# Properties

 Label 1764.2.b.b.1567.3 Level $1764$ Weight $2$ Character 1764.1567 Analytic conductor $14.086$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1764.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.0856109166$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-7})$$ Defining polynomial: $$x^{4} - x^{3} - x^{2} - 2 x + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 252) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1567.3 Root $$1.39564 + 0.228425i$$ of defining polynomial Character $$\chi$$ $$=$$ 1764.1567 Dual form 1764.2.b.b.1567.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 1.32288i) q^{2} +(-1.50000 - 1.32288i) q^{4} -1.73205i q^{5} +(2.50000 - 1.32288i) q^{8} +O(q^{10})$$ $$q+(-0.500000 + 1.32288i) q^{2} +(-1.50000 - 1.32288i) q^{4} -1.73205i q^{5} +(2.50000 - 1.32288i) q^{8} +(2.29129 + 0.866025i) q^{10} -2.64575i q^{11} -3.46410i q^{13} +(0.500000 + 3.96863i) q^{16} +6.92820i q^{17} +(-2.29129 + 2.59808i) q^{20} +(3.50000 + 1.32288i) q^{22} -5.29150i q^{23} +2.00000 q^{25} +(4.58258 + 1.73205i) q^{26} -5.00000 q^{29} +4.58258 q^{31} +(-5.50000 - 1.32288i) q^{32} +(-9.16515 - 3.46410i) q^{34} +(-2.29129 - 4.33013i) q^{40} +3.46410i q^{41} -10.5830i q^{43} +(-3.50000 + 3.96863i) q^{44} +(7.00000 + 2.64575i) q^{46} -9.16515 q^{47} +(-1.00000 + 2.64575i) q^{50} +(-4.58258 + 5.19615i) q^{52} -7.00000 q^{53} -4.58258 q^{55} +(2.50000 - 6.61438i) q^{58} -13.7477 q^{59} -10.3923i q^{61} +(-2.29129 + 6.06218i) q^{62} +(4.50000 - 6.61438i) q^{64} -6.00000 q^{65} +(9.16515 - 10.3923i) q^{68} -5.29150i q^{71} +6.92820i q^{73} -7.93725i q^{79} +(6.87386 - 0.866025i) q^{80} +(-4.58258 - 1.73205i) q^{82} +4.58258 q^{83} +12.0000 q^{85} +(14.0000 + 5.29150i) q^{86} +(-3.50000 - 6.61438i) q^{88} +10.3923i q^{89} +(-7.00000 + 7.93725i) q^{92} +(4.58258 - 12.1244i) q^{94} -8.66025i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} - 6q^{4} + 10q^{8} + O(q^{10})$$ $$4q - 2q^{2} - 6q^{4} + 10q^{8} + 2q^{16} + 14q^{22} + 8q^{25} - 20q^{29} - 22q^{32} - 14q^{44} + 28q^{46} - 4q^{50} - 28q^{53} + 10q^{58} + 18q^{64} - 24q^{65} + 48q^{85} + 56q^{86} - 14q^{88} - 28q^{92} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$883$$ $$1081$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 1.32288i −0.353553 + 0.935414i
$$3$$ 0 0
$$4$$ −1.50000 1.32288i −0.750000 0.661438i
$$5$$ 1.73205i 0.774597i −0.921954 0.387298i $$-0.873408\pi$$
0.921954 0.387298i $$-0.126592\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 2.50000 1.32288i 0.883883 0.467707i
$$9$$ 0 0
$$10$$ 2.29129 + 0.866025i 0.724569 + 0.273861i
$$11$$ 2.64575i 0.797724i −0.917011 0.398862i $$-0.869405\pi$$
0.917011 0.398862i $$-0.130595\pi$$
$$12$$ 0 0
$$13$$ 3.46410i 0.960769i −0.877058 0.480384i $$-0.840497\pi$$
0.877058 0.480384i $$-0.159503\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0.500000 + 3.96863i 0.125000 + 0.992157i
$$17$$ 6.92820i 1.68034i 0.542326 + 0.840168i $$0.317544\pi$$
−0.542326 + 0.840168i $$0.682456\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −2.29129 + 2.59808i −0.512348 + 0.580948i
$$21$$ 0 0
$$22$$ 3.50000 + 1.32288i 0.746203 + 0.282038i
$$23$$ 5.29150i 1.10335i −0.834058 0.551677i $$-0.813988\pi$$
0.834058 0.551677i $$-0.186012\pi$$
$$24$$ 0 0
$$25$$ 2.00000 0.400000
$$26$$ 4.58258 + 1.73205i 0.898717 + 0.339683i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0 0
$$31$$ 4.58258 0.823055 0.411527 0.911397i $$-0.364995\pi$$
0.411527 + 0.911397i $$0.364995\pi$$
$$32$$ −5.50000 1.32288i −0.972272 0.233854i
$$33$$ 0 0
$$34$$ −9.16515 3.46410i −1.57181 0.594089i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −2.29129 4.33013i −0.362284 0.684653i
$$41$$ 3.46410i 0.541002i 0.962720 + 0.270501i $$0.0871893\pi$$
−0.962720 + 0.270501i $$0.912811\pi$$
$$42$$ 0 0
$$43$$ 10.5830i 1.61389i −0.590624 0.806947i $$-0.701119\pi$$
0.590624 0.806947i $$-0.298881\pi$$
$$44$$ −3.50000 + 3.96863i −0.527645 + 0.598293i
$$45$$ 0 0
$$46$$ 7.00000 + 2.64575i 1.03209 + 0.390095i
$$47$$ −9.16515 −1.33687 −0.668437 0.743768i $$-0.733037\pi$$
−0.668437 + 0.743768i $$0.733037\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −1.00000 + 2.64575i −0.141421 + 0.374166i
$$51$$ 0 0
$$52$$ −4.58258 + 5.19615i −0.635489 + 0.720577i
$$53$$ −7.00000 −0.961524 −0.480762 0.876851i $$-0.659640\pi$$
−0.480762 + 0.876851i $$0.659640\pi$$
$$54$$ 0 0
$$55$$ −4.58258 −0.617914
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 2.50000 6.61438i 0.328266 0.868510i
$$59$$ −13.7477 −1.78980 −0.894901 0.446265i $$-0.852754\pi$$
−0.894901 + 0.446265i $$0.852754\pi$$
$$60$$ 0 0
$$61$$ 10.3923i 1.33060i −0.746577 0.665299i $$-0.768304\pi$$
0.746577 0.665299i $$-0.231696\pi$$
$$62$$ −2.29129 + 6.06218i −0.290994 + 0.769897i
$$63$$ 0 0
$$64$$ 4.50000 6.61438i 0.562500 0.826797i
$$65$$ −6.00000 −0.744208
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 9.16515 10.3923i 1.11144 1.26025i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 5.29150i 0.627986i −0.949425 0.313993i $$-0.898333\pi$$
0.949425 0.313993i $$-0.101667\pi$$
$$72$$ 0 0
$$73$$ 6.92820i 0.810885i 0.914121 + 0.405442i $$0.132883\pi$$
−0.914121 + 0.405442i $$0.867117\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 7.93725i 0.893011i −0.894781 0.446505i $$-0.852668\pi$$
0.894781 0.446505i $$-0.147332\pi$$
$$80$$ 6.87386 0.866025i 0.768521 0.0968246i
$$81$$ 0 0
$$82$$ −4.58258 1.73205i −0.506061 0.191273i
$$83$$ 4.58258 0.503003 0.251502 0.967857i $$-0.419076\pi$$
0.251502 + 0.967857i $$0.419076\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 14.0000 + 5.29150i 1.50966 + 0.570597i
$$87$$ 0 0
$$88$$ −3.50000 6.61438i −0.373101 0.705095i
$$89$$ 10.3923i 1.10158i 0.834643 + 0.550791i $$0.185674\pi$$
−0.834643 + 0.550791i $$0.814326\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −7.00000 + 7.93725i −0.729800 + 0.827516i
$$93$$ 0 0
$$94$$ 4.58258 12.1244i 0.472657 1.25053i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 8.66025i 0.879316i −0.898165 0.439658i $$-0.855100\pi$$
0.898165 0.439658i $$-0.144900\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −3.00000 2.64575i −0.300000 0.264575i
$$101$$ 6.92820i 0.689382i −0.938716 0.344691i $$-0.887984\pi$$
0.938716 0.344691i $$-0.112016\pi$$
$$102$$ 0 0
$$103$$ −18.3303 −1.80614 −0.903069 0.429495i $$-0.858692\pi$$
−0.903069 + 0.429495i $$0.858692\pi$$
$$104$$ −4.58258 8.66025i −0.449359 0.849208i
$$105$$ 0 0
$$106$$ 3.50000 9.26013i 0.339950 0.899423i
$$107$$ 18.5203i 1.79042i −0.445644 0.895211i $$-0.647025\pi$$
0.445644 0.895211i $$-0.352975\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 2.29129 6.06218i 0.218466 0.578006i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ −9.16515 −0.854655
$$116$$ 7.50000 + 6.61438i 0.696358 + 0.614130i
$$117$$ 0 0
$$118$$ 6.87386 18.1865i 0.632790 1.67421i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 4.00000 0.363636
$$122$$ 13.7477 + 5.19615i 1.24466 + 0.470438i
$$123$$ 0 0
$$124$$ −6.87386 6.06218i −0.617291 0.544400i
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ 7.93725i 0.704317i 0.935940 + 0.352159i $$0.114552\pi$$
−0.935940 + 0.352159i $$0.885448\pi$$
$$128$$ 6.50000 + 9.26013i 0.574524 + 0.818488i
$$129$$ 0 0
$$130$$ 3.00000 7.93725i 0.263117 0.696143i
$$131$$ −13.7477 −1.20114 −0.600572 0.799570i $$-0.705061\pi$$
−0.600572 + 0.799570i $$0.705061\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 9.16515 + 17.3205i 0.785905 + 1.48522i
$$137$$ 4.00000 0.341743 0.170872 0.985293i $$-0.445342\pi$$
0.170872 + 0.985293i $$0.445342\pi$$
$$138$$ 0 0
$$139$$ −9.16515 −0.777378 −0.388689 0.921369i $$-0.627072\pi$$
−0.388689 + 0.921369i $$0.627072\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 7.00000 + 2.64575i 0.587427 + 0.222027i
$$143$$ −9.16515 −0.766428
$$144$$ 0 0
$$145$$ 8.66025i 0.719195i
$$146$$ −9.16515 3.46410i −0.758513 0.286691i
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −14.0000 −1.14692 −0.573462 0.819232i $$-0.694400\pi$$
−0.573462 + 0.819232i $$0.694400\pi$$
$$150$$ 0 0
$$151$$ 13.2288i 1.07654i −0.842772 0.538270i $$-0.819078\pi$$
0.842772 0.538270i $$-0.180922\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 7.93725i 0.637536i
$$156$$ 0 0
$$157$$ 6.92820i 0.552931i −0.961024 0.276465i $$-0.910837\pi$$
0.961024 0.276465i $$-0.0891631\pi$$
$$158$$ 10.5000 + 3.96863i 0.835335 + 0.315727i
$$159$$ 0 0
$$160$$ −2.29129 + 9.52628i −0.181142 + 0.753119i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 15.8745i 1.24339i 0.783260 + 0.621694i $$0.213555\pi$$
−0.783260 + 0.621694i $$0.786445\pi$$
$$164$$ 4.58258 5.19615i 0.357839 0.405751i
$$165$$ 0 0
$$166$$ −2.29129 + 6.06218i −0.177838 + 0.470516i
$$167$$ 18.3303 1.41844 0.709221 0.704987i $$-0.249047\pi$$
0.709221 + 0.704987i $$0.249047\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ −6.00000 + 15.8745i −0.460179 + 1.21752i
$$171$$ 0 0
$$172$$ −14.0000 + 15.8745i −1.06749 + 1.21042i
$$173$$ 13.8564i 1.05348i 0.850026 + 0.526742i $$0.176586\pi$$
−0.850026 + 0.526742i $$0.823414\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 10.5000 1.32288i 0.791467 0.0997155i
$$177$$ 0 0
$$178$$ −13.7477 5.19615i −1.03044 0.389468i
$$179$$ 5.29150i 0.395505i −0.980252 0.197753i $$-0.936636\pi$$
0.980252 0.197753i $$-0.0633643\pi$$
$$180$$ 0 0
$$181$$ 3.46410i 0.257485i 0.991678 + 0.128742i $$0.0410940\pi$$
−0.991678 + 0.128742i $$0.958906\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −7.00000 13.2288i −0.516047 0.975237i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 18.3303 1.34044
$$188$$ 13.7477 + 12.1244i 1.00266 + 0.884260i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 10.5830i 0.765759i −0.923798 0.382880i $$-0.874932\pi$$
0.923798 0.382880i $$-0.125068\pi$$
$$192$$ 0 0
$$193$$ 3.00000 0.215945 0.107972 0.994154i $$-0.465564\pi$$
0.107972 + 0.994154i $$0.465564\pi$$
$$194$$ 11.4564 + 4.33013i 0.822524 + 0.310885i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −14.0000 −0.997459 −0.498729 0.866758i $$-0.666200\pi$$
−0.498729 + 0.866758i $$0.666200\pi$$
$$198$$ 0 0
$$199$$ 18.3303 1.29940 0.649700 0.760190i $$-0.274894\pi$$
0.649700 + 0.760190i $$0.274894\pi$$
$$200$$ 5.00000 2.64575i 0.353553 0.187083i
$$201$$ 0 0
$$202$$ 9.16515 + 3.46410i 0.644858 + 0.243733i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 6.00000 0.419058
$$206$$ 9.16515 24.2487i 0.638566 1.68949i
$$207$$ 0 0
$$208$$ 13.7477 1.73205i 0.953233 0.120096i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 5.29150i 0.364282i −0.983272 0.182141i $$-0.941697\pi$$
0.983272 0.182141i $$-0.0583027\pi$$
$$212$$ 10.5000 + 9.26013i 0.721143 + 0.635988i
$$213$$ 0 0
$$214$$ 24.5000 + 9.26013i 1.67479 + 0.633009i
$$215$$ −18.3303 −1.25012
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 6.87386 + 6.06218i 0.463436 + 0.408712i
$$221$$ 24.0000 1.61441
$$222$$ 0 0
$$223$$ −4.58258 −0.306872 −0.153436 0.988159i $$-0.549034\pi$$
−0.153436 + 0.988159i $$0.549034\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −7.00000 + 18.5203i −0.465633 + 1.23195i
$$227$$ 4.58258 0.304156 0.152078 0.988368i $$-0.451403\pi$$
0.152078 + 0.988368i $$0.451403\pi$$
$$228$$ 0 0
$$229$$ 10.3923i 0.686743i −0.939200 0.343371i $$-0.888431\pi$$
0.939200 0.343371i $$-0.111569\pi$$
$$230$$ 4.58258 12.1244i 0.302166 0.799456i
$$231$$ 0 0
$$232$$ −12.5000 + 6.61438i −0.820665 + 0.434255i
$$233$$ 20.0000 1.31024 0.655122 0.755523i $$-0.272617\pi$$
0.655122 + 0.755523i $$0.272617\pi$$
$$234$$ 0 0
$$235$$ 15.8745i 1.03554i
$$236$$ 20.6216 + 18.1865i 1.34235 + 1.18384i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 5.29150i 0.342279i 0.985247 + 0.171139i $$0.0547449\pi$$
−0.985247 + 0.171139i $$0.945255\pi$$
$$240$$ 0 0
$$241$$ 5.19615i 0.334714i 0.985896 + 0.167357i $$0.0535232\pi$$
−0.985896 + 0.167357i $$0.946477\pi$$
$$242$$ −2.00000 + 5.29150i −0.128565 + 0.340151i
$$243$$ 0 0
$$244$$ −13.7477 + 15.5885i −0.880108 + 0.997949i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 11.4564 6.06218i 0.727485 0.384949i
$$249$$ 0 0
$$250$$ 16.0390 + 6.06218i 1.01440 + 0.383406i
$$251$$ −4.58258 −0.289250 −0.144625 0.989487i $$-0.546198\pi$$
−0.144625 + 0.989487i $$0.546198\pi$$
$$252$$ 0 0
$$253$$ −14.0000 −0.880172
$$254$$ −10.5000 3.96863i −0.658829 0.249014i
$$255$$ 0 0
$$256$$ −15.5000 + 3.96863i −0.968750 + 0.248039i
$$257$$ 10.3923i 0.648254i −0.946014 0.324127i $$-0.894929\pi$$
0.946014 0.324127i $$-0.105071\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 9.00000 + 7.93725i 0.558156 + 0.492248i
$$261$$ 0 0
$$262$$ 6.87386 18.1865i 0.424669 1.12357i
$$263$$ 10.5830i 0.652576i 0.945270 + 0.326288i $$0.105798\pi$$
−0.945270 + 0.326288i $$0.894202\pi$$
$$264$$ 0 0
$$265$$ 12.1244i 0.744793i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 19.0526i 1.16166i 0.814027 + 0.580828i $$0.197271\pi$$
−0.814027 + 0.580828i $$0.802729\pi$$
$$270$$ 0 0
$$271$$ 13.7477 0.835115 0.417557 0.908651i $$-0.362886\pi$$
0.417557 + 0.908651i $$0.362886\pi$$
$$272$$ −27.4955 + 3.46410i −1.66716 + 0.210042i
$$273$$ 0 0
$$274$$ −2.00000 + 5.29150i −0.120824 + 0.319671i
$$275$$ 5.29150i 0.319090i
$$276$$ 0 0
$$277$$ −4.00000 −0.240337 −0.120168 0.992754i $$-0.538343\pi$$
−0.120168 + 0.992754i $$0.538343\pi$$
$$278$$ 4.58258 12.1244i 0.274845 0.727171i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −16.0000 −0.954480 −0.477240 0.878773i $$-0.658363\pi$$
−0.477240 + 0.878773i $$0.658363\pi$$
$$282$$ 0 0
$$283$$ −18.3303 −1.08962 −0.544812 0.838558i $$-0.683399\pi$$
−0.544812 + 0.838558i $$0.683399\pi$$
$$284$$ −7.00000 + 7.93725i −0.415374 + 0.470989i
$$285$$ 0 0
$$286$$ 4.58258 12.1244i 0.270973 0.716928i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −31.0000 −1.82353
$$290$$ −11.4564 4.33013i −0.672745 0.254274i
$$291$$ 0 0
$$292$$ 9.16515 10.3923i 0.536350 0.608164i
$$293$$ 15.5885i 0.910687i −0.890316 0.455344i $$-0.849516\pi$$
0.890316 0.455344i $$-0.150484\pi$$
$$294$$ 0 0
$$295$$ 23.8118i 1.38637i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 7.00000 18.5203i 0.405499 1.07285i
$$299$$ −18.3303 −1.06007
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 17.5000 + 6.61438i 1.00701 + 0.380615i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −18.0000 −1.03068
$$306$$ 0 0
$$307$$ 27.4955 1.56925 0.784624 0.619972i $$-0.212856\pi$$
0.784624 + 0.619972i $$0.212856\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 10.5000 + 3.96863i 0.596360 + 0.225403i
$$311$$ −9.16515 −0.519708 −0.259854 0.965648i $$-0.583674\pi$$
−0.259854 + 0.965648i $$0.583674\pi$$
$$312$$ 0 0
$$313$$ 22.5167i 1.27272i 0.771393 + 0.636358i $$0.219560\pi$$
−0.771393 + 0.636358i $$0.780440\pi$$
$$314$$ 9.16515 + 3.46410i 0.517219 + 0.195491i
$$315$$ 0 0
$$316$$ −10.5000 + 11.9059i −0.590671 + 0.669758i
$$317$$ −7.00000 −0.393159 −0.196580 0.980488i $$-0.562983\pi$$
−0.196580 + 0.980488i $$0.562983\pi$$
$$318$$ 0 0
$$319$$ 13.2288i 0.740668i
$$320$$ −11.4564 7.79423i −0.640434 0.435711i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 6.92820i 0.384308i
$$326$$ −21.0000 7.93725i −1.16308 0.439604i
$$327$$ 0 0
$$328$$ 4.58258 + 8.66025i 0.253030 + 0.478183i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 10.5830i 0.581695i −0.956769 0.290847i $$-0.906063\pi$$
0.956769 0.290847i $$-0.0939372\pi$$
$$332$$ −6.87386 6.06218i −0.377252 0.332705i
$$333$$ 0 0
$$334$$ −9.16515 + 24.2487i −0.501495 + 1.32683i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −21.0000 −1.14394 −0.571971 0.820274i $$-0.693821\pi$$
−0.571971 + 0.820274i $$0.693821\pi$$
$$338$$ −0.500000 + 1.32288i −0.0271964 + 0.0719549i
$$339$$ 0 0
$$340$$ −18.0000 15.8745i −0.976187 0.860916i
$$341$$ 12.1244i 0.656571i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −14.0000 26.4575i −0.754829 1.42649i
$$345$$ 0 0
$$346$$ −18.3303 6.92820i −0.985443 0.372463i
$$347$$ 5.29150i 0.284063i −0.989862 0.142031i $$-0.954637\pi$$
0.989862 0.142031i $$-0.0453634\pi$$
$$348$$ 0 0
$$349$$ 20.7846i 1.11257i 0.830990 + 0.556287i $$0.187775\pi$$
−0.830990 + 0.556287i $$0.812225\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −3.50000 + 14.5516i −0.186551 + 0.775605i
$$353$$ 6.92820i 0.368751i −0.982856 0.184376i $$-0.940974\pi$$
0.982856 0.184376i $$-0.0590263\pi$$
$$354$$ 0 0
$$355$$ −9.16515 −0.486436
$$356$$ 13.7477 15.5885i 0.728628 0.826187i
$$357$$ 0 0
$$358$$ 7.00000 + 2.64575i 0.369961 + 0.139832i
$$359$$ 10.5830i 0.558550i −0.960211 0.279275i $$-0.909906\pi$$
0.960211 0.279275i $$-0.0900940\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ −4.58258 1.73205i −0.240855 0.0910346i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 12.0000 0.628109
$$366$$ 0 0
$$367$$ −4.58258 −0.239209 −0.119604 0.992822i $$-0.538163\pi$$
−0.119604 + 0.992822i $$0.538163\pi$$
$$368$$ 21.0000 2.64575i 1.09470 0.137919i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 34.0000 1.76045 0.880227 0.474554i $$-0.157390\pi$$
0.880227 + 0.474554i $$0.157390\pi$$
$$374$$ −9.16515 + 24.2487i −0.473919 + 1.25387i
$$375$$ 0 0
$$376$$ −22.9129 + 12.1244i −1.18164 + 0.625266i
$$377$$ 17.3205i 0.892052i
$$378$$ 0 0
$$379$$ 5.29150i 0.271806i −0.990722 0.135903i $$-0.956606\pi$$
0.990722 0.135903i $$-0.0433936\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 14.0000 + 5.29150i 0.716302 + 0.270737i
$$383$$ 27.4955 1.40495 0.702476 0.711707i $$-0.252078\pi$$
0.702476 + 0.711707i $$0.252078\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −1.50000 + 3.96863i −0.0763480 + 0.201998i
$$387$$ 0 0
$$388$$ −11.4564 + 12.9904i −0.581613 + 0.659487i
$$389$$ −10.0000 −0.507020 −0.253510 0.967333i $$-0.581585\pi$$
−0.253510 + 0.967333i $$0.581585\pi$$
$$390$$ 0 0
$$391$$ 36.6606 1.85401
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 7.00000 18.5203i 0.352655 0.933037i
$$395$$ −13.7477 −0.691723
$$396$$ 0 0
$$397$$ 13.8564i 0.695433i 0.937600 + 0.347717i $$0.113043\pi$$
−0.937600 + 0.347717i $$0.886957\pi$$
$$398$$ −9.16515 + 24.2487i −0.459408 + 1.21548i
$$399$$ 0 0
$$400$$ 1.00000 + 7.93725i 0.0500000 + 0.396863i
$$401$$ −8.00000 −0.399501 −0.199750 0.979847i $$-0.564013\pi$$
−0.199750 + 0.979847i $$0.564013\pi$$
$$402$$ 0 0
$$403$$ 15.8745i 0.790766i
$$404$$ −9.16515 + 10.3923i −0.455983 + 0.517036i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 5.19615i 0.256933i −0.991714 0.128467i $$-0.958994\pi$$
0.991714 0.128467i $$-0.0410055\pi$$
$$410$$ −3.00000 + 7.93725i −0.148159 + 0.391993i
$$411$$ 0 0
$$412$$ 27.4955 + 24.2487i 1.35460 + 1.19465i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 7.93725i 0.389624i
$$416$$ −4.58258 + 19.0526i −0.224679 + 0.934129i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ −2.00000 −0.0974740 −0.0487370 0.998812i $$-0.515520\pi$$
−0.0487370 + 0.998812i $$0.515520\pi$$
$$422$$ 7.00000 + 2.64575i 0.340755 + 0.128793i
$$423$$ 0 0
$$424$$ −17.5000 + 9.26013i −0.849875 + 0.449712i
$$425$$ 13.8564i 0.672134i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −24.5000 + 27.7804i −1.18425 + 1.34282i
$$429$$ 0 0
$$430$$ 9.16515 24.2487i 0.441983 1.16938i
$$431$$ 26.4575i 1.27441i −0.770693 0.637207i $$-0.780090\pi$$
0.770693 0.637207i $$-0.219910\pi$$
$$432$$ 0 0
$$433$$ 20.7846i 0.998845i −0.866359 0.499422i $$-0.833546\pi$$
0.866359 0.499422i $$-0.166454\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −4.58258 −0.218714 −0.109357 0.994003i $$-0.534879\pi$$
−0.109357 + 0.994003i $$0.534879\pi$$
$$440$$ −11.4564 + 6.06218i −0.546164 + 0.289003i
$$441$$ 0 0
$$442$$ −12.0000 + 31.7490i −0.570782 + 1.51015i
$$443$$ 18.5203i 0.879924i 0.898016 + 0.439962i $$0.145008\pi$$
−0.898016 + 0.439962i $$0.854992\pi$$
$$444$$ 0 0
$$445$$ 18.0000 0.853282
$$446$$ 2.29129 6.06218i 0.108496 0.287052i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 14.0000 0.660701 0.330350 0.943858i $$-0.392833\pi$$
0.330350 + 0.943858i $$0.392833\pi$$
$$450$$ 0 0
$$451$$ 9.16515 0.431570
$$452$$ −21.0000 18.5203i −0.987757 0.871120i
$$453$$ 0 0
$$454$$ −2.29129 + 6.06218i −0.107535 + 0.284512i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −27.0000 −1.26301 −0.631503 0.775373i $$-0.717562\pi$$
−0.631503 + 0.775373i $$0.717562\pi$$
$$458$$ 13.7477 + 5.19615i 0.642389 + 0.242800i
$$459$$ 0 0
$$460$$ 13.7477 + 12.1244i 0.640991 + 0.565301i
$$461$$ 27.7128i 1.29071i 0.763881 + 0.645357i $$0.223291\pi$$
−0.763881 + 0.645357i $$0.776709\pi$$
$$462$$ 0 0
$$463$$ 15.8745i 0.737751i −0.929479 0.368875i $$-0.879743\pi$$
0.929479 0.368875i $$-0.120257\pi$$
$$464$$ −2.50000 19.8431i −0.116060 0.921194i
$$465$$ 0 0
$$466$$ −10.0000 + 26.4575i −0.463241 + 1.22562i
$$467$$ 36.6606 1.69645 0.848225 0.529636i $$-0.177671\pi$$
0.848225 + 0.529636i $$0.177671\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −21.0000 7.93725i −0.968658 0.366118i
$$471$$ 0 0
$$472$$ −34.3693 + 18.1865i −1.58198 + 0.837103i
$$473$$ −28.0000 −1.28744
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −7.00000 2.64575i −0.320173 0.121014i
$$479$$ 18.3303 0.837533 0.418766 0.908094i $$-0.362463\pi$$
0.418766 + 0.908094i $$0.362463\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −6.87386 2.59808i −0.313096 0.118339i
$$483$$ 0 0
$$484$$ −6.00000 5.29150i −0.272727 0.240523i
$$485$$ −15.0000 −0.681115
$$486$$ 0 0
$$487$$ 2.64575i 0.119890i −0.998202 0.0599452i $$-0.980907\pi$$
0.998202 0.0599452i $$-0.0190926\pi$$
$$488$$ −13.7477 25.9808i −0.622330 1.17609i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2.64575i 0.119401i −0.998216 0.0597005i $$-0.980985\pi$$
0.998216 0.0597005i $$-0.0190146\pi$$
$$492$$ 0 0
$$493$$ 34.6410i 1.56015i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 2.29129 + 18.1865i 0.102882 + 0.816599i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 5.29150i 0.236880i −0.992961 0.118440i $$-0.962211\pi$$
0.992961 0.118440i $$-0.0377894\pi$$
$$500$$ −16.0390 + 18.1865i −0.717287 + 0.813327i
$$501$$ 0 0
$$502$$ 2.29129 6.06218i 0.102265 0.270568i
$$503$$ −36.6606 −1.63462 −0.817308 0.576201i $$-0.804534\pi$$
−0.817308 + 0.576201i $$0.804534\pi$$
$$504$$ 0 0
$$505$$ −12.0000 −0.533993
$$506$$ 7.00000 18.5203i 0.311188 0.823326i
$$507$$ 0 0
$$508$$ 10.5000 11.9059i 0.465862 0.528238i
$$509$$ 1.73205i 0.0767718i 0.999263 + 0.0383859i $$0.0122216\pi$$
−0.999263 + 0.0383859i $$0.987778\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 2.50000 22.4889i 0.110485 0.993878i
$$513$$ 0 0
$$514$$ 13.7477 + 5.19615i 0.606386 + 0.229192i
$$515$$ 31.7490i 1.39903i
$$516$$ 0 0
$$517$$ 24.2487i 1.06646i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −15.0000 + 7.93725i −0.657794 + 0.348072i
$$521$$ 6.92820i 0.303530i −0.988417 0.151765i $$-0.951504\pi$$
0.988417 0.151765i $$-0.0484957\pi$$
$$522$$ 0 0
$$523$$ 27.4955 1.20229 0.601146 0.799139i $$-0.294711\pi$$
0.601146 + 0.799139i $$0.294711\pi$$
$$524$$ 20.6216 + 18.1865i 0.900858 + 0.794482i
$$525$$ 0 0
$$526$$ −14.0000 5.29150i −0.610429 0.230720i
$$527$$ 31.7490i 1.38301i
$$528$$ 0 0
$$529$$ −5.00000 −0.217391
$$530$$ −16.0390 6.06218i −0.696690 0.263324i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ −32.0780 −1.38685
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −25.2042 9.52628i −1.08663 0.410707i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 8.00000 0.343947 0.171973 0.985102i $$-0.444986\pi$$
0.171973 + 0.985102i $$0.444986\pi$$
$$542$$ −6.87386 + 18.1865i −0.295258 + 0.781179i
$$543$$ 0 0
$$544$$ 9.16515 38.1051i 0.392953 1.63374i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 31.7490i 1.35749i 0.734374 + 0.678745i $$0.237476\pi$$
−0.734374 + 0.678745i $$0.762524\pi$$
$$548$$ −6.00000 5.29150i −0.256307 0.226042i
$$549$$ 0 0
$$550$$ 7.00000 + 2.64575i 0.298481 + 0.112815i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 2.00000 5.29150i 0.0849719 0.224814i
$$555$$ 0 0
$$556$$ 13.7477 + 12.1244i 0.583033 + 0.514187i
$$557$$ 7.00000 0.296600 0.148300 0.988942i $$-0.452620\pi$$
0.148300 + 0.988942i $$0.452620\pi$$
$$558$$ 0 0
$$559$$ −36.6606 −1.55058
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 8.00000 21.1660i 0.337460 0.892834i
$$563$$ 22.9129 0.965663 0.482831 0.875713i $$-0.339608\pi$$
0.482831 + 0.875713i $$0.339608\pi$$
$$564$$ 0 0
$$565$$ 24.2487i 1.02015i
$$566$$ 9.16515 24.2487i 0.385240 1.01925i
$$567$$ 0 0
$$568$$ −7.00000 13.2288i −0.293713 0.555066i
$$569$$ 8.00000 0.335377 0.167689 0.985840i $$-0.446370\pi$$
0.167689 + 0.985840i $$0.446370\pi$$
$$570$$ 0 0
$$571$$ 15.8745i 0.664327i 0.943222 + 0.332164i $$0.107779\pi$$
−0.943222 + 0.332164i $$0.892221\pi$$
$$572$$ 13.7477 + 12.1244i 0.574821 + 0.506945i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 10.5830i 0.441342i
$$576$$ 0 0
$$577$$ 43.3013i 1.80266i 0.433138 + 0.901328i $$0.357406\pi$$
−0.433138 + 0.901328i $$0.642594\pi$$
$$578$$ 15.5000 41.0091i 0.644715 1.70576i
$$579$$ 0 0
$$580$$ 11.4564 12.9904i 0.475703 0.539396i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 18.5203i 0.767031i
$$584$$ 9.16515 + 17.3205i 0.379257 + 0.716728i
$$585$$ 0 0
$$586$$ 20.6216 + 7.79423i 0.851870 + 0.321977i
$$587$$ 22.9129 0.945716 0.472858 0.881139i $$-0.343222\pi$$
0.472858 + 0.881139i $$0.343222\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −31.5000 11.9059i −1.29683 0.490157i
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 10.3923i 0.426761i −0.976969 0.213380i $$-0.931553\pi$$
0.976969 0.213380i $$-0.0684474\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 21.0000 + 18.5203i 0.860194 + 0.758619i
$$597$$ 0 0
$$598$$ 9.16515 24.2487i 0.374791 0.991604i
$$599$$ 10.5830i 0.432410i −0.976348 0.216205i $$-0.930632\pi$$
0.976348 0.216205i $$-0.0693679\pi$$
$$600$$ 0 0
$$601$$ 8.66025i 0.353259i 0.984277 + 0.176630i $$0.0565195\pi$$
−0.984277 + 0.176630i $$0.943481\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −17.5000 + 19.8431i −0.712065 + 0.807406i
$$605$$ 6.92820i 0.281672i
$$606$$ 0 0
$$607$$ 13.7477 0.558003 0.279002 0.960291i $$-0.409997\pi$$
0.279002 + 0.960291i $$0.409997\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 9.00000 23.8118i 0.364399 0.964110i
$$611$$ 31.7490i 1.28443i
$$612$$ 0 0
$$613$$ 14.0000 0.565455 0.282727 0.959200i $$-0.408761\pi$$
0.282727 + 0.959200i $$0.408761\pi$$
$$614$$ −13.7477 + 36.3731i −0.554813 + 1.46790i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 2.00000 0.0805170 0.0402585 0.999189i $$-0.487182\pi$$
0.0402585 + 0.999189i $$0.487182\pi$$
$$618$$ 0 0
$$619$$ 27.4955 1.10514 0.552568 0.833468i $$-0.313648\pi$$
0.552568 + 0.833468i $$0.313648\pi$$
$$620$$ −10.5000 + 11.9059i −0.421690 + 0.478152i
$$621$$ 0 0
$$622$$ 4.58258 12.1244i 0.183745 0.486142i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −11.0000 −0.440000
$$626$$ −29.7867 11.2583i −1.19052 0.449973i
$$627$$ 0 0
$$628$$ −9.16515 + 10.3923i −0.365729 + 0.414698i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 7.93725i 0.315977i 0.987441 + 0.157989i $$0.0505009\pi$$
−0.987441 + 0.157989i $$0.949499\pi$$
$$632$$ −10.5000 19.8431i −0.417668 0.789318i
$$633$$ 0 0
$$634$$ 3.50000 9.26013i 0.139003 0.367767i
$$635$$ 13.7477 0.545562
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −17.5000 6.61438i −0.692832 0.261866i
$$639$$ 0 0
$$640$$ 16.0390 11.2583i 0.633998 0.445025i
$$641$$ 38.0000 1.50091 0.750455 0.660922i $$-0.229834\pi$$
0.750455 + 0.660922i $$0.229834\pi$$
$$642$$ 0 0
$$643$$ −18.3303 −0.722877 −0.361438 0.932396i $$-0.617714\pi$$
−0.361438 + 0.932396i $$0.617714\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −9.16515 −0.360319 −0.180160 0.983637i $$-0.557661\pi$$
−0.180160 + 0.983637i $$0.557661\pi$$
$$648$$ 0 0
$$649$$ 36.3731i 1.42777i
$$650$$ 9.16515 + 3.46410i 0.359487 + 0.135873i
$$651$$ 0 0
$$652$$ 21.0000 23.8118i 0.822423 0.932541i
$$653$$ 43.0000 1.68272 0.841360 0.540475i $$-0.181755\pi$$
0.841360 + 0.540475i $$0.181755\pi$$
$$654$$ 0 0
$$655$$ 23.8118i 0.930403i
$$656$$ −13.7477 + 1.73205i −0.536759 + 0.0676252i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 26.4575i 1.03064i 0.856998 + 0.515319i $$0.172327\pi$$
−0.856998 + 0.515319i $$0.827673\pi$$
$$660$$ 0 0
$$661$$ 6.92820i 0.269476i −0.990881 0.134738i $$-0.956981\pi$$
0.990881 0.134738i $$-0.0430193\pi$$
$$662$$ 14.0000 + 5.29150i 0.544125 + 0.205660i
$$663$$ 0 0
$$664$$ 11.4564 6.06218i 0.444596 0.235258i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 26.4575i 1.02444i
$$668$$ −27.4955 24.2487i −1.06383 0.938211i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −27.4955 −1.06145
$$672$$ 0 0
$$673$$ 21.0000 0.809491 0.404745 0.914429i $$-0.367360\pi$$
0.404745 + 0.914429i $$0.367360\pi$$
$$674$$ 10.5000 27.7804i 0.404445 1.07006i
$$675$$ 0 0
$$676$$ −1.50000 1.32288i −0.0576923 0.0508798i
$$677$$ 22.5167i 0.865386i −0.901541 0.432693i $$-0.857563\pi$$
0.901541 0.432693i $$-0.142437\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 30.0000 15.8745i 1.15045 0.608760i
$$681$$ 0 0
$$682$$ 16.0390 + 6.06218i 0.614166 + 0.232133i
$$683$$ 2.64575i 0.101237i −0.998718 0.0506184i $$-0.983881\pi$$
0.998718 0.0506184i $$-0.0161192\pi$$
$$684$$ 0 0
$$685$$ 6.92820i 0.264713i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 42.0000 5.29150i 1.60123 0.201737i
$$689$$ 24.2487i 0.923802i
$$690$$ 0 0
$$691$$ −45.8258 −1.74329 −0.871647 0.490134i $$-0.836948\pi$$
−0.871647 + 0.490134i $$0.836948\pi$$
$$692$$ 18.3303 20.7846i 0.696814 0.790112i
$$693$$ 0 0
$$694$$ 7.00000 + 2.64575i 0.265716 + 0.100431i
$$695$$ 15.8745i 0.602154i
$$696$$ 0 0
$$697$$ −24.0000 −0.909065
$$698$$ −27.4955 10.3923i −1.04072 0.393355i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −23.0000 −0.868698 −0.434349 0.900745i $$-0.643022\pi$$
−0.434349 + 0.900745i $$0.643022\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −17.5000 11.9059i −0.659556 0.448720i
$$705$$ 0 0
$$706$$ 9.16515 + 3.46410i 0.344935 + 0.130373i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 42.0000 1.57734 0.788672 0.614815i $$-0.210769\pi$$
0.788672 + 0.614815i $$0.210769\pi$$
$$710$$ 4.58258 12.1244i 0.171981 0.455019i
$$711$$ 0 0
$$712$$ 13.7477 + 25.9808i 0.515218 + 0.973670i
$$713$$ 24.2487i 0.908121i
$$714$$ 0 0
$$715$$ 15.8745i 0.593673i
$$716$$ −7.00000 + 7.93725i −0.261602 + 0.296629i
$$717$$ 0 0
$$718$$ 14.0000 + 5.29150i 0.522475 + 0.197477i
$$719$$ 27.4955 1.02541 0.512704 0.858566i $$-0.328644\pi$$
0.512704 + 0.858566i $$0.328644\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 9.50000 25.1346i 0.353553 0.935414i
$$723$$ 0 0
$$724$$ 4.58258 5.19615i 0.170310 0.193113i
$$725$$ −10.0000 −0.371391
$$726$$ 0 0
$$727$$ 13.7477 0.509875 0.254937 0.966958i $$-0.417945\pi$$
0.254937 + 0.966958i $$0.417945\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −6.00000 + 15.8745i −0.222070 + 0.587542i
$$731$$ 73.3212 2.71188
$$732$$ 0 0
$$733$$ 34.6410i 1.27950i −0.768585 0.639748i $$-0.779039\pi$$
0.768585 0.639748i $$-0.220961\pi$$
$$734$$ 2.29129 6.06218i 0.0845730 0.223759i
$$735$$ 0 0
$$736$$ −7.00000 + 29.1033i −0.258023 + 1.07276i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 47.6235i 1.75186i −0.482439 0.875930i $$-0.660249\pi$$
0.482439 0.875930i $$-0.339751\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 21.1660i 0.776506i 0.921553 + 0.388253i $$0.126921\pi$$
−0.921553 + 0.388253i $$0.873079\pi$$
$$744$$ 0 0
$$745$$ 24.2487i 0.888404i
$$746$$ −17.0000 + 44.9778i −0.622414 + 1.64675i
$$747$$ 0 0
$$748$$ −27.4955 24.2487i −1.00533 0.886621i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 13.2288i 0.482724i 0.970435 + 0.241362i $$0.0775941\pi$$
−0.970435 + 0.241362i $$0.922406\pi$$
$$752$$ −4.58258 36.3731i −0.167109 1.32639i
$$753$$ 0 0
$$754$$ −22.9129 8.66025i −0.834438 0.315388i
$$755$$ −22.9129 −0.833885
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ 7.00000 + 2.64575i 0.254251 + 0.0960980i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 38.1051i 1.38131i −0.723185 0.690655i $$-0.757322\pi$$
0.723185 0.690655i $$-0.242678\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −14.0000 + 15.8745i −0.506502 + 0.574320i
$$765$$ 0 0
$$766$$ −13.7477 + 36.3731i −0.496726 + 1.31421i
$$767$$ 47.6235i 1.71959i
$$768$$ 0 0
$$769$$ 32.9090i 1.18673i −0.804934 0.593364i $$-0.797800\pi$$
0.804934 0.593364i $$-0.202200\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −4.50000 3.96863i −0.161959 0.142834i
$$773$$ 41.5692i 1.49514i −0.664183 0.747570i $$-0.731220\pi$$
0.664183 0.747570i $$-0.268780\pi$$
$$774$$ 0 0
$$775$$ 9.16515 0.329222
$$776$$ −11.4564 21.6506i −0.411262 0.777213i
$$777$$ 0 0
$$778$$ 5.00000 13.2288i 0.179259 0.474274i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −14.0000 −0.500959
$$782$$ −18.3303 + 48.4974i −0.655490 + 1.73426i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −12.0000 −0.428298
$$786$$ 0 0
$$787$$ 27.4955 0.980107 0.490054 0.871692i $$-0.336977\pi$$
0.490054 + 0.871692i $$0.336977\pi$$
$$788$$ 21.0000 + 18.5203i 0.748094 + 0.659757i
$$789$$ 0 0
$$790$$ 6.87386 18.1865i 0.244561 0.647048i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −36.0000 −1.27840
$$794$$ −18.3303 6.92820i −0.650518 0.245873i
$$795$$ 0 0
$$796$$ −27.4955 24.2487i −0.974551 0.859473i
$$797$$ 15.5885i 0.552171i −0.961133 0.276086i $$-0.910963\pi$$
0.961133 0.276086i $$-0.0890374\pi$$
$$798$$ 0 0
$$799$$ 63.4980i 2.24640i
$$800$$ −11.0000 2.64575i −0.388909 0.0935414i
$$801$$ 0 0
$$802$$ 4.00000 10.5830i 0.141245 0.373699i
$$803$$ 18.3303 0.646862
$$804$$ 0 0
$$805$$ 0 0