# Properties

 Label 105.2.d.a.64.1 Level $105$ Weight $2$ Character 105.64 Analytic conductor $0.838$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 105.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.838429221223$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 64.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 105.64 Dual form 105.2.d.a.64.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +(2.00000 - 1.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} +2.00000i q^{13} -1.00000 q^{14} +(2.00000 - 1.00000i) q^{15} -1.00000 q^{16} +4.00000i q^{17} +1.00000i q^{18} +6.00000 q^{19} +(1.00000 + 2.00000i) q^{20} -1.00000 q^{21} +6.00000i q^{22} -3.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} -1.00000i q^{28} +2.00000 q^{29} +(-1.00000 - 2.00000i) q^{30} -10.0000 q^{31} -5.00000i q^{32} +6.00000i q^{33} +4.00000 q^{34} +(2.00000 - 1.00000i) q^{35} -1.00000 q^{36} -4.00000i q^{37} -6.00000i q^{38} +2.00000 q^{39} +(6.00000 - 3.00000i) q^{40} +2.00000 q^{41} +1.00000i q^{42} +4.00000i q^{43} -6.00000 q^{44} +(-1.00000 - 2.00000i) q^{45} +1.00000i q^{48} -1.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +4.00000 q^{51} +2.00000i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(-6.00000 - 12.0000i) q^{55} -3.00000 q^{56} -6.00000i q^{57} -2.00000i q^{58} +8.00000 q^{59} +(2.00000 - 1.00000i) q^{60} -2.00000 q^{61} +10.0000i q^{62} +1.00000i q^{63} -7.00000 q^{64} +(-4.00000 + 2.00000i) q^{65} +6.00000 q^{66} -16.0000i q^{67} +4.00000i q^{68} +(-1.00000 - 2.00000i) q^{70} +10.0000 q^{71} +3.00000i q^{72} +6.00000i q^{73} -4.00000 q^{74} +(4.00000 + 3.00000i) q^{75} +6.00000 q^{76} +6.00000i q^{77} -2.00000i q^{78} -4.00000 q^{79} +(-1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -2.00000i q^{82} -8.00000i q^{83} -1.00000 q^{84} +(-8.00000 + 4.00000i) q^{85} +4.00000 q^{86} -2.00000i q^{87} +18.0000i q^{88} -6.00000 q^{89} +(-2.00000 + 1.00000i) q^{90} +2.00000 q^{91} +10.0000i q^{93} +(6.00000 + 12.0000i) q^{95} -5.00000 q^{96} -2.00000i q^{97} +1.00000i q^{98} +6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{9} + O(q^{10})$$ $$2 q + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{9} + 4 q^{10} - 12 q^{11} - 2 q^{14} + 4 q^{15} - 2 q^{16} + 12 q^{19} + 2 q^{20} - 2 q^{21} - 6 q^{24} - 6 q^{25} + 4 q^{26} + 4 q^{29} - 2 q^{30} - 20 q^{31} + 8 q^{34} + 4 q^{35} - 2 q^{36} + 4 q^{39} + 12 q^{40} + 4 q^{41} - 12 q^{44} - 2 q^{45} - 2 q^{49} + 8 q^{50} + 8 q^{51} + 2 q^{54} - 12 q^{55} - 6 q^{56} + 16 q^{59} + 4 q^{60} - 4 q^{61} - 14 q^{64} - 8 q^{65} + 12 q^{66} - 2 q^{70} + 20 q^{71} - 8 q^{74} + 8 q^{75} + 12 q^{76} - 8 q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{84} - 16 q^{85} + 8 q^{86} - 12 q^{89} - 4 q^{90} + 4 q^{91} + 12 q^{95} - 10 q^{96} + 12 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$$.

 $$n$$ $$22$$ $$31$$ $$71$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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 −0.935414 0.353553i $$-0.884973\pi$$
0.935414 0.353553i $$-0.115027\pi$$
$$3$$ 1.00000i 0.577350i
$$4$$ 1.00000 0.500000
$$5$$ 1.00000 + 2.00000i 0.447214 + 0.894427i
$$6$$ −1.00000 −0.408248
$$7$$ 1.00000i 0.377964i
$$8$$ 3.00000i 1.06066i
$$9$$ −1.00000 −0.333333
$$10$$ 2.00000 1.00000i 0.632456 0.316228i
$$11$$ −6.00000 −1.80907 −0.904534 0.426401i $$-0.859781\pi$$
−0.904534 + 0.426401i $$0.859781\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 2.00000i 0.554700i 0.960769 + 0.277350i $$0.0894562\pi$$
−0.960769 + 0.277350i $$0.910544\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 2.00000 1.00000i 0.516398 0.258199i
$$16$$ −1.00000 −0.250000
$$17$$ 4.00000i 0.970143i 0.874475 + 0.485071i $$0.161206\pi$$
−0.874475 + 0.485071i $$0.838794\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 6.00000 1.37649 0.688247 0.725476i $$-0.258380\pi$$
0.688247 + 0.725476i $$0.258380\pi$$
$$20$$ 1.00000 + 2.00000i 0.223607 + 0.447214i
$$21$$ −1.00000 −0.218218
$$22$$ 6.00000i 1.27920i
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ −3.00000 −0.612372
$$25$$ −3.00000 + 4.00000i −0.600000 + 0.800000i
$$26$$ 2.00000 0.392232
$$27$$ 1.00000i 0.192450i
$$28$$ 1.00000i 0.188982i
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ −1.00000 2.00000i −0.182574 0.365148i
$$31$$ −10.0000 −1.79605 −0.898027 0.439941i $$-0.854999\pi$$
−0.898027 + 0.439941i $$0.854999\pi$$
$$32$$ 5.00000i 0.883883i
$$33$$ 6.00000i 1.04447i
$$34$$ 4.00000 0.685994
$$35$$ 2.00000 1.00000i 0.338062 0.169031i
$$36$$ −1.00000 −0.166667
$$37$$ 4.00000i 0.657596i −0.944400 0.328798i $$-0.893356\pi$$
0.944400 0.328798i $$-0.106644\pi$$
$$38$$ 6.00000i 0.973329i
$$39$$ 2.00000 0.320256
$$40$$ 6.00000 3.00000i 0.948683 0.474342i
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 1.00000i 0.154303i
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ −6.00000 −0.904534
$$45$$ −1.00000 2.00000i −0.149071 0.298142i
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −1.00000 −0.142857
$$50$$ 4.00000 + 3.00000i 0.565685 + 0.424264i
$$51$$ 4.00000 0.560112
$$52$$ 2.00000i 0.277350i
$$53$$ 6.00000i 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 1.00000 0.136083
$$55$$ −6.00000 12.0000i −0.809040 1.61808i
$$56$$ −3.00000 −0.400892
$$57$$ 6.00000i 0.794719i
$$58$$ 2.00000i 0.262613i
$$59$$ 8.00000 1.04151 0.520756 0.853706i $$-0.325650\pi$$
0.520756 + 0.853706i $$0.325650\pi$$
$$60$$ 2.00000 1.00000i 0.258199 0.129099i
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 10.0000i 1.27000i
$$63$$ 1.00000i 0.125988i
$$64$$ −7.00000 −0.875000
$$65$$ −4.00000 + 2.00000i −0.496139 + 0.248069i
$$66$$ 6.00000 0.738549
$$67$$ 16.0000i 1.95471i −0.211604 0.977356i $$-0.567869\pi$$
0.211604 0.977356i $$-0.432131\pi$$
$$68$$ 4.00000i 0.485071i
$$69$$ 0 0
$$70$$ −1.00000 2.00000i −0.119523 0.239046i
$$71$$ 10.0000 1.18678 0.593391 0.804914i $$-0.297789\pi$$
0.593391 + 0.804914i $$0.297789\pi$$
$$72$$ 3.00000i 0.353553i
$$73$$ 6.00000i 0.702247i 0.936329 + 0.351123i $$0.114200\pi$$
−0.936329 + 0.351123i $$0.885800\pi$$
$$74$$ −4.00000 −0.464991
$$75$$ 4.00000 + 3.00000i 0.461880 + 0.346410i
$$76$$ 6.00000 0.688247
$$77$$ 6.00000i 0.683763i
$$78$$ 2.00000i 0.226455i
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ −1.00000 2.00000i −0.111803 0.223607i
$$81$$ 1.00000 0.111111
$$82$$ 2.00000i 0.220863i
$$83$$ 8.00000i 0.878114i −0.898459 0.439057i $$-0.855313\pi$$
0.898459 0.439057i $$-0.144687\pi$$
$$84$$ −1.00000 −0.109109
$$85$$ −8.00000 + 4.00000i −0.867722 + 0.433861i
$$86$$ 4.00000 0.431331
$$87$$ 2.00000i 0.214423i
$$88$$ 18.0000i 1.91881i
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ −2.00000 + 1.00000i −0.210819 + 0.105409i
$$91$$ 2.00000 0.209657
$$92$$ 0 0
$$93$$ 10.0000i 1.03695i
$$94$$ 0 0
$$95$$ 6.00000 + 12.0000i 0.615587 + 1.23117i
$$96$$ −5.00000 −0.510310
$$97$$ 2.00000i 0.203069i −0.994832 0.101535i $$-0.967625\pi$$
0.994832 0.101535i $$-0.0323753\pi$$
$$98$$ 1.00000i 0.101015i
$$99$$ 6.00000 0.603023
$$100$$ −3.00000 + 4.00000i −0.300000 + 0.400000i
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 4.00000i 0.396059i
$$103$$ 8.00000i 0.788263i −0.919054 0.394132i $$-0.871045\pi$$
0.919054 0.394132i $$-0.128955\pi$$
$$104$$ 6.00000 0.588348
$$105$$ −1.00000 2.00000i −0.0975900 0.195180i
$$106$$ −6.00000 −0.582772
$$107$$ 4.00000i 0.386695i 0.981130 + 0.193347i $$0.0619344\pi$$
−0.981130 + 0.193347i $$0.938066\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ −12.0000 + 6.00000i −1.14416 + 0.572078i
$$111$$ −4.00000 −0.379663
$$112$$ 1.00000i 0.0944911i
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ −6.00000 −0.561951
$$115$$ 0 0
$$116$$ 2.00000 0.185695
$$117$$ 2.00000i 0.184900i
$$118$$ 8.00000i 0.736460i
$$119$$ 4.00000 0.366679
$$120$$ −3.00000 6.00000i −0.273861 0.547723i
$$121$$ 25.0000 2.27273
$$122$$ 2.00000i 0.181071i
$$123$$ 2.00000i 0.180334i
$$124$$ −10.0000 −0.898027
$$125$$ −11.0000 2.00000i −0.983870 0.178885i
$$126$$ 1.00000 0.0890871
$$127$$ 20.0000i 1.77471i 0.461084 + 0.887357i $$0.347461\pi$$
−0.461084 + 0.887357i $$0.652539\pi$$
$$128$$ 3.00000i 0.265165i
$$129$$ 4.00000 0.352180
$$130$$ 2.00000 + 4.00000i 0.175412 + 0.350823i
$$131$$ 4.00000 0.349482 0.174741 0.984614i $$-0.444091\pi$$
0.174741 + 0.984614i $$0.444091\pi$$
$$132$$ 6.00000i 0.522233i
$$133$$ 6.00000i 0.520266i
$$134$$ −16.0000 −1.38219
$$135$$ −2.00000 + 1.00000i −0.172133 + 0.0860663i
$$136$$ 12.0000 1.02899
$$137$$ 6.00000i 0.512615i −0.966595 0.256307i $$-0.917494\pi$$
0.966595 0.256307i $$-0.0825059\pi$$
$$138$$ 0 0
$$139$$ −2.00000 −0.169638 −0.0848189 0.996396i $$-0.527031\pi$$
−0.0848189 + 0.996396i $$0.527031\pi$$
$$140$$ 2.00000 1.00000i 0.169031 0.0845154i
$$141$$ 0 0
$$142$$ 10.0000i 0.839181i
$$143$$ 12.0000i 1.00349i
$$144$$ 1.00000 0.0833333
$$145$$ 2.00000 + 4.00000i 0.166091 + 0.332182i
$$146$$ 6.00000 0.496564
$$147$$ 1.00000i 0.0824786i
$$148$$ 4.00000i 0.328798i
$$149$$ 14.0000 1.14692 0.573462 0.819232i $$-0.305600\pi$$
0.573462 + 0.819232i $$0.305600\pi$$
$$150$$ 3.00000 4.00000i 0.244949 0.326599i
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 18.0000i 1.45999i
$$153$$ 4.00000i 0.323381i
$$154$$ 6.00000 0.483494
$$155$$ −10.0000 20.0000i −0.803219 1.60644i
$$156$$ 2.00000 0.160128
$$157$$ 18.0000i 1.43656i 0.695756 + 0.718278i $$0.255069\pi$$
−0.695756 + 0.718278i $$0.744931\pi$$
$$158$$ 4.00000i 0.318223i
$$159$$ −6.00000 −0.475831
$$160$$ 10.0000 5.00000i 0.790569 0.395285i
$$161$$ 0 0
$$162$$ 1.00000i 0.0785674i
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ 2.00000 0.156174
$$165$$ −12.0000 + 6.00000i −0.934199 + 0.467099i
$$166$$ −8.00000 −0.620920
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ 3.00000i 0.231455i
$$169$$ 9.00000 0.692308
$$170$$ 4.00000 + 8.00000i 0.306786 + 0.613572i
$$171$$ −6.00000 −0.458831
$$172$$ 4.00000i 0.304997i
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ −2.00000 −0.151620
$$175$$ 4.00000 + 3.00000i 0.302372 + 0.226779i
$$176$$ 6.00000 0.452267
$$177$$ 8.00000i 0.601317i
$$178$$ 6.00000i 0.449719i
$$179$$ 14.0000 1.04641 0.523205 0.852207i $$-0.324736\pi$$
0.523205 + 0.852207i $$0.324736\pi$$
$$180$$ −1.00000 2.00000i −0.0745356 0.149071i
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 2.00000i 0.148250i
$$183$$ 2.00000i 0.147844i
$$184$$ 0 0
$$185$$ 8.00000 4.00000i 0.588172 0.294086i
$$186$$ 10.0000 0.733236
$$187$$ 24.0000i 1.75505i
$$188$$ 0 0
$$189$$ 1.00000 0.0727393
$$190$$ 12.0000 6.00000i 0.870572 0.435286i
$$191$$ −18.0000 −1.30243 −0.651217 0.758891i $$-0.725741\pi$$
−0.651217 + 0.758891i $$0.725741\pi$$
$$192$$ 7.00000i 0.505181i
$$193$$ 8.00000i 0.575853i 0.957653 + 0.287926i $$0.0929658\pi$$
−0.957653 + 0.287926i $$0.907034\pi$$
$$194$$ −2.00000 −0.143592
$$195$$ 2.00000 + 4.00000i 0.143223 + 0.286446i
$$196$$ −1.00000 −0.0714286
$$197$$ 2.00000i 0.142494i 0.997459 + 0.0712470i $$0.0226979\pi$$
−0.997459 + 0.0712470i $$0.977302\pi$$
$$198$$ 6.00000i 0.426401i
$$199$$ −14.0000 −0.992434 −0.496217 0.868199i $$-0.665278\pi$$
−0.496217 + 0.868199i $$0.665278\pi$$
$$200$$ 12.0000 + 9.00000i 0.848528 + 0.636396i
$$201$$ −16.0000 −1.12855
$$202$$ 6.00000i 0.422159i
$$203$$ 2.00000i 0.140372i
$$204$$ 4.00000 0.280056
$$205$$ 2.00000 + 4.00000i 0.139686 + 0.279372i
$$206$$ −8.00000 −0.557386
$$207$$ 0 0
$$208$$ 2.00000i 0.138675i
$$209$$ −36.0000 −2.49017
$$210$$ −2.00000 + 1.00000i −0.138013 + 0.0690066i
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 10.0000i 0.685189i
$$214$$ 4.00000 0.273434
$$215$$ −8.00000 + 4.00000i −0.545595 + 0.272798i
$$216$$ 3.00000 0.204124
$$217$$ 10.0000i 0.678844i
$$218$$ 2.00000i 0.135457i
$$219$$ 6.00000 0.405442
$$220$$ −6.00000 12.0000i −0.404520 0.809040i
$$221$$ −8.00000 −0.538138
$$222$$ 4.00000i 0.268462i
$$223$$ 24.0000i 1.60716i 0.595198 + 0.803579i $$0.297074\pi$$
−0.595198 + 0.803579i $$0.702926\pi$$
$$224$$ −5.00000 −0.334077
$$225$$ 3.00000 4.00000i 0.200000 0.266667i
$$226$$ −6.00000 −0.399114
$$227$$ 8.00000i 0.530979i 0.964114 + 0.265489i $$0.0855335\pi$$
−0.964114 + 0.265489i $$0.914466\pi$$
$$228$$ 6.00000i 0.397360i
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 6.00000 0.394771
$$232$$ 6.00000i 0.393919i
$$233$$ 26.0000i 1.70332i 0.524097 + 0.851658i $$0.324403\pi$$
−0.524097 + 0.851658i $$0.675597\pi$$
$$234$$ −2.00000 −0.130744
$$235$$ 0 0
$$236$$ 8.00000 0.520756
$$237$$ 4.00000i 0.259828i
$$238$$ 4.00000i 0.259281i
$$239$$ 6.00000 0.388108 0.194054 0.980991i $$-0.437836\pi$$
0.194054 + 0.980991i $$0.437836\pi$$
$$240$$ −2.00000 + 1.00000i −0.129099 + 0.0645497i
$$241$$ 22.0000 1.41714 0.708572 0.705638i $$-0.249340\pi$$
0.708572 + 0.705638i $$0.249340\pi$$
$$242$$ 25.0000i 1.60706i
$$243$$ 1.00000i 0.0641500i
$$244$$ −2.00000 −0.128037
$$245$$ −1.00000 2.00000i −0.0638877 0.127775i
$$246$$ −2.00000 −0.127515
$$247$$ 12.0000i 0.763542i
$$248$$ 30.0000i 1.90500i
$$249$$ −8.00000 −0.506979
$$250$$ −2.00000 + 11.0000i −0.126491 + 0.695701i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 1.00000i 0.0629941i
$$253$$ 0 0
$$254$$ 20.0000 1.25491
$$255$$ 4.00000 + 8.00000i 0.250490 + 0.500979i
$$256$$ −17.0000 −1.06250
$$257$$ 16.0000i 0.998053i 0.866587 + 0.499026i $$0.166309\pi$$
−0.866587 + 0.499026i $$0.833691\pi$$
$$258$$ 4.00000i 0.249029i
$$259$$ −4.00000 −0.248548
$$260$$ −4.00000 + 2.00000i −0.248069 + 0.124035i
$$261$$ −2.00000 −0.123797
$$262$$ 4.00000i 0.247121i
$$263$$ 24.0000i 1.47990i 0.672660 + 0.739952i $$0.265152\pi$$
−0.672660 + 0.739952i $$0.734848\pi$$
$$264$$ 18.0000 1.10782
$$265$$ 12.0000 6.00000i 0.737154 0.368577i
$$266$$ −6.00000 −0.367884
$$267$$ 6.00000i 0.367194i
$$268$$ 16.0000i 0.977356i
$$269$$ 14.0000 0.853595 0.426798 0.904347i $$-0.359642\pi$$
0.426798 + 0.904347i $$0.359642\pi$$
$$270$$ 1.00000 + 2.00000i 0.0608581 + 0.121716i
$$271$$ −14.0000 −0.850439 −0.425220 0.905090i $$-0.639803\pi$$
−0.425220 + 0.905090i $$0.639803\pi$$
$$272$$ 4.00000i 0.242536i
$$273$$ 2.00000i 0.121046i
$$274$$ −6.00000 −0.362473
$$275$$ 18.0000 24.0000i 1.08544 1.44725i
$$276$$ 0 0
$$277$$ 28.0000i 1.68236i −0.540758 0.841178i $$-0.681862\pi$$
0.540758 0.841178i $$-0.318138\pi$$
$$278$$ 2.00000i 0.119952i
$$279$$ 10.0000 0.598684
$$280$$ −3.00000 6.00000i −0.179284 0.358569i
$$281$$ −2.00000 −0.119310 −0.0596550 0.998219i $$-0.519000\pi$$
−0.0596550 + 0.998219i $$0.519000\pi$$
$$282$$ 0 0
$$283$$ 20.0000i 1.18888i −0.804141 0.594438i $$-0.797374\pi$$
0.804141 0.594438i $$-0.202626\pi$$
$$284$$ 10.0000 0.593391
$$285$$ 12.0000 6.00000i 0.710819 0.355409i
$$286$$ −12.0000 −0.709575
$$287$$ 2.00000i 0.118056i
$$288$$ 5.00000i 0.294628i
$$289$$ 1.00000 0.0588235
$$290$$ 4.00000 2.00000i 0.234888 0.117444i
$$291$$ −2.00000 −0.117242
$$292$$ 6.00000i 0.351123i
$$293$$ 24.0000i 1.40209i −0.713115 0.701047i $$-0.752716\pi$$
0.713115 0.701047i $$-0.247284\pi$$
$$294$$ 1.00000 0.0583212
$$295$$ 8.00000 + 16.0000i 0.465778 + 0.931556i
$$296$$ −12.0000 −0.697486
$$297$$ 6.00000i 0.348155i
$$298$$ 14.0000i 0.810998i
$$299$$ 0 0
$$300$$ 4.00000 + 3.00000i 0.230940 + 0.173205i
$$301$$ 4.00000 0.230556
$$302$$ 8.00000i 0.460348i
$$303$$ 6.00000i 0.344691i
$$304$$ −6.00000 −0.344124
$$305$$ −2.00000 4.00000i −0.114520 0.229039i
$$306$$ −4.00000 −0.228665
$$307$$ 4.00000i 0.228292i 0.993464 + 0.114146i $$0.0364132\pi$$
−0.993464 + 0.114146i $$0.963587\pi$$
$$308$$ 6.00000i 0.341882i
$$309$$ −8.00000 −0.455104
$$310$$ −20.0000 + 10.0000i −1.13592 + 0.567962i
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 6.00000i 0.339683i
$$313$$ 6.00000i 0.339140i −0.985518 0.169570i $$-0.945762\pi$$
0.985518 0.169570i $$-0.0542379\pi$$
$$314$$ 18.0000 1.01580
$$315$$ −2.00000 + 1.00000i −0.112687 + 0.0563436i
$$316$$ −4.00000 −0.225018
$$317$$ 18.0000i 1.01098i −0.862832 0.505490i $$-0.831312\pi$$
0.862832 0.505490i $$-0.168688\pi$$
$$318$$ 6.00000i 0.336463i
$$319$$ −12.0000 −0.671871
$$320$$ −7.00000 14.0000i −0.391312 0.782624i
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ 24.0000i 1.33540i
$$324$$ 1.00000 0.0555556
$$325$$ −8.00000 6.00000i −0.443760 0.332820i
$$326$$ −4.00000 −0.221540
$$327$$ 2.00000i 0.110600i
$$328$$ 6.00000i 0.331295i
$$329$$ 0 0
$$330$$ 6.00000 + 12.0000i 0.330289 + 0.660578i
$$331$$ −24.0000 −1.31916 −0.659580 0.751635i $$-0.729266\pi$$
−0.659580 + 0.751635i $$0.729266\pi$$
$$332$$ 8.00000i 0.439057i
$$333$$ 4.00000i 0.219199i
$$334$$ 12.0000 0.656611
$$335$$ 32.0000 16.0000i 1.74835 0.874173i
$$336$$ 1.00000 0.0545545
$$337$$ 24.0000i 1.30736i −0.756770 0.653682i $$-0.773224\pi$$
0.756770 0.653682i $$-0.226776\pi$$
$$338$$ 9.00000i 0.489535i
$$339$$ −6.00000 −0.325875
$$340$$ −8.00000 + 4.00000i −0.433861 + 0.216930i
$$341$$ 60.0000 3.24918
$$342$$ 6.00000i 0.324443i
$$343$$ 1.00000i 0.0539949i
$$344$$ 12.0000 0.646997
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 12.0000i 0.644194i 0.946707 + 0.322097i $$0.104388\pi$$
−0.946707 + 0.322097i $$0.895612\pi$$
$$348$$ 2.00000i 0.107211i
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 3.00000 4.00000i 0.160357 0.213809i
$$351$$ −2.00000 −0.106752
$$352$$ 30.0000i 1.59901i
$$353$$ 20.0000i 1.06449i −0.846590 0.532246i $$-0.821348\pi$$
0.846590 0.532246i $$-0.178652\pi$$
$$354$$ −8.00000 −0.425195
$$355$$ 10.0000 + 20.0000i 0.530745 + 1.06149i
$$356$$ −6.00000 −0.317999
$$357$$ 4.00000i 0.211702i
$$358$$ 14.0000i 0.739923i
$$359$$ −22.0000 −1.16112 −0.580558 0.814219i $$-0.697165\pi$$
−0.580558 + 0.814219i $$0.697165\pi$$
$$360$$ −6.00000 + 3.00000i −0.316228 + 0.158114i
$$361$$ 17.0000 0.894737
$$362$$ 6.00000i 0.315353i
$$363$$ 25.0000i 1.31216i
$$364$$ 2.00000 0.104828
$$365$$ −12.0000 + 6.00000i −0.628109 + 0.314054i
$$366$$ 2.00000 0.104542
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ −2.00000 −0.104116
$$370$$ −4.00000 8.00000i −0.207950 0.415900i
$$371$$ −6.00000 −0.311504
$$372$$ 10.0000i 0.518476i
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ −24.0000 −1.24101
$$375$$ −2.00000 + 11.0000i −0.103280 + 0.568038i
$$376$$ 0 0
$$377$$ 4.00000i 0.206010i
$$378$$ 1.00000i 0.0514344i
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ 6.00000 + 12.0000i 0.307794 + 0.615587i
$$381$$ 20.0000 1.02463
$$382$$ 18.0000i 0.920960i
$$383$$ 20.0000i 1.02195i 0.859595 + 0.510976i $$0.170716\pi$$
−0.859595 + 0.510976i $$0.829284\pi$$
$$384$$ −3.00000 −0.153093
$$385$$ −12.0000 + 6.00000i −0.611577 + 0.305788i
$$386$$ 8.00000 0.407189
$$387$$ 4.00000i 0.203331i
$$388$$ 2.00000i 0.101535i
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 4.00000 2.00000i 0.202548 0.101274i
$$391$$ 0 0
$$392$$ 3.00000i 0.151523i
$$393$$ 4.00000i 0.201773i
$$394$$ 2.00000 0.100759
$$395$$ −4.00000 8.00000i −0.201262 0.402524i
$$396$$ 6.00000 0.301511
$$397$$ 22.0000i 1.10415i 0.833795 + 0.552074i $$0.186163\pi$$
−0.833795 + 0.552074i $$0.813837\pi$$
$$398$$ 14.0000i 0.701757i
$$399$$ −6.00000 −0.300376
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 16.0000i 0.798007i
$$403$$ 20.0000i 0.996271i
$$404$$ −6.00000 −0.298511
$$405$$ 1.00000 + 2.00000i 0.0496904 + 0.0993808i
$$406$$ −2.00000 −0.0992583
$$407$$ 24.0000i 1.18964i
$$408$$ 12.0000i 0.594089i
$$409$$ 22.0000 1.08783 0.543915 0.839140i $$-0.316941\pi$$
0.543915 + 0.839140i $$0.316941\pi$$
$$410$$ 4.00000 2.00000i 0.197546 0.0987730i
$$411$$ −6.00000 −0.295958
$$412$$ 8.00000i 0.394132i
$$413$$ 8.00000i 0.393654i
$$414$$ 0 0
$$415$$ 16.0000 8.00000i 0.785409 0.392705i
$$416$$ 10.0000 0.490290
$$417$$ 2.00000i 0.0979404i
$$418$$ 36.0000i 1.76082i
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ −1.00000 2.00000i −0.0487950 0.0975900i
$$421$$ 18.0000 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$422$$ 16.0000i 0.778868i
$$423$$ 0 0
$$424$$ −18.0000 −0.874157
$$425$$ −16.0000 12.0000i −0.776114 0.582086i
$$426$$ −10.0000 −0.484502
$$427$$ 2.00000i 0.0967868i
$$428$$ 4.00000i 0.193347i
$$429$$ −12.0000 −0.579365
$$430$$ 4.00000 + 8.00000i 0.192897 + 0.385794i
$$431$$ −14.0000 −0.674356 −0.337178 0.941441i $$-0.609472\pi$$
−0.337178 + 0.941441i $$0.609472\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 34.0000i 1.63394i 0.576683 + 0.816968i $$0.304347\pi$$
−0.576683 + 0.816968i $$0.695653\pi$$
$$434$$ 10.0000 0.480015
$$435$$ 4.00000 2.00000i 0.191785 0.0958927i
$$436$$ −2.00000 −0.0957826
$$437$$ 0 0
$$438$$ 6.00000i 0.286691i
$$439$$ −6.00000 −0.286364 −0.143182 0.989696i $$-0.545733\pi$$
−0.143182 + 0.989696i $$0.545733\pi$$
$$440$$ −36.0000 + 18.0000i −1.71623 + 0.858116i
$$441$$ 1.00000 0.0476190
$$442$$ 8.00000i 0.380521i
$$443$$ 4.00000i 0.190046i 0.995475 + 0.0950229i $$0.0302924\pi$$
−0.995475 + 0.0950229i $$0.969708\pi$$
$$444$$ −4.00000 −0.189832
$$445$$ −6.00000 12.0000i −0.284427 0.568855i
$$446$$ 24.0000 1.13643
$$447$$ 14.0000i 0.662177i
$$448$$ 7.00000i 0.330719i
$$449$$ −10.0000 −0.471929 −0.235965 0.971762i $$-0.575825\pi$$
−0.235965 + 0.971762i $$0.575825\pi$$
$$450$$ −4.00000 3.00000i −0.188562 0.141421i
$$451$$ −12.0000 −0.565058
$$452$$ 6.00000i 0.282216i
$$453$$ 8.00000i 0.375873i
$$454$$ 8.00000 0.375459
$$455$$ 2.00000 + 4.00000i 0.0937614 + 0.187523i
$$456$$ −18.0000 −0.842927
$$457$$ 20.0000i 0.935561i −0.883845 0.467780i $$-0.845054\pi$$
0.883845 0.467780i $$-0.154946\pi$$
$$458$$ 10.0000i 0.467269i
$$459$$ −4.00000 −0.186704
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 6.00000i 0.279145i
$$463$$ 36.0000i 1.67306i −0.547920 0.836531i $$-0.684580\pi$$
0.547920 0.836531i $$-0.315420\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ −20.0000 + 10.0000i −0.927478 + 0.463739i
$$466$$ 26.0000 1.20443
$$467$$ 24.0000i 1.11059i −0.831654 0.555294i $$-0.812606\pi$$
0.831654 0.555294i $$-0.187394\pi$$
$$468$$ 2.00000i 0.0924500i
$$469$$ −16.0000 −0.738811
$$470$$ 0 0
$$471$$ 18.0000 0.829396
$$472$$ 24.0000i 1.10469i
$$473$$ 24.0000i 1.10352i
$$474$$ 4.00000 0.183726
$$475$$ −18.0000 + 24.0000i −0.825897 + 1.10120i
$$476$$ 4.00000 0.183340
$$477$$ 6.00000i 0.274721i
$$478$$ 6.00000i 0.274434i
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ −5.00000 10.0000i −0.228218 0.456435i
$$481$$ 8.00000 0.364769
$$482$$ 22.0000i 1.00207i
$$483$$ 0 0
$$484$$ 25.0000 1.13636
$$485$$ 4.00000 2.00000i 0.181631 0.0908153i
$$486$$ −1.00000 −0.0453609
$$487$$ 12.0000i 0.543772i 0.962329 + 0.271886i $$0.0876473\pi$$
−0.962329 + 0.271886i $$0.912353\pi$$
$$488$$ 6.00000i 0.271607i
$$489$$ −4.00000 −0.180886
$$490$$ −2.00000 + 1.00000i −0.0903508 + 0.0451754i
$$491$$ 10.0000 0.451294 0.225647 0.974209i $$-0.427550\pi$$
0.225647 + 0.974209i $$0.427550\pi$$
$$492$$ 2.00000i 0.0901670i
$$493$$ 8.00000i 0.360302i
$$494$$ 12.0000 0.539906
$$495$$ 6.00000 + 12.0000i 0.269680 + 0.539360i
$$496$$ 10.0000 0.449013
$$497$$ 10.0000i 0.448561i
$$498$$ 8.00000i 0.358489i
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ −11.0000 2.00000i −0.491935 0.0894427i
$$501$$ 12.0000 0.536120
$$502$$ 0 0
$$503$$ 36.0000i 1.60516i 0.596544 + 0.802580i $$0.296540\pi$$
−0.596544 + 0.802580i $$0.703460\pi$$
$$504$$ 3.00000 0.133631
$$505$$ −6.00000 12.0000i −0.266996 0.533993i
$$506$$ 0 0
$$507$$ 9.00000i 0.399704i
$$508$$ 20.0000i 0.887357i
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 8.00000 4.00000i 0.354246 0.177123i
$$511$$ 6.00000 0.265424
$$512$$ 11.0000i 0.486136i
$$513$$ 6.00000i 0.264906i
$$514$$ 16.0000 0.705730
$$515$$ 16.0000 8.00000i 0.705044 0.352522i
$$516$$ 4.00000 0.176090
$$517$$ 0 0
$$518$$ 4.00000i 0.175750i
$$519$$ 0 0
$$520$$ 6.00000 + 12.0000i 0.263117 + 0.526235i
$$521$$ 38.0000 1.66481 0.832405 0.554168i $$-0.186963\pi$$
0.832405 + 0.554168i $$0.186963\pi$$
$$522$$ 2.00000i 0.0875376i
$$523$$ 20.0000i 0.874539i −0.899331 0.437269i $$-0.855946\pi$$
0.899331 0.437269i $$-0.144054\pi$$
$$524$$ 4.00000 0.174741
$$525$$ 3.00000 4.00000i 0.130931 0.174574i
$$526$$ 24.0000 1.04645
$$527$$ 40.0000i 1.74243i
$$528$$ 6.00000i 0.261116i
$$529$$ 23.0000 1.00000
$$530$$ −6.00000 12.0000i −0.260623 0.521247i
$$531$$ −8.00000 −0.347170
$$532$$ 6.00000i 0.260133i
$$533$$ 4.00000i 0.173259i
$$534$$ 6.00000 0.259645
$$535$$ −8.00000 + 4.00000i −0.345870 + 0.172935i
$$536$$ −48.0000 −2.07328
$$537$$ 14.0000i 0.604145i
$$538$$ 14.0000i 0.603583i
$$539$$ 6.00000 0.258438
$$540$$ −2.00000 + 1.00000i −0.0860663 + 0.0430331i
$$541$$ 6.00000 0.257960 0.128980 0.991647i $$-0.458830\pi$$
0.128980 + 0.991647i $$0.458830\pi$$
$$542$$ 14.0000i 0.601351i
$$543$$ 6.00000i 0.257485i
$$544$$ 20.0000 0.857493
$$545$$ −2.00000 4.00000i −0.0856706 0.171341i
$$546$$ −2.00000 −0.0855921
$$547$$ 16.0000i 0.684111i −0.939680 0.342055i $$-0.888877\pi$$
0.939680 0.342055i $$-0.111123\pi$$
$$548$$ 6.00000i 0.256307i
$$549$$ 2.00000 0.0853579
$$550$$ −24.0000 18.0000i −1.02336 0.767523i
$$551$$ 12.0000 0.511217
$$552$$ 0 0
$$553$$ 4.00000i 0.170097i
$$554$$ −28.0000 −1.18961
$$555$$ −4.00000 8.00000i −0.169791 0.339581i
$$556$$ −2.00000 −0.0848189
$$557$$ 38.0000i 1.61011i 0.593199 + 0.805056i $$0.297865\pi$$
−0.593199 + 0.805056i $$0.702135\pi$$
$$558$$ 10.0000i 0.423334i
$$559$$ −8.00000 −0.338364
$$560$$ −2.00000 + 1.00000i −0.0845154 + 0.0422577i
$$561$$ −24.0000 −1.01328
$$562$$ 2.00000i 0.0843649i
$$563$$ 36.0000i 1.51722i 0.651546 + 0.758610i $$0.274121\pi$$
−0.651546 + 0.758610i $$0.725879\pi$$
$$564$$ 0 0
$$565$$ 12.0000 6.00000i 0.504844 0.252422i
$$566$$ −20.0000 −0.840663
$$567$$ 1.00000i 0.0419961i
$$568$$ 30.0000i 1.25877i
$$569$$ 30.0000 1.25767 0.628833 0.777541i $$-0.283533\pi$$
0.628833 + 0.777541i $$0.283533\pi$$
$$570$$ −6.00000 12.0000i −0.251312 0.502625i
$$571$$ 36.0000 1.50655 0.753277 0.657704i $$-0.228472\pi$$
0.753277 + 0.657704i $$0.228472\pi$$
$$572$$ 12.0000i 0.501745i
$$573$$ 18.0000i 0.751961i
$$574$$ −2.00000 −0.0834784
$$575$$ 0 0
$$576$$ 7.00000 0.291667
$$577$$ 14.0000i 0.582828i 0.956597 + 0.291414i $$0.0941257\pi$$
−0.956597 + 0.291414i $$0.905874\pi$$
$$578$$ 1.00000i 0.0415945i
$$579$$ 8.00000 0.332469
$$580$$ 2.00000 + 4.00000i 0.0830455 + 0.166091i
$$581$$ −8.00000 −0.331896
$$582$$ 2.00000i 0.0829027i
$$583$$ 36.0000i 1.49097i
$$584$$ 18.0000 0.744845
$$585$$ 4.00000 2.00000i 0.165380 0.0826898i
$$586$$ −24.0000 −0.991431
$$587$$ 12.0000i 0.495293i −0.968850 0.247647i $$-0.920343\pi$$
0.968850 0.247647i $$-0.0796572\pi$$
$$588$$ 1.00000i 0.0412393i
$$589$$ −60.0000 −2.47226
$$590$$ 16.0000 8.00000i 0.658710 0.329355i
$$591$$ 2.00000 0.0822690
$$592$$ 4.00000i 0.164399i
$$593$$ 44.0000i 1.80686i −0.428732 0.903432i $$-0.641040\pi$$
0.428732 0.903432i $$-0.358960\pi$$
$$594$$ −6.00000 −0.246183
$$595$$ 4.00000 + 8.00000i 0.163984 + 0.327968i
$$596$$ 14.0000 0.573462
$$597$$ 14.0000i 0.572982i
$$598$$ 0 0
$$599$$ 2.00000 0.0817178 0.0408589 0.999165i $$-0.486991\pi$$
0.0408589 + 0.999165i $$0.486991\pi$$
$$600$$ 9.00000 12.0000i 0.367423 0.489898i
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 4.00000i 0.163028i
$$603$$ 16.0000i 0.651570i
$$604$$ 8.00000 0.325515
$$605$$ 25.0000 + 50.0000i 1.01639 + 2.03279i
$$606$$ 6.00000 0.243733
$$607$$ 24.0000i 0.974130i 0.873366 + 0.487065i $$0.161933\pi$$
−0.873366 + 0.487065i $$0.838067\pi$$
$$608$$ 30.0000i 1.21666i
$$609$$ −2.00000 −0.0810441
$$610$$ −4.00000 + 2.00000i −0.161955 + 0.0809776i
$$611$$ 0 0
$$612$$ 4.00000i 0.161690i
$$613$$ 4.00000i 0.161558i −0.996732 0.0807792i $$-0.974259\pi$$
0.996732 0.0807792i $$-0.0257409\pi$$
$$614$$ 4.00000 0.161427
$$615$$ 4.00000 2.00000i 0.161296 0.0806478i
$$616$$ 18.0000 0.725241
$$617$$ 26.0000i 1.04672i −0.852111 0.523360i $$-0.824678\pi$$
0.852111 0.523360i $$-0.175322\pi$$
$$618$$ 8.00000i 0.321807i
$$619$$ −10.0000 −0.401934 −0.200967 0.979598i $$-0.564408\pi$$
−0.200967 + 0.979598i $$0.564408\pi$$
$$620$$ −10.0000 20.0000i −0.401610 0.803219i
$$621$$ 0 0
$$622$$ 24.0000i 0.962312i
$$623$$ 6.00000i 0.240385i
$$624$$ −2.00000 −0.0800641
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ −6.00000 −0.239808
$$627$$ 36.0000i 1.43770i
$$628$$ 18.0000i 0.718278i
$$629$$ 16.0000 0.637962
$$630$$ 1.00000 + 2.00000i 0.0398410 + 0.0796819i
$$631$$ −20.0000 −0.796187 −0.398094 0.917345i $$-0.630328\pi$$
−0.398094 + 0.917345i $$0.630328\pi$$
$$632$$ 12.0000i 0.477334i
$$633$$ 16.0000i 0.635943i
$$634$$ −18.0000 −0.714871
$$635$$ −40.0000 + 20.0000i −1.58735 + 0.793676i
$$636$$ −6.00000 −0.237915
$$637$$ 2.00000i 0.0792429i
$$638$$ 12.0000i 0.475085i
$$639$$ −10.0000 −0.395594
$$640$$ 6.00000 3.00000i 0.237171 0.118585i
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 4.00000i 0.157867i
$$643$$ 20.0000i 0.788723i 0.918955 + 0.394362i $$0.129034\pi$$
−0.918955 + 0.394362i $$0.870966\pi$$
$$644$$ 0 0
$$645$$ 4.00000 + 8.00000i 0.157500 + 0.315000i
$$646$$ 24.0000 0.944267
$$647$$ 20.0000i 0.786281i −0.919478 0.393141i $$-0.871389\pi$$
0.919478 0.393141i $$-0.128611\pi$$
$$648$$ 3.00000i 0.117851i
$$649$$ −48.0000 −1.88416
$$650$$ −6.00000 + 8.00000i −0.235339 + 0.313786i
$$651$$ 10.0000 0.391931
$$652$$ 4.00000i 0.156652i
$$653$$ 2.00000i 0.0782660i −0.999234 0.0391330i $$-0.987540\pi$$
0.999234 0.0391330i $$-0.0124596\pi$$
$$654$$ 2.00000 0.0782062
$$655$$ 4.00000 + 8.00000i 0.156293 + 0.312586i
$$656$$ −2.00000 −0.0780869
$$657$$ 6.00000i 0.234082i
$$658$$ 0 0
$$659$$ 18.0000 0.701180 0.350590 0.936529i $$-0.385981\pi$$
0.350590 + 0.936529i $$0.385981\pi$$
$$660$$ −12.0000 + 6.00000i −0.467099 + 0.233550i
$$661$$ −18.0000 −0.700119 −0.350059 0.936727i $$-0.613839\pi$$
−0.350059 + 0.936727i $$0.613839\pi$$
$$662$$ 24.0000i 0.932786i
$$663$$ 8.00000i 0.310694i
$$664$$ −24.0000 −0.931381
$$665$$ 12.0000 6.00000i 0.465340 0.232670i
$$666$$ 4.00000 0.154997
$$667$$ 0 0
$$668$$ 12.0000i 0.464294i
$$669$$ 24.0000 0.927894
$$670$$ −16.0000 32.0000i −0.618134 1.23627i
$$671$$ 12.0000 0.463255
$$672$$ 5.00000i 0.192879i
$$673$$ 36.0000i 1.38770i 0.720121 + 0.693849i $$0.244086\pi$$
−0.720121 + 0.693849i $$0.755914\pi$$
$$674$$ −24.0000 −0.924445
$$675$$ −4.00000 3.00000i −0.153960 0.115470i
$$676$$ 9.00000 0.346154
$$677$$ 32.0000i 1.22986i 0.788582 + 0.614930i $$0.210816\pi$$
−0.788582 + 0.614930i $$0.789184\pi$$
$$678$$ 6.00000i 0.230429i
$$679$$ −2.00000 −0.0767530
$$680$$ 12.0000 + 24.0000i 0.460179 + 0.920358i
$$681$$ 8.00000 0.306561
$$682$$ 60.0000i 2.29752i
$$683$$ 28.0000i 1.07139i −0.844411 0.535695i $$-0.820050\pi$$
0.844411 0.535695i $$-0.179950\pi$$
$$684$$ −6.00000 −0.229416
$$685$$ 12.0000 6.00000i 0.458496 0.229248i
$$686$$ 1.00000 0.0381802
$$687$$ 10.0000i 0.381524i
$$688$$ 4.00000i 0.152499i
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ −50.0000 −1.90209 −0.951045 0.309053i $$-0.899988\pi$$
−0.951045 + 0.309053i $$0.899988\pi$$
$$692$$ 0 0
$$693$$ 6.00000i 0.227921i
$$694$$ 12.0000 0.455514
$$695$$ −2.00000 4.00000i −0.0758643 0.151729i
$$696$$ −6.00000 −0.227429
$$697$$ 8.00000i 0.303022i
$$698$$ 2.00000i 0.0757011i
$$699$$ 26.0000 0.983410
$$700$$ 4.00000 + 3.00000i 0.151186 + 0.113389i
$$701$$ −10.0000 −0.377695 −0.188847 0.982006i $$-0.560475\pi$$
−0.188847 + 0.982006i $$0.560475\pi$$
$$702$$ 2.00000i 0.0754851i
$$703$$ 24.0000i 0.905177i
$$704$$ 42.0000 1.58293
$$705$$ 0 0
$$706$$ −20.0000 −0.752710
$$707$$ 6.00000i 0.225653i
$$708$$ 8.00000i 0.300658i
$$709$$ −26.0000 −0.976450 −0.488225 0.872718i $$-0.662356\pi$$
−0.488225 + 0.872718i $$0.662356\pi$$
$$710$$ 20.0000 10.0000i 0.750587 0.375293i
$$711$$ 4.00000 0.150012
$$712$$ 18.0000i 0.674579i
$$713$$ 0 0
$$714$$ −4.00000 −0.149696
$$715$$ 24.0000 12.0000i 0.897549 0.448775i
$$716$$ 14.0000 0.523205
$$717$$ 6.00000i 0.224074i
$$718$$ 22.0000i 0.821033i
$$719$$ −12.0000 −0.447524 −0.223762 0.974644i $$-0.571834\pi$$
−0.223762 + 0.974644i $$0.571834\pi$$
$$720$$ 1.00000 + 2.00000i 0.0372678 + 0.0745356i
$$721$$ −8.00000 −0.297936
$$722$$ 17.0000i 0.632674i
$$723$$ 22.0000i 0.818189i
$$724$$ −6.00000 −0.222988
$$725$$ −6.00000 + 8.00000i −0.222834 + 0.297113i
$$726$$ −25.0000 −0.927837
$$727$$ 40.0000i 1.48352i −0.670667 0.741759i $$-0.733992\pi$$
0.670667 0.741759i $$-0.266008\pi$$
$$728$$ 6.00000i 0.222375i
$$729$$ −1.00000 −0.0370370
$$730$$ 6.00000 + 12.0000i 0.222070 + 0.444140i
$$731$$ −16.0000 −0.591781
$$732$$ 2.00000i 0.0739221i
$$733$$ 22.0000i 0.812589i −0.913742 0.406294i $$-0.866821\pi$$
0.913742 0.406294i $$-0.133179\pi$$
$$734$$ 0 0
$$735$$ −2.00000 + 1.00000i −0.0737711 + 0.0368856i
$$736$$ 0 0
$$737$$ 96.0000i 3.53621i
$$738$$ 2.00000i 0.0736210i
$$739$$ 44.0000 1.61857 0.809283 0.587419i $$-0.199856\pi$$
0.809283 + 0.587419i $$0.199856\pi$$
$$740$$ 8.00000 4.00000i 0.294086 0.147043i
$$741$$ 12.0000 0.440831
$$742$$ 6.00000i 0.220267i
$$743$$ 40.0000i 1.46746i −0.679442 0.733729i $$-0.737778\pi$$
0.679442 0.733729i $$-0.262222\pi$$
$$744$$ 30.0000 1.09985
$$745$$ 14.0000 + 28.0000i 0.512920 + 1.02584i
$$746$$ 0 0
$$747$$ 8.00000i 0.292705i
$$748$$ 24.0000i 0.877527i
$$749$$ 4.00000 0.146157
$$750$$ 11.0000 + 2.00000i 0.401663 + 0.0730297i
$$751$$ −12.0000 −0.437886 −0.218943 0.975738i $$-0.570261\pi$$
−0.218943 + 0.975738i $$0.570261\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 4.00000 0.145671
$$755$$ 8.00000 + 16.0000i 0.291150 + 0.582300i
$$756$$ 1.00000 0.0363696
$$757$$ 40.0000i 1.45382i −0.686730 0.726912i $$-0.740955\pi$$
0.686730 0.726912i $$-0.259045\pi$$
$$758$$ 28.0000i 1.01701i
$$759$$ 0 0
$$760$$ 36.0000 18.0000i 1.30586 0.652929i
$$761$$ −22.0000 −0.797499 −0.398750 0.917060i $$-0.630556\pi$$
−0.398750 + 0.917060i $$0.630556\pi$$
$$762$$ 20.0000i 0.724524i
$$763$$ 2.00000i 0.0724049i
$$764$$ −18.0000 −0.651217
$$765$$ 8.00000 4.00000i 0.289241 0.144620i
$$766$$ 20.0000 0.722629
$$767$$ 16.0000i 0.577727i
$$768$$ 17.0000i 0.613435i
$$769$$ 18.0000 0.649097 0.324548 0.945869i $$-0.394788\pi$$
0.324548 + 0.945869i $$0.394788\pi$$
$$770$$ 6.00000 + 12.0000i 0.216225 + 0.432450i
$$771$$ 16.0000 0.576226
$$772$$ 8.00000i 0.287926i
$$773$$ 24.0000i 0.863220i −0.902060 0.431610i $$-0.857946\pi$$
0.902060 0.431610i $$-0.142054\pi$$
$$774$$ −4.00000 −0.143777
$$775$$ 30.0000 40.0000i 1.07763 1.43684i
$$776$$ −6.00000 −0.215387
$$777$$ 4.00000i 0.143499i
$$778$$ 26.0000i 0.932145i
$$779$$ 12.0000 0.429945
$$780$$ 2.00000 + 4.00000i 0.0716115 + 0.143223i
$$781$$ −60.0000 −2.14697
$$782$$ 0 0
$$783$$ 2.00000i 0.0714742i
$$784$$ 1.00000 0.0357143
$$785$$ −36.0000 + 18.0000i −1.28490 + 0.642448i
$$786$$ −4.00000 −0.142675
$$787$$ 4.00000i 0.142585i −0.997455 0.0712923i $$-0.977288\pi$$
0.997455 0.0712923i $$-0.0227123\pi$$
$$788$$ 2.00000i 0.0712470i
$$789$$ 24.0000