# Properties

 Label 1470.2.g.g.589.1 Level $1470$ Weight $2$ Character 1470.589 Analytic conductor $11.738$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1470.g (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.7380090971$$ 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 30) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 589.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1470.589 Dual form 1470.2.g.g.589.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} +2.00000 q^{11} +1.00000i q^{12} +6.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} -2.00000i q^{17} +1.00000i q^{18} +(-2.00000 - 1.00000i) q^{20} -2.00000i q^{22} +4.00000i q^{23} +1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +6.00000 q^{26} +1.00000i q^{27} +(-2.00000 - 1.00000i) q^{30} +8.00000 q^{31} -1.00000i q^{32} -2.00000i q^{33} -2.00000 q^{34} +1.00000 q^{36} +2.00000i q^{37} +6.00000 q^{39} +(-1.00000 + 2.00000i) q^{40} -2.00000 q^{41} +4.00000i q^{43} -2.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} +4.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} -2.00000 q^{51} -6.00000i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(4.00000 + 2.00000i) q^{55} +10.0000 q^{59} +(-1.00000 + 2.00000i) q^{60} -2.00000 q^{61} -8.00000i q^{62} -1.00000 q^{64} +(-6.00000 + 12.0000i) q^{65} -2.00000 q^{66} -8.00000i q^{67} +2.00000i q^{68} +4.00000 q^{69} +12.0000 q^{71} -1.00000i q^{72} -4.00000i q^{73} +2.00000 q^{74} +(4.00000 - 3.00000i) q^{75} -6.00000i q^{78} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} -4.00000i q^{83} +(2.00000 - 4.00000i) q^{85} +4.00000 q^{86} +2.00000i q^{88} -10.0000 q^{89} +(-1.00000 + 2.00000i) q^{90} -4.00000i q^{92} -8.00000i q^{93} +8.00000 q^{94} -1.00000 q^{96} +8.00000i q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{4} + 4q^{5} - 2q^{6} - 2q^{9} + O(q^{10})$$ $$2q - 2q^{4} + 4q^{5} - 2q^{6} - 2q^{9} + 2q^{10} + 4q^{11} + 2q^{15} + 2q^{16} - 4q^{20} + 2q^{24} + 6q^{25} + 12q^{26} - 4q^{30} + 16q^{31} - 4q^{34} + 2q^{36} + 12q^{39} - 2q^{40} - 4q^{41} - 4q^{44} - 4q^{45} + 8q^{46} + 8q^{50} - 4q^{51} + 2q^{54} + 8q^{55} + 20q^{59} - 2q^{60} - 4q^{61} - 2q^{64} - 12q^{65} - 4q^{66} + 8q^{69} + 24q^{71} + 4q^{74} + 8q^{75} + 4q^{80} + 2q^{81} + 4q^{85} + 8q^{86} - 20q^{89} - 2q^{90} + 16q^{94} - 2q^{96} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$$.

 $$n$$ $$491$$ $$1081$$ $$1177$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 1.00000i 0.577350i
$$4$$ −1.00000 −0.500000
$$5$$ 2.00000 + 1.00000i 0.894427 + 0.447214i
$$6$$ −1.00000 −0.408248
$$7$$ 0 0
$$8$$ 1.00000i 0.353553i
$$9$$ −1.00000 −0.333333
$$10$$ 1.00000 2.00000i 0.316228 0.632456i
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 6.00000i 1.66410i 0.554700 + 0.832050i $$0.312833\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ 1.00000 2.00000i 0.258199 0.516398i
$$16$$ 1.00000 0.250000
$$17$$ 2.00000i 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −2.00000 1.00000i −0.447214 0.223607i
$$21$$ 0 0
$$22$$ 2.00000i 0.426401i
$$23$$ 4.00000i 0.834058i 0.908893 + 0.417029i $$0.136929\pi$$
−0.908893 + 0.417029i $$0.863071\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 3.00000 + 4.00000i 0.600000 + 0.800000i
$$26$$ 6.00000 1.17670
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ −2.00000 1.00000i −0.365148 0.182574i
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 2.00000i 0.348155i
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 2.00000i 0.328798i 0.986394 + 0.164399i $$0.0525685\pi$$
−0.986394 + 0.164399i $$0.947432\pi$$
$$38$$ 0 0
$$39$$ 6.00000 0.960769
$$40$$ −1.00000 + 2.00000i −0.158114 + 0.316228i
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 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
$$45$$ −2.00000 1.00000i −0.298142 0.149071i
$$46$$ 4.00000 0.589768
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 0 0
$$50$$ 4.00000 3.00000i 0.565685 0.424264i
$$51$$ −2.00000 −0.280056
$$52$$ 6.00000i 0.832050i
$$53$$ 6.00000i 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 4.00000 + 2.00000i 0.539360 + 0.269680i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ −1.00000 + 2.00000i −0.129099 + 0.258199i
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 8.00000i 1.01600i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −6.00000 + 12.0000i −0.744208 + 1.48842i
$$66$$ −2.00000 −0.246183
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 4.00000i 0.468165i −0.972217 0.234082i $$-0.924791\pi$$
0.972217 0.234082i $$-0.0752085\pi$$
$$74$$ 2.00000 0.232495
$$75$$ 4.00000 3.00000i 0.461880 0.346410i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 6.00000i 0.679366i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 2.00000 + 1.00000i 0.223607 + 0.111803i
$$81$$ 1.00000 0.111111
$$82$$ 2.00000i 0.220863i
$$83$$ 4.00000i 0.439057i −0.975606 0.219529i $$-0.929548\pi$$
0.975606 0.219529i $$-0.0704519\pi$$
$$84$$ 0 0
$$85$$ 2.00000 4.00000i 0.216930 0.433861i
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ 2.00000i 0.213201i
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ −1.00000 + 2.00000i −0.105409 + 0.210819i
$$91$$ 0 0
$$92$$ 4.00000i 0.417029i
$$93$$ 8.00000i 0.829561i
$$94$$ 8.00000 0.825137
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 8.00000i 0.812277i 0.913812 + 0.406138i $$0.133125\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ −3.00000 4.00000i −0.300000 0.400000i
$$101$$ 8.00000 0.796030 0.398015 0.917379i $$-0.369699\pi$$
0.398015 + 0.917379i $$0.369699\pi$$
$$102$$ 2.00000i 0.198030i
$$103$$ 14.0000i 1.37946i −0.724066 0.689730i $$-0.757729\pi$$
0.724066 0.689730i $$-0.242271\pi$$
$$104$$ −6.00000 −0.588348
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000i 1.16008i 0.814587 + 0.580042i $$0.196964\pi$$
−0.814587 + 0.580042i $$0.803036\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 2.00000 4.00000i 0.190693 0.381385i
$$111$$ 2.00000 0.189832
$$112$$ 0 0
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ −4.00000 + 8.00000i −0.373002 + 0.746004i
$$116$$ 0 0
$$117$$ 6.00000i 0.554700i
$$118$$ 10.0000i 0.920575i
$$119$$ 0 0
$$120$$ 2.00000 + 1.00000i 0.182574 + 0.0912871i
$$121$$ −7.00000 −0.636364
$$122$$ 2.00000i 0.181071i
$$123$$ 2.00000i 0.180334i
$$124$$ −8.00000 −0.718421
$$125$$ 2.00000 + 11.0000i 0.178885 + 0.983870i
$$126$$ 0 0
$$127$$ 2.00000i 0.177471i 0.996055 + 0.0887357i $$0.0282826\pi$$
−0.996055 + 0.0887357i $$0.971717\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 4.00000 0.352180
$$130$$ 12.0000 + 6.00000i 1.05247 + 0.526235i
$$131$$ 18.0000 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$132$$ 2.00000i 0.174078i
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ −1.00000 + 2.00000i −0.0860663 + 0.172133i
$$136$$ 2.00000 0.171499
$$137$$ 18.0000i 1.53784i −0.639343 0.768922i $$-0.720793\pi$$
0.639343 0.768922i $$-0.279207\pi$$
$$138$$ 4.00000i 0.340503i
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 12.0000i 1.00702i
$$143$$ 12.0000i 1.00349i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ 2.00000i 0.164399i
$$149$$ 20.0000 1.63846 0.819232 0.573462i $$-0.194400\pi$$
0.819232 + 0.573462i $$0.194400\pi$$
$$150$$ −3.00000 4.00000i −0.244949 0.326599i
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 2.00000i 0.161690i
$$154$$ 0 0
$$155$$ 16.0000 + 8.00000i 1.28515 + 0.642575i
$$156$$ −6.00000 −0.480384
$$157$$ 22.0000i 1.75579i −0.478852 0.877896i $$-0.658947\pi$$
0.478852 0.877896i $$-0.341053\pi$$
$$158$$ 0 0
$$159$$ −6.00000 −0.475831
$$160$$ 1.00000 2.00000i 0.0790569 0.158114i
$$161$$ 0 0
$$162$$ 1.00000i 0.0785674i
$$163$$ 16.0000i 1.25322i −0.779334 0.626608i $$-0.784443\pi$$
0.779334 0.626608i $$-0.215557\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 2.00000 4.00000i 0.155700 0.311400i
$$166$$ −4.00000 −0.310460
$$167$$ 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
$$170$$ −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
$$175$$ 0 0
$$176$$ 2.00000 0.150756
$$177$$ 10.0000i 0.751646i
$$178$$ 10.0000i 0.749532i
$$179$$ −10.0000 −0.747435 −0.373718 0.927543i $$-0.621917\pi$$
−0.373718 + 0.927543i $$0.621917\pi$$
$$180$$ 2.00000 + 1.00000i 0.149071 + 0.0745356i
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 2.00000i 0.147844i
$$184$$ −4.00000 −0.294884
$$185$$ −2.00000 + 4.00000i −0.147043 + 0.294086i
$$186$$ −8.00000 −0.586588
$$187$$ 4.00000i 0.292509i
$$188$$ 8.00000i 0.583460i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ 4.00000i 0.287926i 0.989583 + 0.143963i $$0.0459847\pi$$
−0.989583 + 0.143963i $$0.954015\pi$$
$$194$$ 8.00000 0.574367
$$195$$ 12.0000 + 6.00000i 0.859338 + 0.429669i
$$196$$ 0 0
$$197$$ 22.0000i 1.56744i 0.621117 + 0.783718i $$0.286679\pi$$
−0.621117 + 0.783718i $$0.713321\pi$$
$$198$$ 2.00000i 0.142134i
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ −4.00000 + 3.00000i −0.282843 + 0.212132i
$$201$$ −8.00000 −0.564276
$$202$$ 8.00000i 0.562878i
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ −4.00000 2.00000i −0.279372 0.139686i
$$206$$ −14.0000 −0.975426
$$207$$ 4.00000i 0.278019i
$$208$$ 6.00000i 0.416025i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 12.0000i 0.822226i
$$214$$ 12.0000 0.820303
$$215$$ −4.00000 + 8.00000i −0.272798 + 0.545595i
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 10.0000i 0.677285i
$$219$$ −4.00000 −0.270295
$$220$$ −4.00000 2.00000i −0.269680 0.134840i
$$221$$ 12.0000 0.807207
$$222$$ 2.00000i 0.134231i
$$223$$ 26.0000i 1.74109i 0.492090 + 0.870544i $$0.336233\pi$$
−0.492090 + 0.870544i $$0.663767\pi$$
$$224$$ 0 0
$$225$$ −3.00000 4.00000i −0.200000 0.266667i
$$226$$ −6.00000 −0.399114
$$227$$ 28.0000i 1.85843i 0.369546 + 0.929213i $$0.379513\pi$$
−0.369546 + 0.929213i $$0.620487\pi$$
$$228$$ 0 0
$$229$$ −10.0000 −0.660819 −0.330409 0.943838i $$-0.607187\pi$$
−0.330409 + 0.943838i $$0.607187\pi$$
$$230$$ 8.00000 + 4.00000i 0.527504 + 0.263752i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 14.0000i 0.917170i 0.888650 + 0.458585i $$0.151644\pi$$
−0.888650 + 0.458585i $$0.848356\pi$$
$$234$$ −6.00000 −0.392232
$$235$$ −8.00000 + 16.0000i −0.521862 + 1.04372i
$$236$$ −10.0000 −0.650945
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 1.00000 2.00000i 0.0645497 0.129099i
$$241$$ −22.0000 −1.41714 −0.708572 0.705638i $$-0.750660\pi$$
−0.708572 + 0.705638i $$0.750660\pi$$
$$242$$ 7.00000i 0.449977i
$$243$$ 1.00000i 0.0641500i
$$244$$ 2.00000 0.128037
$$245$$ 0 0
$$246$$ 2.00000 0.127515
$$247$$ 0 0
$$248$$ 8.00000i 0.508001i
$$249$$ −4.00000 −0.253490
$$250$$ 11.0000 2.00000i 0.695701 0.126491i
$$251$$ 18.0000 1.13615 0.568075 0.822977i $$-0.307688\pi$$
0.568075 + 0.822977i $$0.307688\pi$$
$$252$$ 0 0
$$253$$ 8.00000i 0.502956i
$$254$$ 2.00000 0.125491
$$255$$ −4.00000 2.00000i −0.250490 0.125245i
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000i 1.12281i 0.827541 + 0.561405i $$0.189739\pi$$
−0.827541 + 0.561405i $$0.810261\pi$$
$$258$$ 4.00000i 0.249029i
$$259$$ 0 0
$$260$$ 6.00000 12.0000i 0.372104 0.744208i
$$261$$ 0 0
$$262$$ 18.0000i 1.11204i
$$263$$ 4.00000i 0.246651i 0.992366 + 0.123325i $$0.0393559\pi$$
−0.992366 + 0.123325i $$0.960644\pi$$
$$264$$ 2.00000 0.123091
$$265$$ 6.00000 12.0000i 0.368577 0.737154i
$$266$$ 0 0
$$267$$ 10.0000i 0.611990i
$$268$$ 8.00000i 0.488678i
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 2.00000 + 1.00000i 0.121716 + 0.0608581i
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 0 0
$$274$$ −18.0000 −1.08742
$$275$$ 6.00000 + 8.00000i 0.361814 + 0.482418i
$$276$$ −4.00000 −0.240772
$$277$$ 2.00000i 0.120168i 0.998193 + 0.0600842i $$0.0191369\pi$$
−0.998193 + 0.0600842i $$0.980863\pi$$
$$278$$ 20.0000i 1.19952i
$$279$$ −8.00000 −0.478947
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 8.00000i 0.476393i
$$283$$ 16.0000i 0.951101i 0.879688 + 0.475551i $$0.157751\pi$$
−0.879688 + 0.475551i $$0.842249\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ 12.0000 0.709575
$$287$$ 0 0
$$288$$ 1.00000i 0.0589256i
$$289$$ 13.0000 0.764706
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ 4.00000i 0.234082i
$$293$$ 6.00000i 0.350524i 0.984522 + 0.175262i $$0.0560772\pi$$
−0.984522 + 0.175262i $$0.943923\pi$$
$$294$$ 0 0
$$295$$ 20.0000 + 10.0000i 1.16445 + 0.582223i
$$296$$ −2.00000 −0.116248
$$297$$ 2.00000i 0.116052i
$$298$$ 20.0000i 1.15857i
$$299$$ −24.0000 −1.38796
$$300$$ −4.00000 + 3.00000i −0.230940 + 0.173205i
$$301$$ 0 0
$$302$$ 8.00000i 0.460348i
$$303$$ 8.00000i 0.459588i
$$304$$ 0 0
$$305$$ −4.00000 2.00000i −0.229039 0.114520i
$$306$$ 2.00000 0.114332
$$307$$ 12.0000i 0.684876i −0.939540 0.342438i $$-0.888747\pi$$
0.939540 0.342438i $$-0.111253\pi$$
$$308$$ 0 0
$$309$$ −14.0000 −0.796432
$$310$$ 8.00000 16.0000i 0.454369 0.908739i
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 6.00000i 0.339683i
$$313$$ 4.00000i 0.226093i −0.993590 0.113047i $$-0.963939\pi$$
0.993590 0.113047i $$-0.0360610\pi$$
$$314$$ −22.0000 −1.24153
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i 0.998421 + 0.0561656i $$0.0178875\pi$$
−0.998421 + 0.0561656i $$0.982113\pi$$
$$318$$ 6.00000i 0.336463i
$$319$$ 0 0
$$320$$ −2.00000 1.00000i −0.111803 0.0559017i
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.00000 −0.0555556
$$325$$ −24.0000 + 18.0000i −1.33128 + 0.998460i
$$326$$ −16.0000 −0.886158
$$327$$ 10.0000i 0.553001i
$$328$$ 2.00000i 0.110432i
$$329$$ 0 0
$$330$$ −4.00000 2.00000i −0.220193 0.110096i
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ 4.00000i 0.219529i
$$333$$ 2.00000i 0.109599i
$$334$$ −12.0000 −0.656611
$$335$$ 8.00000 16.0000i 0.437087 0.874173i
$$336$$ 0 0
$$337$$ 28.0000i 1.52526i −0.646837 0.762629i $$-0.723908\pi$$
0.646837 0.762629i $$-0.276092\pi$$
$$338$$ 23.0000i 1.25104i
$$339$$ −6.00000 −0.325875
$$340$$ −2.00000 + 4.00000i −0.108465 + 0.216930i
$$341$$ 16.0000 0.866449
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −4.00000 −0.215666
$$345$$ 8.00000 + 4.00000i 0.430706 + 0.215353i
$$346$$ −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
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ −6.00000 −0.320256
$$352$$ 2.00000i 0.106600i
$$353$$ 14.0000i 0.745145i −0.928003 0.372572i $$-0.878476\pi$$
0.928003 0.372572i $$-0.121524\pi$$
$$354$$ −10.0000 −0.531494
$$355$$ 24.0000 + 12.0000i 1.27379 + 0.636894i
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ 10.0000i 0.528516i
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 1.00000 2.00000i 0.0527046 0.105409i
$$361$$ −19.0000 −1.00000
$$362$$ 2.00000i 0.105118i
$$363$$ 7.00000i 0.367405i
$$364$$ 0 0
$$365$$ 4.00000 8.00000i 0.209370 0.418739i
$$366$$ 2.00000 0.104542
$$367$$ 2.00000i 0.104399i −0.998637 0.0521996i $$-0.983377\pi$$
0.998637 0.0521996i $$-0.0166232\pi$$
$$368$$ 4.00000i 0.208514i
$$369$$ 2.00000 0.104116
$$370$$ 4.00000 + 2.00000i 0.207950 + 0.103975i
$$371$$ 0 0
$$372$$ 8.00000i 0.414781i
$$373$$ 6.00000i 0.310668i −0.987862 0.155334i $$-0.950355\pi$$
0.987862 0.155334i $$-0.0496454\pi$$
$$374$$ −4.00000 −0.206835
$$375$$ 11.0000 2.00000i 0.568038 0.103280i
$$376$$ −8.00000 −0.412568
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ 2.00000 0.102463
$$382$$ 12.0000i 0.613973i
$$383$$ 16.0000i 0.817562i 0.912633 + 0.408781i $$0.134046\pi$$
−0.912633 + 0.408781i $$0.865954\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 4.00000 0.203595
$$387$$ 4.00000i 0.203331i
$$388$$ 8.00000i 0.406138i
$$389$$ −20.0000 −1.01404 −0.507020 0.861934i $$-0.669253\pi$$
−0.507020 + 0.861934i $$0.669253\pi$$
$$390$$ 6.00000 12.0000i 0.303822 0.607644i
$$391$$ 8.00000 0.404577
$$392$$ 0 0
$$393$$ 18.0000i 0.907980i
$$394$$ 22.0000 1.10834
$$395$$ 0 0
$$396$$ 2.00000 0.100504
$$397$$ 2.00000i 0.100377i −0.998740 0.0501886i $$-0.984018\pi$$
0.998740 0.0501886i $$-0.0159822\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 3.00000 + 4.00000i 0.150000 + 0.200000i
$$401$$ 22.0000 1.09863 0.549314 0.835616i $$-0.314889\pi$$
0.549314 + 0.835616i $$0.314889\pi$$
$$402$$ 8.00000i 0.399004i
$$403$$ 48.0000i 2.39105i
$$404$$ −8.00000 −0.398015
$$405$$ 2.00000 + 1.00000i 0.0993808 + 0.0496904i
$$406$$ 0 0
$$407$$ 4.00000i 0.198273i
$$408$$ 2.00000i 0.0990148i
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ −2.00000 + 4.00000i −0.0987730 + 0.197546i
$$411$$ −18.0000 −0.887875
$$412$$ 14.0000i 0.689730i
$$413$$ 0 0
$$414$$ −4.00000 −0.196589
$$415$$ 4.00000 8.00000i 0.196352 0.392705i
$$416$$ 6.00000 0.294174
$$417$$ 20.0000i 0.979404i
$$418$$ 0 0
$$419$$ −10.0000 −0.488532 −0.244266 0.969708i $$-0.578547\pi$$
−0.244266 + 0.969708i $$0.578547\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 12.0000i 0.584151i
$$423$$ 8.00000i 0.388973i
$$424$$ 6.00000 0.291386
$$425$$ 8.00000 6.00000i 0.388057 0.291043i
$$426$$ −12.0000 −0.581402
$$427$$ 0 0
$$428$$ 12.0000i 0.580042i
$$429$$ 12.0000 0.579365
$$430$$ 8.00000 + 4.00000i 0.385794 + 0.192897i
$$431$$ 32.0000 1.54139 0.770693 0.637207i $$-0.219910\pi$$
0.770693 + 0.637207i $$0.219910\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 4.00000i 0.192228i −0.995370 0.0961139i $$-0.969359\pi$$
0.995370 0.0961139i $$-0.0306413\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ 0 0
$$438$$ 4.00000i 0.191127i
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ −2.00000 + 4.00000i −0.0953463 + 0.190693i
$$441$$ 0 0
$$442$$ 12.0000i 0.570782i
$$443$$ 36.0000i 1.71041i −0.518289 0.855206i $$-0.673431\pi$$
0.518289 0.855206i $$-0.326569\pi$$
$$444$$ −2.00000 −0.0949158
$$445$$ −20.0000 10.0000i −0.948091 0.474045i
$$446$$ 26.0000 1.23114
$$447$$ 20.0000i 0.945968i
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ −4.00000 + 3.00000i −0.188562 + 0.141421i
$$451$$ −4.00000 −0.188353
$$452$$ 6.00000i 0.282216i
$$453$$ 8.00000i 0.375873i
$$454$$ 28.0000 1.31411
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 32.0000i 1.49690i 0.663193 + 0.748448i $$0.269201\pi$$
−0.663193 + 0.748448i $$0.730799\pi$$
$$458$$ 10.0000i 0.467269i
$$459$$ 2.00000 0.0933520
$$460$$ 4.00000 8.00000i 0.186501 0.373002i
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ 6.00000i 0.278844i −0.990233 0.139422i $$-0.955476\pi$$
0.990233 0.139422i $$-0.0445244\pi$$
$$464$$ 0 0
$$465$$ 8.00000 16.0000i 0.370991 0.741982i
$$466$$ 14.0000 0.648537
$$467$$ 12.0000i 0.555294i −0.960683 0.277647i $$-0.910445\pi$$
0.960683 0.277647i $$-0.0895545\pi$$
$$468$$ 6.00000i 0.277350i
$$469$$ 0 0
$$470$$ 16.0000 + 8.00000i 0.738025 + 0.369012i
$$471$$ −22.0000 −1.01371
$$472$$ 10.0000i 0.460287i
$$473$$ 8.00000i 0.367840i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.00000i 0.274721i
$$478$$ 20.0000i 0.914779i
$$479$$ 20.0000 0.913823 0.456912 0.889512i $$-0.348956\pi$$
0.456912 + 0.889512i $$0.348956\pi$$
$$480$$ −2.00000 1.00000i −0.0912871 0.0456435i
$$481$$ −12.0000 −0.547153
$$482$$ 22.0000i 1.00207i
$$483$$ 0 0
$$484$$ 7.00000 0.318182
$$485$$ −8.00000 + 16.0000i −0.363261 + 0.726523i
$$486$$ −1.00000 −0.0453609
$$487$$ 18.0000i 0.815658i −0.913058 0.407829i $$-0.866286\pi$$
0.913058 0.407829i $$-0.133714\pi$$
$$488$$ 2.00000i 0.0905357i
$$489$$ −16.0000 −0.723545
$$490$$ 0 0
$$491$$ −18.0000 −0.812329 −0.406164 0.913800i $$-0.633134\pi$$
−0.406164 + 0.913800i $$0.633134\pi$$
$$492$$ 2.00000i 0.0901670i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −4.00000 2.00000i −0.179787 0.0898933i
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ 4.00000i 0.179244i
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −2.00000 11.0000i −0.0894427 0.491935i
$$501$$ −12.0000 −0.536120
$$502$$ 18.0000i 0.803379i
$$503$$ 24.0000i 1.07011i −0.844818 0.535054i $$-0.820291\pi$$
0.844818 0.535054i $$-0.179709\pi$$
$$504$$ 0 0
$$505$$ 16.0000 + 8.00000i 0.711991 + 0.355995i
$$506$$ 8.00000 0.355643
$$507$$ 23.0000i 1.02147i
$$508$$ 2.00000i 0.0887357i
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ −2.00000 + 4.00000i −0.0885615 + 0.177123i
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 18.0000 0.793946
$$515$$ 14.0000 28.0000i 0.616914 1.23383i
$$516$$ −4.00000 −0.176090
$$517$$ 16.0000i 0.703679i
$$518$$ 0 0
$$519$$ −14.0000 −0.614532
$$520$$ −12.0000 6.00000i −0.526235 0.263117i
$$521$$ −22.0000 −0.963837 −0.481919 0.876216i $$-0.660060\pi$$
−0.481919 + 0.876216i $$0.660060\pi$$
$$522$$ 0 0
$$523$$ 16.0000i 0.699631i 0.936819 + 0.349816i $$0.113756\pi$$
−0.936819 + 0.349816i $$0.886244\pi$$
$$524$$ −18.0000 −0.786334
$$525$$ 0 0
$$526$$ 4.00000 0.174408
$$527$$ 16.0000i 0.696971i
$$528$$ 2.00000i 0.0870388i
$$529$$ 7.00000 0.304348
$$530$$ −12.0000 6.00000i −0.521247 0.260623i
$$531$$ −10.0000 −0.433963
$$532$$ 0 0
$$533$$ 12.0000i 0.519778i
$$534$$ 10.0000 0.432742
$$535$$ −12.0000 + 24.0000i −0.518805 + 1.03761i
$$536$$ 8.00000 0.345547
$$537$$ 10.0000i 0.431532i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 1.00000 2.00000i 0.0430331 0.0860663i
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 8.00000i 0.343629i
$$543$$ 2.00000i 0.0858282i
$$544$$ −2.00000 −0.0857493
$$545$$ −20.0000 10.0000i −0.856706 0.428353i
$$546$$ 0 0
$$547$$ 28.0000i 1.19719i −0.801050 0.598597i $$-0.795725\pi$$
0.801050 0.598597i $$-0.204275\pi$$
$$548$$ 18.0000i 0.768922i
$$549$$ 2.00000 0.0853579
$$550$$ 8.00000 6.00000i 0.341121 0.255841i
$$551$$ 0 0
$$552$$ 4.00000i 0.170251i
$$553$$ 0 0
$$554$$ 2.00000 0.0849719
$$555$$ 4.00000 + 2.00000i 0.169791 + 0.0848953i
$$556$$ 20.0000 0.848189
$$557$$ 18.0000i 0.762684i −0.924434 0.381342i $$-0.875462\pi$$
0.924434 0.381342i $$-0.124538\pi$$
$$558$$ 8.00000i 0.338667i
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ 18.0000i 0.759284i
$$563$$ 44.0000i 1.85438i −0.374593 0.927189i $$-0.622217\pi$$
0.374593 0.927189i $$-0.377783\pi$$
$$564$$ −8.00000 −0.336861
$$565$$ 6.00000 12.0000i 0.252422 0.504844i
$$566$$ 16.0000 0.672530
$$567$$ 0 0
$$568$$ 12.0000i 0.503509i
$$569$$ 10.0000 0.419222 0.209611 0.977785i $$-0.432780\pi$$
0.209611 + 0.977785i $$0.432780\pi$$
$$570$$ 0 0
$$571$$ −8.00000 −0.334790 −0.167395 0.985890i $$-0.553535\pi$$
−0.167395 + 0.985890i $$0.553535\pi$$
$$572$$ 12.0000i 0.501745i
$$573$$ 12.0000i 0.501307i
$$574$$ 0 0
$$575$$ −16.0000 + 12.0000i −0.667246 + 0.500435i
$$576$$ 1.00000 0.0416667
$$577$$ 32.0000i 1.33218i −0.745873 0.666089i $$-0.767967\pi$$
0.745873 0.666089i $$-0.232033\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 4.00000 0.166234
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 8.00000i 0.331611i
$$583$$ 12.0000i 0.496989i
$$584$$ 4.00000 0.165521
$$585$$ 6.00000 12.0000i 0.248069 0.496139i
$$586$$ 6.00000 0.247858
$$587$$ 12.0000i 0.495293i −0.968850 0.247647i $$-0.920343\pi$$
0.968850 0.247647i $$-0.0796572\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 10.0000 20.0000i 0.411693 0.823387i
$$591$$ 22.0000 0.904959
$$592$$ 2.00000i 0.0821995i
$$593$$ 6.00000i 0.246390i 0.992382 + 0.123195i $$0.0393141\pi$$
−0.992382 + 0.123195i $$0.960686\pi$$
$$594$$ 2.00000 0.0820610
$$595$$ 0 0
$$596$$ −20.0000 −0.819232
$$597$$ 0 0
$$598$$ 24.0000i 0.981433i
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 3.00000 + 4.00000i 0.122474 + 0.163299i
$$601$$ −2.00000 −0.0815817 −0.0407909 0.999168i $$-0.512988\pi$$
−0.0407909 + 0.999168i $$0.512988\pi$$
$$602$$ 0 0
$$603$$ 8.00000i 0.325785i
$$604$$ 8.00000 0.325515
$$605$$ −14.0000 7.00000i −0.569181 0.284590i
$$606$$ −8.00000 −0.324978
$$607$$ 22.0000i 0.892952i −0.894795 0.446476i $$-0.852679\pi$$
0.894795 0.446476i $$-0.147321\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −2.00000 + 4.00000i −0.0809776 + 0.161955i
$$611$$ −48.0000 −1.94187
$$612$$ 2.00000i 0.0808452i
$$613$$ 26.0000i 1.05013i −0.851062 0.525065i $$-0.824041\pi$$
0.851062 0.525065i $$-0.175959\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ −2.00000 + 4.00000i −0.0806478 + 0.161296i
$$616$$ 0 0
$$617$$ 2.00000i 0.0805170i 0.999189 + 0.0402585i $$0.0128181\pi$$
−0.999189 + 0.0402585i $$0.987182\pi$$
$$618$$ 14.0000i 0.563163i
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ −16.0000 8.00000i −0.642575 0.321288i
$$621$$ −4.00000 −0.160514
$$622$$ 12.0000i 0.481156i
$$623$$ 0 0
$$624$$ 6.00000 0.240192
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ −4.00000 −0.159872
$$627$$ 0 0
$$628$$ 22.0000i 0.877896i
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ 32.0000 1.27390 0.636950 0.770905i $$-0.280196\pi$$
0.636950 + 0.770905i $$0.280196\pi$$
$$632$$ 0 0
$$633$$ 12.0000i 0.476957i
$$634$$ 2.00000 0.0794301
$$635$$ −2.00000 + 4.00000i −0.0793676 + 0.158735i
$$636$$ 6.00000 0.237915
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −12.0000 −0.474713
$$640$$ −1.00000 + 2.00000i −0.0395285 + 0.0790569i
$$641$$ 2.00000 0.0789953 0.0394976 0.999220i $$-0.487424\pi$$
0.0394976 + 0.999220i $$0.487424\pi$$
$$642$$ 12.0000i 0.473602i
$$643$$ 24.0000i 0.946468i −0.880937 0.473234i $$-0.843087\pi$$
0.880937 0.473234i $$-0.156913\pi$$
$$644$$ 0 0
$$645$$ 8.00000 + 4.00000i 0.315000 + 0.157500i
$$646$$ 0 0
$$647$$ 48.0000i 1.88707i 0.331266 + 0.943537i $$0.392524\pi$$
−0.331266 + 0.943537i $$0.607476\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ 20.0000 0.785069
$$650$$ 18.0000 + 24.0000i 0.706018 + 0.941357i
$$651$$ 0 0
$$652$$ 16.0000i 0.626608i
$$653$$ 26.0000i 1.01746i −0.860927 0.508729i $$-0.830115\pi$$
0.860927 0.508729i $$-0.169885\pi$$
$$654$$ 10.0000 0.391031
$$655$$ 36.0000 + 18.0000i 1.40664 + 0.703318i
$$656$$ −2.00000 −0.0780869
$$657$$ 4.00000i 0.156055i
$$658$$ 0 0
$$659$$ 50.0000 1.94772 0.973862 0.227142i $$-0.0729380\pi$$
0.973862 + 0.227142i $$0.0729380\pi$$
$$660$$ −2.00000 + 4.00000i −0.0778499 + 0.155700i
$$661$$ −2.00000 −0.0777910 −0.0388955 0.999243i $$-0.512384\pi$$
−0.0388955 + 0.999243i $$0.512384\pi$$
$$662$$ 8.00000i 0.310929i
$$663$$ 12.0000i 0.466041i
$$664$$ 4.00000 0.155230
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ 0 0
$$668$$ 12.0000i 0.464294i
$$669$$ 26.0000 1.00522
$$670$$ −16.0000 8.00000i −0.618134 0.309067i
$$671$$ −4.00000 −0.154418
$$672$$ 0 0
$$673$$ 36.0000i 1.38770i −0.720121 0.693849i $$-0.755914\pi$$
0.720121 0.693849i $$-0.244086\pi$$
$$674$$ −28.0000 −1.07852
$$675$$ −4.00000 + 3.00000i −0.153960 + 0.115470i
$$676$$ 23.0000 0.884615
$$677$$ 2.00000i 0.0768662i −0.999261 0.0384331i $$-0.987763\pi$$
0.999261 0.0384331i $$-0.0122367\pi$$
$$678$$ 6.00000i 0.230429i
$$679$$ 0 0
$$680$$ 4.00000 + 2.00000i 0.153393 + 0.0766965i
$$681$$ 28.0000 1.07296
$$682$$ 16.0000i 0.612672i
$$683$$ 4.00000i 0.153056i 0.997067 + 0.0765279i $$0.0243834\pi$$
−0.997067 + 0.0765279i $$0.975617\pi$$
$$684$$ 0 0
$$685$$ 18.0000 36.0000i 0.687745 1.37549i
$$686$$ 0 0
$$687$$ 10.0000i 0.381524i
$$688$$ 4.00000i 0.152499i
$$689$$ 36.0000 1.37149
$$690$$ 4.00000 8.00000i 0.152277 0.304555i
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ 14.0000i 0.532200i
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ −40.0000 20.0000i −1.51729 0.758643i
$$696$$ 0 0
$$697$$ 4.00000i 0.151511i
$$698$$ 10.0000i 0.378506i
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ 32.0000 1.20862 0.604312 0.796748i $$-0.293448\pi$$
0.604312 + 0.796748i $$0.293448\pi$$
$$702$$ 6.00000i 0.226455i
$$703$$ 0 0
$$704$$ −2.00000 −0.0753778
$$705$$ 16.0000 + 8.00000i 0.602595 + 0.301297i
$$706$$ −14.0000 −0.526897
$$707$$ 0 0
$$708$$ 10.0000i 0.375823i
$$709$$ −30.0000 −1.12667 −0.563337 0.826227i $$-0.690483\pi$$
−0.563337 + 0.826227i $$0.690483\pi$$
$$710$$ 12.0000 24.0000i 0.450352 0.900704i
$$711$$ 0 0
$$712$$ 10.0000i 0.374766i
$$713$$ 32.0000i 1.19841i
$$714$$ 0 0
$$715$$ −12.0000 + 24.0000i −0.448775 + 0.897549i
$$716$$ 10.0000 0.373718
$$717$$ 20.0000i 0.746914i
$$718$$ 0 0
$$719$$ −40.0000 −1.49175 −0.745874 0.666087i $$-0.767968\pi$$
−0.745874 + 0.666087i $$0.767968\pi$$
$$720$$ −2.00000 1.00000i −0.0745356 0.0372678i
$$721$$ 0 0
$$722$$ 19.0000i 0.707107i
$$723$$ 22.0000i 0.818189i
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ 7.00000 0.259794
$$727$$ 18.0000i 0.667583i 0.942647 + 0.333792i $$0.108328\pi$$
−0.942647 + 0.333792i $$0.891672\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ −8.00000 4.00000i −0.296093 0.148047i
$$731$$ 8.00000 0.295891
$$732$$ 2.00000i 0.0739221i
$$733$$ 14.0000i 0.517102i −0.965998 0.258551i $$-0.916755\pi$$
0.965998 0.258551i $$-0.0832450\pi$$
$$734$$ −2.00000 −0.0738213
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 16.0000i 0.589368i
$$738$$ 2.00000i 0.0736210i
$$739$$ −40.0000 −1.47142 −0.735712 0.677295i $$-0.763152\pi$$
−0.735712 + 0.677295i $$0.763152\pi$$
$$740$$ 2.00000 4.00000i 0.0735215 0.147043i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0000i 0.880475i 0.897881 + 0.440237i $$0.145106\pi$$
−0.897881 + 0.440237i $$0.854894\pi$$
$$744$$ 8.00000 0.293294
$$745$$ 40.0000 + 20.0000i 1.46549 + 0.732743i
$$746$$ −6.00000 −0.219676
$$747$$ 4.00000i 0.146352i
$$748$$ 4.00000i 0.146254i
$$749$$ 0 0
$$750$$ −2.00000 11.0000i −0.0730297 0.401663i
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 18.0000i 0.655956i
$$754$$ 0 0
$$755$$ −16.0000 8.00000i −0.582300 0.291150i
$$756$$ 0 0
$$757$$ 2.00000i 0.0726912i 0.999339 + 0.0363456i $$0.0115717\pi$$
−0.999339 + 0.0363456i $$0.988428\pi$$
$$758$$ 20.0000i 0.726433i
$$759$$ 8.00000 0.290382
$$760$$ 0 0
$$761$$ 18.0000 0.652499 0.326250 0.945284i $$-0.394215\pi$$
0.326250 + 0.945284i $$0.394215\pi$$
$$762$$ 2.00000i 0.0724524i
$$763$$ 0 0
$$764$$ −12.0000 −0.434145
$$765$$ −2.00000 + 4.00000i −0.0723102 + 0.144620i
$$766$$ 16.0000 0.578103
$$767$$ 60.0000i 2.16647i
$$768$$ 1.00000i 0.0360844i
$$769$$ −30.0000 −1.08183 −0.540914 0.841078i $$-0.681921\pi$$
−0.540914 + 0.841078i $$0.681921\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 4.00000i 0.143963i
$$773$$ 54.0000i 1.94225i −0.238581 0.971123i $$-0.576682\pi$$
0.238581 0.971123i $$-0.423318\pi$$
$$774$$ −4.00000 −0.143777
$$775$$ 24.0000 + 32.0000i 0.862105 + 1.14947i
$$776$$ −8.00000 −0.287183
$$777$$ 0 0
$$778$$ 20.0000i 0.717035i
$$779$$ 0 0
$$780$$ −12.0000 6.00000i −0.429669 0.214834i
$$781$$ 24.0000 0.858788
$$782$$ 8.00000i 0.286079i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 22.0000 44.0000i 0.785214 1.57043i
$$786$$ −18.0000 −0.642039
$$787$$ 32.0000i 1.14068i −0.821410 0.570338i $$-0.806812\pi$$
0.821410 0.570338i $$-0.193188\pi$$
$$788$$ 22.0000i 0.783718i
$$789$$ 4.00000 0.142404
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 2.00000i 0.0710669i
$$793$$ 12.0000i 0.426132i
$$794$$ −2.00000 −0.0709773
$$795$$ −12.0000