i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 29.3939 1.35296
$$473$$ −14.6969 −0.675766
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 12.0000 + 20.7846i 0.550019 + 0.952661i
$$477$$ 0 0
$$478$$ −14.6969 8.48528i −0.672222 0.388108i
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 4.89898 + 2.82843i 0.223142 + 0.128831i
$$483$$ 0 0
$$484$$ −1.00000 1.73205i −0.0454545 0.0787296i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −7.34847 −0.332991 −0.166495 0.986042i $$-0.553245\pi$$
−0.166495 + 0.986042i $$0.553245\pi$$
$$488$$ −9.79796 −0.443533
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 24.2487i 1.09433i 0.837025 + 0.547165i $$0.184293\pi$$
−0.837025 + 0.547165i $$0.815707\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −8.00000 + 13.8564i −0.359211 + 0.622171i
$$497$$ 29.3939 1.31850
$$498$$ 0 0
$$499$$ 17.3205i 0.775372i 0.921791 + 0.387686i $$0.126726\pi$$
−0.921791 + 0.387686i $$0.873274\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 7.34847 12.7279i 0.327978 0.568075i
$$503$$ −12.2474 −0.546087 −0.273043 0.962002i $$-0.588030\pi$$
−0.273043 + 0.962002i $$0.588030\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 6.00000 10.3923i 0.266733 0.461994i
$$507$$ 0 0
$$508$$ −17.1464 29.6985i −0.760750 1.31766i
$$509$$ 27.7128i 1.22835i 0.789170 + 0.614174i $$0.210511\pi$$
−0.789170 + 0.614174i $$0.789489\pi$$
$$510$$ 0 0
$$511$$ 12.0000 0.530849
$$512$$ 22.6274i 1.00000i
$$513$$ 0 0
$$514$$ 12.0000 + 6.92820i 0.529297 + 0.305590i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 25.4558i 1.11955i
$$518$$ −14.6969 + 25.4558i −0.645746 + 1.11847i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ 12.7279i 0.556553i 0.960501 + 0.278277i $$0.0897632\pi$$
−0.960501 + 0.278277i $$0.910237\pi$$
$$524$$ 6.00000 3.46410i 0.262111 0.151330i
$$525$$ 0 0
$$526$$ −9.00000 5.19615i −0.392419 0.226563i
$$527$$ 19.5959 0.853612
$$528$$ 0 0
$$529$$ −17.0000 −0.739130
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 14.6969 8.48528i 0.637193 0.367884i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −12.0000 −0.518321
$$537$$ 0 0
$$538$$ 7.34847 12.7279i 0.316815 0.548740i
$$539$$ 3.46410i 0.149209i
$$540$$ 0 0
$$541$$ 41.5692i 1.78720i −0.448864 0.893600i $$-0.648171\pi$$
0.448864 0.893600i $$-0.351829\pi$$
$$542$$ 24.4949 + 14.1421i 1.05215 + 0.607457i
$$543$$ 0 0
$$544$$ −24.0000 + 13.8564i −1.02899 + 0.594089i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 4.24264i 0.181402i −0.995878 0.0907011i $$-0.971089\pi$$
0.995878 0.0907011i $$-0.0289108\pi$$
$$548$$ −9.79796 16.9706i −0.418548 0.724947i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 9.79796 0.416652
$$554$$ 18.0000 31.1769i 0.764747 1.32458i
$$555$$ 0 0
$$556$$ 18.0000 10.3923i 0.763370 0.440732i
$$557$$ 14.1421i 0.599222i −0.954062 0.299611i $$-0.903143\pi$$
0.954062 0.299611i $$-0.0968568\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 14.6969 + 8.48528i 0.619953 + 0.357930i
$$563$$ 41.0122i 1.72846i 0.503099 + 0.864229i $$0.332193\pi$$
−0.503099 + 0.864229i $$0.667807\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 15.0000 25.9808i 0.630497 1.09205i
$$567$$ 0 0
$$568$$ 33.9411i 1.42414i
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ 3.46410i 0.144968i −0.997370 0.0724841i $$-0.976907\pi$$
0.997370 0.0724841i $$-0.0230926\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 29.3939 1.22368 0.611842 0.790980i $$-0.290429\pi$$
0.611842 + 0.790980i $$0.290429\pi$$
$$578$$ 8.57321 + 4.94975i 0.356599 + 0.205882i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 24.2487i 1.00601i
$$582$$ 0 0
$$583$$ 19.5959 0.811580
$$584$$ 13.8564i 0.573382i
$$585$$ 0 0
$$586$$ −14.0000 + 24.2487i −0.578335 + 1.00171i
$$587$$ 9.89949i 0.408596i 0.978909 + 0.204298i $$0.0654911\pi$$
−0.978909 + 0.204298i $$0.934509\pi$$
$$588$$ 0 0
$$589$$ 13.8564i 0.570943i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −29.3939 16.9706i −1.20808 0.697486i
$$593$$ −9.79796 −0.402354 −0.201177 0.979555i $$-0.564477\pi$$
−0.201177 + 0.979555i $$0.564477\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 30.0000 17.3205i 1.22885 0.709476i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 12.0000 0.490307 0.245153 0.969484i $$-0.421162\pi$$
0.245153 + 0.969484i $$0.421162\pi$$
$$600$$ 0 0
$$601$$ −28.0000 −1.14214 −0.571072 0.820900i $$-0.693472\pi$$
−0.571072 + 0.820900i $$0.693472\pi$$
$$602$$ −7.34847 + 12.7279i −0.299501 + 0.518751i
$$603$$ 0 0
$$604$$ −16.0000 27.7128i −0.651031 1.12762i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 7.34847 0.298265 0.149133 0.988817i $$-0.452352\pi$$
0.149133 + 0.988817i $$0.452352\pi$$
$$608$$ 9.79796 + 16.9706i 0.397360 + 0.688247i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 33.9411i 1.37087i −0.728134 0.685435i $$-0.759612\pi$$
0.728134 0.685435i $$-0.240388\pi$$
$$614$$ 21.0000 36.3731i 0.847491 1.46790i
$$615$$ 0 0
$$616$$ −24.0000 −0.966988
$$617$$ −34.2929 −1.38058 −0.690289 0.723534i $$-0.742517\pi$$
−0.690289 + 0.723534i $$0.742517\pi$$
$$618$$ 0 0
$$619$$ 10.3923i 0.417702i 0.977947 + 0.208851i $$0.0669724\pi$$
−0.977947 + 0.208851i $$0.933028\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 29.3939 + 16.9706i 1.17859 + 0.680458i
$$623$$ 14.6969 0.588820
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 12.0000 + 6.92820i 0.479616 + 0.276907i
$$627$$ 0 0
$$628$$ 14.6969 8.48528i 0.586472 0.338600i
$$629$$ 41.5692i 1.65747i
$$630$$ 0 0
$$631$$ 16.0000 0.636950 0.318475 0.947931i $$-0.396829\pi$$
0.318475 + 0.947931i $$0.396829\pi$$
$$632$$ 11.3137i 0.450035i
$$633$$ 0 0
$$634$$ 20.0000 34.6410i 0.794301 1.37577i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −12.0000 −0.473972 −0.236986 0.971513i $$-0.576159\pi$$
−0.236986 + 0.971513i $$0.576159\pi$$
$$642$$ 0 0
$$643$$ 29.6985i 1.17119i 0.810602 + 0.585597i $$0.199140\pi$$
−0.810602 + 0.585597i $$0.800860\pi$$
$$644$$ −6.00000 10.3923i −0.236433 0.409514i
$$645$$ 0 0
$$646$$ 12.0000 20.7846i 0.472134 0.817760i
$$647$$ −12.2474 −0.481497 −0.240748 0.970588i $$-0.577393\pi$$
−0.240748 + 0.970588i $$0.577393\pi$$
$$648$$ 0 0
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −36.7423 + 21.2132i −1.43894 + 0.830773i
$$653$$ 11.3137i 0.442740i −0.975190 0.221370i $$-0.928947\pi$$
0.975190 0.221370i $$-0.0710528\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ −22.0454 12.7279i −0.859419 0.496186i
$$659$$ 24.2487i 0.944596i 0.881439 + 0.472298i $$0.156575\pi$$
−0.881439 + 0.472298i $$0.843425\pi$$
$$660$$ 0 0
$$661$$ 10.3923i 0.404214i −0.979363 0.202107i $$-0.935221\pi$$
0.979363 0.202107i $$-0.0647788\pi$$
$$662$$ −22.0454 + 38.1838i −0.856819 + 1.48405i
$$663$$ 0 0
$$664$$ −28.0000 −1.08661
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 12.2474 + 21.2132i 0.473868 + 0.820763i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ 34.2929 1.32189 0.660946 0.750433i $$-0.270155\pi$$
0.660946 + 0.750433i $$0.270155\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 13.0000 + 22.5167i 0.500000 + 0.866025i
$$677$$ 22.6274i 0.869642i 0.900517 + 0.434821i $$0.143188\pi$$
−0.900517 + 0.434821i $$0.856812\pi$$
$$678$$ 0 0
$$679$$ 12.0000 0.460518
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −9.79796 + 16.9706i −0.375183 + 0.649836i
$$683$$ 15.5563i 0.595247i −0.954683 0.297624i $$-0.903806\pi$$
0.954683 0.297624i $$-0.0961940\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −24.0000 13.8564i −0.916324 0.529040i
$$687$$ 0 0
$$688$$ −14.6969 8.48528i −0.560316 0.323498i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 3.46410i 0.131781i 0.997827 + 0.0658903i $$0.0209887\pi$$
−0.997827 + 0.0658903i $$0.979011\pi$$
$$692$$ 4.89898 2.82843i 0.186231 0.107521i
$$693$$ 0 0
$$694$$ −11.0000 + 19.0526i −0.417554 + 0.723225i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −9.79796 + 16.9706i −0.370858 + 0.642345i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 24.2487i 0.915861i −0.888988 0.457931i $$-0.848591\pi$$
0.888988 0.457931i $$-0.151409\pi$$
$$702$$ 0 0
$$703$$ 29.3939 1.10861
$$704$$ 27.7128i 1.04447i
$$705$$ 0 0
$$706$$ 36.0000 + 20.7846i 1.35488 + 0.782239i
$$707$$ 33.9411i 1.27649i
$$708$$ 0 0
$$709$$ 41.5692i 1.56116i 0.625053 + 0.780582i $$0.285077\pi$$
−0.625053 + 0.780582i $$0.714923\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 16.9706i 0.635999i
$$713$$ −9.79796 −0.366936
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 6.00000 3.46410i 0.224231 0.129460i
$$717$$ 0 0
$$718$$ 29.3939 + 16.9706i 1.09697 + 0.633336i
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 0 0
$$721$$ −18.0000 −0.670355
$$722$$ 8.57321 + 4.94975i 0.319062 + 0.184211i
$$723$$ 0 0
$$724$$ 24.0000 13.8564i 0.891953 0.514969i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −46.5403 −1.72608 −0.863042 0.505132i $$-0.831444\pi$$
−0.863042 + 0.505132i $$0.831444\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 20.7846i 0.768747i
$$732$$ 0 0
$$733$$ 42.4264i 1.56706i 0.621357 + 0.783528i $$0.286582\pi$$
−0.621357 + 0.783528i $$0.713418\pi$$
$$734$$ 15.0000 + 8.66025i 0.553660 + 0.319656i
$$735$$ 0 0
$$736$$ 12.0000 6.92820i 0.442326 0.255377i
$$737$$ −14.6969 −0.541369
$$738$$ 0 0
$$739$$ 3.46410i 0.127429i 0.997968 + 0.0637145i $$0.0202947\pi$$
−0.997968 + 0.0637145i $$0.979705\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 9.79796 16.9706i 0.359694 0.623009i
$$743$$ 51.4393 1.88712 0.943562 0.331195i $$-0.107452\pi$$
0.943562 + 0.331195i $$0.107452\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 6.00000 10.3923i 0.219676 0.380489i
$$747$$ 0 0
$$748$$ −29.3939 + 16.9706i −1.07475 + 0.620505i
$$749$$ 3.46410i 0.126576i
$$750$$ 0 0
$$751$$ −32.0000 −1.16770 −0.583848 0.811863i $$-0.698454\pi$$
−0.583848 + 0.811863i $$0.698454\pi$$
$$752$$ 14.6969 25.4558i 0.535942 0.928279i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 25.4558i 0.925208i 0.886565 + 0.462604i $$0.153085\pi$$
−0.886565 + 0.462604i $$0.846915\pi$$
$$758$$ 17.1464 29.6985i 0.622786 1.07870i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 0 0
$$763$$ 8.48528i 0.307188i
$$764$$ −24.0000 41.5692i −0.868290 1.50392i
$$765$$ 0 0
$$766$$ −33.0000 19.0526i −1.19234 0.688397i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 24.4949 + 42.4264i 0.881591 + 1.52696i
$$773$$ 28.2843i 1.01731i −0.860969 0.508657i $$-0.830142\pi$$
0.860969 0.508657i $$-0.169858\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 13.8564i 0.497416i
$$777$$ 0 0
$$778$$ 2.44949 4.24264i 0.0878185 0.152106i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 41.5692i 1.48746i
$$782$$ −14.6969 8.48528i −0.525561 0.303433i
$$783$$ 0 0
$$784$$ 2.00000 3.46410i 0.0714286 0.123718i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 21.2132i 0.756169i 0.925771 + 0.378085i $$0.123417\pi$$
−0.925771 + 0.378085i $$0.876583\pi$$
$$788$$ 9.79796 5.65685i 0.349038 0.201517i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −12.0000 + 20.7846i −0.425864 + 0.737618i
$$795$$ 0 0
$$796$$ −4.00000 6.92820i −0.141776 0.245564i
$$797$$ 39.5980i 1.40263i 0.712850 + 0.701316i $$0.247404\pi$$
−0.712850 + 0.701316i $$0.752596\pi$$
$$798$$ 0 0
$$799$$