# Properties

 Label 144.2.s.a.47.1 Level $144$ Weight $2$ Character 144.47 Analytic conductor $1.150$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 144.s (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.14984578911$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 47.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 144.47 Dual form 144.2.s.a.95.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 - 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(-3.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(-1.50000 - 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(-3.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.00000 - 3.46410i) q^{13} +6.00000 q^{15} -1.73205i q^{17} +1.73205i q^{19} +(3.00000 + 5.19615i) q^{21} +(3.50000 - 6.06218i) q^{25} -5.19615i q^{27} +(-3.00000 - 1.73205i) q^{29} +(4.50000 - 2.59808i) q^{33} +12.0000 q^{35} +2.00000 q^{37} +6.92820i q^{39} +(-4.50000 + 2.59808i) q^{41} +(4.50000 + 2.59808i) q^{43} +(-9.00000 - 5.19615i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(2.50000 + 4.33013i) q^{49} +(-1.50000 + 2.59808i) q^{51} -10.3923i q^{55} +(1.50000 - 2.59808i) q^{57} +(-7.50000 - 12.9904i) q^{59} +(-4.00000 + 6.92820i) q^{61} -10.3923i q^{63} +(12.0000 + 6.92820i) q^{65} +(-7.50000 + 4.33013i) q^{67} -6.00000 q^{71} -11.0000 q^{73} +(-10.5000 + 6.06218i) q^{75} +(9.00000 - 5.19615i) q^{77} +(3.00000 + 1.73205i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 10.3923i) q^{83} +(3.00000 + 5.19615i) q^{85} +(3.00000 + 5.19615i) q^{87} -13.8564i q^{89} +13.8564i q^{91} +(-3.00000 - 5.19615i) q^{95} +(-6.50000 + 11.2583i) q^{97} -9.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 3q^{3} - 6q^{5} - 6q^{7} + 3q^{9} + O(q^{10})$$ $$2q - 3q^{3} - 6q^{5} - 6q^{7} + 3q^{9} - 3q^{11} - 4q^{13} + 12q^{15} + 6q^{21} + 7q^{25} - 6q^{29} + 9q^{33} + 24q^{35} + 4q^{37} - 9q^{41} + 9q^{43} - 18q^{45} - 12q^{47} + 5q^{49} - 3q^{51} + 3q^{57} - 15q^{59} - 8q^{61} + 24q^{65} - 15q^{67} - 12q^{71} - 22q^{73} - 21q^{75} + 18q^{77} + 6q^{79} - 9q^{81} + 12q^{83} + 6q^{85} + 6q^{87} - 6q^{95} - 13q^{97} - 18q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$$.

 $$n$$ $$37$$ $$65$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.50000 0.866025i −0.866025 0.500000i
$$4$$ 0 0
$$5$$ −3.00000 + 1.73205i −1.34164 + 0.774597i −0.987048 0.160424i $$-0.948714\pi$$
−0.354593 + 0.935021i $$0.615380\pi$$
$$6$$ 0 0
$$7$$ −3.00000 1.73205i −1.13389 0.654654i −0.188982 0.981981i $$-0.560519\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ 0 0
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ 0 0
$$13$$ −2.00000 3.46410i −0.554700 0.960769i −0.997927 0.0643593i $$-0.979500\pi$$
0.443227 0.896410i $$-0.353834\pi$$
$$14$$ 0 0
$$15$$ 6.00000 1.54919
$$16$$ 0 0
$$17$$ 1.73205i 0.420084i −0.977692 0.210042i $$-0.932640\pi$$
0.977692 0.210042i $$-0.0673601\pi$$
$$18$$ 0 0
$$19$$ 1.73205i 0.397360i 0.980064 + 0.198680i $$0.0636654\pi$$
−0.980064 + 0.198680i $$0.936335\pi$$
$$20$$ 0 0
$$21$$ 3.00000 + 5.19615i 0.654654 + 1.13389i
$$22$$ 0 0
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 0 0
$$25$$ 3.50000 6.06218i 0.700000 1.21244i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ −3.00000 1.73205i −0.557086 0.321634i 0.194889 0.980825i $$-0.437565\pi$$
−0.751975 + 0.659192i $$0.770899\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$32$$ 0 0
$$33$$ 4.50000 2.59808i 0.783349 0.452267i
$$34$$ 0 0
$$35$$ 12.0000 2.02837
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 6.92820i 1.10940i
$$40$$ 0 0
$$41$$ −4.50000 + 2.59808i −0.702782 + 0.405751i −0.808383 0.588657i $$-0.799657\pi$$
0.105601 + 0.994409i $$0.466323\pi$$
$$42$$ 0 0
$$43$$ 4.50000 + 2.59808i 0.686244 + 0.396203i 0.802203 0.597051i $$-0.203661\pi$$
−0.115960 + 0.993254i $$0.536994\pi$$
$$44$$ 0 0
$$45$$ −9.00000 5.19615i −1.34164 0.774597i
$$46$$ 0 0
$$47$$ −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i $$0.505930\pi$$
−0.856560 + 0.516047i $$0.827403\pi$$
$$48$$ 0 0
$$49$$ 2.50000 + 4.33013i 0.357143 + 0.618590i
$$50$$ 0 0
$$51$$ −1.50000 + 2.59808i −0.210042 + 0.363803i
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 10.3923i 1.40130i
$$56$$ 0 0
$$57$$ 1.50000 2.59808i 0.198680 0.344124i
$$58$$ 0 0
$$59$$ −7.50000 12.9904i −0.976417 1.69120i −0.675178 0.737655i $$-0.735933\pi$$
−0.301239 0.953549i $$-0.597400\pi$$
$$60$$ 0 0
$$61$$ −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i $$0.337817\pi$$
−0.999901 + 0.0140840i $$0.995517\pi$$
$$62$$ 0 0
$$63$$ 10.3923i 1.30931i
$$64$$ 0 0
$$65$$ 12.0000 + 6.92820i 1.48842 + 0.859338i
$$66$$ 0 0
$$67$$ −7.50000 + 4.33013i −0.916271 + 0.529009i −0.882443 0.470418i $$-0.844103\pi$$
−0.0338274 + 0.999428i $$0.510770\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0 0
$$73$$ −11.0000 −1.28745 −0.643726 0.765256i $$-0.722612\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ 0 0
$$75$$ −10.5000 + 6.06218i −1.21244 + 0.700000i
$$76$$ 0 0
$$77$$ 9.00000 5.19615i 1.02565 0.592157i
$$78$$ 0 0
$$79$$ 3.00000 + 1.73205i 0.337526 + 0.194871i 0.659178 0.751987i $$-0.270905\pi$$
−0.321651 + 0.946858i $$0.604238\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i $$-0.604488\pi$$
0.980982 0.194099i $$-0.0621783\pi$$
$$84$$ 0 0
$$85$$ 3.00000 + 5.19615i 0.325396 + 0.563602i
$$86$$ 0 0
$$87$$ 3.00000 + 5.19615i 0.321634 + 0.557086i
$$88$$ 0 0
$$89$$ 13.8564i 1.46878i −0.678730 0.734388i $$-0.737469\pi$$
0.678730 0.734388i $$-0.262531\pi$$
$$90$$ 0 0
$$91$$ 13.8564i 1.45255i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −3.00000 5.19615i −0.307794 0.533114i
$$96$$ 0 0
$$97$$ −6.50000 + 11.2583i −0.659975 + 1.14311i 0.320647 + 0.947199i $$0.396100\pi$$
−0.980622 + 0.195911i $$0.937234\pi$$
$$98$$ 0 0
$$99$$ −9.00000 −0.904534
$$100$$ 0 0
$$101$$ 9.00000 + 5.19615i 0.895533 + 0.517036i 0.875748 0.482768i $$-0.160368\pi$$
0.0197851 + 0.999804i $$0.493702\pi$$
$$102$$ 0 0
$$103$$ 12.0000 6.92820i 1.18240 0.682656i 0.225828 0.974167i $$-0.427491\pi$$
0.956567 + 0.291511i $$0.0941580\pi$$
$$104$$ 0 0
$$105$$ −18.0000 10.3923i −1.75662 1.01419i
$$106$$ 0 0
$$107$$ 3.00000 0.290021 0.145010 0.989430i $$-0.453678\pi$$
0.145010 + 0.989430i $$0.453678\pi$$
$$108$$ 0 0
$$109$$ 4.00000 0.383131 0.191565 0.981480i $$-0.438644\pi$$
0.191565 + 0.981480i $$0.438644\pi$$
$$110$$ 0 0
$$111$$ −3.00000 1.73205i −0.284747 0.164399i
$$112$$ 0 0
$$113$$ −6.00000 + 3.46410i −0.564433 + 0.325875i −0.754923 0.655814i $$-0.772326\pi$$
0.190490 + 0.981689i $$0.438992\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 6.00000 10.3923i 0.554700 0.960769i
$$118$$ 0 0
$$119$$ −3.00000 + 5.19615i −0.275010 + 0.476331i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ 9.00000 0.811503
$$124$$ 0 0
$$125$$ 6.92820i 0.619677i
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ −4.50000 7.79423i −0.396203 0.686244i
$$130$$ 0 0
$$131$$ 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i $$0.00897729\pi$$
−0.475380 + 0.879781i $$0.657689\pi$$
$$132$$ 0 0
$$133$$ 3.00000 5.19615i 0.260133 0.450564i
$$134$$ 0 0
$$135$$ 9.00000 + 15.5885i 0.774597 + 1.34164i
$$136$$ 0 0
$$137$$ −1.50000 0.866025i −0.128154 0.0739895i 0.434553 0.900646i $$-0.356906\pi$$
−0.562706 + 0.826657i $$0.690240\pi$$
$$138$$ 0 0
$$139$$ 16.5000 9.52628i 1.39951 0.808008i 0.405170 0.914241i $$-0.367212\pi$$
0.994341 + 0.106233i $$0.0338788\pi$$
$$140$$ 0 0
$$141$$ 18.0000 10.3923i 1.51587 0.875190i
$$142$$ 0 0
$$143$$ 12.0000 1.00349
$$144$$ 0 0
$$145$$ 12.0000 0.996546
$$146$$ 0 0
$$147$$ 8.66025i 0.714286i
$$148$$ 0 0
$$149$$ 12.0000 6.92820i 0.983078 0.567581i 0.0798802 0.996804i $$-0.474546\pi$$
0.903198 + 0.429224i $$0.141213\pi$$
$$150$$ 0 0
$$151$$ −6.00000 3.46410i −0.488273 0.281905i 0.235585 0.971854i $$-0.424299\pi$$
−0.723858 + 0.689949i $$0.757633\pi$$
$$152$$ 0 0
$$153$$ 4.50000 2.59808i 0.363803 0.210042i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −4.00000 6.92820i −0.319235 0.552931i 0.661094 0.750303i $$-0.270093\pi$$
−0.980329 + 0.197372i $$0.936759\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 3.46410i 0.271329i 0.990755 + 0.135665i $$0.0433170\pi$$
−0.990755 + 0.135665i $$0.956683\pi$$
$$164$$ 0 0
$$165$$ −9.00000 + 15.5885i −0.700649 + 1.21356i
$$166$$ 0 0
$$167$$ −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i $$-0.241242\pi$$
−0.958440 + 0.285295i $$0.907908\pi$$
$$168$$ 0 0
$$169$$ −1.50000 + 2.59808i −0.115385 + 0.199852i
$$170$$ 0 0
$$171$$ −4.50000 + 2.59808i −0.344124 + 0.198680i
$$172$$ 0 0
$$173$$ −21.0000 12.1244i −1.59660 0.921798i −0.992136 0.125166i $$-0.960054\pi$$
−0.604465 0.796632i $$-0.706613\pi$$
$$174$$ 0 0
$$175$$ −21.0000 + 12.1244i −1.58745 + 0.916515i
$$176$$ 0 0
$$177$$ 25.9808i 1.95283i
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ −8.00000 −0.594635 −0.297318 0.954779i $$-0.596092\pi$$
−0.297318 + 0.954779i $$0.596092\pi$$
$$182$$ 0 0
$$183$$ 12.0000 6.92820i 0.887066 0.512148i
$$184$$ 0 0
$$185$$ −6.00000 + 3.46410i −0.441129 + 0.254686i
$$186$$ 0 0
$$187$$ 4.50000 + 2.59808i 0.329073 + 0.189990i
$$188$$ 0 0
$$189$$ −9.00000 + 15.5885i −0.654654 + 1.13389i
$$190$$ 0 0
$$191$$ 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i $$-0.763683\pi$$
0.953912 + 0.300088i $$0.0970159\pi$$
$$192$$ 0 0
$$193$$ −11.5000 19.9186i −0.827788 1.43377i −0.899770 0.436365i $$-0.856266\pi$$
0.0719816 0.997406i $$-0.477068\pi$$
$$194$$ 0 0
$$195$$ −12.0000 20.7846i −0.859338 1.48842i
$$196$$ 0 0
$$197$$ 13.8564i 0.987228i 0.869681 + 0.493614i $$0.164324\pi$$
−0.869681 + 0.493614i $$0.835676\pi$$
$$198$$ 0 0
$$199$$ 3.46410i 0.245564i 0.992434 + 0.122782i $$0.0391815\pi$$
−0.992434 + 0.122782i $$0.960818\pi$$
$$200$$ 0 0
$$201$$ 15.0000 1.05802
$$202$$ 0 0
$$203$$ 6.00000 + 10.3923i 0.421117 + 0.729397i
$$204$$ 0 0
$$205$$ 9.00000 15.5885i 0.628587 1.08875i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −4.50000 2.59808i −0.311272 0.179713i
$$210$$ 0 0
$$211$$ −15.0000 + 8.66025i −1.03264 + 0.596196i −0.917741 0.397180i $$-0.869989\pi$$
−0.114902 + 0.993377i $$0.536655\pi$$
$$212$$ 0 0
$$213$$ 9.00000 + 5.19615i 0.616670 + 0.356034i
$$214$$ 0 0
$$215$$ −18.0000 −1.22759
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 16.5000 + 9.52628i 1.11497 + 0.643726i
$$220$$ 0 0
$$221$$ −6.00000 + 3.46410i −0.403604 + 0.233021i
$$222$$ 0 0
$$223$$ −18.0000 10.3923i −1.20537 0.695920i −0.243625 0.969870i $$-0.578337\pi$$
−0.961744 + 0.273949i $$0.911670\pi$$
$$224$$ 0 0
$$225$$ 21.0000 1.40000
$$226$$ 0 0
$$227$$ −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i $$-0.865076\pi$$
0.811943 + 0.583736i $$0.198410\pi$$
$$228$$ 0 0
$$229$$ 13.0000 + 22.5167i 0.859064 + 1.48794i 0.872823 + 0.488037i $$0.162287\pi$$
−0.0137585 + 0.999905i $$0.504380\pi$$
$$230$$ 0 0
$$231$$ −18.0000 −1.18431
$$232$$ 0 0
$$233$$ 12.1244i 0.794293i 0.917755 + 0.397146i $$0.130000\pi$$
−0.917755 + 0.397146i $$0.870000\pi$$
$$234$$ 0 0
$$235$$ 41.5692i 2.71168i
$$236$$ 0 0
$$237$$ −3.00000 5.19615i −0.194871 0.337526i
$$238$$ 0 0
$$239$$ 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i $$0.116196\pi$$
−0.157893 + 0.987456i $$0.550470\pi$$
$$240$$ 0 0
$$241$$ 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i $$-0.648900\pi$$
0.998443 0.0557856i $$-0.0177663\pi$$
$$242$$ 0 0
$$243$$ 13.5000 7.79423i 0.866025 0.500000i
$$244$$ 0 0
$$245$$ −15.0000 8.66025i −0.958315 0.553283i
$$246$$ 0 0
$$247$$ 6.00000 3.46410i 0.381771 0.220416i
$$248$$ 0 0
$$249$$ −18.0000 + 10.3923i −1.14070 + 0.658586i
$$250$$ 0 0
$$251$$ −21.0000 −1.32551 −0.662754 0.748837i $$-0.730613\pi$$
−0.662754 + 0.748837i $$0.730613\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 10.3923i 0.650791i
$$256$$ 0 0
$$257$$ −16.5000 + 9.52628i −1.02924 + 0.594233i −0.916767 0.399422i $$-0.869211\pi$$
−0.112474 + 0.993655i $$0.535878\pi$$
$$258$$ 0 0
$$259$$ −6.00000 3.46410i −0.372822 0.215249i
$$260$$ 0 0
$$261$$ 10.3923i 0.643268i
$$262$$ 0 0
$$263$$ 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i $$-0.646065\pi$$
0.997906 0.0646755i $$-0.0206012\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.0000 + 20.7846i −0.734388 + 1.27200i
$$268$$ 0 0
$$269$$ 6.92820i 0.422420i 0.977441 + 0.211210i $$0.0677404\pi$$
−0.977441 + 0.211210i $$0.932260\pi$$
$$270$$ 0 0
$$271$$ 6.92820i 0.420858i 0.977609 + 0.210429i $$0.0674861\pi$$
−0.977609 + 0.210429i $$0.932514\pi$$
$$272$$ 0 0
$$273$$ 12.0000 20.7846i 0.726273 1.25794i
$$274$$ 0 0
$$275$$ 10.5000 + 18.1865i 0.633174 + 1.09669i
$$276$$ 0 0
$$277$$ 4.00000 6.92820i 0.240337 0.416275i −0.720473 0.693482i $$-0.756075\pi$$
0.960810 + 0.277207i $$0.0894088\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 6.00000 + 3.46410i 0.357930 + 0.206651i 0.668172 0.744007i $$-0.267077\pi$$
−0.310242 + 0.950657i $$0.600410\pi$$
$$282$$ 0 0
$$283$$ −9.00000 + 5.19615i −0.534994 + 0.308879i −0.743048 0.669238i $$-0.766621\pi$$
0.208053 + 0.978117i $$0.433287\pi$$
$$284$$ 0 0
$$285$$ 10.3923i 0.615587i
$$286$$ 0 0
$$287$$ 18.0000 1.06251
$$288$$ 0 0
$$289$$ 14.0000 0.823529
$$290$$ 0 0
$$291$$ 19.5000 11.2583i 1.14311 0.659975i
$$292$$ 0 0
$$293$$ −3.00000 + 1.73205i −0.175262 + 0.101187i −0.585065 0.810987i $$-0.698931\pi$$
0.409803 + 0.912174i $$0.365598\pi$$
$$294$$ 0 0
$$295$$ 45.0000 + 25.9808i 2.62000 + 1.51266i
$$296$$ 0 0
$$297$$ 13.5000 + 7.79423i 0.783349 + 0.452267i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −9.00000 15.5885i −0.518751 0.898504i
$$302$$ 0 0
$$303$$ −9.00000 15.5885i −0.517036 0.895533i
$$304$$ 0 0
$$305$$ 27.7128i 1.58683i
$$306$$ 0 0
$$307$$ 25.9808i 1.48280i 0.671063 + 0.741400i $$0.265838\pi$$
−0.671063 + 0.741400i $$0.734162\pi$$
$$308$$ 0 0
$$309$$ −24.0000 −1.36531
$$310$$ 0 0
$$311$$ 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i $$-0.112253\pi$$
−0.768345 + 0.640036i $$0.778920\pi$$
$$312$$ 0 0
$$313$$ 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i $$-0.824336\pi$$
0.879810 + 0.475325i $$0.157669\pi$$
$$314$$ 0 0
$$315$$ 18.0000 + 31.1769i 1.01419 + 1.75662i
$$316$$ 0 0
$$317$$ −6.00000 3.46410i −0.336994 0.194563i 0.321948 0.946757i $$-0.395662\pi$$
−0.658942 + 0.752194i $$0.728996\pi$$
$$318$$ 0 0
$$319$$ 9.00000 5.19615i 0.503903 0.290929i
$$320$$ 0 0
$$321$$ −4.50000 2.59808i −0.251166 0.145010i
$$322$$ 0 0
$$323$$ 3.00000 0.166924
$$324$$ 0 0
$$325$$ −28.0000 −1.55316
$$326$$ 0 0
$$327$$ −6.00000 3.46410i −0.331801 0.191565i
$$328$$ 0 0
$$329$$ 36.0000 20.7846i 1.98474 1.14589i
$$330$$ 0 0
$$331$$ −21.0000 12.1244i −1.15426 0.666415i −0.204342 0.978900i $$-0.565505\pi$$
−0.949923 + 0.312485i $$0.898839\pi$$
$$332$$ 0 0
$$333$$ 3.00000 + 5.19615i 0.164399 + 0.284747i
$$334$$ 0 0
$$335$$ 15.0000 25.9808i 0.819538 1.41948i
$$336$$ 0 0
$$337$$ 5.50000 + 9.52628i 0.299604 + 0.518930i 0.976045 0.217567i $$-0.0698121\pi$$
−0.676441 + 0.736497i $$0.736479\pi$$
$$338$$ 0 0
$$339$$ 12.0000 0.651751
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 6.92820i 0.374088i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −13.5000 23.3827i −0.724718 1.25525i −0.959090 0.283101i $$-0.908637\pi$$
0.234372 0.972147i $$-0.424697\pi$$
$$348$$ 0 0
$$349$$ −16.0000 + 27.7128i −0.856460 + 1.48343i 0.0188232 + 0.999823i $$0.494008\pi$$
−0.875284 + 0.483610i $$0.839325\pi$$
$$350$$ 0 0
$$351$$ −18.0000 + 10.3923i −0.960769 + 0.554700i
$$352$$ 0 0
$$353$$ 22.5000 + 12.9904i 1.19755 + 0.691408i 0.960009 0.279968i $$-0.0903240\pi$$
0.237545 + 0.971377i $$0.423657\pi$$
$$354$$ 0 0
$$355$$ 18.0000 10.3923i 0.955341 0.551566i
$$356$$ 0 0
$$357$$ 9.00000 5.19615i 0.476331 0.275010i
$$358$$ 0 0
$$359$$ −30.0000 −1.58334 −0.791670 0.610949i $$-0.790788\pi$$
−0.791670 + 0.610949i $$0.790788\pi$$
$$360$$ 0 0
$$361$$ 16.0000 0.842105
$$362$$ 0 0
$$363$$ 3.46410i 0.181818i
$$364$$ 0 0
$$365$$ 33.0000 19.0526i 1.72730 0.997257i
$$366$$ 0 0
$$367$$ −3.00000 1.73205i −0.156599 0.0904123i 0.419653 0.907685i $$-0.362152\pi$$
−0.576252 + 0.817272i $$0.695485\pi$$
$$368$$ 0 0
$$369$$ −13.5000 7.79423i −0.702782 0.405751i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −10.0000 17.3205i −0.517780 0.896822i −0.999787 0.0206542i $$-0.993425\pi$$
0.482006 0.876168i $$-0.339908\pi$$
$$374$$ 0 0
$$375$$ 6.00000 10.3923i 0.309839 0.536656i
$$376$$ 0 0
$$377$$ 13.8564i 0.713641i
$$378$$ 0 0
$$379$$ 19.0526i 0.978664i −0.872098 0.489332i $$-0.837241\pi$$
0.872098 0.489332i $$-0.162759\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i $$-0.0145596\pi$$
−0.539076 + 0.842257i $$0.681226\pi$$
$$384$$ 0 0
$$385$$ −18.0000 + 31.1769i −0.917365 + 1.58892i
$$386$$ 0 0
$$387$$ 15.5885i 0.792406i
$$388$$ 0 0
$$389$$ −9.00000 5.19615i −0.456318 0.263455i 0.254177 0.967158i $$-0.418196\pi$$
−0.710495 + 0.703702i $$0.751529\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 20.7846i 1.04844i
$$394$$ 0 0
$$395$$ −12.0000 −0.603786
$$396$$ 0 0
$$397$$ 14.0000 0.702640 0.351320 0.936255i $$-0.385733\pi$$
0.351320 + 0.936255i $$0.385733\pi$$
$$398$$ 0 0
$$399$$ −9.00000 + 5.19615i −0.450564 + 0.260133i
$$400$$ 0 0
$$401$$ −7.50000 + 4.33013i −0.374532 + 0.216236i −0.675437 0.737418i $$-0.736045\pi$$
0.300904 + 0.953654i $$0.402711\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 31.1769i 1.54919i
$$406$$ 0 0
$$407$$ −3.00000 + 5.19615i −0.148704 + 0.257564i
$$408$$ 0 0
$$409$$ 11.5000 + 19.9186i 0.568638 + 0.984911i 0.996701 + 0.0811615i $$0.0258630\pi$$
−0.428063 + 0.903749i $$0.640804\pi$$
$$410$$ 0 0
$$411$$ 1.50000 + 2.59808i 0.0739895 + 0.128154i
$$412$$ 0 0
$$413$$ 51.9615i 2.55686i
$$414$$ 0 0
$$415$$ 41.5692i 2.04055i
$$416$$ 0 0
$$417$$ −33.0000 −1.61602
$$418$$ 0 0
$$419$$ −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i $$-0.261360\pi$$
−0.974546 + 0.224189i $$0.928027\pi$$
$$420$$ 0 0
$$421$$ −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i $$-0.911690\pi$$
0.718076 + 0.695965i $$0.245023\pi$$
$$422$$ 0 0
$$423$$ −36.0000 −1.75038
$$424$$ 0 0
$$425$$ −10.5000 6.06218i −0.509325 0.294059i
$$426$$ 0 0
$$427$$ 24.0000 13.8564i 1.16144 0.670559i
$$428$$ 0 0
$$429$$ −18.0000 10.3923i −0.869048 0.501745i
$$430$$ 0 0
$$431$$ 18.0000 0.867029 0.433515 0.901146i $$-0.357273\pi$$
0.433515 + 0.901146i $$0.357273\pi$$
$$432$$ 0 0
$$433$$ −31.0000 −1.48976 −0.744882 0.667196i $$-0.767494\pi$$
−0.744882 + 0.667196i $$0.767494\pi$$
$$434$$ 0 0
$$435$$ −18.0000 10.3923i −0.863034 0.498273i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −18.0000 10.3923i −0.859093 0.495998i 0.00461537 0.999989i $$-0.498531\pi$$
−0.863708 + 0.503992i $$0.831864\pi$$
$$440$$ 0 0
$$441$$ −7.50000 + 12.9904i −0.357143 + 0.618590i
$$442$$ 0 0
$$443$$ −4.50000 + 7.79423i −0.213801 + 0.370315i −0.952901 0.303281i $$-0.901918\pi$$
0.739100 + 0.673596i $$0.235251\pi$$
$$444$$ 0 0
$$445$$ 24.0000 + 41.5692i 1.13771 + 1.97057i
$$446$$ 0 0
$$447$$ −24.0000 −1.13516
$$448$$ 0 0
$$449$$ 25.9808i 1.22611i −0.790041 0.613054i $$-0.789941\pi$$
0.790041 0.613054i $$-0.210059\pi$$
$$450$$ 0 0
$$451$$ 15.5885i 0.734032i
$$452$$ 0 0
$$453$$ 6.00000 + 10.3923i 0.281905 + 0.488273i
$$454$$ 0 0
$$455$$ −24.0000 41.5692i −1.12514 1.94880i
$$456$$ 0 0
$$457$$ 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i $$-0.750507\pi$$
0.965512 + 0.260358i $$0.0838407\pi$$
$$458$$ 0 0
$$459$$ −9.00000 −0.420084
$$460$$ 0 0
$$461$$ 18.0000 + 10.3923i 0.838344 + 0.484018i 0.856701 0.515814i $$-0.172510\pi$$
−0.0183573 + 0.999831i $$0.505844\pi$$
$$462$$ 0 0
$$463$$ −15.0000 + 8.66025i −0.697109 + 0.402476i −0.806270 0.591548i $$-0.798517\pi$$
0.109161 + 0.994024i $$0.465184\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 3.00000 0.138823 0.0694117 0.997588i $$-0.477888\pi$$
0.0694117 + 0.997588i $$0.477888\pi$$
$$468$$ 0 0
$$469$$ 30.0000 1.38527
$$470$$ 0 0
$$471$$ 13.8564i 0.638470i
$$472$$ 0 0
$$473$$ −13.5000 + 7.79423i −0.620731 + 0.358379i
$$474$$ 0 0
$$475$$ 10.5000 + 6.06218i 0.481773 + 0.278152i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 15.0000 25.9808i 0.685367 1.18709i −0.287954 0.957644i $$-0.592975\pi$$
0.973321 0.229447i $$-0.0736918\pi$$
$$480$$ 0 0
$$481$$ −4.00000 6.92820i −0.182384 0.315899i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 45.0333i 2.04486i
$$486$$ 0 0
$$487$$ 17.3205i 0.784867i −0.919780 0.392434i $$-0.871633\pi$$
0.919780 0.392434i $$-0.128367\pi$$
$$488$$ 0 0
$$489$$ 3.00000 5.19615i 0.135665 0.234978i
$$490$$ 0 0
$$491$$ 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i $$-0.0567572\pi$$
−0.645675 + 0.763612i $$0.723424\pi$$
$$492$$ 0 0
$$493$$ −3.00000 + 5.19615i −0.135113 + 0.234023i
$$494$$ 0 0
$$495$$ 27.0000 15.5885i 1.21356 0.700649i
$$496$$ 0 0
$$497$$ 18.0000 + 10.3923i 0.807410 + 0.466159i
$$498$$ 0 0
$$499$$ −13.5000 + 7.79423i −0.604343 + 0.348918i −0.770748 0.637140i $$-0.780117\pi$$
0.166405 + 0.986057i $$0.446784\pi$$
$$500$$ 0 0
$$501$$ 10.3923i 0.464294i
$$502$$ 0 0
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ −36.0000 −1.60198
$$506$$ 0 0
$$507$$ 4.50000 2.59808i 0.199852 0.115385i
$$508$$ 0 0
$$509$$ 18.0000 10.3923i 0.797836 0.460631i −0.0448779 0.998992i $$-0.514290\pi$$
0.842714 + 0.538362i $$0.180957\pi$$
$$510$$ 0 0
$$511$$ 33.0000 + 19.0526i 1.45983 + 0.842836i
$$512$$ 0 0
$$513$$ 9.00000 0.397360
$$514$$ 0 0
$$515$$ −24.0000 + 41.5692i −1.05757 + 1.83176i
$$516$$ 0 0
$$517$$ −18.0000 31.1769i −0.791639 1.37116i
$$518$$ 0 0
$$519$$ 21.0000 + 36.3731i 0.921798 + 1.59660i
$$520$$ 0 0
$$521$$ 15.5885i 0.682943i 0.939892 + 0.341471i $$0.110925\pi$$
−0.939892 + 0.341471i $$0.889075\pi$$
$$522$$ 0 0
$$523$$ 17.3205i 0.757373i 0.925525 + 0.378686i $$0.123624\pi$$
−0.925525 + 0.378686i $$0.876376\pi$$
$$524$$ 0 0
$$525$$ 42.0000 1.83303
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 0 0
$$531$$ 22.5000 38.9711i 0.976417 1.69120i
$$532$$ 0 0
$$533$$ 18.0000 + 10.3923i 0.779667 + 0.450141i
$$534$$ 0 0
$$535$$ −9.00000 + 5.19615i −0.389104 + 0.224649i
$$536$$ 0 0
$$537$$ 18.0000 + 10.3923i 0.776757 + 0.448461i
$$538$$ 0 0
$$539$$ −15.0000 −0.646096
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 0 0
$$543$$ 12.0000 + 6.92820i 0.514969 + 0.297318i
$$544$$ 0 0
$$545$$ −12.0000 + 6.92820i −0.514024 + 0.296772i
$$546$$ 0 0
$$547$$ −7.50000 4.33013i −0.320677 0.185143i 0.331017 0.943625i $$-0.392608\pi$$
−0.651694 + 0.758482i $$0.725941\pi$$
$$548$$ 0 0
$$549$$ −24.0000 −1.02430
$$550$$ 0 0
$$551$$ 3.00000 5.19615i 0.127804 0.221364i
$$552$$ 0 0
$$553$$ −6.00000 10.3923i −0.255146 0.441926i
$$554$$ 0 0
$$555$$ 12.0000 0.509372
$$556$$ 0 0
$$557$$ 38.1051i 1.61457i −0.590165 0.807283i $$-0.700937\pi$$
0.590165 0.807283i $$-0.299063\pi$$
$$558$$ 0 0
$$559$$ 20.7846i 0.879095i
$$560$$ 0 0
$$561$$ −4.50000 7.79423i −0.189990 0.329073i
$$562$$ 0 0
$$563$$ 4.50000 + 7.79423i 0.189652 + 0.328488i 0.945134 0.326682i $$-0.105931\pi$$
−0.755482 + 0.655169i $$0.772597\pi$$
$$564$$ 0 0
$$565$$ 12.0000 20.7846i 0.504844 0.874415i
$$566$$ 0 0
$$567$$ 27.0000 15.5885i 1.13389 0.654654i
$$568$$ 0 0
$$569$$ −16.5000 9.52628i −0.691716 0.399362i 0.112539 0.993647i $$-0.464102\pi$$
−0.804255 + 0.594285i $$0.797435\pi$$
$$570$$ 0 0
$$571$$ 10.5000 6.06218i 0.439411 0.253694i −0.263937 0.964540i $$-0.585021\pi$$
0.703348 + 0.710846i $$0.251688\pi$$
$$572$$ 0 0
$$573$$ −9.00000 + 5.19615i −0.375980 + 0.217072i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −7.00000 −0.291414 −0.145707 0.989328i $$-0.546546\pi$$
−0.145707 + 0.989328i $$0.546546\pi$$
$$578$$ 0 0
$$579$$ 39.8372i 1.65558i
$$580$$ 0 0
$$581$$ −36.0000 + 20.7846i −1.49353 + 0.862291i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 41.5692i 1.71868i
$$586$$ 0 0
$$587$$ −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i $$-0.853053\pi$$
0.833408 + 0.552658i $$0.186386\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 12.0000 20.7846i 0.493614 0.854965i
$$592$$ 0 0
$$593$$ 6.92820i 0.284507i 0.989830 + 0.142254i $$0.0454349\pi$$
−0.989830 + 0.142254i $$0.954565\pi$$
$$594$$ 0 0
$$595$$ 20.7846i 0.852086i
$$596$$ 0 0
$$597$$ 3.00000 5.19615i 0.122782 0.212664i
$$598$$ 0 0
$$599$$ 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i $$-0.0468017\pi$$
−0.621480 + 0.783430i $$0.713468\pi$$
$$600$$ 0 0
$$601$$ 3.50000 6.06218i 0.142768 0.247281i −0.785770 0.618519i $$-0.787733\pi$$
0.928538 + 0.371237i $$0.121066\pi$$
$$602$$ 0 0
$$603$$ −22.5000 12.9904i −0.916271 0.529009i
$$604$$ 0 0
$$605$$ −6.00000 3.46410i −0.243935 0.140836i
$$606$$ 0 0
$$607$$ −24.0000 + 13.8564i −0.974130 + 0.562414i −0.900493 0.434871i $$-0.856794\pi$$
−0.0736371 + 0.997285i $$0.523461\pi$$
$$608$$ 0 0
$$609$$ 20.7846i 0.842235i
$$610$$ 0 0
$$611$$ 48.0000 1.94187
$$612$$ 0 0
$$613$$ 26.0000 1.05013 0.525065 0.851062i $$-0.324041\pi$$
0.525065 + 0.851062i $$0.324041\pi$$
$$614$$ 0 0
$$615$$ −27.0000 + 15.5885i −1.08875 + 0.628587i
$$616$$ 0 0
$$617$$ −25.5000 + 14.7224i −1.02659 + 0.592703i −0.916006 0.401164i $$-0.868606\pi$$
−0.110585 + 0.993867i $$0.535272\pi$$
$$618$$ 0 0
$$619$$ 25.5000 + 14.7224i 1.02493 + 0.591744i 0.915529 0.402253i $$-0.131773\pi$$
0.109403 + 0.993997i $$0.465106\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −24.0000 + 41.5692i −0.961540 + 1.66544i
$$624$$ 0 0
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ 0 0
$$627$$ 4.50000 + 7.79423i 0.179713 + 0.311272i
$$628$$ 0 0
$$629$$ 3.46410i 0.138123i
$$630$$ 0 0
$$631$$ 3.46410i 0.137904i −0.997620 0.0689519i $$-0.978035\pi$$
0.997620 0.0689519i $$-0.0219655\pi$$
$$632$$ 0 0
$$633$$ 30.0000 1.19239
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 10.0000 17.3205i 0.396214 0.686264i
$$638$$ 0 0
$$639$$ −9.00000 15.5885i −0.356034 0.616670i
$$640$$ 0 0
$$641$$ −37.5000 21.6506i −1.48116 0.855149i −0.481389 0.876507i $$-0.659868\pi$$
−0.999772 + 0.0213584i $$0.993201\pi$$
$$642$$ 0 0
$$643$$ −22.5000 + 12.9904i −0.887313 + 0.512291i −0.873063 0.487608i $$-0.837870\pi$$
−0.0142506 + 0.999898i $$0.504536\pi$$
$$644$$ 0 0
$$645$$ 27.0000 + 15.5885i 1.06312 + 0.613795i
$$646$$ 0 0
$$647$$ 42.0000 1.65119 0.825595 0.564263i $$-0.190840\pi$$
0.825595 + 0.564263i $$0.190840\pi$$
$$648$$ 0 0
$$649$$ 45.0000 1.76640
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −27.0000 + 15.5885i −1.05659 + 0.610023i −0.924487 0.381212i $$-0.875507\pi$$
−0.132104 + 0.991236i $$0.542173\pi$$
$$654$$ 0 0
$$655$$ −36.0000 20.7846i −1.40664 0.812122i
$$656$$ 0 0
$$657$$ −16.5000 28.5788i −0.643726 1.11497i
$$658$$ 0 0
$$659$$ 12.0000 20.7846i 0.467454 0.809653i −0.531855 0.846836i $$-0.678505\pi$$
0.999309 + 0.0371821i $$0.0118382\pi$$
$$660$$ 0 0
$$661$$ −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i $$-0.254441\pi$$
−0.969442 + 0.245319i $$0.921107\pi$$
$$662$$ 0 0
$$663$$ 12.0000 0.466041
$$664$$ 0 0
$$665$$ 20.7846i 0.805993i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 18.0000 + 31.1769i 0.695920 + 1.20537i
$$670$$ 0 0
$$671$$ −12.0000 20.7846i −0.463255 0.802381i
$$672$$ 0 0
$$673$$ 23.0000 39.8372i 0.886585 1.53561i 0.0426985 0.999088i $$-0.486405\pi$$
0.843886 0.536522i $$-0.180262\pi$$
$$674$$ 0 0
$$675$$ −31.5000 18.1865i −1.21244 0.700000i
$$676$$ 0 0
$$677$$ 18.0000 + 10.3923i 0.691796 + 0.399409i 0.804285 0.594244i $$-0.202549\pi$$
−0.112488 + 0.993653i $$0.535882\pi$$
$$678$$ 0 0
$$679$$ 39.0000 22.5167i 1.49668 0.864110i
$$680$$ 0 0
$$681$$ 4.50000 2.59808i 0.172440 0.0995585i
$$682$$ 0 0
$$683$$ −15.0000 −0.573959 −0.286980 0.957937i $$-0.592651\pi$$
−0.286980 + 0.957937i $$0.592651\pi$$
$$684$$ 0 0
$$685$$ 6.00000 0.229248
$$686$$ 0 0
$$687$$ 45.0333i 1.71813i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −27.0000 15.5885i −1.02713 0.593013i −0.110968 0.993824i $$-0.535395\pi$$
−0.916161 + 0.400811i $$0.868728\pi$$
$$692$$ 0 0
$$693$$ 27.0000 + 15.5885i 1.02565 + 0.592157i
$$694$$ 0 0
$$695$$ −33.0000 + 57.1577i −1.25176 + 2.16811i
$$696$$ 0 0
$$697$$ 4.50000 + 7.79423i 0.170450 + 0.295227i
$$698$$ 0 0
$$699$$ 10.5000 18.1865i 0.397146 0.687878i
$$700$$ 0 0
$$701$$ 27.7128i 1.04670i 0.852118 + 0.523349i $$0.175318\pi$$
−0.852118 + 0.523349i $$0.824682\pi$$
$$702$$ 0 0
$$703$$ 3.46410i 0.130651i
$$704$$ 0 0
$$705$$ −36.0000 + 62.3538i −1.35584 + 2.34838i
$$706$$ 0 0
$$707$$ −18.0000 31.1769i −0.676960 1.17253i
$$708$$ 0 0
$$709$$ −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i $$0.342894\pi$$
−0.999549 + 0.0300298i $$0.990440\pi$$
$$710$$ 0 0
$$711$$ 10.3923i 0.389742i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −36.0000 + 20.7846i −1.34632 + 0.777300i
$$716$$ 0 0
$$717$$ 41.5692i 1.55243i
$$718$$ 0 0
$$719$$ −42.0000 −1.56634 −0.783168 0.621810i $$-0.786397\pi$$
−0.783168 + 0.621810i $$0.786397\pi$$
$$720$$ 0 0
$$721$$ −48.0000 −1.78761
$$722$$ 0 0
$$723$$ −25.5000 + 14.7224i −0.948355 + 0.547533i
$$724$$ 0 0
$$725$$ −21.0000 + 12.1244i −0.779920 + 0.450287i
$$726$$ 0 0
$$727$$ −36.0000 20.7846i −1.33517 0.770859i −0.349080 0.937093i $$-0.613506\pi$$
−0.986086 + 0.166234i $$0.946839\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 4.50000 7.79423i 0.166439 0.288280i
$$732$$ 0 0
$$733$$ −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i $$-0.299846\pi$$
−0.994471 + 0.105010i $$0.966513\pi$$
$$734$$ 0 0
$$735$$ 15.0000 + 25.9808i 0.553283 + 0.958315i
$$736$$ 0 0
$$737$$ 25.9808i 0.957014i
$$738$$ 0 0
$$739$$ 25.9808i 0.955718i 0.878437 + 0.477859i $$0.158587\pi$$
−0.878437 + 0.477859i $$0.841413\pi$$
$$740$$ 0 0
$$741$$ −12.0000 −0.440831
$$742$$ 0 0
$$743$$ −9.00000 15.5885i −0.330178 0.571885i 0.652369 0.757902i $$-0.273775\pi$$
−0.982547 + 0.186017i $$0.940442\pi$$
$$744$$ 0 0
$$745$$ −24.0000 + 41.5692i −0.879292 + 1.52298i
$$746$$ 0 0
$$747$$ 36.0000 1.31717
$$748$$ 0 0
$$749$$ −9.00000 5.19615i −0.328853 0.189863i
$$750$$ 0 0
$$751$$ 33.0000 19.0526i 1.20419 0.695238i 0.242704 0.970100i $$-0.421966\pi$$
0.961483 + 0.274863i $$0.0886324\pi$$
$$752$$ 0 0
$$753$$ 31.5000 + 18.1865i 1.14792 + 0.662754i
$$754$$ 0 0
$$755$$ 24.0000 0.873449
$$756$$ 0 0
$$757$$ −26.0000 −0.944986 −0.472493 0.881334i $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 42.0000 24.2487i 1.52250 0.879015i 0.522852 0.852423i $$-0.324868\pi$$
0.999646 0.0265919i $$-0.00846546\pi$$
$$762$$ 0 0
$$763$$ −12.0000 6.92820i −0.434429 0.250818i
$$764$$ 0 0
$$765$$ −9.00000 + 15.5885i −0.325396 + 0.563602i
$$766$$ 0 0
$$767$$ −30.0000 + 51.9615i −1.08324 + 1.87622i
$$768$$ 0 0
$$769$$ −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i $$-0.247895\pi$$
−0.964193 + 0.265200i $$0.914562\pi$$
$$770$$ 0 0
$$771$$ 33.0000 1.18847
$$772$$ 0 0
$$773$$ 6.92820i 0.249190i −0.992208 0.124595i $$-0.960237\pi$$
0.992208 0.124595i $$-0.0397632\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 6.00000 + 10.3923i 0.215249 + 0.372822i
$$778$$ 0 0
$$779$$ −4.50000 7.79423i −0.161229 0.279257i
$$780$$ 0 0
$$781$$ 9.00000 15.5885i 0.322045 0.557799i
$$782$$ 0 0
$$783$$ −9.00000 + 15.5885i −0.321634 + 0.557086i
$$784$$ 0 0
$$785$$ 24.0000 + 13.8564i 0.856597 + 0.494556i
$$786$$ 0 0
$$787$$ 15.0000 8.66025i 0.534692 0.308705i −0.208233 0.978079i $$-0.566771\pi$$
0.742925 + 0.669375i $$0.233438\pi$$
$$788$$ 0 0
$$789$$ −27.0000 + 15.5885i −0.961225 + 0.554964i
$$790$$ 0 0
$$791$$ 24.0000 0.853342
$$792$$ 0 0
$$793$$ 32.0000 1.13635
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 3.00000