# Properties

 Label 570.2.d.a.229.1 Level $570$ Weight $2$ Character 570.229 Analytic conductor $4.551$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ 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 229.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.229 Dual form 570.2.d.a.229.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} -4.00000 q^{11} +1.00000i q^{12} +2.00000i q^{13} +(2.00000 + 1.00000i) q^{15} +1.00000 q^{16} +6.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} +(1.00000 - 2.00000i) q^{20} +4.00000i q^{22} +6.00000i q^{23} +1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} +2.00000 q^{29} +(1.00000 - 2.00000i) q^{30} -6.00000 q^{31} -1.00000i q^{32} +4.00000i q^{33} +6.00000 q^{34} +1.00000 q^{36} +10.0000i q^{37} -1.00000i q^{38} +2.00000 q^{39} +(-2.00000 - 1.00000i) q^{40} -6.00000i q^{43} +4.00000 q^{44} +(1.00000 - 2.00000i) q^{45} +6.00000 q^{46} -6.00000i q^{47} -1.00000i q^{48} +7.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +6.00000 q^{51} -2.00000i q^{52} +10.0000i q^{53} +1.00000 q^{54} +(4.00000 - 8.00000i) q^{55} -1.00000i q^{57} -2.00000i q^{58} -2.00000 q^{59} +(-2.00000 - 1.00000i) q^{60} -6.00000 q^{61} +6.00000i q^{62} -1.00000 q^{64} +(-4.00000 - 2.00000i) q^{65} +4.00000 q^{66} -8.00000i q^{67} -6.00000i q^{68} +6.00000 q^{69} -12.0000 q^{71} -1.00000i q^{72} -16.0000i q^{73} +10.0000 q^{74} +(-4.00000 + 3.00000i) q^{75} -1.00000 q^{76} -2.00000i q^{78} +14.0000 q^{79} +(-1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +12.0000i q^{83} +(-12.0000 - 6.00000i) q^{85} -6.00000 q^{86} -2.00000i q^{87} -4.00000i q^{88} -4.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} -6.00000i q^{92} +6.00000i q^{93} -6.00000 q^{94} +(-1.00000 + 2.00000i) q^{95} -1.00000 q^{96} +10.0000i q^{97} -7.00000i q^{98} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} + O(q^{10})$$ $$2q - 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} + 4q^{10} - 8q^{11} + 4q^{15} + 2q^{16} + 2q^{19} + 2q^{20} + 2q^{24} - 6q^{25} + 4q^{26} + 4q^{29} + 2q^{30} - 12q^{31} + 12q^{34} + 2q^{36} + 4q^{39} - 4q^{40} + 8q^{44} + 2q^{45} + 12q^{46} + 14q^{49} - 8q^{50} + 12q^{51} + 2q^{54} + 8q^{55} - 4q^{59} - 4q^{60} - 12q^{61} - 2q^{64} - 8q^{65} + 8q^{66} + 12q^{69} - 24q^{71} + 20q^{74} - 8q^{75} - 2q^{76} + 28q^{79} - 2q^{80} + 2q^{81} - 24q^{85} - 12q^{86} - 8q^{89} - 4q^{90} - 12q^{94} - 2q^{95} - 2q^{96} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$5$$ −1.00000 + 2.00000i −0.447214 + 0.894427i
$$6$$ −1.00000 −0.408248
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −1.00000 −0.333333
$$10$$ 2.00000 + 1.00000i 0.632456 + 0.316228i
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 2.00000i 0.554700i 0.960769 + 0.277350i $$0.0894562\pi$$
−0.960769 + 0.277350i $$0.910544\pi$$
$$14$$ 0 0
$$15$$ 2.00000 + 1.00000i 0.516398 + 0.258199i
$$16$$ 1.00000 0.250000
$$17$$ 6.00000i 1.45521i 0.685994 + 0.727607i $$0.259367\pi$$
−0.685994 + 0.727607i $$0.740633\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 1.00000 0.229416
$$20$$ 1.00000 2.00000i 0.223607 0.447214i
$$21$$ 0 0
$$22$$ 4.00000i 0.852803i
$$23$$ 6.00000i 1.25109i 0.780189 + 0.625543i $$0.215123\pi$$
−0.780189 + 0.625543i $$0.784877\pi$$
$$24$$ 1.00000 0.204124
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ 2.00000 0.392232
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 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
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 4.00000i 0.696311i
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 10.0000i 1.64399i 0.569495 + 0.821995i $$0.307139\pi$$
−0.569495 + 0.821995i $$0.692861\pi$$
$$38$$ 1.00000i 0.162221i
$$39$$ 2.00000 0.320256
$$40$$ −2.00000 1.00000i −0.316228 0.158114i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 6.00000i 0.914991i −0.889212 0.457496i $$-0.848747\pi$$
0.889212 0.457496i $$-0.151253\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 1.00000 2.00000i 0.149071 0.298142i
$$46$$ 6.00000 0.884652
$$47$$ 6.00000i 0.875190i −0.899172 0.437595i $$-0.855830\pi$$
0.899172 0.437595i $$-0.144170\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 7.00000 1.00000
$$50$$ −4.00000 + 3.00000i −0.565685 + 0.424264i
$$51$$ 6.00000 0.840168
$$52$$ 2.00000i 0.277350i
$$53$$ 10.0000i 1.37361i 0.726844 + 0.686803i $$0.240986\pi$$
−0.726844 + 0.686803i $$0.759014\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 4.00000 8.00000i 0.539360 1.07872i
$$56$$ 0 0
$$57$$ 1.00000i 0.132453i
$$58$$ 2.00000i 0.262613i
$$59$$ −2.00000 −0.260378 −0.130189 0.991489i $$-0.541558\pi$$
−0.130189 + 0.991489i $$0.541558\pi$$
$$60$$ −2.00000 1.00000i −0.258199 0.129099i
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 6.00000i 0.762001i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −4.00000 2.00000i −0.496139 0.248069i
$$66$$ 4.00000 0.492366
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 6.00000i 0.727607i
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 16.0000i 1.87266i −0.351123 0.936329i $$-0.614200\pi$$
0.351123 0.936329i $$-0.385800\pi$$
$$74$$ 10.0000 1.16248
$$75$$ −4.00000 + 3.00000i −0.461880 + 0.346410i
$$76$$ −1.00000 −0.114708
$$77$$ 0 0
$$78$$ 2.00000i 0.226455i
$$79$$ 14.0000 1.57512 0.787562 0.616236i $$-0.211343\pi$$
0.787562 + 0.616236i $$0.211343\pi$$
$$80$$ −1.00000 + 2.00000i −0.111803 + 0.223607i
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 12.0000i 1.31717i 0.752506 + 0.658586i $$0.228845\pi$$
−0.752506 + 0.658586i $$0.771155\pi$$
$$84$$ 0 0
$$85$$ −12.0000 6.00000i −1.30158 0.650791i
$$86$$ −6.00000 −0.646997
$$87$$ 2.00000i 0.214423i
$$88$$ 4.00000i 0.426401i
$$89$$ −4.00000 −0.423999 −0.212000 0.977270i $$-0.567998\pi$$
−0.212000 + 0.977270i $$0.567998\pi$$
$$90$$ −2.00000 1.00000i −0.210819 0.105409i
$$91$$ 0 0
$$92$$ 6.00000i 0.625543i
$$93$$ 6.00000i 0.622171i
$$94$$ −6.00000 −0.618853
$$95$$ −1.00000 + 2.00000i −0.102598 + 0.205196i
$$96$$ −1.00000 −0.102062
$$97$$ 10.0000i 1.01535i 0.861550 + 0.507673i $$0.169494\pi$$
−0.861550 + 0.507673i $$0.830506\pi$$
$$98$$ 7.00000i 0.707107i
$$99$$ 4.00000 0.402015
$$100$$ 3.00000 + 4.00000i 0.300000 + 0.400000i
$$101$$ −18.0000 −1.79107 −0.895533 0.444994i $$-0.853206\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 6.00000i 0.594089i
$$103$$ 8.00000i 0.788263i 0.919054 + 0.394132i $$0.128955\pi$$
−0.919054 + 0.394132i $$0.871045\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ 10.0000 0.971286
$$107$$ 4.00000i 0.386695i 0.981130 + 0.193347i $$0.0619344\pi$$
−0.981130 + 0.193347i $$0.938066\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ −4.00000 −0.383131 −0.191565 0.981480i $$-0.561356\pi$$
−0.191565 + 0.981480i $$0.561356\pi$$
$$110$$ −8.00000 4.00000i −0.762770 0.381385i
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ 2.00000i 0.188144i 0.995565 + 0.0940721i $$0.0299884\pi$$
−0.995565 + 0.0940721i $$0.970012\pi$$
$$114$$ −1.00000 −0.0936586
$$115$$ −12.0000 6.00000i −1.11901 0.559503i
$$116$$ −2.00000 −0.185695
$$117$$ 2.00000i 0.184900i
$$118$$ 2.00000i 0.184115i
$$119$$ 0 0
$$120$$ −1.00000 + 2.00000i −0.0912871 + 0.182574i
$$121$$ 5.00000 0.454545
$$122$$ 6.00000i 0.543214i
$$123$$ 0 0
$$124$$ 6.00000 0.538816
$$125$$ 11.0000 2.00000i 0.983870 0.178885i
$$126$$ 0 0
$$127$$ 8.00000i 0.709885i −0.934888 0.354943i $$-0.884500\pi$$
0.934888 0.354943i $$-0.115500\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −6.00000 −0.528271
$$130$$ −2.00000 + 4.00000i −0.175412 + 0.350823i
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 4.00000i 0.348155i
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ −2.00000 1.00000i −0.172133 0.0860663i
$$136$$ −6.00000 −0.514496
$$137$$ 6.00000i 0.512615i −0.966595 0.256307i $$-0.917494\pi$$
0.966595 0.256307i $$-0.0825059\pi$$
$$138$$ 6.00000i 0.510754i
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 12.0000i 1.00702i
$$143$$ 8.00000i 0.668994i
$$144$$ −1.00000 −0.0833333
$$145$$ −2.00000 + 4.00000i −0.166091 + 0.332182i
$$146$$ −16.0000 −1.32417
$$147$$ 7.00000i 0.577350i
$$148$$ 10.0000i 0.821995i
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 3.00000 + 4.00000i 0.244949 + 0.326599i
$$151$$ 10.0000 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$152$$ 1.00000i 0.0811107i
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 6.00000 12.0000i 0.481932 0.963863i
$$156$$ −2.00000 −0.160128
$$157$$ 18.0000i 1.43656i 0.695756 + 0.718278i $$0.255069\pi$$
−0.695756 + 0.718278i $$0.744931\pi$$
$$158$$ 14.0000i 1.11378i
$$159$$ 10.0000 0.793052
$$160$$ 2.00000 + 1.00000i 0.158114 + 0.0790569i
$$161$$ 0 0
$$162$$ 1.00000i 0.0785674i
$$163$$ 10.0000i 0.783260i −0.920123 0.391630i $$-0.871911\pi$$
0.920123 0.391630i $$-0.128089\pi$$
$$164$$ 0 0
$$165$$ −8.00000 4.00000i −0.622799 0.311400i
$$166$$ 12.0000 0.931381
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 9.00000 0.692308
$$170$$ −6.00000 + 12.0000i −0.460179 + 0.920358i
$$171$$ −1.00000 −0.0764719
$$172$$ 6.00000i 0.457496i
$$173$$ 14.0000i 1.06440i −0.846619 0.532200i $$-0.821365\pi$$
0.846619 0.532200i $$-0.178635\pi$$
$$174$$ −2.00000 −0.151620
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ 2.00000i 0.150329i
$$178$$ 4.00000i 0.299813i
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ −1.00000 + 2.00000i −0.0745356 + 0.149071i
$$181$$ −4.00000 −0.297318 −0.148659 0.988889i $$-0.547496\pi$$
−0.148659 + 0.988889i $$0.547496\pi$$
$$182$$ 0 0
$$183$$ 6.00000i 0.443533i
$$184$$ −6.00000 −0.442326
$$185$$ −20.0000 10.0000i −1.47043 0.735215i
$$186$$ 6.00000 0.439941
$$187$$ 24.0000i 1.75505i
$$188$$ 6.00000i 0.437595i
$$189$$ 0 0
$$190$$ 2.00000 + 1.00000i 0.145095 + 0.0725476i
$$191$$ 24.0000 1.73658 0.868290 0.496058i $$-0.165220\pi$$
0.868290 + 0.496058i $$0.165220\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ 14.0000i 1.00774i 0.863779 + 0.503871i $$0.168091\pi$$
−0.863779 + 0.503871i $$0.831909\pi$$
$$194$$ 10.0000 0.717958
$$195$$ −2.00000 + 4.00000i −0.143223 + 0.286446i
$$196$$ −7.00000 −0.500000
$$197$$ 8.00000i 0.569976i −0.958531 0.284988i $$-0.908010\pi$$
0.958531 0.284988i $$-0.0919897\pi$$
$$198$$ 4.00000i 0.284268i
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ 4.00000 3.00000i 0.282843 0.212132i
$$201$$ −8.00000 −0.564276
$$202$$ 18.0000i 1.26648i
$$203$$ 0 0
$$204$$ −6.00000 −0.420084
$$205$$ 0 0
$$206$$ 8.00000 0.557386
$$207$$ 6.00000i 0.417029i
$$208$$ 2.00000i 0.138675i
$$209$$ −4.00000 −0.276686
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ 10.0000i 0.686803i
$$213$$ 12.0000i 0.822226i
$$214$$ 4.00000 0.273434
$$215$$ 12.0000 + 6.00000i 0.818393 + 0.409197i
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 4.00000i 0.270914i
$$219$$ −16.0000 −1.08118
$$220$$ −4.00000 + 8.00000i −0.269680 + 0.539360i
$$221$$ −12.0000 −0.807207
$$222$$ 10.0000i 0.671156i
$$223$$ 8.00000i 0.535720i −0.963458 0.267860i $$-0.913684\pi$$
0.963458 0.267860i $$-0.0863164\pi$$
$$224$$ 0 0
$$225$$ 3.00000 + 4.00000i 0.200000 + 0.266667i
$$226$$ 2.00000 0.133038
$$227$$ 12.0000i 0.796468i 0.917284 + 0.398234i $$0.130377\pi$$
−0.917284 + 0.398234i $$0.869623\pi$$
$$228$$ 1.00000i 0.0662266i
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ −6.00000 + 12.0000i −0.395628 + 0.791257i
$$231$$ 0 0
$$232$$ 2.00000i 0.131306i
$$233$$ 14.0000i 0.917170i 0.888650 + 0.458585i $$0.151644\pi$$
−0.888650 + 0.458585i $$0.848356\pi$$
$$234$$ −2.00000 −0.130744
$$235$$ 12.0000 + 6.00000i 0.782794 + 0.391397i
$$236$$ 2.00000 0.130189
$$237$$ 14.0000i 0.909398i
$$238$$ 0 0
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 2.00000 + 1.00000i 0.129099 + 0.0645497i
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 5.00000i 0.321412i
$$243$$ 1.00000i 0.0641500i
$$244$$ 6.00000 0.384111
$$245$$ −7.00000 + 14.0000i −0.447214 + 0.894427i
$$246$$ 0 0
$$247$$ 2.00000i 0.127257i
$$248$$ 6.00000i 0.381000i
$$249$$ 12.0000 0.760469
$$250$$ −2.00000 11.0000i −0.126491 0.695701i
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 24.0000i 1.50887i
$$254$$ −8.00000 −0.501965
$$255$$ −6.00000 + 12.0000i −0.375735 + 0.751469i
$$256$$ 1.00000 0.0625000
$$257$$ 22.0000i 1.37232i −0.727450 0.686161i $$-0.759294\pi$$
0.727450 0.686161i $$-0.240706\pi$$
$$258$$ 6.00000i 0.373544i
$$259$$ 0 0
$$260$$ 4.00000 + 2.00000i 0.248069 + 0.124035i
$$261$$ −2.00000 −0.123797
$$262$$ 8.00000i 0.494242i
$$263$$ 2.00000i 0.123325i −0.998097 0.0616626i $$-0.980360\pi$$
0.998097 0.0616626i $$-0.0196403\pi$$
$$264$$ −4.00000 −0.246183
$$265$$ −20.0000 10.0000i −1.22859 0.614295i
$$266$$ 0 0
$$267$$ 4.00000i 0.244796i
$$268$$ 8.00000i 0.488678i
$$269$$ 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
$$271$$ 32.0000 1.94386 0.971931 0.235267i $$-0.0755965\pi$$
0.971931 + 0.235267i $$0.0755965\pi$$
$$272$$ 6.00000i 0.363803i
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 12.0000 + 16.0000i 0.723627 + 0.964836i
$$276$$ −6.00000 −0.361158
$$277$$ 26.0000i 1.56219i 0.624413 + 0.781094i $$0.285338\pi$$
−0.624413 + 0.781094i $$0.714662\pi$$
$$278$$ 12.0000i 0.719712i
$$279$$ 6.00000 0.359211
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 6.00000i 0.357295i
$$283$$ 22.0000i 1.30776i 0.756596 + 0.653882i $$0.226861\pi$$
−0.756596 + 0.653882i $$0.773139\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 2.00000 + 1.00000i 0.118470 + 0.0592349i
$$286$$ −8.00000 −0.473050
$$287$$ 0 0
$$288$$ 1.00000i 0.0589256i
$$289$$ −19.0000 −1.11765
$$290$$ 4.00000 + 2.00000i 0.234888 + 0.117444i
$$291$$ 10.0000 0.586210
$$292$$ 16.0000i 0.936329i
$$293$$ 2.00000i 0.116841i 0.998292 + 0.0584206i $$0.0186065\pi$$
−0.998292 + 0.0584206i $$0.981394\pi$$
$$294$$ −7.00000 −0.408248
$$295$$ 2.00000 4.00000i 0.116445 0.232889i
$$296$$ −10.0000 −0.581238
$$297$$ 4.00000i 0.232104i
$$298$$ 6.00000i 0.347571i
$$299$$ −12.0000 −0.693978
$$300$$ 4.00000 3.00000i 0.230940 0.173205i
$$301$$ 0 0
$$302$$ 10.0000i 0.575435i
$$303$$ 18.0000i 1.03407i
$$304$$ 1.00000 0.0573539
$$305$$ 6.00000 12.0000i 0.343559 0.687118i
$$306$$ −6.00000 −0.342997
$$307$$ 12.0000i 0.684876i 0.939540 + 0.342438i $$0.111253\pi$$
−0.939540 + 0.342438i $$0.888747\pi$$
$$308$$ 0 0
$$309$$ 8.00000 0.455104
$$310$$ −12.0000 6.00000i −0.681554 0.340777i
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 2.00000i 0.113228i
$$313$$ 28.0000i 1.58265i 0.611393 + 0.791327i $$0.290609\pi$$
−0.611393 + 0.791327i $$0.709391\pi$$
$$314$$ 18.0000 1.01580
$$315$$ 0 0
$$316$$ −14.0000 −0.787562
$$317$$ 6.00000i 0.336994i −0.985702 0.168497i $$-0.946109\pi$$
0.985702 0.168497i $$-0.0538913\pi$$
$$318$$ 10.0000i 0.560772i
$$319$$ −8.00000 −0.447914
$$320$$ 1.00000 2.00000i 0.0559017 0.111803i
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ 6.00000i 0.333849i
$$324$$ −1.00000 −0.0555556
$$325$$ 8.00000 6.00000i 0.443760 0.332820i
$$326$$ −10.0000 −0.553849
$$327$$ 4.00000i 0.221201i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ −4.00000 + 8.00000i −0.220193 + 0.440386i
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ 12.0000i 0.658586i
$$333$$ 10.0000i 0.547997i
$$334$$ 0 0
$$335$$ 16.0000 + 8.00000i 0.874173 + 0.437087i
$$336$$ 0 0
$$337$$ 6.00000i 0.326841i −0.986557 0.163420i $$-0.947747\pi$$
0.986557 0.163420i $$-0.0522527\pi$$
$$338$$ 9.00000i 0.489535i
$$339$$ 2.00000 0.108625
$$340$$ 12.0000 + 6.00000i 0.650791 + 0.325396i
$$341$$ 24.0000 1.29967
$$342$$ 1.00000i 0.0540738i
$$343$$ 0 0
$$344$$ 6.00000 0.323498
$$345$$ −6.00000 + 12.0000i −0.323029 + 0.646058i
$$346$$ −14.0000 −0.752645
$$347$$ 20.0000i 1.07366i −0.843692 0.536828i $$-0.819622\pi$$
0.843692 0.536828i $$-0.180378\pi$$
$$348$$ 2.00000i 0.107211i
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ 4.00000i 0.213201i
$$353$$ 2.00000i 0.106449i −0.998583 0.0532246i $$-0.983050\pi$$
0.998583 0.0532246i $$-0.0169499\pi$$
$$354$$ 2.00000 0.106299
$$355$$ 12.0000 24.0000i 0.636894 1.27379i
$$356$$ 4.00000 0.212000
$$357$$ 0 0
$$358$$ 18.0000i 0.951330i
$$359$$ 8.00000 0.422224 0.211112 0.977462i $$-0.432292\pi$$
0.211112 + 0.977462i $$0.432292\pi$$
$$360$$ 2.00000 + 1.00000i 0.105409 + 0.0527046i
$$361$$ 1.00000 0.0526316
$$362$$ 4.00000i 0.210235i
$$363$$ 5.00000i 0.262432i
$$364$$ 0 0
$$365$$ 32.0000 + 16.0000i 1.67496 + 0.837478i
$$366$$ 6.00000 0.313625
$$367$$ 12.0000i 0.626395i −0.949688 0.313197i $$-0.898600\pi$$
0.949688 0.313197i $$-0.101400\pi$$
$$368$$ 6.00000i 0.312772i
$$369$$ 0 0
$$370$$ −10.0000 + 20.0000i −0.519875 + 1.03975i
$$371$$ 0 0
$$372$$ 6.00000i 0.311086i
$$373$$ 6.00000i 0.310668i 0.987862 + 0.155334i $$0.0496454\pi$$
−0.987862 + 0.155334i $$0.950355\pi$$
$$374$$ −24.0000 −1.24101
$$375$$ −2.00000 11.0000i −0.103280 0.568038i
$$376$$ 6.00000 0.309426
$$377$$ 4.00000i 0.206010i
$$378$$ 0 0
$$379$$ −24.0000 −1.23280 −0.616399 0.787434i $$-0.711409\pi$$
−0.616399 + 0.787434i $$0.711409\pi$$
$$380$$ 1.00000 2.00000i 0.0512989 0.102598i
$$381$$ −8.00000 −0.409852
$$382$$ 24.0000i 1.22795i
$$383$$ 36.0000i 1.83951i 0.392488 + 0.919757i $$0.371614\pi$$
−0.392488 + 0.919757i $$0.628386\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 14.0000 0.712581
$$387$$ 6.00000i 0.304997i
$$388$$ 10.0000i 0.507673i
$$389$$ −38.0000 −1.92668 −0.963338 0.268290i $$-0.913542\pi$$
−0.963338 + 0.268290i $$0.913542\pi$$
$$390$$ 4.00000 + 2.00000i 0.202548 + 0.101274i
$$391$$ −36.0000 −1.82060
$$392$$ 7.00000i 0.353553i
$$393$$ 8.00000i 0.403547i
$$394$$ −8.00000 −0.403034
$$395$$ −14.0000 + 28.0000i −0.704416 + 1.40883i
$$396$$ −4.00000 −0.201008
$$397$$ 30.0000i 1.50566i 0.658217 + 0.752828i $$0.271311\pi$$
−0.658217 + 0.752828i $$0.728689\pi$$
$$398$$ 16.0000i 0.802008i
$$399$$ 0 0
$$400$$ −3.00000 4.00000i −0.150000 0.200000i
$$401$$ 16.0000 0.799002 0.399501 0.916733i $$-0.369183\pi$$
0.399501 + 0.916733i $$0.369183\pi$$
$$402$$ 8.00000i 0.399004i
$$403$$ 12.0000i 0.597763i
$$404$$ 18.0000 0.895533
$$405$$ −1.00000 + 2.00000i −0.0496904 + 0.0993808i
$$406$$ 0 0
$$407$$ 40.0000i 1.98273i
$$408$$ 6.00000i 0.297044i
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 0 0
$$411$$ −6.00000 −0.295958
$$412$$ 8.00000i 0.394132i
$$413$$ 0 0
$$414$$ −6.00000 −0.294884
$$415$$ −24.0000 12.0000i −1.17811 0.589057i
$$416$$ 2.00000 0.0980581
$$417$$ 12.0000i 0.587643i
$$418$$ 4.00000i 0.195646i
$$419$$ −8.00000 −0.390826 −0.195413 0.980721i $$-0.562605\pi$$
−0.195413 + 0.980721i $$0.562605\pi$$
$$420$$ 0 0
$$421$$ 16.0000 0.779792 0.389896 0.920859i $$-0.372511\pi$$
0.389896 + 0.920859i $$0.372511\pi$$
$$422$$ 8.00000i 0.389434i
$$423$$ 6.00000i 0.291730i
$$424$$ −10.0000 −0.485643
$$425$$ 24.0000 18.0000i 1.16417 0.873128i
$$426$$ 12.0000 0.581402
$$427$$ 0 0
$$428$$ 4.00000i 0.193347i
$$429$$ −8.00000 −0.386244
$$430$$ 6.00000 12.0000i 0.289346 0.578691i
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 6.00000i 0.288342i 0.989553 + 0.144171i $$0.0460515\pi$$
−0.989553 + 0.144171i $$0.953949\pi$$
$$434$$ 0 0
$$435$$ 4.00000 + 2.00000i 0.191785 + 0.0958927i
$$436$$ 4.00000 0.191565
$$437$$ 6.00000i 0.287019i
$$438$$ 16.0000i 0.764510i
$$439$$ 14.0000 0.668184 0.334092 0.942541i $$-0.391570\pi$$
0.334092 + 0.942541i $$0.391570\pi$$
$$440$$ 8.00000 + 4.00000i 0.381385 + 0.190693i
$$441$$ −7.00000 −0.333333
$$442$$ 12.0000i 0.570782i
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ −10.0000 −0.474579
$$445$$ 4.00000 8.00000i 0.189618 0.379236i
$$446$$ −8.00000 −0.378811
$$447$$ 6.00000i 0.283790i
$$448$$ 0 0
$$449$$ −4.00000 −0.188772 −0.0943858 0.995536i $$-0.530089\pi$$
−0.0943858 + 0.995536i $$0.530089\pi$$
$$450$$ 4.00000 3.00000i 0.188562 0.141421i
$$451$$ 0 0
$$452$$ 2.00000i 0.0940721i
$$453$$ 10.0000i 0.469841i
$$454$$ 12.0000 0.563188
$$455$$ 0 0
$$456$$ 1.00000 0.0468293
$$457$$ 16.0000i 0.748448i −0.927338 0.374224i $$-0.877909\pi$$
0.927338 0.374224i $$-0.122091\pi$$
$$458$$ 10.0000i 0.467269i
$$459$$ −6.00000 −0.280056
$$460$$ 12.0000 + 6.00000i 0.559503 + 0.279751i
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ 8.00000i 0.371792i −0.982569 0.185896i $$-0.940481\pi$$
0.982569 0.185896i $$-0.0595187\pi$$
$$464$$ 2.00000 0.0928477
$$465$$ −12.0000 6.00000i −0.556487 0.278243i
$$466$$ 14.0000 0.648537
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 2.00000i 0.0924500i
$$469$$ 0 0
$$470$$ 6.00000 12.0000i 0.276759 0.553519i
$$471$$ 18.0000 0.829396
$$472$$ 2.00000i 0.0920575i
$$473$$ 24.0000i 1.10352i
$$474$$ −14.0000 −0.643041
$$475$$ −3.00000 4.00000i −0.137649 0.183533i
$$476$$ 0 0
$$477$$ 10.0000i 0.457869i
$$478$$ 8.00000i 0.365911i
$$479$$ 16.0000 0.731059 0.365529 0.930800i $$-0.380888\pi$$
0.365529 + 0.930800i $$0.380888\pi$$
$$480$$ 1.00000 2.00000i 0.0456435 0.0912871i
$$481$$ −20.0000 −0.911922
$$482$$ 10.0000i 0.455488i
$$483$$ 0 0
$$484$$ −5.00000 −0.227273
$$485$$ −20.0000 10.0000i −0.908153 0.454077i
$$486$$ −1.00000 −0.0453609
$$487$$ 24.0000i 1.08754i −0.839233 0.543772i $$-0.816996\pi$$
0.839233 0.543772i $$-0.183004\pi$$
$$488$$ 6.00000i 0.271607i
$$489$$ −10.0000 −0.452216
$$490$$ 14.0000 + 7.00000i 0.632456 + 0.316228i
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 12.0000i 0.540453i
$$494$$ 2.00000 0.0899843
$$495$$ −4.00000 + 8.00000i −0.179787 + 0.359573i
$$496$$ −6.00000 −0.269408
$$497$$ 0 0
$$498$$ 12.0000i 0.537733i
$$499$$ −20.0000 −0.895323 −0.447661 0.894203i $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ −11.0000 + 2.00000i −0.491935 + 0.0894427i
$$501$$ 0 0
$$502$$ 12.0000i 0.535586i
$$503$$ 14.0000i 0.624229i −0.950044 0.312115i $$-0.898963\pi$$
0.950044 0.312115i $$-0.101037\pi$$
$$504$$ 0 0
$$505$$ 18.0000 36.0000i 0.800989 1.60198i
$$506$$ −24.0000 −1.06693
$$507$$ 9.00000i 0.399704i
$$508$$ 8.00000i 0.354943i
$$509$$ −6.00000 −0.265945 −0.132973 0.991120i $$-0.542452\pi$$
−0.132973 + 0.991120i $$0.542452\pi$$
$$510$$ 12.0000 + 6.00000i 0.531369 + 0.265684i
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ 1.00000i 0.0441511i
$$514$$ −22.0000 −0.970378
$$515$$ −16.0000 8.00000i −0.705044 0.352522i
$$516$$ 6.00000 0.264135
$$517$$ 24.0000i 1.05552i
$$518$$ 0 0
$$519$$ −14.0000 −0.614532
$$520$$ 2.00000 4.00000i 0.0877058 0.175412i
$$521$$ −24.0000 −1.05146 −0.525730 0.850652i $$-0.676208\pi$$
−0.525730 + 0.850652i $$0.676208\pi$$
$$522$$ 2.00000i 0.0875376i
$$523$$ 36.0000i 1.57417i 0.616844 + 0.787085i $$0.288411\pi$$
−0.616844 + 0.787085i $$0.711589\pi$$
$$524$$ 8.00000 0.349482
$$525$$ 0 0
$$526$$ −2.00000 −0.0872041
$$527$$ 36.0000i 1.56818i
$$528$$ 4.00000i 0.174078i
$$529$$ −13.0000 −0.565217
$$530$$ −10.0000 + 20.0000i −0.434372 + 0.868744i
$$531$$ 2.00000 0.0867926
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 4.00000 0.173097
$$535$$ −8.00000 4.00000i −0.345870 0.172935i
$$536$$ 8.00000 0.345547
$$537$$ 18.0000i 0.776757i
$$538$$ 14.0000i 0.603583i
$$539$$ −28.0000 −1.20605
$$540$$ 2.00000 + 1.00000i 0.0860663 + 0.0430331i
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ 32.0000i 1.37452i
$$543$$ 4.00000i 0.171656i
$$544$$ 6.00000 0.257248
$$545$$ 4.00000 8.00000i 0.171341 0.342682i
$$546$$ 0 0
$$547$$ 36.0000i 1.53925i 0.638497 + 0.769624i $$0.279557\pi$$
−0.638497 + 0.769624i $$0.720443\pi$$
$$548$$ 6.00000i 0.256307i
$$549$$ 6.00000 0.256074
$$550$$ 16.0000 12.0000i 0.682242 0.511682i
$$551$$ 2.00000 0.0852029
$$552$$ 6.00000i 0.255377i
$$553$$ 0 0
$$554$$ 26.0000 1.10463
$$555$$ −10.0000 + 20.0000i −0.424476 + 0.848953i
$$556$$ 12.0000 0.508913
$$557$$ 24.0000i 1.01691i −0.861088 0.508456i $$-0.830216\pi$$
0.861088 0.508456i $$-0.169784\pi$$
$$558$$ 6.00000i 0.254000i
$$559$$ 12.0000 0.507546
$$560$$ 0 0
$$561$$ −24.0000 −1.01328
$$562$$ 0 0
$$563$$ 12.0000i 0.505740i −0.967500 0.252870i $$-0.918626\pi$$
0.967500 0.252870i $$-0.0813744\pi$$
$$564$$ 6.00000 0.252646
$$565$$ −4.00000 2.00000i −0.168281 0.0841406i
$$566$$ 22.0000 0.924729
$$567$$ 0 0
$$568$$ 12.0000i 0.503509i
$$569$$ 28.0000 1.17382 0.586911 0.809652i $$-0.300344\pi$$
0.586911 + 0.809652i $$0.300344\pi$$
$$570$$ 1.00000 2.00000i 0.0418854 0.0837708i
$$571$$ −20.0000 −0.836974 −0.418487 0.908223i $$-0.637439\pi$$
−0.418487 + 0.908223i $$0.637439\pi$$
$$572$$ 8.00000i 0.334497i
$$573$$ 24.0000i 1.00261i
$$574$$ 0 0
$$575$$ 24.0000 18.0000i 1.00087 0.750652i
$$576$$ 1.00000 0.0416667
$$577$$ 8.00000i 0.333044i 0.986038 + 0.166522i $$0.0532537\pi$$
−0.986038 + 0.166522i $$0.946746\pi$$
$$578$$ 19.0000i 0.790296i
$$579$$ 14.0000 0.581820
$$580$$ 2.00000 4.00000i 0.0830455 0.166091i
$$581$$ 0 0
$$582$$ 10.0000i 0.414513i
$$583$$ 40.0000i 1.65663i
$$584$$ 16.0000 0.662085
$$585$$ 4.00000 + 2.00000i 0.165380 + 0.0826898i
$$586$$ 2.00000 0.0826192
$$587$$ 28.0000i 1.15568i 0.816149 + 0.577842i $$0.196105\pi$$
−0.816149 + 0.577842i $$0.803895\pi$$
$$588$$ 7.00000i 0.288675i
$$589$$ −6.00000 −0.247226
$$590$$ −4.00000 2.00000i −0.164677 0.0823387i
$$591$$ −8.00000 −0.329076
$$592$$ 10.0000i 0.410997i
$$593$$ 46.0000i 1.88899i −0.328521 0.944497i $$-0.606550\pi$$
0.328521 0.944497i $$-0.393450\pi$$
$$594$$ −4.00000 −0.164122
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 16.0000i 0.654836i
$$598$$ 12.0000i 0.490716i
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ −3.00000 4.00000i −0.122474 0.163299i
$$601$$ 30.0000 1.22373 0.611863 0.790964i $$-0.290420\pi$$
0.611863 + 0.790964i $$0.290420\pi$$
$$602$$ 0 0
$$603$$ 8.00000i 0.325785i
$$604$$ −10.0000 −0.406894
$$605$$ −5.00000 + 10.0000i −0.203279 + 0.406558i
$$606$$ 18.0000 0.731200
$$607$$ 24.0000i 0.974130i 0.873366 + 0.487065i $$0.161933\pi$$
−0.873366 + 0.487065i $$0.838067\pi$$
$$608$$ 1.00000i 0.0405554i
$$609$$ 0 0
$$610$$ −12.0000 6.00000i −0.485866 0.242933i
$$611$$ 12.0000 0.485468
$$612$$ 6.00000i 0.242536i
$$613$$ 22.0000i 0.888572i −0.895885 0.444286i $$-0.853457\pi$$
0.895885 0.444286i $$-0.146543\pi$$
$$614$$ 12.0000 0.484281
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000i 0.724653i 0.932051 + 0.362326i $$0.118017\pi$$
−0.932051 + 0.362326i $$0.881983\pi$$
$$618$$ 8.00000i 0.321807i
$$619$$ −44.0000 −1.76851 −0.884255 0.467005i $$-0.845333\pi$$
−0.884255 + 0.467005i $$0.845333\pi$$
$$620$$ −6.00000 + 12.0000i −0.240966 + 0.481932i
$$621$$ −6.00000 −0.240772
$$622$$ 24.0000i 0.962312i
$$623$$ 0 0
$$624$$ 2.00000 0.0800641
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 28.0000 1.11911
$$627$$ 4.00000i 0.159745i
$$628$$ 18.0000i 0.718278i
$$629$$ −60.0000 −2.39236
$$630$$ 0 0
$$631$$ −20.0000 −0.796187 −0.398094 0.917345i $$-0.630328\pi$$
−0.398094 + 0.917345i $$0.630328\pi$$
$$632$$ 14.0000i 0.556890i
$$633$$ 8.00000i 0.317971i
$$634$$ −6.00000 −0.238290
$$635$$ 16.0000 + 8.00000i 0.634941 + 0.317470i
$$636$$ −10.0000 −0.396526
$$637$$ 14.0000i 0.554700i
$$638$$ 8.00000i 0.316723i
$$639$$ 12.0000 0.474713
$$640$$ −2.00000 1.00000i −0.0790569 0.0395285i
$$641$$ 48.0000 1.89589 0.947943 0.318440i $$-0.103159\pi$$
0.947943 + 0.318440i $$0.103159\pi$$
$$642$$ 4.00000i 0.157867i
$$643$$ 26.0000i 1.02534i −0.858586 0.512670i $$-0.828656\pi$$
0.858586 0.512670i $$-0.171344\pi$$
$$644$$ 0 0
$$645$$ 6.00000 12.0000i 0.236250 0.472500i
$$646$$ 6.00000 0.236067
$$647$$ 6.00000i 0.235884i −0.993020 0.117942i $$-0.962370\pi$$
0.993020 0.117942i $$-0.0376297\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ 8.00000 0.314027
$$650$$ −6.00000 8.00000i −0.235339 0.313786i
$$651$$ 0 0
$$652$$ 10.0000i 0.391630i
$$653$$ 48.0000i 1.87839i 0.343391 + 0.939193i $$0.388424\pi$$
−0.343391 + 0.939193i $$0.611576\pi$$
$$654$$ 4.00000 0.156412
$$655$$ 8.00000 16.0000i 0.312586 0.625172i
$$656$$ 0 0
$$657$$ 16.0000i 0.624219i
$$658$$ 0 0
$$659$$ −46.0000 −1.79191 −0.895953 0.444149i $$-0.853506\pi$$
−0.895953 + 0.444149i $$0.853506\pi$$
$$660$$ 8.00000 + 4.00000i 0.311400 + 0.155700i
$$661$$ −8.00000 −0.311164 −0.155582 0.987823i $$-0.549725\pi$$
−0.155582 + 0.987823i $$0.549725\pi$$
$$662$$ 4.00000i 0.155464i
$$663$$ 12.0000i 0.466041i
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ −10.0000 −0.387492
$$667$$ 12.0000i 0.464642i
$$668$$ 0 0
$$669$$ −8.00000 −0.309298
$$670$$ 8.00000 16.0000i 0.309067 0.618134i
$$671$$ 24.0000 0.926510
$$672$$ 0 0
$$673$$ 26.0000i 1.00223i 0.865382 + 0.501113i $$0.167076\pi$$
−0.865382 + 0.501113i $$0.832924\pi$$
$$674$$ −6.00000 −0.231111
$$675$$ 4.00000 3.00000i 0.153960 0.115470i
$$676$$ −9.00000 −0.346154
$$677$$ 6.00000i 0.230599i 0.993331 + 0.115299i $$0.0367827\pi$$
−0.993331 + 0.115299i $$0.963217\pi$$
$$678$$ 2.00000i 0.0768095i
$$679$$ 0 0
$$680$$ 6.00000 12.0000i 0.230089 0.460179i
$$681$$ 12.0000 0.459841
$$682$$ 24.0000i 0.919007i
$$683$$ 36.0000i 1.37750i −0.724998 0.688751i $$-0.758159\pi$$
0.724998 0.688751i $$-0.241841\pi$$
$$684$$ 1.00000 0.0382360
$$685$$ 12.0000 + 6.00000i 0.458496 + 0.229248i
$$686$$ 0 0
$$687$$ 10.0000i 0.381524i
$$688$$ 6.00000i 0.228748i
$$689$$ −20.0000 −0.761939
$$690$$ 12.0000 + 6.00000i 0.456832 + 0.228416i
$$691$$ 44.0000 1.67384 0.836919 0.547326i $$-0.184354\pi$$
0.836919 + 0.547326i $$0.184354\pi$$
$$692$$ 14.0000i 0.532200i
$$693$$ 0 0
$$694$$ −20.0000 −0.759190
$$695$$ 12.0000 24.0000i 0.455186 0.910372i
$$696$$ 2.00000 0.0758098
$$697$$ 0 0
$$698$$ 26.0000i 0.984115i
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ −22.0000 −0.830929 −0.415464 0.909610i $$-0.636381\pi$$
−0.415464 + 0.909610i $$0.636381\pi$$
$$702$$ 2.00000i 0.0754851i
$$703$$ 10.0000i 0.377157i
$$704$$ 4.00000 0.150756
$$705$$ 6.00000 12.0000i 0.225973 0.451946i
$$706$$ −2.00000 −0.0752710
$$707$$ 0 0
$$708$$ 2.00000i 0.0751646i
$$709$$ 2.00000 0.0751116 0.0375558 0.999295i $$-0.488043\pi$$
0.0375558 + 0.999295i $$0.488043\pi$$
$$710$$ −24.0000 12.0000i −0.900704 0.450352i
$$711$$ −14.0000 −0.525041
$$712$$ 4.00000i 0.149906i
$$713$$ 36.0000i 1.34821i
$$714$$ 0 0
$$715$$ 16.0000 + 8.00000i 0.598366 + 0.299183i
$$716$$ −18.0000 −0.672692
$$717$$ 8.00000i 0.298765i
$$718$$ 8.00000i 0.298557i
$$719$$ −48.0000 −1.79010 −0.895049 0.445968i $$-0.852860\pi$$
−0.895049 + 0.445968i $$0.852860\pi$$
$$720$$ 1.00000 2.00000i 0.0372678 0.0745356i
$$721$$ 0 0
$$722$$ 1.00000i 0.0372161i
$$723$$ 10.0000i 0.371904i
$$724$$ 4.00000 0.148659
$$725$$ −6.00000 8.00000i −0.222834 0.297113i
$$726$$ −5.00000 −0.185567
$$727$$ 28.0000i 1.03846i 0.854634 + 0.519231i $$0.173782\pi$$
−0.854634 + 0.519231i $$0.826218\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 16.0000 32.0000i 0.592187 1.18437i
$$731$$ 36.0000 1.33151
$$732$$ 6.00000i 0.221766i
$$733$$ 46.0000i 1.69905i 0.527549 + 0.849524i $$0.323111\pi$$
−0.527549 + 0.849524i $$0.676889\pi$$
$$734$$ −12.0000 −0.442928
$$735$$ 14.0000 + 7.00000i 0.516398 + 0.258199i
$$736$$ 6.00000 0.221163
$$737$$ 32.0000i 1.17874i
$$738$$ 0 0
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ 20.0000 + 10.0000i 0.735215 + 0.367607i
$$741$$ 2.00000 0.0734718
$$742$$ 0 0
$$743$$ 8.00000i 0.293492i −0.989174 0.146746i $$-0.953120\pi$$
0.989174 0.146746i $$-0.0468799\pi$$
$$744$$ −6.00000 −0.219971
$$745$$ −6.00000 + 12.0000i −0.219823 + 0.439646i
$$746$$ 6.00000 0.219676
$$747$$ 12.0000i 0.439057i
$$748$$ 24.0000i 0.877527i
$$749$$ 0 0
$$750$$ −11.0000 + 2.00000i −0.401663 + 0.0730297i
$$751$$ −26.0000 −0.948753 −0.474377 0.880322i $$-0.657327\pi$$
−0.474377 + 0.880322i $$0.657327\pi$$
$$752$$ 6.00000i 0.218797i
$$753$$ 12.0000i 0.437304i
$$754$$ 4.00000 0.145671
$$755$$ −10.0000 + 20.0000i −0.363937 + 0.727875i
$$756$$ 0 0
$$757$$ 2.00000i 0.0726912i 0.999339 + 0.0363456i $$0.0115717\pi$$
−0.999339 + 0.0363456i $$0.988428\pi$$
$$758$$ 24.0000i 0.871719i
$$759$$ −24.0000 −0.871145
$$760$$ −2.00000 1.00000i −0.0725476 0.0362738i
$$761$$ 30.0000 1.08750 0.543750 0.839248i $$-0.317004\pi$$
0.543750 + 0.839248i $$0.317004\pi$$
$$762$$ 8.00000i 0.289809i
$$763$$ 0 0
$$764$$ −24.0000 −0.868290
$$765$$ 12.0000 + 6.00000i 0.433861 + 0.216930i
$$766$$ 36.0000 1.30073
$$767$$ 4.00000i 0.144432i
$$768$$ 1.00000i 0.0360844i
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ −22.0000 −0.792311
$$772$$ 14.0000i 0.503871i
$$773$$ 50.0000i 1.79838i −0.437564 0.899188i $$-0.644158\pi$$
0.437564 0.899188i $$-0.355842\pi$$
$$774$$ 6.00000 0.215666
$$775$$ 18.0000 + 24.0000i 0.646579 + 0.862105i
$$776$$ −10.0000 −0.358979
$$777$$ 0 0
$$778$$ 38.0000i 1.36237i
$$779$$ 0 0
$$780$$ 2.00000 4.00000i 0.0716115 0.143223i
$$781$$ 48.0000 1.71758
$$782$$ 36.0000i 1.28736i
$$783$$ 2.00000i 0.0714742i
$$784$$ 7.00000 0.250000
$$785$$ −36.0000 18.0000i −1.28490 0.642448i
$$786$$ 8.00000 0.285351
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 8.00000i 0.284988i
$$789$$ −2.00000 −0.0712019
$$790$$ 28.0000 + 14.0000i 0.996195 + 0.498098i
$$791$$ 0 0
$$792$$ 4.00000i 0.142134i