# Properties

 Label 1170.2.e.a.469.2 Level $1170$ Weight $2$ Character 1170.469 Analytic conductor $9.342$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.34249703649$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 469.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1170.469 Dual form 1170.2.e.a.469.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} -2.00000 q^{11} -1.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} +2.00000i q^{17} +4.00000 q^{19} +(2.00000 - 1.00000i) q^{20} -2.00000i q^{22} +(3.00000 - 4.00000i) q^{25} +1.00000 q^{26} +2.00000i q^{28} +4.00000 q^{29} +8.00000 q^{31} +1.00000i q^{32} -2.00000 q^{34} +(2.00000 + 4.00000i) q^{35} -6.00000i q^{37} +4.00000i q^{38} +(1.00000 + 2.00000i) q^{40} +6.00000 q^{41} +4.00000i q^{43} +2.00000 q^{44} -8.00000i q^{47} +3.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +1.00000i q^{52} -2.00000i q^{53} +(4.00000 - 2.00000i) q^{55} -2.00000 q^{56} +4.00000i q^{58} +10.0000 q^{59} -14.0000 q^{61} +8.00000i q^{62} -1.00000 q^{64} +(1.00000 + 2.00000i) q^{65} +16.0000i q^{67} -2.00000i q^{68} +(-4.00000 + 2.00000i) q^{70} +4.00000 q^{71} +8.00000i q^{73} +6.00000 q^{74} -4.00000 q^{76} +4.00000i q^{77} +8.00000 q^{79} +(-2.00000 + 1.00000i) q^{80} +6.00000i q^{82} -12.0000i q^{83} +(-2.00000 - 4.00000i) q^{85} -4.00000 q^{86} +2.00000i q^{88} +6.00000 q^{89} -2.00000 q^{91} +8.00000 q^{94} +(-8.00000 + 4.00000i) q^{95} -12.0000i q^{97} +3.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{4} - 4 q^{5} + O(q^{10})$$ $$2 q - 2 q^{4} - 4 q^{5} - 2 q^{10} - 4 q^{11} + 4 q^{14} + 2 q^{16} + 8 q^{19} + 4 q^{20} + 6 q^{25} + 2 q^{26} + 8 q^{29} + 16 q^{31} - 4 q^{34} + 4 q^{35} + 2 q^{40} + 12 q^{41} + 4 q^{44} + 6 q^{49} + 8 q^{50} + 8 q^{55} - 4 q^{56} + 20 q^{59} - 28 q^{61} - 2 q^{64} + 2 q^{65} - 8 q^{70} + 8 q^{71} + 12 q^{74} - 8 q^{76} + 16 q^{79} - 4 q^{80} - 4 q^{85} - 8 q^{86} + 12 q^{89} - 4 q^{91} + 16 q^{94} - 16 q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$$.

 $$n$$ $$911$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ −2.00000 + 1.00000i −0.894427 + 0.447214i
$$6$$ 0 0
$$7$$ 2.00000i 0.755929i −0.925820 0.377964i $$-0.876624\pi$$
0.925820 0.377964i $$-0.123376\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ −1.00000 2.00000i −0.316228 0.632456i
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 1.00000i 0.277350i
$$14$$ 2.00000 0.534522
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.00000i 0.485071i 0.970143 + 0.242536i $$0.0779791\pi$$
−0.970143 + 0.242536i $$0.922021\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 2.00000 1.00000i 0.447214 0.223607i
$$21$$ 0 0
$$22$$ 2.00000i 0.426401i
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 1.00000 0.196116
$$27$$ 0 0
$$28$$ 2.00000i 0.377964i
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 2.00000 + 4.00000i 0.338062 + 0.676123i
$$36$$ 0 0
$$37$$ 6.00000i 0.986394i −0.869918 0.493197i $$-0.835828\pi$$
0.869918 0.493197i $$-0.164172\pi$$
$$38$$ 4.00000i 0.648886i
$$39$$ 0 0
$$40$$ 1.00000 + 2.00000i 0.158114 + 0.316228i
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.00000i 1.16692i −0.812142 0.583460i $$-0.801699\pi$$
0.812142 0.583460i $$-0.198301\pi$$
$$48$$ 0 0
$$49$$ 3.00000 0.428571
$$50$$ 4.00000 + 3.00000i 0.565685 + 0.424264i
$$51$$ 0 0
$$52$$ 1.00000i 0.138675i
$$53$$ 2.00000i 0.274721i −0.990521 0.137361i $$-0.956138\pi$$
0.990521 0.137361i $$-0.0438619\pi$$
$$54$$ 0 0
$$55$$ 4.00000 2.00000i 0.539360 0.269680i
$$56$$ −2.00000 −0.267261
$$57$$ 0 0
$$58$$ 4.00000i 0.525226i
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ −14.0000 −1.79252 −0.896258 0.443533i $$-0.853725\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 8.00000i 1.01600i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 1.00000 + 2.00000i 0.124035 + 0.248069i
$$66$$ 0 0
$$67$$ 16.0000i 1.95471i 0.211604 + 0.977356i $$0.432131\pi$$
−0.211604 + 0.977356i $$0.567869\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ 0 0
$$70$$ −4.00000 + 2.00000i −0.478091 + 0.239046i
$$71$$ 4.00000 0.474713 0.237356 0.971423i $$-0.423719\pi$$
0.237356 + 0.971423i $$0.423719\pi$$
$$72$$ 0 0
$$73$$ 8.00000i 0.936329i 0.883641 + 0.468165i $$0.155085\pi$$
−0.883641 + 0.468165i $$0.844915\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 4.00000i 0.455842i
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ −2.00000 + 1.00000i −0.223607 + 0.111803i
$$81$$ 0 0
$$82$$ 6.00000i 0.662589i
$$83$$ 12.0000i 1.31717i −0.752506 0.658586i $$-0.771155\pi$$
0.752506 0.658586i $$-0.228845\pi$$
$$84$$ 0 0
$$85$$ −2.00000 4.00000i −0.216930 0.433861i
$$86$$ −4.00000 −0.431331
$$87$$ 0 0
$$88$$ 2.00000i 0.213201i
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ −2.00000 −0.209657
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 8.00000 0.825137
$$95$$ −8.00000 + 4.00000i −0.820783 + 0.410391i
$$96$$ 0 0
$$97$$ 12.0000i 1.21842i −0.793011 0.609208i $$-0.791488\pi$$
0.793011 0.609208i $$-0.208512\pi$$
$$98$$ 3.00000i 0.303046i
$$99$$ 0 0
$$100$$ −3.00000 + 4.00000i −0.300000 + 0.400000i
$$101$$ −4.00000 −0.398015 −0.199007 0.979998i $$-0.563772\pi$$
−0.199007 + 0.979998i $$0.563772\pi$$
$$102$$ 0 0
$$103$$ 6.00000i 0.591198i 0.955312 + 0.295599i $$0.0955191\pi$$
−0.955312 + 0.295599i $$0.904481\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 2.00000 0.194257
$$107$$ 4.00000i 0.386695i −0.981130 0.193347i $$-0.938066\pi$$
0.981130 0.193347i $$-0.0619344\pi$$
$$108$$ 0 0
$$109$$ 18.0000 1.72409 0.862044 0.506834i $$-0.169184\pi$$
0.862044 + 0.506834i $$0.169184\pi$$
$$110$$ 2.00000 + 4.00000i 0.190693 + 0.381385i
$$111$$ 0 0
$$112$$ 2.00000i 0.188982i
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −4.00000 −0.371391
$$117$$ 0 0
$$118$$ 10.0000i 0.920575i
$$119$$ 4.00000 0.366679
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 14.0000i 1.26750i
$$123$$ 0 0
$$124$$ −8.00000 −0.718421
$$125$$ −2.00000 + 11.0000i −0.178885 + 0.983870i
$$126$$ 0 0
$$127$$ 6.00000i 0.532414i −0.963916 0.266207i $$-0.914230\pi$$
0.963916 0.266207i $$-0.0857705\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ −2.00000 + 1.00000i −0.175412 + 0.0877058i
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ 8.00000i 0.693688i
$$134$$ −16.0000 −1.38219
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ 14.0000i 1.19610i −0.801459 0.598050i $$-0.795942\pi$$
0.801459 0.598050i $$-0.204058\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ −2.00000 4.00000i −0.169031 0.338062i
$$141$$ 0 0
$$142$$ 4.00000i 0.335673i
$$143$$ 2.00000i 0.167248i
$$144$$ 0 0
$$145$$ −8.00000 + 4.00000i −0.664364 + 0.332182i
$$146$$ −8.00000 −0.662085
$$147$$ 0 0
$$148$$ 6.00000i 0.493197i
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 4.00000i 0.324443i
$$153$$ 0 0
$$154$$ −4.00000 −0.322329
$$155$$ −16.0000 + 8.00000i −1.28515 + 0.642575i
$$156$$ 0 0
$$157$$ 10.0000i 0.798087i −0.916932 0.399043i $$-0.869342\pi$$
0.916932 0.399043i $$-0.130658\pi$$
$$158$$ 8.00000i 0.636446i
$$159$$ 0 0
$$160$$ −1.00000 2.00000i −0.0790569 0.158114i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 8.00000i 0.626608i −0.949653 0.313304i $$-0.898564\pi$$
0.949653 0.313304i $$-0.101436\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ 0 0
$$169$$ −1.00000 −0.0769231
$$170$$ 4.00000 2.00000i 0.306786 0.153393i
$$171$$ 0 0
$$172$$ 4.00000i 0.304997i
$$173$$ 14.0000i 1.06440i −0.846619 0.532200i $$-0.821365\pi$$
0.846619 0.532200i $$-0.178635\pi$$
$$174$$ 0 0
$$175$$ −8.00000 6.00000i −0.604743 0.453557i
$$176$$ −2.00000 −0.150756
$$177$$ 0 0
$$178$$ 6.00000i 0.449719i
$$179$$ −18.0000 −1.34538 −0.672692 0.739923i $$-0.734862\pi$$
−0.672692 + 0.739923i $$0.734862\pi$$
$$180$$ 0 0
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 2.00000i 0.148250i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 6.00000 + 12.0000i 0.441129 + 0.882258i
$$186$$ 0 0
$$187$$ 4.00000i 0.292509i
$$188$$ 8.00000i 0.583460i
$$189$$ 0 0
$$190$$ −4.00000 8.00000i −0.290191 0.580381i
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 12.0000 0.861550
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ 10.0000i 0.712470i 0.934396 + 0.356235i $$0.115940\pi$$
−0.934396 + 0.356235i $$0.884060\pi$$
$$198$$ 0 0
$$199$$ 24.0000 1.70131 0.850657 0.525720i $$-0.176204\pi$$
0.850657 + 0.525720i $$0.176204\pi$$
$$200$$ −4.00000 3.00000i −0.282843 0.212132i
$$201$$ 0 0
$$202$$ 4.00000i 0.281439i
$$203$$ 8.00000i 0.561490i
$$204$$ 0 0
$$205$$ −12.0000 + 6.00000i −0.838116 + 0.419058i
$$206$$ −6.00000 −0.418040
$$207$$ 0 0
$$208$$ 1.00000i 0.0693375i
$$209$$ −8.00000 −0.553372
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 2.00000i 0.137361i
$$213$$ 0 0
$$214$$ 4.00000 0.273434
$$215$$ −4.00000 8.00000i −0.272798 0.545595i
$$216$$ 0 0
$$217$$ 16.0000i 1.08615i
$$218$$ 18.0000i 1.21911i
$$219$$ 0 0
$$220$$ −4.00000 + 2.00000i −0.269680 + 0.134840i
$$221$$ 2.00000 0.134535
$$222$$ 0 0
$$223$$ 14.0000i 0.937509i −0.883328 0.468755i $$-0.844703\pi$$
0.883328 0.468755i $$-0.155297\pi$$
$$224$$ 2.00000 0.133631
$$225$$ 0 0
$$226$$ 6.00000 0.399114
$$227$$ 12.0000i 0.796468i 0.917284 + 0.398234i $$0.130377\pi$$
−0.917284 + 0.398234i $$0.869623\pi$$
$$228$$ 0 0
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 4.00000i 0.262613i
$$233$$ 14.0000i 0.917170i 0.888650 + 0.458585i $$0.151644\pi$$
−0.888650 + 0.458585i $$0.848356\pi$$
$$234$$ 0 0
$$235$$ 8.00000 + 16.0000i 0.521862 + 1.04372i
$$236$$ −10.0000 −0.650945
$$237$$ 0 0
$$238$$ 4.00000i 0.259281i
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 7.00000i 0.449977i
$$243$$ 0 0
$$244$$ 14.0000 0.896258
$$245$$ −6.00000 + 3.00000i −0.383326 + 0.191663i
$$246$$ 0 0
$$247$$ 4.00000i 0.254514i
$$248$$ 8.00000i 0.508001i
$$249$$ 0 0
$$250$$ −11.0000 2.00000i −0.695701 0.126491i
$$251$$ −18.0000 −1.13615 −0.568075 0.822977i $$-0.692312\pi$$
−0.568075 + 0.822977i $$0.692312\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 6.00000 0.376473
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000i 1.12281i −0.827541 0.561405i $$-0.810261\pi$$
0.827541 0.561405i $$-0.189739\pi$$
$$258$$ 0 0
$$259$$ −12.0000 −0.745644
$$260$$ −1.00000 2.00000i −0.0620174 0.124035i
$$261$$ 0 0
$$262$$ 6.00000i 0.370681i
$$263$$ 8.00000i 0.493301i 0.969104 + 0.246651i $$0.0793300\pi$$
−0.969104 + 0.246651i $$0.920670\pi$$
$$264$$ 0 0
$$265$$ 2.00000 + 4.00000i 0.122859 + 0.245718i
$$266$$ 8.00000 0.490511
$$267$$ 0 0
$$268$$ 16.0000i 0.977356i
$$269$$ −20.0000 −1.21942 −0.609711 0.792624i $$-0.708714\pi$$
−0.609711 + 0.792624i $$0.708714\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 0 0
$$274$$ 14.0000 0.845771
$$275$$ −6.00000 + 8.00000i −0.361814 + 0.482418i
$$276$$ 0 0
$$277$$ 2.00000i 0.120168i 0.998193 + 0.0600842i $$0.0191369\pi$$
−0.998193 + 0.0600842i $$0.980863\pi$$
$$278$$ 4.00000i 0.239904i
$$279$$ 0 0
$$280$$ 4.00000 2.00000i 0.239046 0.119523i
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 16.0000i 0.951101i 0.879688 + 0.475551i $$0.157751\pi$$
−0.879688 + 0.475551i $$0.842249\pi$$
$$284$$ −4.00000 −0.237356
$$285$$ 0 0
$$286$$ −2.00000 −0.118262
$$287$$ 12.0000i 0.708338i
$$288$$ 0 0
$$289$$ 13.0000 0.764706
$$290$$ −4.00000 8.00000i −0.234888 0.469776i
$$291$$ 0 0
$$292$$ 8.00000i 0.468165i
$$293$$ 26.0000i 1.51894i −0.650545 0.759468i $$-0.725459\pi$$
0.650545 0.759468i $$-0.274541\pi$$
$$294$$ 0 0
$$295$$ −20.0000 + 10.0000i −1.16445 + 0.582223i
$$296$$ −6.00000 −0.348743
$$297$$ 0 0
$$298$$ 12.0000i 0.695141i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 8.00000 0.461112
$$302$$ 16.0000i 0.920697i
$$303$$ 0 0
$$304$$ 4.00000 0.229416
$$305$$ 28.0000 14.0000i 1.60328 0.801638i
$$306$$ 0 0
$$307$$ 28.0000i 1.59804i 0.601302 + 0.799022i $$0.294649\pi$$
−0.601302 + 0.799022i $$0.705351\pi$$
$$308$$ 4.00000i 0.227921i
$$309$$ 0 0
$$310$$ −8.00000 16.0000i −0.454369 0.908739i
$$311$$ −20.0000 −1.13410 −0.567048 0.823685i $$-0.691915\pi$$
−0.567048 + 0.823685i $$0.691915\pi$$
$$312$$ 0 0
$$313$$ 20.0000i 1.13047i −0.824931 0.565233i $$-0.808786\pi$$
0.824931 0.565233i $$-0.191214\pi$$
$$314$$ 10.0000 0.564333
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ 18.0000i 1.01098i −0.862832 0.505490i $$-0.831312\pi$$
0.862832 0.505490i $$-0.168688\pi$$
$$318$$ 0 0
$$319$$ −8.00000 −0.447914
$$320$$ 2.00000 1.00000i 0.111803 0.0559017i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000i 0.445132i
$$324$$ 0 0
$$325$$ −4.00000 3.00000i −0.221880 0.166410i
$$326$$ 8.00000 0.443079
$$327$$ 0 0
$$328$$ 6.00000i 0.331295i
$$329$$ −16.0000 −0.882109
$$330$$ 0 0
$$331$$ −12.0000 −0.659580 −0.329790 0.944054i $$-0.606978\pi$$
−0.329790 + 0.944054i $$0.606978\pi$$
$$332$$ 12.0000i 0.658586i
$$333$$ 0 0
$$334$$ −12.0000 −0.656611
$$335$$ −16.0000 32.0000i −0.874173 1.74835i
$$336$$ 0 0
$$337$$ 20.0000i 1.08947i −0.838608 0.544735i $$-0.816630\pi$$
0.838608 0.544735i $$-0.183370\pi$$
$$338$$ 1.00000i 0.0543928i
$$339$$ 0 0
$$340$$ 2.00000 + 4.00000i 0.108465 + 0.216930i
$$341$$ −16.0000 −0.866449
$$342$$ 0 0
$$343$$ 20.0000i 1.07990i
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ 14.0000 0.752645
$$347$$ 12.0000i 0.644194i 0.946707 + 0.322097i $$0.104388\pi$$
−0.946707 + 0.322097i $$0.895612\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 6.00000 8.00000i 0.320713 0.427618i
$$351$$ 0 0
$$352$$ 2.00000i 0.106600i
$$353$$ 34.0000i 1.80964i 0.425797 + 0.904819i $$0.359994\pi$$
−0.425797 + 0.904819i $$0.640006\pi$$
$$354$$ 0 0
$$355$$ −8.00000 + 4.00000i −0.424596 + 0.212298i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 18.0000i 0.951330i
$$359$$ 32.0000 1.68890 0.844448 0.535638i $$-0.179929\pi$$
0.844448 + 0.535638i $$0.179929\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 6.00000i 0.315353i
$$363$$ 0 0
$$364$$ 2.00000 0.104828
$$365$$ −8.00000 16.0000i −0.418739 0.837478i
$$366$$ 0 0
$$367$$ 10.0000i 0.521996i 0.965339 + 0.260998i $$0.0840516\pi$$
−0.965339 + 0.260998i $$0.915948\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −12.0000 + 6.00000i −0.623850 + 0.311925i
$$371$$ −4.00000 −0.207670
$$372$$ 0 0
$$373$$ 22.0000i 1.13912i −0.821951 0.569558i $$-0.807114\pi$$
0.821951 0.569558i $$-0.192886\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ −8.00000 −0.412568
$$377$$ 4.00000i 0.206010i
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 8.00000 4.00000i 0.410391 0.205196i
$$381$$ 0 0
$$382$$ 12.0000i 0.613973i
$$383$$ 24.0000i 1.22634i −0.789950 0.613171i $$-0.789894\pi$$
0.789950 0.613171i $$-0.210106\pi$$
$$384$$ 0 0
$$385$$ −4.00000 8.00000i −0.203859 0.407718i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 12.0000i 0.609208i
$$389$$ 16.0000 0.811232 0.405616 0.914044i $$-0.367057\pi$$
0.405616 + 0.914044i $$0.367057\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 3.00000i 0.151523i
$$393$$ 0 0
$$394$$ −10.0000 −0.503793
$$395$$ −16.0000 + 8.00000i −0.805047 + 0.402524i
$$396$$ 0 0
$$397$$ 18.0000i 0.903394i 0.892171 + 0.451697i $$0.149181\pi$$
−0.892171 + 0.451697i $$0.850819\pi$$
$$398$$ 24.0000i 1.20301i
$$399$$ 0 0
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 8.00000i 0.398508i
$$404$$ 4.00000 0.199007
$$405$$ 0 0
$$406$$ 8.00000 0.397033
$$407$$ 12.0000i 0.594818i
$$408$$ 0 0
$$409$$ 26.0000 1.28562 0.642809 0.766027i $$-0.277769\pi$$
0.642809 + 0.766027i $$0.277769\pi$$
$$410$$ −6.00000 12.0000i −0.296319 0.592638i
$$411$$ 0 0
$$412$$ 6.00000i 0.295599i
$$413$$ 20.0000i 0.984136i
$$414$$ 0 0
$$415$$ 12.0000 + 24.0000i 0.589057 + 1.17811i
$$416$$ 1.00000 0.0490290
$$417$$ 0 0
$$418$$ 8.00000i 0.391293i
$$419$$ −14.0000 −0.683945 −0.341972 0.939710i $$-0.611095\pi$$
−0.341972 + 0.939710i $$0.611095\pi$$
$$420$$ 0 0
$$421$$ 34.0000 1.65706 0.828529 0.559946i $$-0.189178\pi$$
0.828529 + 0.559946i $$0.189178\pi$$
$$422$$ 4.00000i 0.194717i
$$423$$ 0 0
$$424$$ −2.00000 −0.0971286
$$425$$ 8.00000 + 6.00000i 0.388057 + 0.291043i
$$426$$ 0 0
$$427$$ 28.0000i 1.35501i
$$428$$ 4.00000i 0.193347i
$$429$$ 0 0
$$430$$ 8.00000 4.00000i 0.385794 0.192897i
$$431$$ −16.0000 −0.770693 −0.385346 0.922772i $$-0.625918\pi$$
−0.385346 + 0.922772i $$0.625918\pi$$
$$432$$ 0 0
$$433$$ 12.0000i 0.576683i 0.957528 + 0.288342i $$0.0931039\pi$$
−0.957528 + 0.288342i $$0.906896\pi$$
$$434$$ 16.0000 0.768025
$$435$$ 0 0
$$436$$ −18.0000 −0.862044
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ −2.00000 4.00000i −0.0953463 0.190693i
$$441$$ 0 0
$$442$$ 2.00000i 0.0951303i
$$443$$ 4.00000i 0.190046i −0.995475 0.0950229i $$-0.969708\pi$$
0.995475 0.0950229i $$-0.0302924\pi$$
$$444$$ 0 0
$$445$$ −12.0000 + 6.00000i −0.568855 + 0.284427i
$$446$$ 14.0000 0.662919
$$447$$ 0 0
$$448$$ 2.00000i 0.0944911i
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ −12.0000 −0.565058
$$452$$ 6.00000i 0.282216i
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ 4.00000 2.00000i 0.187523 0.0937614i
$$456$$ 0 0
$$457$$ 28.0000i 1.30978i 0.755722 + 0.654892i $$0.227286\pi$$
−0.755722 + 0.654892i $$0.772714\pi$$
$$458$$ 22.0000i 1.02799i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −20.0000 −0.931493 −0.465746 0.884918i $$-0.654214\pi$$
−0.465746 + 0.884918i $$0.654214\pi$$
$$462$$ 0 0
$$463$$ 6.00000i 0.278844i 0.990233 + 0.139422i $$0.0445244\pi$$
−0.990233 + 0.139422i $$0.955476\pi$$
$$464$$ 4.00000 0.185695
$$465$$ 0 0
$$466$$ −14.0000 −0.648537
$$467$$ 28.0000i 1.29569i 0.761774 + 0.647843i $$0.224329\pi$$
−0.761774 + 0.647843i $$0.775671\pi$$
$$468$$ 0 0
$$469$$ 32.0000 1.47762
$$470$$ −16.0000 + 8.00000i −0.738025 + 0.369012i
$$471$$ 0 0
$$472$$ 10.0000i 0.460287i
$$473$$ 8.00000i 0.367840i
$$474$$ 0 0
$$475$$ 12.0000 16.0000i 0.550598 0.734130i
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ 12.0000i 0.548867i
$$479$$ 36.0000 1.64488 0.822441 0.568850i $$-0.192612\pi$$
0.822441 + 0.568850i $$0.192612\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 18.0000i 0.819878i
$$483$$ 0 0
$$484$$ 7.00000 0.318182
$$485$$ 12.0000 + 24.0000i 0.544892 + 1.08978i
$$486$$ 0 0
$$487$$ 26.0000i 1.17817i 0.808070 + 0.589086i $$0.200512\pi$$
−0.808070 + 0.589086i $$0.799488\pi$$
$$488$$ 14.0000i 0.633750i
$$489$$ 0 0
$$490$$ −3.00000 6.00000i −0.135526 0.271052i
$$491$$ 22.0000 0.992846 0.496423 0.868081i $$-0.334646\pi$$
0.496423 + 0.868081i $$0.334646\pi$$
$$492$$ 0 0
$$493$$ 8.00000i 0.360302i
$$494$$ 4.00000 0.179969
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 8.00000i 0.358849i
$$498$$ 0 0
$$499$$ −36.0000 −1.61158 −0.805791 0.592200i $$-0.798259\pi$$
−0.805791 + 0.592200i $$0.798259\pi$$
$$500$$ 2.00000 11.0000i 0.0894427 0.491935i
$$501$$ 0 0
$$502$$ 18.0000i 0.803379i
$$503$$ 36.0000i 1.60516i 0.596544 + 0.802580i $$0.296540\pi$$
−0.596544 + 0.802580i $$0.703460\pi$$
$$504$$ 0 0
$$505$$ 8.00000 4.00000i 0.355995 0.177998i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 6.00000i 0.266207i
$$509$$ −40.0000 −1.77297 −0.886484 0.462758i $$-0.846860\pi$$
−0.886484 + 0.462758i $$0.846860\pi$$
$$510$$ 0 0
$$511$$ 16.0000 0.707798
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 18.0000 0.793946
$$515$$ −6.00000 12.0000i −0.264392 0.528783i
$$516$$ 0 0
$$517$$ 16.0000i 0.703679i
$$518$$ 12.0000i 0.527250i
$$519$$ 0 0
$$520$$ 2.00000 1.00000i 0.0877058 0.0438529i
$$521$$ 10.0000 0.438108 0.219054 0.975713i $$-0.429703\pi$$
0.219054 + 0.975713i $$0.429703\pi$$
$$522$$ 0 0
$$523$$ 16.0000i 0.699631i 0.936819 + 0.349816i $$0.113756\pi$$
−0.936819 + 0.349816i $$0.886244\pi$$
$$524$$ −6.00000 −0.262111
$$525$$ 0 0
$$526$$ −8.00000 −0.348817
$$527$$ 16.0000i 0.696971i
$$528$$ 0 0
$$529$$ 23.0000 1.00000
$$530$$ −4.00000 + 2.00000i −0.173749 + 0.0868744i
$$531$$ 0 0
$$532$$ 8.00000i 0.346844i
$$533$$ 6.00000i 0.259889i
$$534$$ 0 0
$$535$$ 4.00000 + 8.00000i 0.172935 + 0.345870i
$$536$$ 16.0000 0.691095
$$537$$ 0 0
$$538$$ 20.0000i 0.862261i
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 16.0000i 0.687259i
$$543$$ 0 0
$$544$$ −2.00000 −0.0857493
$$545$$ −36.0000 + 18.0000i −1.54207 + 0.771035i
$$546$$ 0 0
$$547$$ 20.0000i 0.855138i 0.903983 + 0.427569i $$0.140630\pi$$
−0.903983 + 0.427569i $$0.859370\pi$$
$$548$$ 14.0000i 0.598050i
$$549$$ 0 0
$$550$$ −8.00000 6.00000i −0.341121 0.255841i
$$551$$ 16.0000 0.681623
$$552$$ 0 0
$$553$$ 16.0000i 0.680389i
$$554$$ −2.00000 −0.0849719
$$555$$ 0 0
$$556$$ 4.00000 0.169638
$$557$$ 14.0000i 0.593199i −0.955002 0.296600i $$-0.904147\pi$$
0.955002 0.296600i $$-0.0958526\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ 2.00000 + 4.00000i 0.0845154 + 0.169031i
$$561$$ 0 0
$$562$$ 18.0000i 0.759284i
$$563$$ 44.0000i 1.85438i 0.374593 + 0.927189i $$0.377783\pi$$
−0.374593 + 0.927189i $$0.622217\pi$$
$$564$$ 0 0
$$565$$ 6.00000 + 12.0000i 0.252422 + 0.504844i
$$566$$ −16.0000 −0.672530
$$567$$ 0 0
$$568$$ 4.00000i 0.167836i
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 2.00000i 0.0836242i
$$573$$ 0 0
$$574$$ 12.0000 0.500870
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 28.0000i 1.16566i −0.812596 0.582828i $$-0.801946\pi$$
0.812596 0.582828i $$-0.198054\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 0 0
$$580$$ 8.00000 4.00000i 0.332182 0.166091i
$$581$$ −24.0000 −0.995688
$$582$$ 0 0
$$583$$ 4.00000i 0.165663i
$$584$$ 8.00000 0.331042
$$585$$ 0 0
$$586$$ 26.0000 1.07405
$$587$$ 36.0000i 1.48588i 0.669359 + 0.742940i $$0.266569\pi$$
−0.669359 + 0.742940i $$0.733431\pi$$
$$588$$ 0 0
$$589$$ 32.0000 1.31854
$$590$$ −10.0000 20.0000i −0.411693 0.823387i
$$591$$ 0 0
$$592$$ 6.00000i 0.246598i
$$593$$ 34.0000i 1.39621i −0.715994 0.698106i $$-0.754026\pi$$
0.715994 0.698106i $$-0.245974\pi$$
$$594$$ 0 0
$$595$$ −8.00000 + 4.00000i −0.327968 + 0.163984i
$$596$$ −12.0000 −0.491539
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 32.0000 1.30748 0.653742 0.756717i $$-0.273198\pi$$
0.653742 + 0.756717i $$0.273198\pi$$
$$600$$ 0 0
$$601$$ −46.0000 −1.87638 −0.938190 0.346122i $$-0.887498\pi$$
−0.938190 + 0.346122i $$0.887498\pi$$
$$602$$ 8.00000i 0.326056i
$$603$$ 0 0
$$604$$ 16.0000 0.651031
$$605$$ 14.0000 7.00000i 0.569181 0.284590i
$$606$$ 0 0
$$607$$ 18.0000i 0.730597i −0.930890 0.365299i $$-0.880967\pi$$
0.930890 0.365299i $$-0.119033\pi$$
$$608$$ 4.00000i 0.162221i
$$609$$ 0 0
$$610$$ 14.0000 + 28.0000i 0.566843 + 1.13369i
$$611$$ −8.00000 −0.323645
$$612$$ 0 0
$$613$$ 2.00000i 0.0807792i −0.999184 0.0403896i $$-0.987140\pi$$
0.999184 0.0403896i $$-0.0128599\pi$$
$$614$$ −28.0000 −1.12999
$$615$$ 0 0
$$616$$ 4.00000 0.161165
$$617$$ 46.0000i 1.85189i 0.377658 + 0.925945i $$0.376729\pi$$
−0.377658 + 0.925945i $$0.623271\pi$$
$$618$$ 0 0
$$619$$ 24.0000 0.964641 0.482321 0.875995i $$-0.339794\pi$$
0.482321 + 0.875995i $$0.339794\pi$$
$$620$$ 16.0000 8.00000i 0.642575 0.321288i
$$621$$ 0 0
$$622$$ 20.0000i 0.801927i
$$623$$ 12.0000i 0.480770i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 20.0000 0.799361
$$627$$ 0 0
$$628$$ 10.0000i 0.399043i
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 8.00000i 0.318223i
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ 6.00000 + 12.0000i 0.238103 + 0.476205i
$$636$$ 0 0
$$637$$ 3.00000i 0.118864i
$$638$$ 8.00000i 0.316723i
$$639$$ 0 0
$$640$$ 1.00000 + 2.00000i 0.0395285 + 0.0790569i
$$641$$ 38.0000 1.50091 0.750455 0.660922i $$-0.229834\pi$$
0.750455 + 0.660922i $$0.229834\pi$$
$$642$$ 0 0
$$643$$ 32.0000i 1.26196i 0.775800 + 0.630978i $$0.217346\pi$$
−0.775800 + 0.630978i $$0.782654\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −8.00000 −0.314756
$$647$$ 36.0000i 1.41531i 0.706560 + 0.707653i $$0.250246\pi$$
−0.706560 + 0.707653i $$0.749754\pi$$
$$648$$ 0 0
$$649$$ −20.0000 −0.785069
$$650$$ 3.00000 4.00000i 0.117670 0.156893i
$$651$$ 0 0
$$652$$ 8.00000i 0.313304i
$$653$$ 34.0000i 1.33052i 0.746611 + 0.665261i $$0.231680\pi$$
−0.746611 + 0.665261i $$0.768320\pi$$
$$654$$ 0 0
$$655$$ −12.0000 + 6.00000i −0.468879 + 0.234439i
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 16.0000i 0.623745i
$$659$$ 10.0000 0.389545 0.194772 0.980848i $$-0.437603\pi$$
0.194772 + 0.980848i $$0.437603\pi$$
$$660$$ 0 0
$$661$$ 30.0000 1.16686 0.583432 0.812162i $$-0.301709\pi$$
0.583432 + 0.812162i $$0.301709\pi$$
$$662$$ 12.0000i 0.466393i
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ 8.00000 + 16.0000i 0.310227 + 0.620453i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 12.0000i 0.464294i
$$669$$ 0 0
$$670$$ 32.0000 16.0000i 1.23627 0.618134i
$$671$$ 28.0000 1.08093
$$672$$ 0 0
$$673$$ 36.0000i 1.38770i −0.720121 0.693849i $$-0.755914\pi$$
0.720121 0.693849i $$-0.244086\pi$$
$$674$$ 20.0000 0.770371
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ 10.0000i 0.384331i −0.981363 0.192166i $$-0.938449\pi$$
0.981363 0.192166i $$-0.0615511\pi$$
$$678$$ 0 0
$$679$$ −24.0000 −0.921035
$$680$$ −4.00000 + 2.00000i −0.153393 + 0.0766965i
$$681$$ 0 0
$$682$$ 16.0000i 0.612672i
$$683$$ 12.0000i 0.459167i −0.973289 0.229584i $$-0.926264\pi$$
0.973289 0.229584i $$-0.0737364\pi$$
$$684$$ 0 0
$$685$$ 14.0000 + 28.0000i 0.534913 + 1.06983i
$$686$$ 20.0000 0.763604
$$687$$ 0 0
$$688$$ 4.00000i 0.152499i
$$689$$ −2.00000 −0.0761939
$$690$$ 0 0
$$691$$ −28.0000 −1.06517 −0.532585 0.846376i $$-0.678779\pi$$
−0.532585 + 0.846376i $$0.678779\pi$$
$$692$$ 14.0000i 0.532200i
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ 8.00000 4.00000i 0.303457 0.151729i
$$696$$ 0 0
$$697$$ 12.0000i 0.454532i
$$698$$ 14.0000i 0.529908i
$$699$$ 0 0
$$700$$ 8.00000 + 6.00000i 0.302372 + 0.226779i
$$701$$ −12.0000 −0.453234 −0.226617 0.973984i $$-0.572767\pi$$
−0.226617 + 0.973984i $$0.572767\pi$$
$$702$$ 0 0
$$703$$ 24.0000i 0.905177i
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ −34.0000 −1.27961
$$707$$ 8.00000i 0.300871i
$$708$$ 0 0
$$709$$ −34.0000 −1.27690 −0.638448 0.769665i $$-0.720423\pi$$
−0.638448 + 0.769665i $$0.720423\pi$$
$$710$$ −4.00000 8.00000i −0.150117 0.300235i
$$711$$ 0 0
$$712$$ 6.00000i 0.224860i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −2.00000 4.00000i −0.0747958 0.149592i
$$716$$ 18.0000 0.672692
$$717$$ 0 0
$$718$$ 32.0000i 1.19423i
$$719$$ −24.0000 −0.895049 −0.447524 0.894272i $$-0.647694\pi$$
−0.447524 + 0.894272i $$0.647694\pi$$
$$720$$ 0 0
$$721$$ 12.0000 0.446903
$$722$$ 3.00000i 0.111648i
$$723$$ 0 0
$$724$$ 6.00000 0.222988
$$725$$ 12.0000 16.0000i 0.445669 0.594225i
$$726$$ 0 0
$$727$$ 34.0000i 1.26099i −0.776193 0.630495i $$-0.782852\pi$$
0.776193 0.630495i $$-0.217148\pi$$
$$728$$ 2.00000i 0.0741249i
$$729$$ 0 0
$$730$$ 16.0000 8.00000i 0.592187 0.296093i
$$731$$ −8.00000 −0.295891
$$732$$ 0 0
$$733$$ 14.0000i 0.517102i 0.965998 + 0.258551i $$0.0832450\pi$$
−0.965998 + 0.258551i $$0.916755\pi$$
$$734$$ −10.0000 −0.369107
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 32.0000i 1.17874i
$$738$$ 0 0
$$739$$ −28.0000 −1.03000 −0.514998 0.857191i $$-0.672207\pi$$
−0.514998 + 0.857191i $$0.672207\pi$$
$$740$$ −6.00000 12.0000i −0.220564 0.441129i
$$741$$ 0 0
$$742$$ 4.00000i 0.146845i
$$743$$ 16.0000i 0.586983i −0.955962 0.293492i $$-0.905183\pi$$
0.955962 0.293492i $$-0.0948173\pi$$
$$744$$ 0 0
$$745$$ −24.0000 + 12.0000i −0.879292 + 0.439646i
$$746$$ 22.0000 0.805477
$$747$$ 0 0
$$748$$ 4.00000i 0.146254i
$$749$$ −8.00000 −0.292314
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 0 0
$$754$$ 4.00000 0.145671
$$755$$ 32.0000 16.0000i 1.16460 0.582300i
$$756$$ 0 0
$$757$$ 26.0000i 0.944986i 0.881334 + 0.472493i $$0.156646\pi$$
−0.881334 + 0.472493i $$0.843354\pi$$
$$758$$ 8.00000i 0.290573i
$$759$$ 0 0
$$760$$ 4.00000 + 8.00000i 0.145095 + 0.290191i
$$761$$ −38.0000 −1.37750 −0.688749 0.724999i $$-0.741840\pi$$
−0.688749 + 0.724999i $$0.741840\pi$$
$$762$$ 0 0
$$763$$ 36.0000i 1.30329i
$$764$$ −12.0000 −0.434145
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ 10.0000i 0.361079i
$$768$$ 0 0
$$769$$ −2.00000 −0.0721218 −0.0360609 0.999350i $$-0.511481\pi$$
−0.0360609 + 0.999350i $$0.511481\pi$$
$$770$$ 8.00000 4.00000i 0.288300 0.144150i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 22.0000i 0.791285i −0.918405 0.395643i $$-0.870522\pi$$
0.918405 0.395643i $$-0.129478\pi$$
$$774$$ 0 0
$$775$$ 24.0000 32.0000i 0.862105 1.14947i
$$776$$ −12.0000 −0.430775
$$777$$ 0 0
$$778$$ 16.0000i 0.573628i
$$779$$ 24.0000 0.859889
$$780$$ 0 0
$$781$$ −8.00000 −0.286263
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 3.00000 0.107143
$$785$$ 10.0000 + 20.0000i 0.356915 + 0.713831i
$$786$$ 0 0
$$787$$ 8.00000i 0.285169i 0.989783 + 0.142585i $$0.0455413\pi$$
−0.989783 + 0.142585i $$0.954459\pi$$
$$788$$ 10.0000i 0.356235i
$$789$$ 0 0
$$790$$ −8.00000 16.0000i −0.284627 0.569254i
$$791$$ −12.0000 −0.426671
$$792$$ 0 0
$$793$$ 14.0000i 0.497155i
$$794$$ −18.0000 −0.638796
$$795$$ 0 0
$$796$$ −24.0000 −0.850657
$$797$$ 14.0000i 0.495905i 0.968772 + 0.247953i \(0.079