# Properties

 Label 2352.2.q.p.1537.1 Level $2352$ Weight $2$ Character 2352.1537 Analytic conductor $18.781$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2352.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.7808145554$$ 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: no (minimal twist has level 588) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1537.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2352.1537 Dual form 2352.2.q.p.961.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -4.00000 q^{13} -2.00000 q^{15} +(-3.00000 + 5.19615i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -10.0000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(-3.00000 - 5.19615i) q^{37} +(-2.00000 + 3.46410i) q^{39} -6.00000 q^{41} -4.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(4.00000 + 6.92820i) q^{47} +(3.00000 + 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{53} -4.00000 q^{55} +8.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} +(4.00000 + 6.92820i) q^{61} +(4.00000 + 6.92820i) q^{65} +(-4.00000 + 6.92820i) q^{67} -6.00000 q^{69} +10.0000 q^{71} +(-2.00000 + 3.46410i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(2.00000 + 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} +12.0000 q^{85} +(-5.00000 + 8.66025i) q^{87} +(7.00000 + 12.1244i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(8.00000 - 13.8564i) q^{95} +4.00000 q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{3} - 2q^{5} - q^{9} + O(q^{10})$$ $$2q + q^{3} - 2q^{5} - q^{9} + 2q^{11} - 8q^{13} - 4q^{15} - 6q^{17} + 8q^{19} - 6q^{23} + q^{25} - 2q^{27} - 20q^{29} + 4q^{31} - 2q^{33} - 6q^{37} - 4q^{39} - 12q^{41} - 8q^{43} - 2q^{45} + 8q^{47} + 6q^{51} - 2q^{53} - 8q^{55} + 16q^{57} - 4q^{59} + 8q^{61} + 8q^{65} - 8q^{67} - 12q^{69} + 20q^{71} - 4q^{73} - q^{75} + 4q^{79} - q^{81} - 24q^{83} + 24q^{85} - 10q^{87} + 14q^{89} - 4q^{93} + 16q^{95} + 8q^{97} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$1471$$ $$1765$$ $$2257$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ 0 0
$$5$$ −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i $$-0.314250\pi$$
−0.998203 + 0.0599153i $$0.980917\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i $$-0.735842\pi$$
0.976478 + 0.215615i $$0.0691756\pi$$
$$12$$ 0 0
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ −2.00000 −0.516398
$$16$$ 0 0
$$17$$ −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i $$0.426034\pi$$
−0.957892 + 0.287129i $$0.907299\pi$$
$$18$$ 0 0
$$19$$ 4.00000 + 6.92820i 0.917663 + 1.58944i 0.802955 + 0.596040i $$0.203260\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −10.0000 −1.85695 −0.928477 0.371391i $$-0.878881\pi$$
−0.928477 + 0.371391i $$0.878881\pi$$
$$30$$ 0 0
$$31$$ 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i $$-0.716379\pi$$
0.987829 + 0.155543i $$0.0497126\pi$$
$$32$$ 0 0
$$33$$ −1.00000 1.73205i −0.174078 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.00000 5.19615i −0.493197 0.854242i 0.506772 0.862080i $$-0.330838\pi$$
−0.999969 + 0.00783774i $$0.997505\pi$$
$$38$$ 0 0
$$39$$ −2.00000 + 3.46410i −0.320256 + 0.554700i
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 1.73205i −0.149071 + 0.258199i
$$46$$ 0 0
$$47$$ 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i $$0.0316348\pi$$
−0.411606 + 0.911362i $$0.635032\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 3.00000 + 5.19615i 0.420084 + 0.727607i
$$52$$ 0 0
$$53$$ −1.00000 + 1.73205i −0.137361 + 0.237915i −0.926497 0.376303i $$-0.877195\pi$$
0.789136 + 0.614218i $$0.210529\pi$$
$$54$$ 0 0
$$55$$ −4.00000 −0.539360
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ 0 0
$$59$$ −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i $$-0.917180\pi$$
0.705965 + 0.708247i $$0.250514\pi$$
$$60$$ 0 0
$$61$$ 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i $$0.00448323\pi$$
−0.487753 + 0.872982i $$0.662183\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 4.00000 + 6.92820i 0.496139 + 0.859338i
$$66$$ 0 0
$$67$$ −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i $$-0.995854\pi$$
0.511237 + 0.859440i $$0.329187\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 10.0000 1.18678 0.593391 0.804914i $$-0.297789\pi$$
0.593391 + 0.804914i $$0.297789\pi$$
$$72$$ 0 0
$$73$$ −2.00000 + 3.46410i −0.234082 + 0.405442i −0.959006 0.283387i $$-0.908542\pi$$
0.724923 + 0.688830i $$0.241875\pi$$
$$74$$ 0 0
$$75$$ −0.500000 0.866025i −0.0577350 0.100000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i $$-0.0944227\pi$$
−0.731307 + 0.682048i $$0.761089\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 0 0
$$87$$ −5.00000 + 8.66025i −0.536056 + 0.928477i
$$88$$ 0 0
$$89$$ 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i $$0.0994552\pi$$
−0.209585 + 0.977790i $$0.567211\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −2.00000 3.46410i −0.207390 0.359211i
$$94$$ 0 0
$$95$$ 8.00000 13.8564i 0.820783 1.42164i
$$96$$ 0 0
$$97$$ 4.00000 0.406138 0.203069 0.979164i $$-0.434908\pi$$
0.203069 + 0.979164i $$0.434908\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i $$-0.667578\pi$$
0.999996 + 0.00286291i $$0.000911295\pi$$
$$102$$ 0 0
$$103$$ −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i $$-0.229808\pi$$
−0.947576 + 0.319531i $$0.896475\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −7.00000 12.1244i −0.676716 1.17211i −0.975964 0.217931i $$-0.930069\pi$$
0.299249 0.954175i $$-0.403264\pi$$
$$108$$ 0 0
$$109$$ −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i $$-0.992302\pi$$
0.520794 + 0.853682i $$0.325636\pi$$
$$110$$ 0 0
$$111$$ −6.00000 −0.569495
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ −6.00000 + 10.3923i −0.559503 + 0.969087i
$$116$$ 0 0
$$117$$ 2.00000 + 3.46410i 0.184900 + 0.320256i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ 0 0
$$123$$ −3.00000 + 5.19615i −0.270501 + 0.468521i
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 4.00000 0.354943 0.177471 0.984126i $$-0.443208\pi$$
0.177471 + 0.984126i $$0.443208\pi$$
$$128$$ 0 0
$$129$$ −2.00000 + 3.46410i −0.176090 + 0.304997i
$$130$$ 0 0
$$131$$ −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i $$-0.991023\pi$$
0.475380 0.879781i $$-0.342311\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 1.00000 + 1.73205i 0.0860663 + 0.149071i
$$136$$ 0 0
$$137$$ 5.00000 8.66025i 0.427179 0.739895i −0.569442 0.822031i $$-0.692841\pi$$
0.996621 + 0.0821359i $$0.0261741\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 0 0
$$143$$ −4.00000 + 6.92820i −0.334497 + 0.579365i
$$144$$ 0 0
$$145$$ 10.0000 + 17.3205i 0.830455 + 1.43839i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.00000 1.73205i −0.0819232 0.141895i 0.822153 0.569267i $$-0.192773\pi$$
−0.904076 + 0.427372i $$0.859440\pi$$
$$150$$ 0 0
$$151$$ −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i $$-0.938871\pi$$
0.656101 + 0.754673i $$0.272204\pi$$
$$152$$ 0 0
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ −8.00000 −0.642575
$$156$$ 0 0
$$157$$ 8.00000 13.8564i 0.638470 1.10586i −0.347299 0.937754i $$-0.612901\pi$$
0.985769 0.168107i $$-0.0537655\pi$$
$$158$$ 0 0
$$159$$ 1.00000 + 1.73205i 0.0793052 + 0.137361i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 12.0000 + 20.7846i 0.939913 + 1.62798i 0.765631 + 0.643280i $$0.222427\pi$$
0.174282 + 0.984696i $$0.444240\pi$$
$$164$$ 0 0
$$165$$ −2.00000 + 3.46410i −0.155700 + 0.269680i
$$166$$ 0 0
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 4.00000 6.92820i 0.305888 0.529813i
$$172$$ 0 0
$$173$$ 1.00000 + 1.73205i 0.0760286 + 0.131685i 0.901533 0.432710i $$-0.142443\pi$$
−0.825505 + 0.564396i $$0.809109\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 2.00000 + 3.46410i 0.150329 + 0.260378i
$$178$$ 0 0
$$179$$ 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i $$-0.761346\pi$$
0.956088 + 0.293079i $$0.0946798\pi$$
$$180$$ 0 0
$$181$$ −20.0000 −1.48659 −0.743294 0.668965i $$-0.766738\pi$$
−0.743294 + 0.668965i $$0.766738\pi$$
$$182$$ 0 0
$$183$$ 8.00000 0.591377
$$184$$ 0 0
$$185$$ −6.00000 + 10.3923i −0.441129 + 0.764057i
$$186$$ 0 0
$$187$$ 6.00000 + 10.3923i 0.438763 + 0.759961i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i $$-0.0970159\pi$$
−0.736839 + 0.676068i $$0.763683\pi$$
$$192$$ 0 0
$$193$$ 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i $$-0.716141\pi$$
0.987945 + 0.154805i $$0.0494748\pi$$
$$194$$ 0 0
$$195$$ 8.00000 0.572892
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ 0 0
$$201$$ 4.00000 + 6.92820i 0.282138 + 0.488678i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 6.00000 + 10.3923i 0.419058 + 0.725830i
$$206$$ 0 0
$$207$$ −3.00000 + 5.19615i −0.208514 + 0.361158i
$$208$$ 0 0
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ 5.00000 8.66025i 0.342594 0.593391i
$$214$$ 0 0
$$215$$ 4.00000 + 6.92820i 0.272798 + 0.472500i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 2.00000 + 3.46410i 0.135147 + 0.234082i
$$220$$ 0 0
$$221$$ 12.0000 20.7846i 0.807207 1.39812i
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ 2.00000 3.46410i 0.132745 0.229920i −0.791989 0.610535i $$-0.790954\pi$$
0.924734 + 0.380615i $$0.124288\pi$$
$$228$$ 0 0
$$229$$ −10.0000 17.3205i −0.660819 1.14457i −0.980401 0.197013i $$-0.936876\pi$$
0.319582 0.947559i $$-0.396457\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i $$-0.318310\pi$$
−0.998886 + 0.0471787i $$0.984977\pi$$
$$234$$ 0 0
$$235$$ 8.00000 13.8564i 0.521862 0.903892i
$$236$$ 0 0
$$237$$ 4.00000 0.259828
$$238$$ 0 0
$$239$$ −18.0000 −1.16432 −0.582162 0.813073i $$-0.697793\pi$$
−0.582162 + 0.813073i $$0.697793\pi$$
$$240$$ 0 0
$$241$$ −14.0000 + 24.2487i −0.901819 + 1.56200i −0.0766885 + 0.997055i $$0.524435\pi$$
−0.825131 + 0.564942i $$0.808899\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −16.0000 27.7128i −1.01806 1.76332i
$$248$$ 0 0
$$249$$ −6.00000 + 10.3923i −0.380235 + 0.658586i
$$250$$ 0 0
$$251$$ 28.0000 1.76734 0.883672 0.468106i $$-0.155064\pi$$
0.883672 + 0.468106i $$0.155064\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 0 0
$$255$$ 6.00000 10.3923i 0.375735 0.650791i
$$256$$ 0 0
$$257$$ −5.00000 8.66025i −0.311891 0.540212i 0.666880 0.745165i $$-0.267629\pi$$
−0.978772 + 0.204953i $$0.934296\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 5.00000 + 8.66025i 0.309492 + 0.536056i
$$262$$ 0 0
$$263$$ 13.0000 22.5167i 0.801614 1.38844i −0.116939 0.993139i $$-0.537308\pi$$
0.918553 0.395298i $$-0.129359\pi$$
$$264$$ 0 0
$$265$$ 4.00000 0.245718
$$266$$ 0 0
$$267$$ 14.0000 0.856786
$$268$$ 0 0
$$269$$ −1.00000 + 1.73205i −0.0609711 + 0.105605i −0.894900 0.446267i $$-0.852753\pi$$
0.833929 + 0.551872i $$0.186086\pi$$
$$270$$ 0 0
$$271$$ −2.00000 3.46410i −0.121491 0.210429i 0.798865 0.601511i $$-0.205434\pi$$
−0.920356 + 0.391082i $$0.872101\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.00000 1.73205i −0.0603023 0.104447i
$$276$$ 0 0
$$277$$ −5.00000 + 8.66025i −0.300421 + 0.520344i −0.976231 0.216731i $$-0.930460\pi$$
0.675810 + 0.737075i $$0.263794\pi$$
$$278$$ 0 0
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 8.00000 13.8564i 0.475551 0.823678i −0.524057 0.851683i $$-0.675582\pi$$
0.999608 + 0.0280052i $$0.00891551\pi$$
$$284$$ 0 0
$$285$$ −8.00000 13.8564i −0.473879 0.820783i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 0 0
$$291$$ 2.00000 3.46410i 0.117242 0.203069i
$$292$$ 0 0
$$293$$ −18.0000 −1.05157 −0.525786 0.850617i $$-0.676229\pi$$
−0.525786 + 0.850617i $$0.676229\pi$$
$$294$$ 0 0
$$295$$ 8.00000 0.465778
$$296$$ 0 0
$$297$$ −1.00000 + 1.73205i −0.0580259 + 0.100504i
$$298$$ 0 0
$$299$$ 12.0000 + 20.7846i 0.693978 + 1.20201i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −5.00000 8.66025i −0.287242 0.497519i
$$304$$ 0 0
$$305$$ 8.00000 13.8564i 0.458079 0.793416i
$$306$$ 0 0
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ 0 0
$$309$$ −4.00000 −0.227552
$$310$$ 0 0
$$311$$ 8.00000 13.8564i 0.453638 0.785725i −0.544970 0.838455i $$-0.683459\pi$$
0.998609 + 0.0527306i $$0.0167924\pi$$
$$312$$ 0 0
$$313$$ −12.0000 20.7846i −0.678280 1.17482i −0.975499 0.220006i $$-0.929392\pi$$
0.297218 0.954810i $$-0.403941\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i $$-0.997978\pi$$
0.494489 0.869184i $$-0.335355\pi$$
$$318$$ 0 0
$$319$$ −10.0000 + 17.3205i −0.559893 + 0.969762i
$$320$$ 0 0
$$321$$ −14.0000 −0.781404
$$322$$ 0 0
$$323$$ −48.0000 −2.67079
$$324$$ 0 0
$$325$$ −2.00000 + 3.46410i −0.110940 + 0.192154i
$$326$$ 0 0
$$327$$ 5.00000 + 8.66025i 0.276501 + 0.478913i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i $$-0.201729\pi$$
−0.915742 + 0.401768i $$0.868396\pi$$
$$332$$ 0 0
$$333$$ −3.00000 + 5.19615i −0.164399 + 0.284747i
$$334$$ 0 0
$$335$$ 16.0000 0.874173
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ −7.00000 + 12.1244i −0.380188 + 0.658505i
$$340$$ 0 0
$$341$$ −4.00000 6.92820i −0.216612 0.375183i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 6.00000 + 10.3923i 0.323029 + 0.559503i
$$346$$ 0 0
$$347$$ −9.00000 + 15.5885i −0.483145 + 0.836832i −0.999813 0.0193540i $$-0.993839\pi$$
0.516667 + 0.856186i $$0.327172\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 4.00000 0.213504
$$352$$ 0 0
$$353$$ −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i $$-0.884378\pi$$
0.775077 + 0.631867i $$0.217711\pi$$
$$354$$ 0 0
$$355$$ −10.0000 17.3205i −0.530745 0.919277i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 11.0000 + 19.0526i 0.580558 + 1.00556i 0.995413 + 0.0956683i $$0.0304988\pi$$
−0.414855 + 0.909887i $$0.636168\pi$$
$$360$$ 0 0
$$361$$ −22.5000 + 38.9711i −1.18421 + 2.05111i
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 8.00000 0.418739
$$366$$ 0 0
$$367$$ 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i $$-0.696206\pi$$
0.995697 + 0.0926670i $$0.0295392\pi$$
$$368$$ 0 0
$$369$$ 3.00000 + 5.19615i 0.156174 + 0.270501i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i $$0.0683772\pi$$
−0.303902 + 0.952703i $$0.598289\pi$$
$$374$$ 0 0
$$375$$ −6.00000 + 10.3923i −0.309839 + 0.536656i
$$376$$ 0 0
$$377$$ 40.0000 2.06010
$$378$$ 0 0
$$379$$ 36.0000 1.84920 0.924598 0.380945i $$-0.124401\pi$$
0.924598 + 0.380945i $$0.124401\pi$$
$$380$$ 0 0
$$381$$ 2.00000 3.46410i 0.102463 0.177471i
$$382$$ 0 0
$$383$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 2.00000 + 3.46410i 0.101666 + 0.176090i
$$388$$ 0 0
$$389$$ 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i $$-0.682501\pi$$
0.998763 + 0.0497253i $$0.0158346\pi$$
$$390$$ 0 0
$$391$$ 36.0000 1.82060
$$392$$ 0 0
$$393$$ −12.0000 −0.605320
$$394$$ 0 0
$$395$$ 4.00000 6.92820i 0.201262 0.348596i
$$396$$ 0 0
$$397$$ −16.0000 27.7128i −0.803017 1.39087i −0.917622 0.397455i $$-0.869893\pi$$
0.114605 0.993411i $$-0.463440\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i $$-0.897170\pi$$
0.199207 0.979957i $$-0.436163\pi$$
$$402$$ 0 0
$$403$$ −8.00000 + 13.8564i −0.398508 + 0.690237i
$$404$$ 0 0
$$405$$ 2.00000 0.0993808
$$406$$ 0 0
$$407$$ −12.0000 −0.594818
$$408$$ 0 0
$$409$$ −6.00000 + 10.3923i −0.296681 + 0.513866i −0.975375 0.220555i $$-0.929213\pi$$
0.678694 + 0.734422i $$0.262546\pi$$
$$410$$ 0 0
$$411$$ −5.00000 8.66025i −0.246632 0.427179i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 12.0000 + 20.7846i 0.589057 + 1.02028i
$$416$$ 0 0
$$417$$ −6.00000 + 10.3923i −0.293821 + 0.508913i
$$418$$ 0 0
$$419$$ 4.00000 0.195413 0.0977064 0.995215i $$-0.468849\pi$$
0.0977064 + 0.995215i $$0.468849\pi$$
$$420$$ 0 0
$$421$$ −6.00000 −0.292422 −0.146211 0.989253i $$-0.546708\pi$$
−0.146211 + 0.989253i $$0.546708\pi$$
$$422$$ 0 0
$$423$$ 4.00000 6.92820i 0.194487 0.336861i
$$424$$ 0 0
$$425$$ 3.00000 + 5.19615i 0.145521 + 0.252050i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 4.00000 + 6.92820i 0.193122 + 0.334497i
$$430$$ 0 0
$$431$$ −1.00000 + 1.73205i −0.0481683 + 0.0834300i −0.889104 0.457705i $$-0.848672\pi$$
0.840936 + 0.541135i $$0.182005\pi$$
$$432$$ 0 0
$$433$$ 32.0000 1.53782 0.768911 0.639356i $$-0.220799\pi$$
0.768911 + 0.639356i $$0.220799\pi$$
$$434$$ 0 0
$$435$$ 20.0000 0.958927
$$436$$ 0 0
$$437$$ 24.0000 41.5692i 1.14808 1.98853i
$$438$$ 0 0
$$439$$ −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i $$-0.972552\pi$$
0.423556 0.905870i $$-0.360782\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −9.00000 15.5885i −0.427603 0.740630i 0.569057 0.822298i $$-0.307309\pi$$
−0.996660 + 0.0816684i $$0.973975\pi$$
$$444$$ 0 0
$$445$$ 14.0000 24.2487i 0.663664 1.14950i
$$446$$ 0 0
$$447$$ −2.00000 −0.0945968
$$448$$ 0 0
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ 0 0
$$453$$ 4.00000 + 6.92820i 0.187936 + 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i $$0.00537742\pi$$
−0.485299 + 0.874348i $$0.661289\pi$$
$$458$$ 0 0
$$459$$ 3.00000 5.19615i 0.140028 0.242536i
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ 4.00000 0.185896 0.0929479 0.995671i $$-0.470371\pi$$
0.0929479 + 0.995671i $$0.470371\pi$$
$$464$$ 0 0
$$465$$ −4.00000 + 6.92820i −0.185496 + 0.321288i
$$466$$ 0 0
$$467$$ −10.0000 17.3205i −0.462745 0.801498i 0.536352 0.843995i $$-0.319802\pi$$
−0.999097 + 0.0424970i $$0.986469\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −8.00000 13.8564i −0.368621 0.638470i
$$472$$ 0 0
$$473$$ −4.00000 + 6.92820i −0.183920 + 0.318559i
$$474$$ 0 0
$$475$$ 8.00000 0.367065
$$476$$ 0 0
$$477$$ 2.00000 0.0915737
$$478$$ 0 0
$$479$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$480$$ 0 0
$$481$$ 12.0000 + 20.7846i 0.547153 + 0.947697i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −4.00000 6.92820i −0.181631 0.314594i
$$486$$ 0 0
$$487$$ 8.00000 13.8564i 0.362515 0.627894i −0.625859 0.779936i $$-0.715252\pi$$
0.988374 + 0.152042i $$0.0485850\pi$$
$$488$$ 0 0
$$489$$ 24.0000 1.08532
$$490$$ 0 0
$$491$$ −6.00000 −0.270776 −0.135388 0.990793i $$-0.543228\pi$$
−0.135388 + 0.990793i $$0.543228\pi$$
$$492$$ 0 0
$$493$$ 30.0000 51.9615i 1.35113 2.34023i
$$494$$ 0 0
$$495$$ 2.00000 + 3.46410i 0.0898933 + 0.155700i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −18.0000 31.1769i −0.805791 1.39567i −0.915756 0.401735i $$-0.868407\pi$$
0.109965 0.993935i $$-0.464926\pi$$
$$500$$ 0 0
$$501$$ −8.00000 + 13.8564i −0.357414 + 0.619059i
$$502$$ 0 0
$$503$$ −16.0000 −0.713405 −0.356702 0.934218i $$-0.616099\pi$$
−0.356702 + 0.934218i $$0.616099\pi$$
$$504$$ 0 0
$$505$$ −20.0000 −0.889988
$$506$$ 0 0
$$507$$ 1.50000 2.59808i 0.0666173 0.115385i
$$508$$ 0 0
$$509$$ −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i $$-0.237801\pi$$
−0.955300 + 0.295637i $$0.904468\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −4.00000 6.92820i −0.176604 0.305888i
$$514$$ 0 0
$$515$$ −4.00000 + 6.92820i −0.176261 + 0.305293i
$$516$$ 0 0
$$517$$ 16.0000 0.703679
$$518$$ 0 0
$$519$$ 2.00000 0.0877903
$$520$$ 0 0
$$521$$ −11.0000 + 19.0526i −0.481919 + 0.834708i −0.999785 0.0207541i $$-0.993393\pi$$
0.517866 + 0.855462i $$0.326727\pi$$
$$522$$ 0 0
$$523$$ −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i $$-0.194540\pi$$
−0.906434 + 0.422347i $$0.861206\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 12.0000 + 20.7846i 0.522728 + 0.905392i
$$528$$ 0 0
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 24.0000 1.03956
$$534$$ 0 0
$$535$$ −14.0000 + 24.2487i −0.605273 + 1.04836i
$$536$$ 0 0
$$537$$ −3.00000 5.19615i −0.129460 0.224231i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −17.0000 29.4449i −0.730887 1.26593i −0.956504 0.291718i $$-0.905773\pi$$
0.225617 0.974216i $$-0.427560\pi$$
$$542$$ 0 0
$$543$$ −10.0000 + 17.3205i −0.429141 + 0.743294i
$$544$$ 0 0
$$545$$ 20.0000 0.856706
$$546$$ 0 0
$$547$$ −16.0000 −0.684111 −0.342055 0.939680i $$-0.611123\pi$$
−0.342055 + 0.939680i $$0.611123\pi$$
$$548$$ 0 0
$$549$$ 4.00000 6.92820i 0.170716 0.295689i
$$550$$ 0 0
$$551$$ −40.0000 69.2820i −1.70406 2.95151i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 6.00000 + 10.3923i 0.254686 + 0.441129i
$$556$$ 0 0
$$557$$ 3.00000 5.19615i 0.127114 0.220168i −0.795443 0.606028i $$-0.792762\pi$$
0.922557 + 0.385860i $$0.126095\pi$$
$$558$$ 0 0
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ 0 0
$$563$$ 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i $$-0.806471\pi$$
0.905088 + 0.425223i $$0.139804\pi$$
$$564$$ 0 0
$$565$$ 14.0000 + 24.2487i 0.588984 + 1.02015i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i $$-0.206806\pi$$
−0.922032 + 0.387113i $$0.873472\pi$$
$$570$$ 0 0
$$571$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$572$$ 0 0
$$573$$ 6.00000 0.250654
$$574$$ 0 0
$$575$$ −6.00000 −0.250217
$$576$$ 0 0
$$577$$ 4.00000 6.92820i 0.166522 0.288425i −0.770673 0.637231i $$-0.780080\pi$$
0.937195 + 0.348806i $$0.113413\pi$$
$$578$$ 0 0
$$579$$ −5.00000 8.66025i −0.207793 0.359908i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 2.00000 + 3.46410i 0.0828315 + 0.143468i
$$584$$ 0 0
$$585$$ 4.00000 6.92820i 0.165380 0.286446i
$$586$$ 0 0
$$587$$ 4.00000 0.165098 0.0825488 0.996587i $$-0.473694\pi$$
0.0825488 + 0.996587i $$0.473694\pi$$
$$588$$ 0 0
$$589$$ 32.0000 1.31854
$$590$$ 0 0
$$591$$ −3.00000 + 5.19615i −0.123404 + 0.213741i
$$592$$ 0 0
$$593$$ −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i $$-0.205981\pi$$
−0.921026 + 0.389501i $$0.872647\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 4.00000 + 6.92820i 0.163709 + 0.283552i
$$598$$ 0 0
$$599$$ 15.0000 25.9808i 0.612883 1.06155i −0.377869 0.925859i $$-0.623343\pi$$
0.990752 0.135686i $$-0.0433238\pi$$
$$600$$ 0 0
$$601$$ 8.00000 0.326327 0.163163 0.986599i $$-0.447830\pi$$
0.163163 + 0.986599i $$0.447830\pi$$
$$602$$ 0 0
$$603$$ 8.00000 0.325785
$$604$$ 0 0
$$605$$ 7.00000 12.1244i 0.284590 0.492925i
$$606$$ 0 0
$$607$$ 12.0000 + 20.7846i 0.487065 + 0.843621i 0.999889 0.0148722i $$-0.00473415\pi$$
−0.512824 + 0.858494i $$0.671401\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −16.0000 27.7128i −0.647291 1.12114i
$$612$$ 0 0
$$613$$ −13.0000 + 22.5167i −0.525065 + 0.909439i 0.474509 + 0.880251i $$0.342626\pi$$
−0.999574 + 0.0291886i $$0.990708\pi$$
$$614$$ 0 0
$$615$$ 12.0000 0.483887
$$616$$ 0 0
$$617$$ −2.00000 −0.0805170 −0.0402585 0.999189i $$-0.512818\pi$$
−0.0402585 + 0.999189i $$0.512818\pi$$
$$618$$ 0 0
$$619$$ 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i $$-0.807718\pi$$
0.903416 + 0.428765i $$0.141051\pi$$
$$620$$ 0 0
$$621$$ 3.00000 + 5.19615i 0.120386 + 0.208514i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0 0
$$627$$ 8.00000 13.8564i 0.319489 0.553372i
$$628$$ 0 0
$$629$$ 36.0000 1.43541
$$630$$ 0 0
$$631$$ −12.0000 −0.477712 −0.238856 0.971055i $$-0.576772\pi$$
−0.238856 + 0.971055i $$0.576772\pi$$
$$632$$ 0 0
$$633$$ 2.00000 3.46410i 0.0794929 0.137686i
$$634$$ 0 0
$$635$$ −4.00000 6.92820i −0.158735 0.274937i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −5.00000 8.66025i −0.197797 0.342594i
$$640$$ 0 0
$$641$$ 13.0000 22.5167i 0.513469 0.889355i −0.486409 0.873731i $$-0.661693\pi$$
0.999878 0.0156233i $$-0.00497325\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 8.00000 0.315000
$$646$$ 0 0
$$647$$ −24.0000 + 41.5692i −0.943537 + 1.63425i −0.184884 + 0.982760i $$0.559191\pi$$
−0.758654 + 0.651494i $$0.774142\pi$$
$$648$$ 0 0
$$649$$ 4.00000 + 6.92820i 0.157014 + 0.271956i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 17.0000 + 29.4449i 0.665261 + 1.15227i 0.979214 + 0.202828i $$0.0650132\pi$$
−0.313953 + 0.949439i $$0.601653\pi$$
$$654$$ 0 0
$$655$$ −12.0000 + 20.7846i −0.468879 + 0.812122i
$$656$$ 0 0
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ 14.0000 0.545363 0.272681 0.962104i $$-0.412090\pi$$
0.272681 + 0.962104i $$0.412090\pi$$
$$660$$ 0 0
$$661$$ −4.00000 + 6.92820i −0.155582 + 0.269476i −0.933271 0.359174i $$-0.883059\pi$$
0.777689 + 0.628649i $$0.216392\pi$$
$$662$$ 0 0
$$663$$ −12.0000 20.7846i −0.466041 0.807207i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 30.0000 + 51.9615i 1.16160 + 2.01196i
$$668$$ 0 0
$$669$$ 4.00000 6.92820i 0.154649 0.267860i
$$670$$ 0 0
$$671$$ 16.0000 0.617673
$$672$$ 0 0
$$673$$ −22.0000 −0.848038 −0.424019 0.905653i $$-0.639381\pi$$
−0.424019 + 0.905653i $$0.639381\pi$$
$$674$$ 0 0
$$675$$ −0.500000 + 0.866025i −0.0192450 + 0.0333333i
$$676$$ 0 0
$$677$$ −15.0000 25.9808i −0.576497 0.998522i −0.995877 0.0907112i $$-0.971086\pi$$
0.419380 0.907811i $$-0.362247\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −2.00000 3.46410i −0.0766402 0.132745i
$$682$$ 0 0
$$683$$ 11.0000 19.0526i 0.420903 0.729026i −0.575125 0.818066i $$-0.695047\pi$$
0.996028 + 0.0890398i $$0.0283798\pi$$
$$684$$ 0 0
$$685$$ −20.0000 −0.764161
$$686$$ 0 0
$$687$$ −20.0000 −0.763048
$$688$$ 0 0
$$689$$ 4.00000 6.92820i 0.152388 0.263944i
$$690$$ 0 0
$$691$$ −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i $$-0.290887\pi$$
−0.991122 + 0.132956i $$0.957553\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 12.0000 + 20.7846i 0.455186 + 0.788405i
$$696$$ 0 0
$$697$$ 18.0000 31.1769i 0.681799 1.18091i
$$698$$ 0 0
$$699$$ −14.0000 −0.529529
$$700$$ 0 0
$$701$$ −50.0000 −1.88847 −0.944237 0.329267i $$-0.893198\pi$$
−0.944237 + 0.329267i $$0.893198\pi$$
$$702$$ 0 0
$$703$$ 24.0000 41.5692i 0.905177 1.56781i
$$704$$ 0 0
$$705$$ −8.00000 13.8564i −0.301297 0.521862i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 7.00000 + 12.1244i 0.262891 + 0.455340i 0.967009 0.254743i $$-0.0819909\pi$$
−0.704118 + 0.710083i $$0.748658\pi$$
$$710$$ 0 0
$$711$$ 2.00000 3.46410i 0.0750059 0.129914i
$$712$$ 0 0
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 16.0000 0.598366
$$716$$ 0 0
$$717$$ −9.00000 + 15.5885i −0.336111 + 0.582162i
$$718$$ 0 0
$$719$$ 24.0000 + 41.5692i 0.895049 + 1.55027i 0.833744 + 0.552151i $$0.186193\pi$$
0.0613050 + 0.998119i $$0.480474\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 14.0000 + 24.2487i 0.520666 + 0.901819i
$$724$$ 0 0
$$725$$ −5.00000 + 8.66025i −0.185695 + 0.321634i
$$726$$ 0 0
$$727$$ −44.0000 −1.63187 −0.815935 0.578144i $$-0.803777\pi$$
−0.815935 + 0.578144i $$0.803777\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 12.0000 20.7846i 0.443836 0.768747i
$$732$$ 0 0
$$733$$ −2.00000 3.46410i −0.0738717 0.127950i 0.826723 0.562609i $$-0.190202\pi$$
−0.900595 + 0.434659i $$0.856869\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 8.00000 + 13.8564i 0.294684 + 0.510407i
$$738$$ 0 0
$$739$$ 20.0000 34.6410i 0.735712 1.27429i −0.218698 0.975793i $$-0.570181\pi$$
0.954410 0.298498i $$-0.0964856\pi$$
$$740$$ 0 0
$$741$$ −32.0000 −1.17555
$$742$$ 0 0
$$743$$ 18.0000 0.660356 0.330178 0.943919i $$-0.392891\pi$$
0.330178 + 0.943919i $$0.392891\pi$$
$$744$$ 0 0
$$745$$ −2.00000 + 3.46410i −0.0732743 + 0.126915i
$$746$$ 0 0
$$747$$ 6.00000 + 10.3923i 0.219529 + 0.380235i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −24.0000 41.5692i −0.875772 1.51688i −0.855938 0.517079i $$-0.827019\pi$$
−0.0198348 0.999803i $$-0.506314\pi$$
$$752$$ 0 0
$$753$$ 14.0000 24.2487i 0.510188 0.883672i
$$754$$ 0 0
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ −14.0000 −0.508839 −0.254419 0.967094i $$-0.581884\pi$$
−0.254419 + 0.967094i $$0.581884\pi$$
$$758$$ 0 0
$$759$$ −6.00000 + 10.3923i −0.217786 + 0.377217i
$$760$$ 0 0
$$761$$ 11.0000 + 19.0526i 0.398750 + 0.690655i 0.993572 0.113203i $$-0.0361109\pi$$
−0.594822 + 0.803857i $$0.702778\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −6.00000 10.3923i −0.216930 0.375735i
$$766$$ 0 0
$$767$$ 8.00000 13.8564i 0.288863 0.500326i
$$768$$ 0 0
$$769$$ 32.0000 1.15395 0.576975 0.816762i $$-0.304233\pi$$
0.576975 + 0.816762i $$0.304233\pi$$
$$770$$ 0 0
$$771$$ −10.0000 −0.360141
$$772$$ 0 0
$$773$$ −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i $$-0.867747\pi$$
0.807018 + 0.590527i $$0.201080\pi$$
$$774$$ 0 0
$$775$$ −2.00000 3.46410i −0.0718421 0.124434i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −24.0000 41.5692i −0.859889 1.48937i
$$780$$ 0 0
$$781$$ 10.0000 17.3205i 0.357828 0.619777i
$$782$$ 0 0
$$783$$ 10.0000 0.357371
$$784$$ 0 0
$$785$$ −32.0000 −1.14213
$$786$$ 0 0
$$787$$ 2.00000 3.46410i 0.0712923 0.123482i −0.828176 0.560469i $$-0.810621\pi$$
0.899468 + 0.436987i $$0.143954\pi$$
$$788$$ 0 0
$$789$$ −13.0000 22.5167i −0.462812 0.801614i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −16.0000 27.7128i −0.568177 0.984111i
$$794$$ 0 0
$$795$$ 2.00000 3.46410i 0.0709327 0.122859i
$$796$$ 0 0
$$797$$ 6.00000 0.212531 0.106265 0.994338i $$-0.466111\pi$$
0.106265 + 0.994338i $$0.466111\pi$$
$$798$$ 0 0
$$799$$ −48.0000 −1.69812
\(800\