# Properties

 Label 1800.2.d.l.1549.4 Level $1800$ Weight $2$ Character 1800.1549 Analytic conductor $14.373$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1800.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.3730723638$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ 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 1549.4 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1800.1549 Dual form 1800.2.d.l.1549.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +0.732051i q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$$ $$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +0.732051i q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{11} +3.46410 q^{13} +(-1.00000 + 0.267949i) q^{14} +(2.00000 - 3.46410i) q^{16} -3.46410i q^{17} +0.535898i q^{19} +(2.73205 - 0.732051i) q^{22} -6.19615i q^{23} +(1.26795 + 4.73205i) q^{26} +(-0.732051 - 1.26795i) q^{28} -6.92820i q^{29} -5.46410 q^{31} +(5.46410 + 1.46410i) q^{32} +(4.73205 - 1.26795i) q^{34} -2.00000 q^{37} +(-0.732051 + 0.196152i) q^{38} -1.46410 q^{41} +5.26795 q^{43} +(2.00000 + 3.46410i) q^{44} +(8.46410 - 2.26795i) q^{46} -3.26795i q^{47} +6.46410 q^{49} +(-6.00000 + 3.46410i) q^{52} +11.4641 q^{53} +(1.46410 - 1.46410i) q^{56} +(9.46410 - 2.53590i) q^{58} +7.46410i q^{59} +8.92820i q^{61} +(-2.00000 - 7.46410i) q^{62} +8.00000i q^{64} +10.7321 q^{67} +(3.46410 + 6.00000i) q^{68} -5.46410 q^{71} -7.46410i q^{73} +(-0.732051 - 2.73205i) q^{74} +(-0.535898 - 0.928203i) q^{76} +1.46410 q^{77} +1.07180 q^{79} +(-0.535898 - 2.00000i) q^{82} +1.26795 q^{83} +(1.92820 + 7.19615i) q^{86} +(-4.00000 + 4.00000i) q^{88} +8.92820 q^{89} +2.53590i q^{91} +(6.19615 + 10.7321i) q^{92} +(4.46410 - 1.19615i) q^{94} -14.3923i q^{97} +(2.36603 + 8.83013i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 8 q^{8} + O(q^{10})$$ $$4 q - 2 q^{2} - 8 q^{8} - 4 q^{14} + 8 q^{16} + 4 q^{22} + 12 q^{26} + 4 q^{28} - 8 q^{31} + 8 q^{32} + 12 q^{34} - 8 q^{37} + 4 q^{38} + 8 q^{41} + 28 q^{43} + 8 q^{44} + 20 q^{46} + 12 q^{49} - 24 q^{52} + 32 q^{53} - 8 q^{56} + 24 q^{58} - 8 q^{62} + 36 q^{67} - 8 q^{71} + 4 q^{74} - 16 q^{76} - 8 q^{77} + 32 q^{79} - 16 q^{82} + 12 q^{83} - 20 q^{86} - 16 q^{88} + 8 q^{89} + 4 q^{92} + 4 q^{94} + 6 q^{98} + O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.366025 + 1.36603i 0.258819 + 0.965926i
$$3$$ 0 0
$$4$$ −1.73205 + 1.00000i −0.866025 + 0.500000i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0.732051i 0.276689i 0.990384 + 0.138345i $$0.0441781\pi$$
−0.990384 + 0.138345i $$0.955822\pi$$
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.00000i 0.603023i −0.953463 0.301511i $$-0.902509\pi$$
0.953463 0.301511i $$-0.0974911\pi$$
$$12$$ 0 0
$$13$$ 3.46410 0.960769 0.480384 0.877058i $$-0.340497\pi$$
0.480384 + 0.877058i $$0.340497\pi$$
$$14$$ −1.00000 + 0.267949i −0.267261 + 0.0716124i
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ 3.46410i 0.840168i −0.907485 0.420084i $$-0.862001\pi$$
0.907485 0.420084i $$-0.137999\pi$$
$$18$$ 0 0
$$19$$ 0.535898i 0.122944i 0.998109 + 0.0614718i $$0.0195794\pi$$
−0.998109 + 0.0614718i $$0.980421\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 2.73205 0.732051i 0.582475 0.156074i
$$23$$ 6.19615i 1.29199i −0.763343 0.645994i $$-0.776443\pi$$
0.763343 0.645994i $$-0.223557\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 1.26795 + 4.73205i 0.248665 + 0.928032i
$$27$$ 0 0
$$28$$ −0.732051 1.26795i −0.138345 0.239620i
$$29$$ 6.92820i 1.28654i −0.765641 0.643268i $$-0.777578\pi$$
0.765641 0.643268i $$-0.222422\pi$$
$$30$$ 0 0
$$31$$ −5.46410 −0.981382 −0.490691 0.871334i $$-0.663256\pi$$
−0.490691 + 0.871334i $$0.663256\pi$$
$$32$$ 5.46410 + 1.46410i 0.965926 + 0.258819i
$$33$$ 0 0
$$34$$ 4.73205 1.26795i 0.811540 0.217451i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −0.732051 + 0.196152i −0.118754 + 0.0318201i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.46410 −0.228654 −0.114327 0.993443i $$-0.536471\pi$$
−0.114327 + 0.993443i $$0.536471\pi$$
$$42$$ 0 0
$$43$$ 5.26795 0.803355 0.401677 0.915781i $$-0.368427\pi$$
0.401677 + 0.915781i $$0.368427\pi$$
$$44$$ 2.00000 + 3.46410i 0.301511 + 0.522233i
$$45$$ 0 0
$$46$$ 8.46410 2.26795i 1.24796 0.334391i
$$47$$ 3.26795i 0.476679i −0.971182 0.238340i $$-0.923397\pi$$
0.971182 0.238340i $$-0.0766032\pi$$
$$48$$ 0 0
$$49$$ 6.46410 0.923443
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −6.00000 + 3.46410i −0.832050 + 0.480384i
$$53$$ 11.4641 1.57472 0.787358 0.616496i $$-0.211449\pi$$
0.787358 + 0.616496i $$0.211449\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.46410 1.46410i 0.195649 0.195649i
$$57$$ 0 0
$$58$$ 9.46410 2.53590i 1.24270 0.332980i
$$59$$ 7.46410i 0.971743i 0.874030 + 0.485872i $$0.161498\pi$$
−0.874030 + 0.485872i $$0.838502\pi$$
$$60$$ 0 0
$$61$$ 8.92820i 1.14314i 0.820554 + 0.571570i $$0.193665\pi$$
−0.820554 + 0.571570i $$0.806335\pi$$
$$62$$ −2.00000 7.46410i −0.254000 0.947942i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 10.7321 1.31113 0.655564 0.755139i $$-0.272431\pi$$
0.655564 + 0.755139i $$0.272431\pi$$
$$68$$ 3.46410 + 6.00000i 0.420084 + 0.727607i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −5.46410 −0.648470 −0.324235 0.945977i $$-0.605107\pi$$
−0.324235 + 0.945977i $$0.605107\pi$$
$$72$$ 0 0
$$73$$ 7.46410i 0.873607i −0.899557 0.436804i $$-0.856111\pi$$
0.899557 0.436804i $$-0.143889\pi$$
$$74$$ −0.732051 2.73205i −0.0850992 0.317594i
$$75$$ 0 0
$$76$$ −0.535898 0.928203i −0.0614718 0.106472i
$$77$$ 1.46410 0.166850
$$78$$ 0 0
$$79$$ 1.07180 0.120587 0.0602933 0.998181i $$-0.480796\pi$$
0.0602933 + 0.998181i $$0.480796\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −0.535898 2.00000i −0.0591801 0.220863i
$$83$$ 1.26795 0.139176 0.0695878 0.997576i $$-0.477832\pi$$
0.0695878 + 0.997576i $$0.477832\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.92820 + 7.19615i 0.207924 + 0.775981i
$$87$$ 0 0
$$88$$ −4.00000 + 4.00000i −0.426401 + 0.426401i
$$89$$ 8.92820 0.946388 0.473194 0.880958i $$-0.343101\pi$$
0.473194 + 0.880958i $$0.343101\pi$$
$$90$$ 0 0
$$91$$ 2.53590i 0.265834i
$$92$$ 6.19615 + 10.7321i 0.645994 + 1.11889i
$$93$$ 0 0
$$94$$ 4.46410 1.19615i 0.460437 0.123374i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 14.3923i 1.46132i −0.682743 0.730659i $$-0.739213\pi$$
0.682743 0.730659i $$-0.260787\pi$$
$$98$$ 2.36603 + 8.83013i 0.239005 + 0.891978i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 2.92820i 0.291367i 0.989331 + 0.145684i $$0.0465381\pi$$
−0.989331 + 0.145684i $$0.953462\pi$$
$$102$$ 0 0
$$103$$ 15.6603i 1.54305i −0.636199 0.771525i $$-0.719494\pi$$
0.636199 0.771525i $$-0.280506\pi$$
$$104$$ −6.92820 6.92820i −0.679366 0.679366i
$$105$$ 0 0
$$106$$ 4.19615 + 15.6603i 0.407566 + 1.52106i
$$107$$ −2.73205 −0.264117 −0.132059 0.991242i $$-0.542159\pi$$
−0.132059 + 0.991242i $$0.542159\pi$$
$$108$$ 0 0
$$109$$ 16.9282i 1.62143i 0.585443 + 0.810714i $$0.300921\pi$$
−0.585443 + 0.810714i $$0.699079\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 2.53590 + 1.46410i 0.239620 + 0.138345i
$$113$$ 12.9282i 1.21618i −0.793867 0.608092i $$-0.791935\pi$$
0.793867 0.608092i $$-0.208065\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 6.92820 + 12.0000i 0.643268 + 1.11417i
$$117$$ 0 0
$$118$$ −10.1962 + 2.73205i −0.938632 + 0.251506i
$$119$$ 2.53590 0.232465
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ −12.1962 + 3.26795i −1.10419 + 0.295866i
$$123$$ 0 0
$$124$$ 9.46410 5.46410i 0.849901 0.490691i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 16.7321i 1.48473i 0.669996 + 0.742365i $$0.266296\pi$$
−0.669996 + 0.742365i $$0.733704\pi$$
$$128$$ −10.9282 + 2.92820i −0.965926 + 0.258819i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 19.8564i 1.73486i −0.497557 0.867431i $$-0.665770\pi$$
0.497557 0.867431i $$-0.334230\pi$$
$$132$$ 0 0
$$133$$ −0.392305 −0.0340171
$$134$$ 3.92820 + 14.6603i 0.339345 + 1.26645i
$$135$$ 0 0
$$136$$ −6.92820 + 6.92820i −0.594089 + 0.594089i
$$137$$ 4.92820i 0.421045i −0.977589 0.210522i $$-0.932484\pi$$
0.977589 0.210522i $$-0.0675165\pi$$
$$138$$ 0 0
$$139$$ 0.535898i 0.0454543i −0.999742 0.0227272i $$-0.992765\pi$$
0.999742 0.0227272i $$-0.00723490\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −2.00000 7.46410i −0.167836 0.626373i
$$143$$ 6.92820i 0.579365i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 10.1962 2.73205i 0.843840 0.226106i
$$147$$ 0 0
$$148$$ 3.46410 2.00000i 0.284747 0.164399i
$$149$$ 7.85641i 0.643622i 0.946804 + 0.321811i $$0.104292\pi$$
−0.946804 + 0.321811i $$0.895708\pi$$
$$150$$ 0 0
$$151$$ −12.3923 −1.00847 −0.504236 0.863566i $$-0.668226\pi$$
−0.504236 + 0.863566i $$0.668226\pi$$
$$152$$ 1.07180 1.07180i 0.0869342 0.0869342i
$$153$$ 0 0
$$154$$ 0.535898 + 2.00000i 0.0431839 + 0.161165i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −3.07180 −0.245156 −0.122578 0.992459i $$-0.539116\pi$$
−0.122578 + 0.992459i $$0.539116\pi$$
$$158$$ 0.392305 + 1.46410i 0.0312101 + 0.116478i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.53590 0.357479
$$162$$ 0 0
$$163$$ 0.196152 0.0153638 0.00768192 0.999970i $$-0.497555\pi$$
0.00768192 + 0.999970i $$0.497555\pi$$
$$164$$ 2.53590 1.46410i 0.198020 0.114327i
$$165$$ 0 0
$$166$$ 0.464102 + 1.73205i 0.0360213 + 0.134433i
$$167$$ 9.80385i 0.758645i 0.925265 + 0.379322i $$0.123843\pi$$
−0.925265 + 0.379322i $$0.876157\pi$$
$$168$$ 0 0
$$169$$ −1.00000 −0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −9.12436 + 5.26795i −0.695726 + 0.401677i
$$173$$ 2.00000 0.152057 0.0760286 0.997106i $$-0.475776\pi$$
0.0760286 + 0.997106i $$0.475776\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −6.92820 4.00000i −0.522233 0.301511i
$$177$$ 0 0
$$178$$ 3.26795 + 12.1962i 0.244943 + 0.914140i
$$179$$ 8.53590i 0.638003i 0.947754 + 0.319002i $$0.103348\pi$$
−0.947754 + 0.319002i $$0.896652\pi$$
$$180$$ 0 0
$$181$$ 16.0000i 1.18927i −0.803996 0.594635i $$-0.797296\pi$$
0.803996 0.594635i $$-0.202704\pi$$
$$182$$ −3.46410 + 0.928203i −0.256776 + 0.0688030i
$$183$$ 0 0
$$184$$ −12.3923 + 12.3923i −0.913573 + 0.913573i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −6.92820 −0.506640
$$188$$ 3.26795 + 5.66025i 0.238340 + 0.412816i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −15.3205 −1.10855 −0.554277 0.832333i $$-0.687005\pi$$
−0.554277 + 0.832333i $$0.687005\pi$$
$$192$$ 0 0
$$193$$ 0.535898i 0.0385748i −0.999814 0.0192874i $$-0.993860\pi$$
0.999814 0.0192874i $$-0.00613975\pi$$
$$194$$ 19.6603 5.26795i 1.41152 0.378217i
$$195$$ 0 0
$$196$$ −11.1962 + 6.46410i −0.799725 + 0.461722i
$$197$$ 19.4641 1.38676 0.693380 0.720572i $$-0.256121\pi$$
0.693380 + 0.720572i $$0.256121\pi$$
$$198$$ 0 0
$$199$$ 1.85641 0.131597 0.0657986 0.997833i $$-0.479041\pi$$
0.0657986 + 0.997833i $$0.479041\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −4.00000 + 1.07180i −0.281439 + 0.0754114i
$$203$$ 5.07180 0.355970
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 21.3923 5.73205i 1.49047 0.399371i
$$207$$ 0 0
$$208$$ 6.92820 12.0000i 0.480384 0.832050i
$$209$$ 1.07180 0.0741377
$$210$$ 0 0
$$211$$ 26.7846i 1.84393i −0.387275 0.921964i $$-0.626584\pi$$
0.387275 0.921964i $$-0.373416\pi$$
$$212$$ −19.8564 + 11.4641i −1.36374 + 0.787358i
$$213$$ 0 0
$$214$$ −1.00000 3.73205i −0.0683586 0.255118i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 4.00000i 0.271538i
$$218$$ −23.1244 + 6.19615i −1.56618 + 0.419656i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 12.0000i 0.807207i
$$222$$ 0 0
$$223$$ 5.80385i 0.388654i 0.980937 + 0.194327i $$0.0622523\pi$$
−0.980937 + 0.194327i $$0.937748\pi$$
$$224$$ −1.07180 + 4.00000i −0.0716124 + 0.267261i
$$225$$ 0 0
$$226$$ 17.6603 4.73205i 1.17474 0.314771i
$$227$$ −10.0526 −0.667212 −0.333606 0.942713i $$-0.608265\pi$$
−0.333606 + 0.942713i $$0.608265\pi$$
$$228$$ 0 0
$$229$$ 4.00000i 0.264327i −0.991228 0.132164i $$-0.957808\pi$$
0.991228 0.132164i $$-0.0421925\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −13.8564 + 13.8564i −0.909718 + 0.909718i
$$233$$ 5.32051i 0.348558i −0.984696 0.174279i $$-0.944241\pi$$
0.984696 0.174279i $$-0.0557595\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −7.46410 12.9282i −0.485872 0.841554i
$$237$$ 0 0
$$238$$ 0.928203 + 3.46410i 0.0601665 + 0.224544i
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 0 0
$$241$$ 16.3923 1.05592 0.527961 0.849269i $$-0.322957\pi$$
0.527961 + 0.849269i $$0.322957\pi$$
$$242$$ 2.56218 + 9.56218i 0.164703 + 0.614680i
$$243$$ 0 0
$$244$$ −8.92820 15.4641i −0.571570 0.989988i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.85641i 0.118120i
$$248$$ 10.9282 + 10.9282i 0.693942 + 0.693942i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 24.9282i 1.57345i 0.617301 + 0.786727i $$0.288226\pi$$
−0.617301 + 0.786727i $$0.711774\pi$$
$$252$$ 0 0
$$253$$ −12.3923 −0.779098
$$254$$ −22.8564 + 6.12436i −1.43414 + 0.384276i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 2.00000i 0.124757i 0.998053 + 0.0623783i $$0.0198685\pi$$
−0.998053 + 0.0623783i $$0.980131\pi$$
$$258$$ 0 0
$$259$$ 1.46410i 0.0909748i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 27.1244 7.26795i 1.67575 0.449015i
$$263$$ 11.6603i 0.719002i −0.933145 0.359501i $$-0.882947\pi$$
0.933145 0.359501i $$-0.117053\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −0.143594 0.535898i −0.00880428 0.0328580i
$$267$$ 0 0
$$268$$ −18.5885 + 10.7321i −1.13547 + 0.655564i
$$269$$ 8.92820i 0.544362i 0.962246 + 0.272181i $$0.0877450\pi$$
−0.962246 + 0.272181i $$0.912255\pi$$
$$270$$ 0 0
$$271$$ −19.3205 −1.17364 −0.586819 0.809718i $$-0.699620\pi$$
−0.586819 + 0.809718i $$0.699620\pi$$
$$272$$ −12.0000 6.92820i −0.727607 0.420084i
$$273$$ 0 0
$$274$$ 6.73205 1.80385i 0.406698 0.108974i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 0.732051 0.196152i 0.0439055 0.0117644i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −10.5359 −0.628519 −0.314260 0.949337i $$-0.601756\pi$$
−0.314260 + 0.949337i $$0.601756\pi$$
$$282$$ 0 0
$$283$$ 9.66025 0.574242 0.287121 0.957894i $$-0.407302\pi$$
0.287121 + 0.957894i $$0.407302\pi$$
$$284$$ 9.46410 5.46410i 0.561591 0.324235i
$$285$$ 0 0
$$286$$ 9.46410 2.53590i 0.559624 0.149951i
$$287$$ 1.07180i 0.0632662i
$$288$$ 0 0
$$289$$ 5.00000 0.294118
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 7.46410 + 12.9282i 0.436804 + 0.756566i
$$293$$ −15.8564 −0.926341 −0.463171 0.886269i $$-0.653288\pi$$
−0.463171 + 0.886269i $$0.653288\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 4.00000 + 4.00000i 0.232495 + 0.232495i
$$297$$ 0 0
$$298$$ −10.7321 + 2.87564i −0.621691 + 0.166582i
$$299$$ 21.4641i 1.24130i
$$300$$ 0 0
$$301$$ 3.85641i 0.222280i
$$302$$ −4.53590 16.9282i −0.261012 0.974109i
$$303$$ 0 0
$$304$$ 1.85641 + 1.07180i 0.106472 + 0.0614718i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −24.9808 −1.42573 −0.712864 0.701303i $$-0.752602\pi$$
−0.712864 + 0.701303i $$0.752602\pi$$
$$308$$ −2.53590 + 1.46410i −0.144496 + 0.0834249i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −31.3205 −1.77602 −0.888012 0.459821i $$-0.847914\pi$$
−0.888012 + 0.459821i $$0.847914\pi$$
$$312$$ 0 0
$$313$$ 4.14359i 0.234210i 0.993120 + 0.117105i $$0.0373614\pi$$
−0.993120 + 0.117105i $$0.962639\pi$$
$$314$$ −1.12436 4.19615i −0.0634511 0.236803i
$$315$$ 0 0
$$316$$ −1.85641 + 1.07180i −0.104431 + 0.0602933i
$$317$$ −8.53590 −0.479424 −0.239712 0.970844i $$-0.577053\pi$$
−0.239712 + 0.970844i $$0.577053\pi$$
$$318$$ 0 0
$$319$$ −13.8564 −0.775810
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 1.66025 + 6.19615i 0.0925223 + 0.345298i
$$323$$ 1.85641 0.103293
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0.0717968 + 0.267949i 0.00397646 + 0.0148403i
$$327$$ 0 0
$$328$$ 2.92820 + 2.92820i 0.161683 + 0.161683i
$$329$$ 2.39230 0.131892
$$330$$ 0 0
$$331$$ 14.0000i 0.769510i 0.923019 + 0.384755i $$0.125714\pi$$
−0.923019 + 0.384755i $$0.874286\pi$$
$$332$$ −2.19615 + 1.26795i −0.120530 + 0.0695878i
$$333$$ 0 0
$$334$$ −13.3923 + 3.58846i −0.732794 + 0.196352i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 19.8564i 1.08165i −0.841136 0.540824i $$-0.818113\pi$$
0.841136 0.540824i $$-0.181887\pi$$
$$338$$ −0.366025 1.36603i −0.0199092 0.0743020i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 10.9282i 0.591795i
$$342$$ 0 0
$$343$$ 9.85641i 0.532196i
$$344$$ −10.5359 10.5359i −0.568058 0.568058i
$$345$$ 0 0
$$346$$ 0.732051 + 2.73205i 0.0393553 + 0.146876i
$$347$$ 1.66025 0.0891271 0.0445636 0.999007i $$-0.485810\pi$$
0.0445636 + 0.999007i $$0.485810\pi$$
$$348$$ 0 0
$$349$$ 28.0000i 1.49881i −0.662114 0.749403i $$-0.730341\pi$$
0.662114 0.749403i $$-0.269659\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 2.92820 10.9282i 0.156074 0.582475i
$$353$$ 12.9282i 0.688099i 0.938952 + 0.344049i $$0.111799\pi$$
−0.938952 + 0.344049i $$0.888201\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −15.4641 + 8.92820i −0.819596 + 0.473194i
$$357$$ 0 0
$$358$$ −11.6603 + 3.12436i −0.616264 + 0.165127i
$$359$$ 18.9282 0.998992 0.499496 0.866316i $$-0.333518\pi$$
0.499496 + 0.866316i $$0.333518\pi$$
$$360$$ 0 0
$$361$$ 18.7128 0.984885
$$362$$ 21.8564 5.85641i 1.14875 0.307806i
$$363$$ 0 0
$$364$$ −2.53590 4.39230i −0.132917 0.230219i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 2.87564i 0.150107i 0.997179 + 0.0750537i $$0.0239128\pi$$
−0.997179 + 0.0750537i $$0.976087\pi$$
$$368$$ −21.4641 12.3923i −1.11889 0.645994i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 8.39230i 0.435707i
$$372$$ 0 0
$$373$$ 25.7128 1.33136 0.665679 0.746238i $$-0.268142\pi$$
0.665679 + 0.746238i $$0.268142\pi$$
$$374$$ −2.53590 9.46410i −0.131128 0.489377i
$$375$$ 0 0
$$376$$ −6.53590 + 6.53590i −0.337063 + 0.337063i
$$377$$ 24.0000i 1.23606i
$$378$$ 0 0
$$379$$ 36.2487i 1.86197i −0.365056 0.930986i $$-0.618950\pi$$
0.365056 0.930986i $$-0.381050\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −5.60770 20.9282i −0.286915 1.07078i
$$383$$ 21.1244i 1.07940i 0.841856 + 0.539702i $$0.181463\pi$$
−0.841856 + 0.539702i $$0.818537\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0.732051 0.196152i 0.0372604 0.00998390i
$$387$$ 0 0
$$388$$ 14.3923 + 24.9282i 0.730659 + 1.26554i
$$389$$ 6.78461i 0.343993i −0.985098 0.171997i $$-0.944978\pi$$
0.985098 0.171997i $$-0.0550218\pi$$
$$390$$ 0 0
$$391$$ −21.4641 −1.08549
$$392$$ −12.9282 12.9282i −0.652973 0.652973i
$$393$$ 0 0
$$394$$ 7.12436 + 26.5885i 0.358920 + 1.33951i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 32.2487 1.61852 0.809258 0.587453i $$-0.199869\pi$$
0.809258 + 0.587453i $$0.199869\pi$$
$$398$$ 0.679492 + 2.53590i 0.0340599 + 0.127113i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 7.85641 0.392330 0.196165 0.980571i $$-0.437151\pi$$
0.196165 + 0.980571i $$0.437151\pi$$
$$402$$ 0 0
$$403$$ −18.9282 −0.942881
$$404$$ −2.92820 5.07180i −0.145684 0.252331i
$$405$$ 0 0
$$406$$ 1.85641 + 6.92820i 0.0921319 + 0.343841i
$$407$$ 4.00000i 0.198273i
$$408$$ 0 0
$$409$$ 11.3205 0.559763 0.279882 0.960035i $$-0.409705\pi$$
0.279882 + 0.960035i $$0.409705\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 15.6603 + 27.1244i 0.771525 + 1.33632i
$$413$$ −5.46410 −0.268871
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 18.9282 + 5.07180i 0.928032 + 0.248665i
$$417$$ 0 0
$$418$$ 0.392305 + 1.46410i 0.0191883 + 0.0716116i
$$419$$ 18.3923i 0.898523i −0.893400 0.449261i $$-0.851687\pi$$
0.893400 0.449261i $$-0.148313\pi$$
$$420$$ 0 0
$$421$$ 0.143594i 0.00699832i −0.999994 0.00349916i $$-0.998886\pi$$
0.999994 0.00349916i $$-0.00111382\pi$$
$$422$$ 36.5885 9.80385i 1.78110 0.477244i
$$423$$ 0 0
$$424$$ −22.9282 22.9282i −1.11349 1.11349i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −6.53590 −0.316294
$$428$$ 4.73205 2.73205i 0.228732 0.132059i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 21.4641 1.03389 0.516945 0.856019i $$-0.327069\pi$$
0.516945 + 0.856019i $$0.327069\pi$$
$$432$$ 0 0
$$433$$ 19.4641i 0.935385i 0.883891 + 0.467693i $$0.154915\pi$$
−0.883891 + 0.467693i $$0.845085\pi$$
$$434$$ 5.46410 1.46410i 0.262285 0.0702791i
$$435$$ 0 0
$$436$$ −16.9282 29.3205i −0.810714 1.40420i
$$437$$ 3.32051 0.158841
$$438$$ 0 0
$$439$$ −40.7846 −1.94654 −0.973272 0.229657i $$-0.926240\pi$$
−0.973272 + 0.229657i $$0.926240\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 16.3923 4.39230i 0.779702 0.208921i
$$443$$ 20.9808 0.996826 0.498413 0.866940i $$-0.333916\pi$$
0.498413 + 0.866940i $$0.333916\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −7.92820 + 2.12436i −0.375411 + 0.100591i
$$447$$ 0 0
$$448$$ −5.85641 −0.276689
$$449$$ −23.3205 −1.10056 −0.550281 0.834979i $$-0.685480\pi$$
−0.550281 + 0.834979i $$0.685480\pi$$
$$450$$ 0 0
$$451$$ 2.92820i 0.137884i
$$452$$ 12.9282 + 22.3923i 0.608092 + 1.05325i
$$453$$ 0 0
$$454$$ −3.67949 13.7321i −0.172687 0.644477i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 26.7846i 1.25293i −0.779449 0.626466i $$-0.784501\pi$$
0.779449 0.626466i $$-0.215499\pi$$
$$458$$ 5.46410 1.46410i 0.255321 0.0684130i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 10.9282i 0.508977i −0.967076 0.254489i $$-0.918093\pi$$
0.967076 0.254489i $$-0.0819071\pi$$
$$462$$ 0 0
$$463$$ 11.2679i 0.523666i 0.965113 + 0.261833i $$0.0843270\pi$$
−0.965113 + 0.261833i $$0.915673\pi$$
$$464$$ −24.0000 13.8564i −1.11417 0.643268i
$$465$$ 0 0
$$466$$ 7.26795 1.94744i 0.336681 0.0902135i
$$467$$ 25.6603 1.18741 0.593707 0.804681i $$-0.297664\pi$$
0.593707 + 0.804681i $$0.297664\pi$$
$$468$$ 0 0
$$469$$ 7.85641i 0.362775i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 14.9282 14.9282i 0.687126 0.687126i
$$473$$ 10.5359i 0.484441i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −4.39230 + 2.53590i −0.201321 + 0.116233i
$$477$$ 0 0
$$478$$ −7.32051 27.3205i −0.334832 1.24961i
$$479$$ 5.85641 0.267586 0.133793 0.991009i $$-0.457284\pi$$
0.133793 + 0.991009i $$0.457284\pi$$
$$480$$ 0 0
$$481$$ −6.92820 −0.315899
$$482$$ 6.00000 + 22.3923i 0.273293 + 1.01994i
$$483$$ 0 0
$$484$$ −12.1244 + 7.00000i −0.551107 + 0.318182i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 6.58846i 0.298551i 0.988796 + 0.149276i $$0.0476942\pi$$
−0.988796 + 0.149276i $$0.952306\pi$$
$$488$$ 17.8564 17.8564i 0.808322 0.808322i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 16.9282i 0.763959i −0.924171 0.381980i $$-0.875242\pi$$
0.924171 0.381980i $$-0.124758\pi$$
$$492$$ 0 0
$$493$$ −24.0000 −1.08091
$$494$$ −2.53590 + 0.679492i −0.114095 + 0.0305718i
$$495$$ 0 0
$$496$$ −10.9282 + 18.9282i −0.490691 + 0.849901i
$$497$$ 4.00000i 0.179425i
$$498$$ 0 0
$$499$$ 31.4641i 1.40853i 0.709939 + 0.704263i $$0.248723\pi$$
−0.709939 + 0.704263i $$0.751277\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −34.0526 + 9.12436i −1.51984 + 0.407240i
$$503$$ 0.339746i 0.0151485i −0.999971 0.00757426i $$-0.997589\pi$$
0.999971 0.00757426i $$-0.00241099\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −4.53590 16.9282i −0.201645 0.752550i
$$507$$ 0 0
$$508$$ −16.7321 28.9808i −0.742365 1.28581i
$$509$$ 1.85641i 0.0822838i 0.999153 + 0.0411419i $$0.0130996\pi$$
−0.999153 + 0.0411419i $$0.986900\pi$$
$$510$$ 0 0
$$511$$ 5.46410 0.241718
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ 0 0
$$514$$ −2.73205 + 0.732051i −0.120506 + 0.0322894i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −6.53590 −0.287448
$$518$$ 2.00000 0.535898i 0.0878750 0.0235460i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 43.8564 1.92138 0.960692 0.277616i $$-0.0895444\pi$$
0.960692 + 0.277616i $$0.0895444\pi$$
$$522$$ 0 0
$$523$$ 11.8038 0.516146 0.258073 0.966125i $$-0.416912\pi$$
0.258073 + 0.966125i $$0.416912\pi$$
$$524$$ 19.8564 + 34.3923i 0.867431 + 1.50243i
$$525$$ 0 0
$$526$$ 15.9282 4.26795i 0.694503 0.186091i
$$527$$ 18.9282i 0.824525i
$$528$$ 0 0
$$529$$ −15.3923 −0.669231
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0.679492 0.392305i 0.0294597 0.0170086i
$$533$$ −5.07180 −0.219684
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −21.4641 21.4641i −0.927108 0.927108i
$$537$$ 0 0
$$538$$ −12.1962 + 3.26795i −0.525813 + 0.140891i
$$539$$ 12.9282i 0.556857i
$$540$$ 0 0
$$541$$ 26.9282i 1.15773i 0.815422 + 0.578867i $$0.196505\pi$$
−0.815422 + 0.578867i $$0.803495\pi$$
$$542$$ −7.07180 26.3923i −0.303760 1.13365i
$$543$$ 0 0
$$544$$ 5.07180 18.9282i 0.217451 0.811540i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 33.2679 1.42243 0.711217 0.702972i $$-0.248144\pi$$
0.711217 + 0.702972i $$0.248144\pi$$
$$548$$ 4.92820 + 8.53590i 0.210522 + 0.364636i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 3.71281 0.158171
$$552$$ 0 0
$$553$$ 0.784610i 0.0333650i
$$554$$ 0.732051 + 2.73205i 0.0311019 + 0.116074i
$$555$$ 0 0
$$556$$ 0.535898 + 0.928203i 0.0227272 + 0.0393646i
$$557$$ −14.7846 −0.626444 −0.313222 0.949680i $$-0.601408\pi$$
−0.313222 + 0.949680i $$0.601408\pi$$
$$558$$ 0 0
$$559$$ 18.2487 0.771838
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −3.85641 14.3923i −0.162673 0.607103i
$$563$$ −22.0526 −0.929405 −0.464702 0.885467i $$-0.653839\pi$$
−0.464702 + 0.885467i $$0.653839\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 3.53590 + 13.1962i 0.148625 + 0.554676i
$$567$$ 0 0
$$568$$ 10.9282 + 10.9282i 0.458537 + 0.458537i
$$569$$ −13.4641 −0.564445 −0.282222 0.959349i $$-0.591072\pi$$
−0.282222 + 0.959349i $$0.591072\pi$$
$$570$$ 0 0
$$571$$ 6.78461i 0.283927i −0.989872 0.141964i $$-0.954658\pi$$
0.989872 0.141964i $$-0.0453416\pi$$
$$572$$ 6.92820 + 12.0000i 0.289683 + 0.501745i
$$573$$ 0 0
$$574$$ 1.46410 0.392305i 0.0611104 0.0163745i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 39.5692i 1.64729i 0.567107 + 0.823644i $$0.308063\pi$$
−0.567107 + 0.823644i $$0.691937\pi$$
$$578$$ 1.83013 + 6.83013i 0.0761232 + 0.284096i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0.928203i 0.0385084i
$$582$$ 0 0
$$583$$ 22.9282i 0.949589i
$$584$$ −14.9282 + 14.9282i −0.617733 + 0.617733i
$$585$$ 0 0
$$586$$ −5.80385 21.6603i −0.239755 0.894777i
$$587$$ 3.80385 0.157002 0.0785008 0.996914i $$-0.474987\pi$$
0.0785008 + 0.996914i $$0.474987\pi$$
$$588$$ 0 0
$$589$$ 2.92820i 0.120655i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −4.00000 + 6.92820i −0.164399 + 0.284747i
$$593$$ 32.6410i 1.34041i 0.742178 + 0.670203i $$0.233793\pi$$
−0.742178 + 0.670203i $$0.766207\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −7.85641 13.6077i −0.321811 0.557393i
$$597$$ 0 0
$$598$$ 29.3205 7.85641i 1.19900 0.321272i
$$599$$ −34.6410 −1.41539 −0.707697 0.706516i $$-0.750266\pi$$
−0.707697 + 0.706516i $$0.750266\pi$$
$$600$$ 0 0
$$601$$ 18.5359 0.756095 0.378048 0.925786i $$-0.376596\pi$$
0.378048 + 0.925786i $$0.376596\pi$$
$$602$$ −5.26795 + 1.41154i −0.214706 + 0.0575302i
$$603$$ 0 0
$$604$$ 21.4641 12.3923i 0.873362 0.504236i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 30.9808i 1.25747i 0.777619 + 0.628735i $$0.216427\pi$$
−0.777619 + 0.628735i $$0.783573\pi$$
$$608$$ −0.784610 + 2.92820i −0.0318201 + 0.118754i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 11.3205i 0.457979i
$$612$$ 0 0
$$613$$ −26.3923 −1.06598 −0.532988 0.846123i $$-0.678931\pi$$
−0.532988 + 0.846123i $$0.678931\pi$$
$$614$$ −9.14359 34.1244i −0.369005 1.37715i
$$615$$ 0 0
$$616$$ −2.92820 2.92820i −0.117981 0.117981i
$$617$$ 20.5359i 0.826744i 0.910562 + 0.413372i $$0.135649\pi$$
−0.910562 + 0.413372i $$0.864351\pi$$
$$618$$ 0 0
$$619$$ 1.32051i 0.0530757i 0.999648 + 0.0265379i $$0.00844825\pi$$
−0.999648 + 0.0265379i $$0.991552\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −11.4641 42.7846i −0.459669 1.71551i
$$623$$ 6.53590i 0.261855i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −5.66025 + 1.51666i −0.226229 + 0.0606179i
$$627$$ 0 0
$$628$$ 5.32051 3.07180i 0.212311 0.122578i
$$629$$ 6.92820i 0.276246i
$$630$$ 0 0
$$631$$ −23.3205 −0.928375 −0.464187 0.885737i $$-0.653654\pi$$
−0.464187 + 0.885737i $$0.653654\pi$$
$$632$$ −2.14359 2.14359i −0.0852676 0.0852676i
$$633$$ 0 0
$$634$$ −3.12436 11.6603i −0.124084 0.463088i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 22.3923 0.887215
$$638$$ −5.07180 18.9282i −0.200794 0.749375i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −0.392305 −0.0154951 −0.00774755 0.999970i $$-0.502466\pi$$
−0.00774755 + 0.999970i $$0.502466\pi$$
$$642$$ 0 0
$$643$$ −39.1244 −1.54291 −0.771457 0.636281i $$-0.780472\pi$$
−0.771457 + 0.636281i $$0.780472\pi$$
$$644$$ −7.85641 + 4.53590i −0.309586 + 0.178739i
$$645$$ 0 0
$$646$$ 0.679492 + 2.53590i 0.0267343 + 0.0997736i
$$647$$ 16.7321i 0.657805i −0.944364 0.328902i $$-0.893321\pi$$
0.944364 0.328902i $$-0.106679\pi$$
$$648$$ 0 0
$$649$$ 14.9282 0.585983
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −0.339746 + 0.196152i −0.0133055 + 0.00768192i
$$653$$ 12.2487 0.479329 0.239665 0.970856i $$-0.422963\pi$$
0.239665 + 0.970856i $$0.422963\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −2.92820 + 5.07180i −0.114327 + 0.198020i
$$657$$ 0 0
$$658$$ 0.875644 + 3.26795i 0.0341362 + 0.127398i
$$659$$ 17.3205i 0.674711i 0.941377 + 0.337356i $$0.109532\pi$$
−0.941377 + 0.337356i $$0.890468\pi$$
$$660$$ 0 0
$$661$$ 8.14359i 0.316749i 0.987379 + 0.158375i $$0.0506253\pi$$
−0.987379 + 0.158375i $$0.949375\pi$$
$$662$$ −19.1244 + 5.12436i −0.743289 + 0.199164i
$$663$$ 0 0
$$664$$ −2.53590 2.53590i −0.0984119 0.0984119i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −42.9282 −1.66219
$$668$$ −9.80385 16.9808i −0.379322 0.657005i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 17.8564 0.689339
$$672$$ 0 0
$$673$$ 12.5359i 0.483223i −0.970373 0.241612i $$-0.922324\pi$$
0.970373 0.241612i $$-0.0776760\pi$$
$$674$$ 27.1244 7.26795i 1.04479 0.279951i
$$675$$ 0 0
$$676$$ 1.73205 1.00000i 0.0666173 0.0384615i
$$677$$ −17.6077 −0.676719 −0.338359 0.941017i $$-0.609872\pi$$
−0.338359 + 0.941017i $$0.609872\pi$$
$$678$$ 0 0
$$679$$ 10.5359 0.404331
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −14.9282 + 4.00000i −0.571630 + 0.153168i
$$683$$ −16.9808 −0.649751 −0.324875 0.945757i $$-0.605322\pi$$
−0.324875 + 0.945757i $$0.605322\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −13.4641 + 3.60770i −0.514062 + 0.137742i
$$687$$ 0 0
$$688$$ 10.5359 18.2487i 0.401677 0.695726i
$$689$$ 39.7128 1.51294
$$690$$ 0 0
$$691$$ 18.0000i 0.684752i −0.939563 0.342376i $$-0.888768\pi$$
0.939563 0.342376i $$-0.111232\pi$$
$$692$$ −3.46410 + 2.00000i −0.131685 + 0.0760286i
$$693$$ 0 0
$$694$$ 0.607695 + 2.26795i 0.0230678 + 0.0860902i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 5.07180i 0.192108i
$$698$$ 38.2487 10.2487i 1.44774 0.387919i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 19.0718i 0.720332i 0.932888 + 0.360166i $$0.117280\pi$$
−0.932888 + 0.360166i $$0.882720\pi$$
$$702$$ 0 0
$$703$$ 1.07180i 0.0404236i
$$704$$ 16.0000 0.603023
$$705$$ 0 0
$$706$$ −17.6603 + 4.73205i −0.664652 + 0.178093i
$$707$$ −2.14359 −0.0806181
$$708$$ 0 0
$$709$$ 12.7846i 0.480136i −0.970756 0.240068i $$-0.922830\pi$$
0.970756 0.240068i $$-0.0771698\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −17.8564 17.8564i −0.669197 0.669197i
$$713$$ 33.8564i 1.26793i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −8.53590 14.7846i −0.319002 0.552527i
$$717$$ 0 0
$$718$$ 6.92820 + 25.8564i 0.258558 + 0.964953i
$$719$$ −1.85641 −0.0692323 −0.0346161 0.999401i $$-0.511021\pi$$
−0.0346161 + 0.999401i $$0.511021\pi$$
$$720$$ 0 0
$$721$$ 11.4641 0.426945
$$722$$ 6.84936 + 25.5622i 0.254907 + 0.951326i
$$723$$ 0 0
$$724$$ 16.0000 + 27.7128i 0.594635 + 1.02994i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 24.0526i 0.892060i −0.895018 0.446030i $$-0.852837\pi$$
0.895018 0.446030i $$-0.147163\pi$$
$$728$$ 5.07180 5.07180i 0.187973 0.187973i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 18.2487i 0.674953i
$$732$$ 0 0
$$733$$ 35.0718 1.29541 0.647703 0.761893i $$-0.275730\pi$$
0.647703 + 0.761893i $$0.275730\pi$$
$$734$$ −3.92820 + 1.05256i −0.144993 + 0.0388507i
$$735$$ 0 0
$$736$$ 9.07180 33.8564i 0.334391 1.24796i
$$737$$ 21.4641i 0.790640i
$$738$$ 0 0
$$739$$ 29.3205i 1.07857i 0.842123 + 0.539286i $$0.181306\pi$$
−0.842123 + 0.539286i $$0.818694\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −11.4641 + 3.07180i −0.420860 + 0.112769i
$$743$$ 10.9808i 0.402845i 0.979504 + 0.201423i $$0.0645564\pi$$
−0.979504 + 0.201423i $$0.935444\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 9.41154 + 35.1244i 0.344581 + 1.28599i
$$747$$ 0 0
$$748$$ 12.0000 6.92820i 0.438763 0.253320i
$$749$$ 2.00000i 0.0730784i
$$750$$ 0 0
$$751$$ 26.2487 0.957829 0.478915 0.877862i $$-0.341030\pi$$
0.478915 + 0.877862i $$0.341030\pi$$
$$752$$ −11.3205 6.53590i −0.412816 0.238340i
$$753$$ 0 0
$$754$$ 32.7846 8.78461i 1.19395 0.319917i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −19.0718 −0.693176 −0.346588 0.938017i $$-0.612660\pi$$
−0.346588 + 0.938017i $$0.612660\pi$$
$$758$$ 49.5167 13.2679i 1.79853 0.481914i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 5.71281 0.207089 0.103545 0.994625i $$-0.466982\pi$$
0.103545 + 0.994625i $$0.466982\pi$$
$$762$$ 0 0
$$763$$ −12.3923 −0.448632
$$764$$ 26.5359 15.3205i 0.960035 0.554277i
$$765$$ 0 0
$$766$$ −28.8564 + 7.73205i −1.04262 + 0.279370i
$$767$$ 25.8564i 0.933621i
$$768$$ 0 0
$$769$$ −12.9282 −0.466203 −0.233101 0.972452i $$-0.574887\pi$$
−0.233101 + 0.972452i $$0.574887\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0.535898 + 0.928203i 0.0192874 + 0.0334068i
$$773$$ −22.3923 −0.805395 −0.402698 0.915333i $$-0.631927\pi$$
−0.402698 + 0.915333i $$0.631927\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −28.7846 + 28.7846i −1.03331 + 1.03331i
$$777$$ 0 0
$$778$$ 9.26795 2.48334i 0.332272 0.0890320i
$$779$$ 0.784610i 0.0281116i
$$780$$ 0 0
$$781$$ 10.9282i 0.391042i
$$782$$ −7.85641 29.3205i −0.280945 1.04850i
$$783$$ 0 0
$$784$$ 12.9282 22.3923i 0.461722 0.799725i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 16.5885 0.591315 0.295657 0.955294i $$-0.404461\pi$$
0.295657 + 0.955294i $$0.404461\pi$$
$$788$$ −33.7128 + 19.4641i −1.20097 + 0.693380i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 9.46410 0.336505
$$792$$ 0 0
$$793$$ 30.9282i 1.09829i
$$794$$ 11.8038 + 44.0526i 0.418903 + 1.56337i
$$795$$ 0 0
$$796$$ −3.21539 + 1.85641i −0.113966 + 0.0657986i
$$797$$ −50.1051 −1.77481