Properties

 Label 3360.2.t.c.2689.1 Level $3360$ Weight $2$ Character 3360.2689 Analytic conductor $26.830$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

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Newspace parameters

 Level: $$N$$ $$=$$ $$3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3360.t (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$26.8297350792$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 2689.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 3360.2689 Dual form 3360.2.t.c.2689.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{3} +(1.00000 - 2.00000i) q^{5} -1.00000i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{3} +(1.00000 - 2.00000i) q^{5} -1.00000i q^{7} -1.00000 q^{9} -6.00000 q^{11} -6.00000i q^{13} +(-2.00000 - 1.00000i) q^{15} +2.00000 q^{19} -1.00000 q^{21} -8.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +1.00000i q^{27} +10.0000 q^{29} -2.00000 q^{31} +6.00000i q^{33} +(-2.00000 - 1.00000i) q^{35} +8.00000i q^{37} -6.00000 q^{39} -6.00000 q^{41} +12.0000i q^{43} +(-1.00000 + 2.00000i) q^{45} +8.00000i q^{47} -1.00000 q^{49} -10.0000i q^{53} +(-6.00000 + 12.0000i) q^{55} -2.00000i q^{57} +4.00000 q^{59} -2.00000 q^{61} +1.00000i q^{63} +(-12.0000 - 6.00000i) q^{65} -8.00000i q^{67} -8.00000 q^{69} -10.0000 q^{71} -6.00000i q^{73} +(-4.00000 + 3.00000i) q^{75} +6.00000i q^{77} -8.00000 q^{79} +1.00000 q^{81} -10.0000i q^{87} -6.00000 q^{89} -6.00000 q^{91} +2.00000i q^{93} +(2.00000 - 4.00000i) q^{95} +10.0000i q^{97} +6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{5} - 2 q^{9}+O(q^{10})$$ 2 * q + 2 * q^5 - 2 * q^9 $$2 q + 2 q^{5} - 2 q^{9} - 12 q^{11} - 4 q^{15} + 4 q^{19} - 2 q^{21} - 6 q^{25} + 20 q^{29} - 4 q^{31} - 4 q^{35} - 12 q^{39} - 12 q^{41} - 2 q^{45} - 2 q^{49} - 12 q^{55} + 8 q^{59} - 4 q^{61} - 24 q^{65} - 16 q^{69} - 20 q^{71} - 8 q^{75} - 16 q^{79} + 2 q^{81} - 12 q^{89} - 12 q^{91} + 4 q^{95} + 12 q^{99}+O(q^{100})$$ 2 * q + 2 * q^5 - 2 * q^9 - 12 * q^11 - 4 * q^15 + 4 * q^19 - 2 * q^21 - 6 * q^25 + 20 * q^29 - 4 * q^31 - 4 * q^35 - 12 * q^39 - 12 * q^41 - 2 * q^45 - 2 * q^49 - 12 * q^55 + 8 * q^59 - 4 * q^61 - 24 * q^65 - 16 * q^69 - 20 * q^71 - 8 * q^75 - 16 * q^79 + 2 * q^81 - 12 * q^89 - 12 * q^91 + 4 * q^95 + 12 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3360\mathbb{Z}\right)^\times$$.

 $$n$$ $$421$$ $$1121$$ $$1471$$ $$1921$$ $$2017$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ 1.00000 2.00000i 0.447214 0.894427i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ −6.00000 −1.80907 −0.904534 0.426401i $$-0.859781\pi$$
−0.904534 + 0.426401i $$0.859781\pi$$
$$12$$ 0 0
$$13$$ 6.00000i 1.66410i −0.554700 0.832050i $$-0.687167\pi$$
0.554700 0.832050i $$-0.312833\pi$$
$$14$$ 0 0
$$15$$ −2.00000 1.00000i −0.516398 0.258199i
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ 8.00000i 1.66812i −0.551677 0.834058i $$-0.686012\pi$$
0.551677 0.834058i $$-0.313988\pi$$
$$24$$ 0 0
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 10.0000 1.85695 0.928477 0.371391i $$-0.121119\pi$$
0.928477 + 0.371391i $$0.121119\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0 0
$$33$$ 6.00000i 1.04447i
$$34$$ 0 0
$$35$$ −2.00000 1.00000i −0.338062 0.169031i
$$36$$ 0 0
$$37$$ 8.00000i 1.31519i 0.753371 + 0.657596i $$0.228427\pi$$
−0.753371 + 0.657596i $$0.771573\pi$$
$$38$$ 0 0
$$39$$ −6.00000 −0.960769
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 12.0000i 1.82998i 0.403473 + 0.914991i $$0.367803\pi$$
−0.403473 + 0.914991i $$0.632197\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 2.00000i −0.149071 + 0.298142i
$$46$$ 0 0
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 10.0000i 1.37361i −0.726844 0.686803i $$-0.759014\pi$$
0.726844 0.686803i $$-0.240986\pi$$
$$54$$ 0 0
$$55$$ −6.00000 + 12.0000i −0.809040 + 1.61808i
$$56$$ 0 0
$$57$$ 2.00000i 0.264906i
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 0 0
$$63$$ 1.00000i 0.125988i
$$64$$ 0 0
$$65$$ −12.0000 6.00000i −1.48842 0.744208i
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 0 0
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ 6.00000i 0.702247i −0.936329 0.351123i $$-0.885800\pi$$
0.936329 0.351123i $$-0.114200\pi$$
$$74$$ 0 0
$$75$$ −4.00000 + 3.00000i −0.461880 + 0.346410i
$$76$$ 0 0
$$77$$ 6.00000i 0.683763i
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 10.0000i 1.07211i
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ −6.00000 −0.628971
$$92$$ 0 0
$$93$$ 2.00000i 0.207390i
$$94$$ 0 0
$$95$$ 2.00000 4.00000i 0.205196 0.410391i
$$96$$ 0 0
$$97$$ 10.0000i 1.01535i 0.861550 + 0.507673i $$0.169494\pi$$
−0.861550 + 0.507673i $$0.830506\pi$$
$$98$$ 0 0
$$99$$ 6.00000 0.603023
$$100$$ 0 0
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ 16.0000i 1.57653i 0.615338 + 0.788263i $$0.289020\pi$$
−0.615338 + 0.788263i $$0.710980\pi$$
$$104$$ 0 0
$$105$$ −1.00000 + 2.00000i −0.0975900 + 0.195180i
$$106$$ 0 0
$$107$$ 4.00000i 0.386695i 0.981130 + 0.193347i $$0.0619344\pi$$
−0.981130 + 0.193347i $$0.938066\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ 8.00000 0.759326
$$112$$ 0 0
$$113$$ 2.00000i 0.188144i 0.995565 + 0.0940721i $$0.0299884\pi$$
−0.995565 + 0.0940721i $$0.970012\pi$$
$$114$$ 0 0
$$115$$ −16.0000 8.00000i −1.49201 0.746004i
$$116$$ 0 0
$$117$$ 6.00000i 0.554700i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 0 0
$$123$$ 6.00000i 0.541002i
$$124$$ 0 0
$$125$$ −11.0000 + 2.00000i −0.983870 + 0.178885i
$$126$$ 0 0
$$127$$ 4.00000i 0.354943i −0.984126 0.177471i $$-0.943208\pi$$
0.984126 0.177471i $$-0.0567917\pi$$
$$128$$ 0 0
$$129$$ 12.0000 1.05654
$$130$$ 0 0
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 0 0
$$133$$ 2.00000i 0.173422i
$$134$$ 0 0
$$135$$ 2.00000 + 1.00000i 0.172133 + 0.0860663i
$$136$$ 0 0
$$137$$ 14.0000i 1.19610i −0.801459 0.598050i $$-0.795942\pi$$
0.801459 0.598050i $$-0.204058\pi$$
$$138$$ 0 0
$$139$$ 10.0000 0.848189 0.424094 0.905618i $$-0.360592\pi$$
0.424094 + 0.905618i $$0.360592\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 0 0
$$143$$ 36.0000i 3.01047i
$$144$$ 0 0
$$145$$ 10.0000 20.0000i 0.830455 1.66091i
$$146$$ 0 0
$$147$$ 1.00000i 0.0824786i
$$148$$ 0 0
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ −4.00000 −0.325515 −0.162758 0.986666i $$-0.552039\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −2.00000 + 4.00000i −0.160644 + 0.321288i
$$156$$ 0 0
$$157$$ 10.0000i 0.798087i 0.916932 + 0.399043i $$0.130658\pi$$
−0.916932 + 0.399043i $$0.869342\pi$$
$$158$$ 0 0
$$159$$ −10.0000 −0.793052
$$160$$ 0 0
$$161$$ −8.00000 −0.630488
$$162$$ 0 0
$$163$$ 12.0000i 0.939913i −0.882690 0.469956i $$-0.844270\pi$$
0.882690 0.469956i $$-0.155730\pi$$
$$164$$ 0 0
$$165$$ 12.0000 + 6.00000i 0.934199 + 0.467099i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i −0.885681 0.464294i $$-0.846308\pi$$
0.885681 0.464294i $$-0.153692\pi$$
$$168$$ 0 0
$$169$$ −23.0000 −1.76923
$$170$$ 0 0
$$171$$ −2.00000 −0.152944
$$172$$ 0 0
$$173$$ 16.0000i 1.21646i 0.793762 + 0.608229i $$0.208120\pi$$
−0.793762 + 0.608229i $$0.791880\pi$$
$$174$$ 0 0
$$175$$ −4.00000 + 3.00000i −0.302372 + 0.226779i
$$176$$ 0 0
$$177$$ 4.00000i 0.300658i
$$178$$ 0 0
$$179$$ −10.0000 −0.747435 −0.373718 0.927543i $$-0.621917\pi$$
−0.373718 + 0.927543i $$0.621917\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 2.00000i 0.147844i
$$184$$ 0 0
$$185$$ 16.0000 + 8.00000i 1.17634 + 0.588172i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 1.00000 0.0727393
$$190$$ 0 0
$$191$$ −6.00000 −0.434145 −0.217072 0.976156i $$-0.569651\pi$$
−0.217072 + 0.976156i $$0.569651\pi$$
$$192$$ 0 0
$$193$$ 16.0000i 1.15171i −0.817554 0.575853i $$-0.804670\pi$$
0.817554 0.575853i $$-0.195330\pi$$
$$194$$ 0 0
$$195$$ −6.00000 + 12.0000i −0.429669 + 0.859338i
$$196$$ 0 0
$$197$$ 18.0000i 1.28245i −0.767354 0.641223i $$-0.778427\pi$$
0.767354 0.641223i $$-0.221573\pi$$
$$198$$ 0 0
$$199$$ −22.0000 −1.55954 −0.779769 0.626067i $$-0.784664\pi$$
−0.779769 + 0.626067i $$0.784664\pi$$
$$200$$ 0 0
$$201$$ −8.00000 −0.564276
$$202$$ 0 0
$$203$$ 10.0000i 0.701862i
$$204$$ 0 0
$$205$$ −6.00000 + 12.0000i −0.419058 + 0.838116i
$$206$$ 0 0
$$207$$ 8.00000i 0.556038i
$$208$$ 0 0
$$209$$ −12.0000 −0.830057
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ 0 0
$$213$$ 10.0000i 0.685189i
$$214$$ 0 0
$$215$$ 24.0000 + 12.0000i 1.63679 + 0.818393i
$$216$$ 0 0
$$217$$ 2.00000i 0.135769i
$$218$$ 0 0
$$219$$ −6.00000 −0.405442
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 8.00000i 0.535720i −0.963458 0.267860i $$-0.913684\pi$$
0.963458 0.267860i $$-0.0863164\pi$$
$$224$$ 0 0
$$225$$ 3.00000 + 4.00000i 0.200000 + 0.266667i
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 18.0000 1.18947 0.594737 0.803921i $$-0.297256\pi$$
0.594737 + 0.803921i $$0.297256\pi$$
$$230$$ 0 0
$$231$$ 6.00000 0.394771
$$232$$ 0 0
$$233$$ 6.00000i 0.393073i −0.980497 0.196537i $$-0.937031\pi$$
0.980497 0.196537i $$-0.0629694\pi$$
$$234$$ 0 0
$$235$$ 16.0000 + 8.00000i 1.04372 + 0.521862i
$$236$$ 0 0
$$237$$ 8.00000i 0.519656i
$$238$$ 0 0
$$239$$ 2.00000 0.129369 0.0646846 0.997906i $$-0.479396\pi$$
0.0646846 + 0.997906i $$0.479396\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ −1.00000 + 2.00000i −0.0638877 + 0.127775i
$$246$$ 0 0
$$247$$ 12.0000i 0.763542i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ 48.0000i 3.01773i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 28.0000i 1.74659i −0.487190 0.873296i $$-0.661978\pi$$
0.487190 0.873296i $$-0.338022\pi$$
$$258$$ 0 0
$$259$$ 8.00000 0.497096
$$260$$ 0 0
$$261$$ −10.0000 −0.618984
$$262$$ 0 0
$$263$$ 8.00000i 0.493301i 0.969104 + 0.246651i $$0.0793300\pi$$
−0.969104 + 0.246651i $$0.920670\pi$$
$$264$$ 0 0
$$265$$ −20.0000 10.0000i −1.22859 0.614295i
$$266$$ 0 0
$$267$$ 6.00000i 0.367194i
$$268$$ 0 0
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ 2.00000 0.121491 0.0607457 0.998153i $$-0.480652\pi$$
0.0607457 + 0.998153i $$0.480652\pi$$
$$272$$ 0 0
$$273$$ 6.00000i 0.363137i
$$274$$ 0 0
$$275$$ 18.0000 + 24.0000i 1.08544 + 1.44725i
$$276$$ 0 0
$$277$$ 8.00000i 0.480673i −0.970690 0.240337i $$-0.922742\pi$$
0.970690 0.240337i $$-0.0772579\pi$$
$$278$$ 0 0
$$279$$ 2.00000 0.119737
$$280$$ 0 0
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ 0 0
$$283$$ 4.00000i 0.237775i 0.992908 + 0.118888i $$0.0379328\pi$$
−0.992908 + 0.118888i $$0.962067\pi$$
$$284$$ 0 0
$$285$$ −4.00000 2.00000i −0.236940 0.118470i
$$286$$ 0 0
$$287$$ 6.00000i 0.354169i
$$288$$ 0 0
$$289$$ 17.0000 1.00000
$$290$$ 0 0
$$291$$ 10.0000 0.586210
$$292$$ 0 0
$$293$$ 16.0000i 0.934730i −0.884064 0.467365i $$-0.845203\pi$$
0.884064 0.467365i $$-0.154797\pi$$
$$294$$ 0 0
$$295$$ 4.00000 8.00000i 0.232889 0.465778i
$$296$$ 0 0
$$297$$ 6.00000i 0.348155i
$$298$$ 0 0
$$299$$ −48.0000 −2.77591
$$300$$ 0 0
$$301$$ 12.0000 0.691669
$$302$$ 0 0
$$303$$ 6.00000i 0.344691i
$$304$$ 0 0
$$305$$ −2.00000 + 4.00000i −0.114520 + 0.229039i
$$306$$ 0 0
$$307$$ 4.00000i 0.228292i 0.993464 + 0.114146i $$0.0364132\pi$$
−0.993464 + 0.114146i $$0.963587\pi$$
$$308$$ 0 0
$$309$$ 16.0000 0.910208
$$310$$ 0 0
$$311$$ −32.0000 −1.81455 −0.907277 0.420534i $$-0.861843\pi$$
−0.907277 + 0.420534i $$0.861843\pi$$
$$312$$ 0 0
$$313$$ 22.0000i 1.24351i 0.783210 + 0.621757i $$0.213581\pi$$
−0.783210 + 0.621757i $$0.786419\pi$$
$$314$$ 0 0
$$315$$ 2.00000 + 1.00000i 0.112687 + 0.0563436i
$$316$$ 0 0
$$317$$ 18.0000i 1.01098i 0.862832 + 0.505490i $$0.168688\pi$$
−0.862832 + 0.505490i $$0.831312\pi$$
$$318$$ 0 0
$$319$$ −60.0000 −3.35936
$$320$$ 0 0
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −24.0000 + 18.0000i −1.33128 + 0.998460i
$$326$$ 0 0
$$327$$ 14.0000i 0.774202i
$$328$$ 0 0
$$329$$ 8.00000 0.441054
$$330$$ 0 0
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ 0 0
$$333$$ 8.00000i 0.438397i
$$334$$ 0 0
$$335$$ −16.0000 8.00000i −0.874173 0.437087i
$$336$$ 0 0
$$337$$ 32.0000i 1.74315i 0.490261 + 0.871576i $$0.336901\pi$$
−0.490261 + 0.871576i $$0.663099\pi$$
$$338$$ 0 0
$$339$$ 2.00000 0.108625
$$340$$ 0 0
$$341$$ 12.0000 0.649836
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ −8.00000 + 16.0000i −0.430706 + 0.861411i
$$346$$ 0 0
$$347$$ 28.0000i 1.50312i −0.659665 0.751559i $$-0.729302\pi$$
0.659665 0.751559i $$-0.270698\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ 6.00000 0.320256
$$352$$ 0 0
$$353$$ 24.0000i 1.27739i −0.769460 0.638696i $$-0.779474\pi$$
0.769460 0.638696i $$-0.220526\pi$$
$$354$$ 0 0
$$355$$ −10.0000 + 20.0000i −0.530745 + 1.06149i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 30.0000 1.58334 0.791670 0.610949i $$-0.209212\pi$$
0.791670 + 0.610949i $$0.209212\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 25.0000i 1.31216i
$$364$$ 0 0
$$365$$ −12.0000 6.00000i −0.628109 0.314054i
$$366$$ 0 0
$$367$$ 24.0000i 1.25279i −0.779506 0.626395i $$-0.784530\pi$$
0.779506 0.626395i $$-0.215470\pi$$
$$368$$ 0 0
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ −10.0000 −0.519174
$$372$$ 0 0
$$373$$ 4.00000i 0.207112i 0.994624 + 0.103556i $$0.0330221\pi$$
−0.994624 + 0.103556i $$0.966978\pi$$
$$374$$ 0 0
$$375$$ 2.00000 + 11.0000i 0.103280 + 0.568038i
$$376$$ 0 0
$$377$$ 60.0000i 3.09016i
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 0 0
$$381$$ −4.00000 −0.204926
$$382$$ 0 0
$$383$$ 36.0000i 1.83951i −0.392488 0.919757i $$-0.628386\pi$$
0.392488 0.919757i $$-0.371614\pi$$
$$384$$ 0 0
$$385$$ 12.0000 + 6.00000i 0.611577 + 0.305788i
$$386$$ 0 0
$$387$$ 12.0000i 0.609994i
$$388$$ 0 0
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 8.00000i 0.403547i
$$394$$ 0 0
$$395$$ −8.00000 + 16.0000i −0.402524 + 0.805047i
$$396$$ 0 0
$$397$$ 14.0000i 0.702640i 0.936255 + 0.351320i $$0.114267\pi$$
−0.936255 + 0.351320i $$0.885733\pi$$
$$398$$ 0 0
$$399$$ −2.00000 −0.100125
$$400$$ 0 0
$$401$$ 10.0000 0.499376 0.249688 0.968326i $$-0.419672\pi$$
0.249688 + 0.968326i $$0.419672\pi$$
$$402$$ 0 0
$$403$$ 12.0000i 0.597763i
$$404$$ 0 0
$$405$$ 1.00000 2.00000i 0.0496904 0.0993808i
$$406$$ 0 0
$$407$$ 48.0000i 2.37927i
$$408$$ 0 0
$$409$$ −2.00000 −0.0988936 −0.0494468 0.998777i $$-0.515746\pi$$
−0.0494468 + 0.998777i $$0.515746\pi$$
$$410$$ 0 0
$$411$$ −14.0000 −0.690569
$$412$$ 0 0
$$413$$ 4.00000i 0.196827i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 10.0000i 0.489702i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 0 0
$$423$$ 8.00000i 0.388973i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 2.00000i 0.0967868i
$$428$$ 0 0
$$429$$ 36.0000 1.73810
$$430$$ 0 0
$$431$$ 38.0000 1.83040 0.915198 0.403005i $$-0.132034\pi$$
0.915198 + 0.403005i $$0.132034\pi$$
$$432$$ 0 0
$$433$$ 2.00000i 0.0961139i −0.998845 0.0480569i $$-0.984697\pi$$
0.998845 0.0480569i $$-0.0153029\pi$$
$$434$$ 0 0
$$435$$ −20.0000 10.0000i −0.958927 0.479463i
$$436$$ 0 0
$$437$$ 16.0000i 0.765384i
$$438$$ 0 0
$$439$$ 18.0000 0.859093 0.429547 0.903045i $$-0.358673\pi$$
0.429547 + 0.903045i $$0.358673\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ 12.0000i 0.570137i 0.958507 + 0.285069i $$0.0920164\pi$$
−0.958507 + 0.285069i $$0.907984\pi$$
$$444$$ 0 0
$$445$$ −6.00000 + 12.0000i −0.284427 + 0.568855i
$$446$$ 0 0
$$447$$ 6.00000i 0.283790i
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 36.0000 1.69517
$$452$$ 0 0
$$453$$ 4.00000i 0.187936i
$$454$$ 0 0
$$455$$ −6.00000 + 12.0000i −0.281284 + 0.562569i
$$456$$ 0 0
$$457$$ 12.0000i 0.561336i −0.959805 0.280668i $$-0.909444\pi$$
0.959805 0.280668i $$-0.0905560\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −34.0000 −1.58354 −0.791769 0.610821i $$-0.790840\pi$$
−0.791769 + 0.610821i $$0.790840\pi$$
$$462$$ 0 0
$$463$$ 20.0000i 0.929479i 0.885448 + 0.464739i $$0.153852\pi$$
−0.885448 + 0.464739i $$0.846148\pi$$
$$464$$ 0 0
$$465$$ 4.00000 + 2.00000i 0.185496 + 0.0927478i
$$466$$ 0 0
$$467$$ 32.0000i 1.48078i −0.672176 0.740392i $$-0.734640\pi$$
0.672176 0.740392i $$-0.265360\pi$$
$$468$$ 0 0
$$469$$ −8.00000 −0.369406
$$470$$ 0 0
$$471$$ 10.0000 0.460776
$$472$$ 0 0
$$473$$ 72.0000i 3.31056i
$$474$$ 0 0
$$475$$ −6.00000 8.00000i −0.275299 0.367065i
$$476$$ 0 0
$$477$$ 10.0000i 0.457869i
$$478$$ 0 0
$$479$$ 40.0000 1.82765 0.913823 0.406112i $$-0.133116\pi$$
0.913823 + 0.406112i $$0.133116\pi$$
$$480$$ 0 0
$$481$$ 48.0000 2.18861
$$482$$ 0 0
$$483$$ 8.00000i 0.364013i
$$484$$ 0 0
$$485$$ 20.0000 + 10.0000i 0.908153 + 0.454077i
$$486$$ 0 0
$$487$$ 20.0000i 0.906287i 0.891438 + 0.453143i $$0.149697\pi$$
−0.891438 + 0.453143i $$0.850303\pi$$
$$488$$ 0 0
$$489$$ −12.0000 −0.542659
$$490$$ 0 0
$$491$$ −22.0000 −0.992846 −0.496423 0.868081i $$-0.665354\pi$$
−0.496423 + 0.868081i $$0.665354\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 6.00000 12.0000i 0.269680 0.539360i
$$496$$ 0 0
$$497$$ 10.0000i 0.448561i
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 0 0
$$501$$ −12.0000 −0.536120
$$502$$ 0 0
$$503$$ 28.0000i 1.24846i 0.781241 + 0.624229i $$0.214587\pi$$
−0.781241 + 0.624229i $$0.785413\pi$$
$$504$$ 0 0
$$505$$ −6.00000 + 12.0000i −0.266996 + 0.533993i
$$506$$ 0 0
$$507$$ 23.0000i 1.02147i
$$508$$ 0 0
$$509$$ 2.00000 0.0886484 0.0443242 0.999017i $$-0.485887\pi$$
0.0443242 + 0.999017i $$0.485887\pi$$
$$510$$ 0 0
$$511$$ −6.00000 −0.265424
$$512$$ 0 0
$$513$$ 2.00000i 0.0883022i
$$514$$ 0 0
$$515$$ 32.0000 + 16.0000i 1.41009 + 0.705044i
$$516$$ 0 0
$$517$$ 48.0000i 2.11104i
$$518$$ 0 0
$$519$$ 16.0000 0.702322
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ 4.00000i 0.174908i −0.996169 0.0874539i $$-0.972127\pi$$
0.996169 0.0874539i $$-0.0278730\pi$$
$$524$$ 0 0
$$525$$ 3.00000 + 4.00000i 0.130931 + 0.174574i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −41.0000 −1.78261
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ 36.0000i 1.55933i
$$534$$ 0 0
$$535$$ 8.00000 + 4.00000i 0.345870 + 0.172935i
$$536$$ 0 0
$$537$$ 10.0000i 0.431532i
$$538$$ 0 0
$$539$$ 6.00000 0.258438
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 0 0
$$543$$ 10.0000i 0.429141i
$$544$$ 0 0
$$545$$ 14.0000 28.0000i 0.599694 1.19939i
$$546$$ 0 0
$$547$$ 8.00000i 0.342055i −0.985266 0.171028i $$-0.945291\pi$$
0.985266 0.171028i $$-0.0547087\pi$$
$$548$$ 0 0
$$549$$ 2.00000 0.0853579
$$550$$ 0 0
$$551$$ 20.0000 0.852029
$$552$$ 0 0
$$553$$ 8.00000i 0.340195i
$$554$$ 0 0
$$555$$ 8.00000 16.0000i 0.339581 0.679162i
$$556$$ 0 0
$$557$$ 34.0000i 1.44063i 0.693649 + 0.720313i $$0.256002\pi$$
−0.693649 + 0.720313i $$0.743998\pi$$
$$558$$ 0 0
$$559$$ 72.0000 3.04528
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 4.00000i 0.168580i 0.996441 + 0.0842900i $$0.0268622\pi$$
−0.996441 + 0.0842900i $$0.973138\pi$$
$$564$$ 0 0
$$565$$ 4.00000 + 2.00000i 0.168281 + 0.0841406i
$$566$$ 0 0
$$567$$ 1.00000i 0.0419961i
$$568$$ 0 0
$$569$$ −26.0000 −1.08998 −0.544988 0.838444i $$-0.683466\pi$$
−0.544988 + 0.838444i $$0.683466\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 0 0
$$573$$ 6.00000i 0.250654i
$$574$$ 0 0
$$575$$ −32.0000 + 24.0000i −1.33449 + 1.00087i
$$576$$ 0 0
$$577$$ 10.0000i 0.416305i 0.978096 + 0.208153i $$0.0667451\pi$$
−0.978096 + 0.208153i $$0.933255\pi$$
$$578$$ 0 0
$$579$$ −16.0000 −0.664937
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 60.0000i 2.48495i
$$584$$ 0 0
$$585$$ 12.0000 + 6.00000i 0.496139 + 0.248069i
$$586$$ 0 0
$$587$$ 12.0000i 0.495293i −0.968850 0.247647i $$-0.920343\pi$$
0.968850 0.247647i $$-0.0796572\pi$$
$$588$$ 0 0
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ −18.0000 −0.740421
$$592$$ 0 0
$$593$$ 24.0000i 0.985562i 0.870153 + 0.492781i $$0.164020\pi$$
−0.870153 + 0.492781i $$0.835980\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 22.0000i 0.900400i
$$598$$ 0 0
$$599$$ 6.00000 0.245153 0.122577 0.992459i $$-0.460884\pi$$
0.122577 + 0.992459i $$0.460884\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ 8.00000i 0.325785i
$$604$$ 0 0
$$605$$ 25.0000 50.0000i 1.01639 2.03279i
$$606$$ 0 0
$$607$$ 32.0000i 1.29884i −0.760430 0.649420i $$-0.775012\pi$$
0.760430 0.649420i $$-0.224988\pi$$
$$608$$ 0 0
$$609$$ −10.0000 −0.405220
$$610$$ 0 0
$$611$$ 48.0000 1.94187
$$612$$ 0 0
$$613$$ 16.0000i 0.646234i 0.946359 + 0.323117i $$0.104731\pi$$
−0.946359 + 0.323117i $$0.895269\pi$$
$$614$$ 0 0
$$615$$ 12.0000 + 6.00000i 0.483887 + 0.241943i
$$616$$ 0 0
$$617$$ 6.00000i 0.241551i 0.992680 + 0.120775i $$0.0385381\pi$$
−0.992680 + 0.120775i $$0.961462\pi$$
$$618$$ 0 0
$$619$$ 34.0000 1.36658 0.683288 0.730149i $$-0.260549\pi$$
0.683288 + 0.730149i $$0.260549\pi$$
$$620$$ 0 0
$$621$$ 8.00000 0.321029
$$622$$ 0 0
$$623$$ 6.00000i 0.240385i
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 0 0
$$627$$ 12.0000i 0.479234i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 8.00000i 0.317971i
$$634$$ 0 0
$$635$$ −8.00000 4.00000i −0.317470 0.158735i
$$636$$ 0 0
$$637$$ 6.00000i 0.237729i
$$638$$ 0 0
$$639$$ 10.0000 0.395594
$$640$$ 0 0
$$641$$ −10.0000 −0.394976 −0.197488 0.980305i $$-0.563278\pi$$
−0.197488 + 0.980305i $$0.563278\pi$$
$$642$$ 0 0
$$643$$ 28.0000i 1.10421i −0.833774 0.552106i $$-0.813824\pi$$
0.833774 0.552106i $$-0.186176\pi$$
$$644$$ 0 0
$$645$$ 12.0000 24.0000i 0.472500 0.944999i
$$646$$ 0 0
$$647$$ 12.0000i 0.471769i −0.971781 0.235884i $$-0.924201\pi$$
0.971781 0.235884i $$-0.0757987\pi$$
$$648$$ 0 0
$$649$$ −24.0000 −0.942082
$$650$$ 0 0
$$651$$ 2.00000 0.0783862
$$652$$ 0 0
$$653$$ 38.0000i 1.48705i −0.668705 0.743527i $$-0.733151\pi$$
0.668705 0.743527i $$-0.266849\pi$$
$$654$$ 0 0
$$655$$ −8.00000 + 16.0000i −0.312586 + 0.625172i
$$656$$ 0 0
$$657$$ 6.00000i 0.234082i
$$658$$ 0 0
$$659$$ 26.0000 1.01282 0.506408 0.862294i $$-0.330973\pi$$
0.506408 + 0.862294i $$0.330973\pi$$
$$660$$ 0 0
$$661$$ 30.0000 1.16686 0.583432 0.812162i $$-0.301709\pi$$
0.583432 + 0.812162i $$0.301709\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −4.00000 2.00000i −0.155113 0.0775567i
$$666$$ 0 0
$$667$$ 80.0000i 3.09761i
$$668$$ 0 0
$$669$$ −8.00000 −0.309298
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ 44.0000i 1.69608i −0.529936 0.848038i $$-0.677784\pi$$
0.529936 0.848038i $$-0.322216\pi$$
$$674$$ 0 0
$$675$$ 4.00000 3.00000i 0.153960 0.115470i
$$676$$ 0 0
$$677$$ 48.0000i 1.84479i −0.386248 0.922395i $$-0.626229\pi$$
0.386248 0.922395i $$-0.373771\pi$$
$$678$$ 0 0
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 12.0000i 0.459167i −0.973289 0.229584i $$-0.926264\pi$$
0.973289 0.229584i $$-0.0737364\pi$$
$$684$$ 0 0
$$685$$ −28.0000 14.0000i −1.06983 0.534913i
$$686$$ 0 0
$$687$$ 18.0000i 0.686743i
$$688$$ 0 0
$$689$$ −60.0000 −2.28582
$$690$$ 0 0
$$691$$ 10.0000 0.380418 0.190209 0.981744i $$-0.439083\pi$$
0.190209 + 0.981744i $$0.439083\pi$$
$$692$$ 0 0
$$693$$ 6.00000i 0.227921i
$$694$$ 0 0
$$695$$ 10.0000 20.0000i 0.379322 0.758643i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ −26.0000 −0.982006 −0.491003 0.871158i $$-0.663370\pi$$
−0.491003 + 0.871158i $$0.663370\pi$$
$$702$$ 0 0
$$703$$ 16.0000i 0.603451i
$$704$$ 0 0
$$705$$ 8.00000 16.0000i 0.301297 0.602595i
$$706$$ 0 0
$$707$$ 6.00000i 0.225653i
$$708$$ 0 0
$$709$$ 14.0000 0.525781 0.262891 0.964826i $$-0.415324\pi$$
0.262891 + 0.964826i $$0.415324\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ 0 0
$$713$$ 16.0000i 0.599205i
$$714$$ 0 0
$$715$$ 72.0000 + 36.0000i 2.69265 + 1.34632i
$$716$$ 0 0
$$717$$ 2.00000i 0.0746914i
$$718$$ 0 0
$$719$$ 20.0000 0.745874 0.372937 0.927857i $$-0.378351\pi$$
0.372937 + 0.927857i $$0.378351\pi$$
$$720$$ 0 0
$$721$$ 16.0000 0.595871
$$722$$ 0 0
$$723$$ 18.0000i 0.669427i
$$724$$ 0 0
$$725$$ −30.0000 40.0000i −1.11417 1.48556i
$$726$$ 0 0
$$727$$ 8.00000i 0.296704i −0.988935 0.148352i $$-0.952603\pi$$
0.988935 0.148352i $$-0.0473968\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 26.0000i 0.960332i 0.877178 + 0.480166i $$0.159424\pi$$
−0.877178 + 0.480166i $$0.840576\pi$$
$$734$$ 0 0
$$735$$ 2.00000 + 1.00000i 0.0737711 + 0.0368856i
$$736$$ 0 0
$$737$$ 48.0000i 1.76810i
$$738$$ 0 0
$$739$$ −28.0000 −1.03000 −0.514998 0.857191i $$-0.672207\pi$$
−0.514998 + 0.857191i $$0.672207\pi$$
$$740$$ 0 0
$$741$$ −12.0000 −0.440831
$$742$$ 0 0
$$743$$ 48.0000i 1.76095i −0.474093 0.880475i $$-0.657224\pi$$
0.474093 0.880475i $$-0.342776\pi$$
$$744$$ 0 0
$$745$$ 6.00000 12.0000i 0.219823 0.439646i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 4.00000 0.146157
$$750$$ 0 0
$$751$$ −8.00000 −0.291924 −0.145962 0.989290i $$-0.546628\pi$$
−0.145962 + 0.989290i $$0.546628\pi$$
$$752$$ 0 0
$$753$$ 12.0000i 0.437304i
$$754$$ 0 0
$$755$$ −4.00000 + 8.00000i −0.145575 + 0.291150i
$$756$$ 0 0
$$757$$ 20.0000i 0.726912i 0.931611 + 0.363456i $$0.118403\pi$$
−0.931611 + 0.363456i $$0.881597\pi$$
$$758$$ 0 0
$$759$$ 48.0000 1.74229
$$760$$ 0 0
$$761$$ −38.0000 −1.37750 −0.688749 0.724999i $$-0.741840\pi$$
−0.688749 + 0.724999i $$0.741840\pi$$
$$762$$ 0 0
$$763$$ 14.0000i 0.506834i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 24.0000i 0.866590i
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 0 0
$$771$$ −28.0000 −1.00840
$$772$$ 0 0
$$773$$ 32.0000i 1.15096i −0.817816 0.575480i $$-0.804815\pi$$
0.817816 0.575480i $$-0.195185\pi$$
$$774$$ 0 0
$$775$$ 6.00000 + 8.00000i 0.215526 + 0.287368i
$$776$$ 0 0
$$777$$ 8.00000i 0.286998i
$$778$$ 0 0
$$779$$ −12.0000 −0.429945
$$780$$ 0 0
$$781$$ 60.0000 2.14697
$$782$$ 0 0
$$783$$ 10.0000i 0.357371i
$$784$$ 0 0
$$785$$ 20.0000 + 10.0000i 0.713831 + 0.356915i
$$786$$ 0 0
$$787$$ 20.0000i 0.712923i −0.934310 0.356462i $$-0.883983\pi$$
0.934310 0.356462i $$-0.116017\pi$$
$$788$$ 0 0
$$789$$ 8.00000 0.284808
$$790$$ 0 0
$$791$$ 2.00000 0.0711118
$$792$$ 0 0
$$793$$ 12.0000i 0.426132i
$$794$$ 0 0
$$795$$ −10.0000 + 20.0000i −0.354663 + 0.709327i
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 6.00000