# Properties

 Label 390.2.l.b.287.2 Level $390$ Weight $2$ Character 390.287 Analytic conductor $3.114$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$390 = 2 \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 390.l (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.11416567883$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ x^4 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 287.2 Root $$0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 390.287 Dual form 390.2.l.b.53.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 - 0.707107i) q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +(1.70711 + 0.292893i) q^{6} +(0.585786 + 0.585786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$$ $$q+(0.707107 - 0.707107i) q^{2} +(1.00000 + 1.41421i) q^{3} -1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +(1.70711 + 0.292893i) q^{6} +(0.585786 + 0.585786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.00000 + 2.82843i) q^{9} +(1.00000 + 2.00000i) q^{10} +4.00000i q^{11} +(1.41421 - 1.00000i) q^{12} +(-0.707107 + 0.707107i) q^{13} +0.828427 q^{14} +(-3.70711 + 1.12132i) q^{15} -1.00000 q^{16} +(3.00000 - 3.00000i) q^{17} +(1.29289 + 2.70711i) q^{18} -6.82843i q^{19} +(2.12132 + 0.707107i) q^{20} +(-0.242641 + 1.41421i) q^{21} +(2.82843 + 2.82843i) q^{22} +(2.82843 + 2.82843i) q^{23} +(0.292893 - 1.70711i) q^{24} +(-4.00000 - 3.00000i) q^{25} +1.00000i q^{26} +(-5.00000 + 1.41421i) q^{27} +(0.585786 - 0.585786i) q^{28} +6.00000 q^{29} +(-1.82843 + 3.41421i) q^{30} +3.41421 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.65685 + 4.00000i) q^{33} -4.24264i q^{34} +(-1.65685 + 0.828427i) q^{35} +(2.82843 + 1.00000i) q^{36} +(-2.58579 - 2.58579i) q^{37} +(-4.82843 - 4.82843i) q^{38} +(-1.70711 - 0.292893i) q^{39} +(2.00000 - 1.00000i) q^{40} +2.00000i q^{41} +(0.828427 + 1.17157i) q^{42} +(1.24264 - 1.24264i) q^{43} +4.00000 q^{44} +(-5.29289 - 4.12132i) q^{45} +4.00000 q^{46} +(2.24264 - 2.24264i) q^{47} +(-1.00000 - 1.41421i) q^{48} -6.31371i q^{49} +(-4.94975 + 0.707107i) q^{50} +(7.24264 + 1.24264i) q^{51} +(0.707107 + 0.707107i) q^{52} +(-0.585786 - 0.585786i) q^{53} +(-2.53553 + 4.53553i) q^{54} +(-8.48528 - 2.82843i) q^{55} -0.828427i q^{56} +(9.65685 - 6.82843i) q^{57} +(4.24264 - 4.24264i) q^{58} -4.48528 q^{59} +(1.12132 + 3.70711i) q^{60} +4.82843 q^{61} +(2.41421 - 2.41421i) q^{62} +(-2.24264 + 1.07107i) q^{63} +1.00000i q^{64} +(-1.00000 - 2.00000i) q^{65} +(-1.17157 + 6.82843i) q^{66} +(-0.828427 - 0.828427i) q^{67} +(-3.00000 - 3.00000i) q^{68} +(-1.17157 + 6.82843i) q^{69} +(-0.585786 + 1.75736i) q^{70} -14.2426i q^{71} +(2.70711 - 1.29289i) q^{72} +(-11.0711 + 11.0711i) q^{73} -3.65685 q^{74} +(0.242641 - 8.65685i) q^{75} -6.82843 q^{76} +(-2.34315 + 2.34315i) q^{77} +(-1.41421 + 1.00000i) q^{78} -12.4853i q^{79} +(0.707107 - 2.12132i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(1.41421 + 1.41421i) q^{82} +(6.82843 + 6.82843i) q^{83} +(1.41421 + 0.242641i) q^{84} +(4.24264 + 8.48528i) q^{85} -1.75736i q^{86} +(6.00000 + 8.48528i) q^{87} +(2.82843 - 2.82843i) q^{88} -11.1716 q^{89} +(-6.65685 + 0.828427i) q^{90} -0.828427 q^{91} +(2.82843 - 2.82843i) q^{92} +(3.41421 + 4.82843i) q^{93} -3.17157i q^{94} +(14.4853 + 4.82843i) q^{95} +(-1.70711 - 0.292893i) q^{96} +(9.07107 + 9.07107i) q^{97} +(-4.46447 - 4.46447i) q^{98} +(-11.3137 - 4.00000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{3} + 4 q^{6} + 8 q^{7} - 4 q^{9}+O(q^{10})$$ 4 * q + 4 * q^3 + 4 * q^6 + 8 * q^7 - 4 * q^9 $$4 q + 4 q^{3} + 4 q^{6} + 8 q^{7} - 4 q^{9} + 4 q^{10} - 8 q^{14} - 12 q^{15} - 4 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} + 4 q^{24} - 16 q^{25} - 20 q^{27} + 8 q^{28} + 24 q^{29} + 4 q^{30} + 8 q^{31} + 16 q^{35} - 16 q^{37} - 8 q^{38} - 4 q^{39} + 8 q^{40} - 8 q^{42} - 12 q^{43} + 16 q^{44} - 24 q^{45} + 16 q^{46} - 8 q^{47} - 4 q^{48} + 12 q^{51} - 8 q^{53} + 4 q^{54} + 16 q^{57} + 16 q^{59} - 4 q^{60} + 8 q^{61} + 4 q^{62} + 8 q^{63} - 4 q^{65} - 16 q^{66} + 8 q^{67} - 12 q^{68} - 16 q^{69} - 8 q^{70} + 8 q^{72} - 16 q^{73} + 8 q^{74} - 16 q^{75} - 16 q^{76} - 32 q^{77} - 28 q^{81} + 16 q^{83} + 24 q^{87} - 56 q^{89} - 4 q^{90} + 8 q^{91} + 8 q^{93} + 24 q^{95} - 4 q^{96} + 8 q^{97} - 32 q^{98}+O(q^{100})$$ 4 * q + 4 * q^3 + 4 * q^6 + 8 * q^7 - 4 * q^9 + 4 * q^10 - 8 * q^14 - 12 * q^15 - 4 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 + 4 * q^24 - 16 * q^25 - 20 * q^27 + 8 * q^28 + 24 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^35 - 16 * q^37 - 8 * q^38 - 4 * q^39 + 8 * q^40 - 8 * q^42 - 12 * q^43 + 16 * q^44 - 24 * q^45 + 16 * q^46 - 8 * q^47 - 4 * q^48 + 12 * q^51 - 8 * q^53 + 4 * q^54 + 16 * q^57 + 16 * q^59 - 4 * q^60 + 8 * q^61 + 4 * q^62 + 8 * q^63 - 4 * q^65 - 16 * q^66 + 8 * q^67 - 12 * q^68 - 16 * q^69 - 8 * q^70 + 8 * q^72 - 16 * q^73 + 8 * q^74 - 16 * q^75 - 16 * q^76 - 32 * q^77 - 28 * q^81 + 16 * q^83 + 24 * q^87 - 56 * q^89 - 4 * q^90 + 8 * q^91 + 8 * q^93 + 24 * q^95 - 4 * q^96 + 8 * q^97 - 32 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$$.

 $$n$$ $$131$$ $$157$$ $$301$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 0.707107i 0.500000 0.500000i
$$3$$ 1.00000 + 1.41421i 0.577350 + 0.816497i
$$4$$ 1.00000i 0.500000i
$$5$$ −0.707107 + 2.12132i −0.316228 + 0.948683i
$$6$$ 1.70711 + 0.292893i 0.696923 + 0.119573i
$$7$$ 0.585786 + 0.585786i 0.221406 + 0.221406i 0.809091 0.587684i $$-0.199960\pi$$
−0.587684 + 0.809091i $$0.699960\pi$$
$$8$$ −0.707107 0.707107i −0.250000 0.250000i
$$9$$ −1.00000 + 2.82843i −0.333333 + 0.942809i
$$10$$ 1.00000 + 2.00000i 0.316228 + 0.632456i
$$11$$ 4.00000i 1.20605i 0.797724 + 0.603023i $$0.206037\pi$$
−0.797724 + 0.603023i $$0.793963\pi$$
$$12$$ 1.41421 1.00000i 0.408248 0.288675i
$$13$$ −0.707107 + 0.707107i −0.196116 + 0.196116i
$$14$$ 0.828427 0.221406
$$15$$ −3.70711 + 1.12132i −0.957171 + 0.289524i
$$16$$ −1.00000 −0.250000
$$17$$ 3.00000 3.00000i 0.727607 0.727607i −0.242536 0.970143i $$-0.577979\pi$$
0.970143 + 0.242536i $$0.0779791\pi$$
$$18$$ 1.29289 + 2.70711i 0.304738 + 0.638071i
$$19$$ 6.82843i 1.56655i −0.621676 0.783274i $$-0.713548\pi$$
0.621676 0.783274i $$-0.286452\pi$$
$$20$$ 2.12132 + 0.707107i 0.474342 + 0.158114i
$$21$$ −0.242641 + 1.41421i −0.0529485 + 0.308607i
$$22$$ 2.82843 + 2.82843i 0.603023 + 0.603023i
$$23$$ 2.82843 + 2.82843i 0.589768 + 0.589768i 0.937568 0.347801i $$-0.113071\pi$$
−0.347801 + 0.937568i $$0.613071\pi$$
$$24$$ 0.292893 1.70711i 0.0597866 0.348462i
$$25$$ −4.00000 3.00000i −0.800000 0.600000i
$$26$$ 1.00000i 0.196116i
$$27$$ −5.00000 + 1.41421i −0.962250 + 0.272166i
$$28$$ 0.585786 0.585786i 0.110703 0.110703i
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ −1.82843 + 3.41421i −0.333824 + 0.623347i
$$31$$ 3.41421 0.613211 0.306605 0.951837i $$-0.400807\pi$$
0.306605 + 0.951837i $$0.400807\pi$$
$$32$$ −0.707107 + 0.707107i −0.125000 + 0.125000i
$$33$$ −5.65685 + 4.00000i −0.984732 + 0.696311i
$$34$$ 4.24264i 0.727607i
$$35$$ −1.65685 + 0.828427i −0.280059 + 0.140030i
$$36$$ 2.82843 + 1.00000i 0.471405 + 0.166667i
$$37$$ −2.58579 2.58579i −0.425101 0.425101i 0.461855 0.886956i $$-0.347184\pi$$
−0.886956 + 0.461855i $$0.847184\pi$$
$$38$$ −4.82843 4.82843i −0.783274 0.783274i
$$39$$ −1.70711 0.292893i −0.273356 0.0469005i
$$40$$ 2.00000 1.00000i 0.316228 0.158114i
$$41$$ 2.00000i 0.312348i 0.987730 + 0.156174i $$0.0499160\pi$$
−0.987730 + 0.156174i $$0.950084\pi$$
$$42$$ 0.828427 + 1.17157i 0.127829 + 0.180778i
$$43$$ 1.24264 1.24264i 0.189501 0.189501i −0.605979 0.795480i $$-0.707219\pi$$
0.795480 + 0.605979i $$0.207219\pi$$
$$44$$ 4.00000 0.603023
$$45$$ −5.29289 4.12132i −0.789018 0.614370i
$$46$$ 4.00000 0.589768
$$47$$ 2.24264 2.24264i 0.327123 0.327123i −0.524369 0.851491i $$-0.675699\pi$$
0.851491 + 0.524369i $$0.175699\pi$$
$$48$$ −1.00000 1.41421i −0.144338 0.204124i
$$49$$ 6.31371i 0.901958i
$$50$$ −4.94975 + 0.707107i −0.700000 + 0.100000i
$$51$$ 7.24264 + 1.24264i 1.01417 + 0.174005i
$$52$$ 0.707107 + 0.707107i 0.0980581 + 0.0980581i
$$53$$ −0.585786 0.585786i −0.0804640 0.0804640i 0.665729 0.746193i $$-0.268121\pi$$
−0.746193 + 0.665729i $$0.768121\pi$$
$$54$$ −2.53553 + 4.53553i −0.345042 + 0.617208i
$$55$$ −8.48528 2.82843i −1.14416 0.381385i
$$56$$ 0.828427i 0.110703i
$$57$$ 9.65685 6.82843i 1.27908 0.904447i
$$58$$ 4.24264 4.24264i 0.557086 0.557086i
$$59$$ −4.48528 −0.583934 −0.291967 0.956428i $$-0.594310\pi$$
−0.291967 + 0.956428i $$0.594310\pi$$
$$60$$ 1.12132 + 3.70711i 0.144762 + 0.478585i
$$61$$ 4.82843 0.618217 0.309108 0.951027i $$-0.399969\pi$$
0.309108 + 0.951027i $$0.399969\pi$$
$$62$$ 2.41421 2.41421i 0.306605 0.306605i
$$63$$ −2.24264 + 1.07107i −0.282546 + 0.134942i
$$64$$ 1.00000i 0.125000i
$$65$$ −1.00000 2.00000i −0.124035 0.248069i
$$66$$ −1.17157 + 6.82843i −0.144211 + 0.840521i
$$67$$ −0.828427 0.828427i −0.101208 0.101208i 0.654689 0.755898i $$-0.272799\pi$$
−0.755898 + 0.654689i $$0.772799\pi$$
$$68$$ −3.00000 3.00000i −0.363803 0.363803i
$$69$$ −1.17157 + 6.82843i −0.141041 + 0.822046i
$$70$$ −0.585786 + 1.75736i −0.0700149 + 0.210045i
$$71$$ 14.2426i 1.69029i −0.534537 0.845145i $$-0.679514\pi$$
0.534537 0.845145i $$-0.320486\pi$$
$$72$$ 2.70711 1.29289i 0.319036 0.152369i
$$73$$ −11.0711 + 11.0711i −1.29577 + 1.29577i −0.364610 + 0.931160i $$0.618798\pi$$
−0.931160 + 0.364610i $$0.881202\pi$$
$$74$$ −3.65685 −0.425101
$$75$$ 0.242641 8.65685i 0.0280177 0.999607i
$$76$$ −6.82843 −0.783274
$$77$$ −2.34315 + 2.34315i −0.267026 + 0.267026i
$$78$$ −1.41421 + 1.00000i −0.160128 + 0.113228i
$$79$$ 12.4853i 1.40470i −0.711830 0.702352i $$-0.752133\pi$$
0.711830 0.702352i $$-0.247867\pi$$
$$80$$ 0.707107 2.12132i 0.0790569 0.237171i
$$81$$ −7.00000 5.65685i −0.777778 0.628539i
$$82$$ 1.41421 + 1.41421i 0.156174 + 0.156174i
$$83$$ 6.82843 + 6.82843i 0.749517 + 0.749517i 0.974388 0.224871i $$-0.0721961\pi$$
−0.224871 + 0.974388i $$0.572196\pi$$
$$84$$ 1.41421 + 0.242641i 0.154303 + 0.0264743i
$$85$$ 4.24264 + 8.48528i 0.460179 + 0.920358i
$$86$$ 1.75736i 0.189501i
$$87$$ 6.00000 + 8.48528i 0.643268 + 0.909718i
$$88$$ 2.82843 2.82843i 0.301511 0.301511i
$$89$$ −11.1716 −1.18418 −0.592092 0.805870i $$-0.701698\pi$$
−0.592092 + 0.805870i $$0.701698\pi$$
$$90$$ −6.65685 + 0.828427i −0.701694 + 0.0873239i
$$91$$ −0.828427 −0.0868428
$$92$$ 2.82843 2.82843i 0.294884 0.294884i
$$93$$ 3.41421 + 4.82843i 0.354037 + 0.500685i
$$94$$ 3.17157i 0.327123i
$$95$$ 14.4853 + 4.82843i 1.48616 + 0.495386i
$$96$$ −1.70711 0.292893i −0.174231 0.0298933i
$$97$$ 9.07107 + 9.07107i 0.921027 + 0.921027i 0.997102 0.0760747i $$-0.0242388\pi$$
−0.0760747 + 0.997102i $$0.524239\pi$$
$$98$$ −4.46447 4.46447i −0.450979 0.450979i
$$99$$ −11.3137 4.00000i −1.13707 0.402015i
$$100$$ −3.00000 + 4.00000i −0.300000 + 0.400000i
$$101$$ 3.17157i 0.315583i 0.987472 + 0.157792i $$0.0504374\pi$$
−0.987472 + 0.157792i $$0.949563\pi$$
$$102$$ 6.00000 4.24264i 0.594089 0.420084i
$$103$$ 12.4853 12.4853i 1.23021 1.23021i 0.266329 0.963882i $$-0.414189\pi$$
0.963882 0.266329i $$-0.0858108\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ −2.82843 1.51472i −0.276026 0.147821i
$$106$$ −0.828427 −0.0804640
$$107$$ −12.0711 + 12.0711i −1.16695 + 1.16695i −0.184034 + 0.982920i $$0.558916\pi$$
−0.982920 + 0.184034i $$0.941084\pi$$
$$108$$ 1.41421 + 5.00000i 0.136083 + 0.481125i
$$109$$ 4.92893i 0.472106i 0.971740 + 0.236053i $$0.0758539\pi$$
−0.971740 + 0.236053i $$0.924146\pi$$
$$110$$ −8.00000 + 4.00000i −0.762770 + 0.381385i
$$111$$ 1.07107 6.24264i 0.101661 0.592525i
$$112$$ −0.585786 0.585786i −0.0553516 0.0553516i
$$113$$ −7.00000 7.00000i −0.658505 0.658505i 0.296522 0.955026i $$-0.404173\pi$$
−0.955026 + 0.296522i $$0.904173\pi$$
$$114$$ 2.00000 11.6569i 0.187317 1.09176i
$$115$$ −8.00000 + 4.00000i −0.746004 + 0.373002i
$$116$$ 6.00000i 0.557086i
$$117$$ −1.29289 2.70711i −0.119528 0.250272i
$$118$$ −3.17157 + 3.17157i −0.291967 + 0.291967i
$$119$$ 3.51472 0.322194
$$120$$ 3.41421 + 1.82843i 0.311674 + 0.166912i
$$121$$ −5.00000 −0.454545
$$122$$ 3.41421 3.41421i 0.309108 0.309108i
$$123$$ −2.82843 + 2.00000i −0.255031 + 0.180334i
$$124$$ 3.41421i 0.306605i
$$125$$ 9.19239 6.36396i 0.822192 0.569210i
$$126$$ −0.828427 + 2.34315i −0.0738022 + 0.208744i
$$127$$ −3.17157 3.17157i −0.281432 0.281432i 0.552248 0.833680i $$-0.313770\pi$$
−0.833680 + 0.552248i $$0.813770\pi$$
$$128$$ 0.707107 + 0.707107i 0.0625000 + 0.0625000i
$$129$$ 3.00000 + 0.514719i 0.264135 + 0.0453184i
$$130$$ −2.12132 0.707107i −0.186052 0.0620174i
$$131$$ 12.9706i 1.13324i −0.823978 0.566622i $$-0.808250\pi$$
0.823978 0.566622i $$-0.191750\pi$$
$$132$$ 4.00000 + 5.65685i 0.348155 + 0.492366i
$$133$$ 4.00000 4.00000i 0.346844 0.346844i
$$134$$ −1.17157 −0.101208
$$135$$ 0.535534 11.6066i 0.0460914 0.998937i
$$136$$ −4.24264 −0.363803
$$137$$ −15.0711 + 15.0711i −1.28761 + 1.28761i −0.351372 + 0.936236i $$0.614285\pi$$
−0.936236 + 0.351372i $$0.885715\pi$$
$$138$$ 4.00000 + 5.65685i 0.340503 + 0.481543i
$$139$$ 1.65685i 0.140533i 0.997528 + 0.0702663i $$0.0223849\pi$$
−0.997528 + 0.0702663i $$0.977615\pi$$
$$140$$ 0.828427 + 1.65685i 0.0700149 + 0.140030i
$$141$$ 5.41421 + 0.928932i 0.455959 + 0.0782302i
$$142$$ −10.0711 10.0711i −0.845145 0.845145i
$$143$$ −2.82843 2.82843i −0.236525 0.236525i
$$144$$ 1.00000 2.82843i 0.0833333 0.235702i
$$145$$ −4.24264 + 12.7279i −0.352332 + 1.05700i
$$146$$ 15.6569i 1.29577i
$$147$$ 8.92893 6.31371i 0.736446 0.520746i
$$148$$ −2.58579 + 2.58579i −0.212550 + 0.212550i
$$149$$ −22.3848 −1.83383 −0.916916 0.399080i $$-0.869330\pi$$
−0.916916 + 0.399080i $$0.869330\pi$$
$$150$$ −5.94975 6.29289i −0.485795 0.513813i
$$151$$ 1.07107 0.0871623 0.0435811 0.999050i $$-0.486123\pi$$
0.0435811 + 0.999050i $$0.486123\pi$$
$$152$$ −4.82843 + 4.82843i −0.391637 + 0.391637i
$$153$$ 5.48528 + 11.4853i 0.443459 + 0.928530i
$$154$$ 3.31371i 0.267026i
$$155$$ −2.41421 + 7.24264i −0.193914 + 0.581743i
$$156$$ −0.292893 + 1.70711i −0.0234502 + 0.136678i
$$157$$ 16.2426 + 16.2426i 1.29630 + 1.29630i 0.930816 + 0.365488i $$0.119098\pi$$
0.365488 + 0.930816i $$0.380902\pi$$
$$158$$ −8.82843 8.82843i −0.702352 0.702352i
$$159$$ 0.242641 1.41421i 0.0192427 0.112154i
$$160$$ −1.00000 2.00000i −0.0790569 0.158114i
$$161$$ 3.31371i 0.261157i
$$162$$ −8.94975 + 0.949747i −0.703159 + 0.0746192i
$$163$$ 2.34315 2.34315i 0.183529 0.183529i −0.609362 0.792892i $$-0.708575\pi$$
0.792892 + 0.609362i $$0.208575\pi$$
$$164$$ 2.00000 0.156174
$$165$$ −4.48528 14.8284i −0.349179 1.15439i
$$166$$ 9.65685 0.749517
$$167$$ −3.41421 + 3.41421i −0.264200 + 0.264200i −0.826758 0.562558i $$-0.809817\pi$$
0.562558 + 0.826758i $$0.309817\pi$$
$$168$$ 1.17157 0.828427i 0.0903888 0.0639145i
$$169$$ 1.00000i 0.0769231i
$$170$$ 9.00000 + 3.00000i 0.690268 + 0.230089i
$$171$$ 19.3137 + 6.82843i 1.47696 + 0.522183i
$$172$$ −1.24264 1.24264i −0.0947505 0.0947505i
$$173$$ 17.0711 + 17.0711i 1.29789 + 1.29789i 0.929784 + 0.368105i $$0.119993\pi$$
0.368105 + 0.929784i $$0.380007\pi$$
$$174$$ 10.2426 + 1.75736i 0.776493 + 0.133225i
$$175$$ −0.585786 4.10051i −0.0442813 0.309969i
$$176$$ 4.00000i 0.301511i
$$177$$ −4.48528 6.34315i −0.337134 0.476780i
$$178$$ −7.89949 + 7.89949i −0.592092 + 0.592092i
$$179$$ 17.6569 1.31974 0.659868 0.751382i $$-0.270612\pi$$
0.659868 + 0.751382i $$0.270612\pi$$
$$180$$ −4.12132 + 5.29289i −0.307185 + 0.394509i
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ −0.585786 + 0.585786i −0.0434214 + 0.0434214i
$$183$$ 4.82843 + 6.82843i 0.356928 + 0.504772i
$$184$$ 4.00000i 0.294884i
$$185$$ 7.31371 3.65685i 0.537715 0.268857i
$$186$$ 5.82843 + 1.00000i 0.427361 + 0.0733236i
$$187$$ 12.0000 + 12.0000i 0.877527 + 0.877527i
$$188$$ −2.24264 2.24264i −0.163561 0.163561i
$$189$$ −3.75736 2.10051i −0.273308 0.152789i
$$190$$ 13.6569 6.82843i 0.990772 0.495386i
$$191$$ 2.82843i 0.204658i −0.994751 0.102329i $$-0.967371\pi$$
0.994751 0.102329i $$-0.0326294\pi$$
$$192$$ −1.41421 + 1.00000i −0.102062 + 0.0721688i
$$193$$ 11.4142 11.4142i 0.821613 0.821613i −0.164726 0.986339i $$-0.552674\pi$$
0.986339 + 0.164726i $$0.0526741\pi$$
$$194$$ 12.8284 0.921027
$$195$$ 1.82843 3.41421i 0.130936 0.244497i
$$196$$ −6.31371 −0.450979
$$197$$ −3.75736 + 3.75736i −0.267701 + 0.267701i −0.828173 0.560472i $$-0.810620\pi$$
0.560472 + 0.828173i $$0.310620\pi$$
$$198$$ −10.8284 + 5.17157i −0.769543 + 0.367528i
$$199$$ 22.1421i 1.56961i −0.619740 0.784807i $$-0.712762\pi$$
0.619740 0.784807i $$-0.287238\pi$$
$$200$$ 0.707107 + 4.94975i 0.0500000 + 0.350000i
$$201$$ 0.343146 2.00000i 0.0242036 0.141069i
$$202$$ 2.24264 + 2.24264i 0.157792 + 0.157792i
$$203$$ 3.51472 + 3.51472i 0.246685 + 0.246685i
$$204$$ 1.24264 7.24264i 0.0870023 0.507086i
$$205$$ −4.24264 1.41421i −0.296319 0.0987730i
$$206$$ 17.6569i 1.23021i
$$207$$ −10.8284 + 5.17157i −0.752628 + 0.359449i
$$208$$ 0.707107 0.707107i 0.0490290 0.0490290i
$$209$$ 27.3137 1.88933
$$210$$ −3.07107 + 0.928932i −0.211924 + 0.0641024i
$$211$$ 1.65685 0.114063 0.0570313 0.998372i $$-0.481837\pi$$
0.0570313 + 0.998372i $$0.481837\pi$$
$$212$$ −0.585786 + 0.585786i −0.0402320 + 0.0402320i
$$213$$ 20.1421 14.2426i 1.38012 0.975890i
$$214$$ 17.0711i 1.16695i
$$215$$ 1.75736 + 3.51472i 0.119851 + 0.239702i
$$216$$ 4.53553 + 2.53553i 0.308604 + 0.172521i
$$217$$ 2.00000 + 2.00000i 0.135769 + 0.135769i
$$218$$ 3.48528 + 3.48528i 0.236053 + 0.236053i
$$219$$ −26.7279 4.58579i −1.80611 0.309879i
$$220$$ −2.82843 + 8.48528i −0.190693 + 0.572078i
$$221$$ 4.24264i 0.285391i
$$222$$ −3.65685 5.17157i −0.245432 0.347093i
$$223$$ −9.65685 + 9.65685i −0.646671 + 0.646671i −0.952187 0.305516i $$-0.901171\pi$$
0.305516 + 0.952187i $$0.401171\pi$$
$$224$$ −0.828427 −0.0553516
$$225$$ 12.4853 8.31371i 0.832352 0.554247i
$$226$$ −9.89949 −0.658505
$$227$$ −2.00000 + 2.00000i −0.132745 + 0.132745i −0.770357 0.637613i $$-0.779922\pi$$
0.637613 + 0.770357i $$0.279922\pi$$
$$228$$ −6.82843 9.65685i −0.452224 0.639541i
$$229$$ 17.8995i 1.18283i 0.806367 + 0.591416i $$0.201431\pi$$
−0.806367 + 0.591416i $$0.798569\pi$$
$$230$$ −2.82843 + 8.48528i −0.186501 + 0.559503i
$$231$$ −5.65685 0.970563i −0.372194 0.0638583i
$$232$$ −4.24264 4.24264i −0.278543 0.278543i
$$233$$ 8.65685 + 8.65685i 0.567129 + 0.567129i 0.931323 0.364194i $$-0.118655\pi$$
−0.364194 + 0.931323i $$0.618655\pi$$
$$234$$ −2.82843 1.00000i −0.184900 0.0653720i
$$235$$ 3.17157 + 6.34315i 0.206891 + 0.413781i
$$236$$ 4.48528i 0.291967i
$$237$$ 17.6569 12.4853i 1.14694 0.811006i
$$238$$ 2.48528 2.48528i 0.161097 0.161097i
$$239$$ 19.8995 1.28719 0.643596 0.765366i $$-0.277442\pi$$
0.643596 + 0.765366i $$0.277442\pi$$
$$240$$ 3.70711 1.12132i 0.239293 0.0723809i
$$241$$ −3.65685 −0.235559 −0.117779 0.993040i $$-0.537578\pi$$
−0.117779 + 0.993040i $$0.537578\pi$$
$$242$$ −3.53553 + 3.53553i −0.227273 + 0.227273i
$$243$$ 1.00000 15.5563i 0.0641500 0.997940i
$$244$$ 4.82843i 0.309108i
$$245$$ 13.3934 + 4.46447i 0.855673 + 0.285224i
$$246$$ −0.585786 + 3.41421i −0.0373484 + 0.217682i
$$247$$ 4.82843 + 4.82843i 0.307225 + 0.307225i
$$248$$ −2.41421 2.41421i −0.153303 0.153303i
$$249$$ −2.82843 + 16.4853i −0.179244 + 1.04471i
$$250$$ 2.00000 11.0000i 0.126491 0.695701i
$$251$$ 14.3431i 0.905331i −0.891680 0.452666i $$-0.850473\pi$$
0.891680 0.452666i $$-0.149527\pi$$
$$252$$ 1.07107 + 2.24264i 0.0674709 + 0.141273i
$$253$$ −11.3137 + 11.3137i −0.711287 + 0.711287i
$$254$$ −4.48528 −0.281432
$$255$$ −7.75736 + 14.4853i −0.485785 + 0.907104i
$$256$$ 1.00000 0.0625000
$$257$$ −7.00000 + 7.00000i −0.436648 + 0.436648i −0.890882 0.454234i $$-0.849913\pi$$
0.454234 + 0.890882i $$0.349913\pi$$
$$258$$ 2.48528 1.75736i 0.154727 0.109408i
$$259$$ 3.02944i 0.188240i
$$260$$ −2.00000 + 1.00000i −0.124035 + 0.0620174i
$$261$$ −6.00000 + 16.9706i −0.371391 + 1.05045i
$$262$$ −9.17157 9.17157i −0.566622 0.566622i
$$263$$ −16.0000 16.0000i −0.986602 0.986602i 0.0133092 0.999911i $$-0.495763\pi$$
−0.999911 + 0.0133092i $$0.995763\pi$$
$$264$$ 6.82843 + 1.17157i 0.420261 + 0.0721053i
$$265$$ 1.65685 0.828427i 0.101780 0.0508899i
$$266$$ 5.65685i 0.346844i
$$267$$ −11.1716 15.7990i −0.683689 0.966882i
$$268$$ −0.828427 + 0.828427i −0.0506042 + 0.0506042i
$$269$$ −15.1716 −0.925027 −0.462514 0.886612i $$-0.653052\pi$$
−0.462514 + 0.886612i $$0.653052\pi$$
$$270$$ −7.82843 8.58579i −0.476423 0.522514i
$$271$$ −2.24264 −0.136231 −0.0681154 0.997677i $$-0.521699\pi$$
−0.0681154 + 0.997677i $$0.521699\pi$$
$$272$$ −3.00000 + 3.00000i −0.181902 + 0.181902i
$$273$$ −0.828427 1.17157i −0.0501387 0.0709068i
$$274$$ 21.3137i 1.28761i
$$275$$ 12.0000 16.0000i 0.723627 0.964836i
$$276$$ 6.82843 + 1.17157i 0.411023 + 0.0705204i
$$277$$ −15.8995 15.8995i −0.955308 0.955308i 0.0437351 0.999043i $$-0.486074\pi$$
−0.999043 + 0.0437351i $$0.986074\pi$$
$$278$$ 1.17157 + 1.17157i 0.0702663 + 0.0702663i
$$279$$ −3.41421 + 9.65685i −0.204404 + 0.578141i
$$280$$ 1.75736 + 0.585786i 0.105022 + 0.0350074i
$$281$$ 0.828427i 0.0494198i 0.999695 + 0.0247099i $$0.00786621\pi$$
−0.999695 + 0.0247099i $$0.992134\pi$$
$$282$$ 4.48528 3.17157i 0.267095 0.188864i
$$283$$ −17.2426 + 17.2426i −1.02497 + 1.02497i −0.0252884 + 0.999680i $$0.508050\pi$$
−0.999680 + 0.0252884i $$0.991950\pi$$
$$284$$ −14.2426 −0.845145
$$285$$ 7.65685 + 25.3137i 0.453553 + 1.49945i
$$286$$ −4.00000 −0.236525
$$287$$ −1.17157 + 1.17157i −0.0691558 + 0.0691558i
$$288$$ −1.29289 2.70711i −0.0761845 0.159518i
$$289$$ 1.00000i 0.0588235i
$$290$$ 6.00000 + 12.0000i 0.352332 + 0.704664i
$$291$$ −3.75736 + 21.8995i −0.220260 + 1.28377i
$$292$$ 11.0711 + 11.0711i 0.647885 + 0.647885i
$$293$$ 4.48528 + 4.48528i 0.262033 + 0.262033i 0.825880 0.563847i $$-0.190679\pi$$
−0.563847 + 0.825880i $$0.690679\pi$$
$$294$$ 1.84924 10.7782i 0.107850 0.628596i
$$295$$ 3.17157 9.51472i 0.184656 0.553968i
$$296$$ 3.65685i 0.212550i
$$297$$ −5.65685 20.0000i −0.328244 1.16052i
$$298$$ −15.8284 + 15.8284i −0.916916 + 0.916916i
$$299$$ −4.00000 −0.231326
$$300$$ −8.65685 0.242641i −0.499804 0.0140089i
$$301$$ 1.45584 0.0839135
$$302$$ 0.757359 0.757359i 0.0435811 0.0435811i
$$303$$ −4.48528 + 3.17157i −0.257673 + 0.182202i
$$304$$ 6.82843i 0.391637i
$$305$$ −3.41421 + 10.2426i −0.195497 + 0.586492i
$$306$$ 12.0000 + 4.24264i 0.685994 + 0.242536i
$$307$$ 7.17157 + 7.17157i 0.409303 + 0.409303i 0.881496 0.472192i $$-0.156537\pi$$
−0.472192 + 0.881496i $$0.656537\pi$$
$$308$$ 2.34315 + 2.34315i 0.133513 + 0.133513i
$$309$$ 30.1421 + 5.17157i 1.71473 + 0.294201i
$$310$$ 3.41421 + 6.82843i 0.193914 + 0.387829i
$$311$$ 28.0000i 1.58773i −0.608091 0.793867i $$-0.708065\pi$$
0.608091 0.793867i $$-0.291935\pi$$
$$312$$ 1.00000 + 1.41421i 0.0566139 + 0.0800641i
$$313$$ 1.34315 1.34315i 0.0759191 0.0759191i −0.668128 0.744047i $$-0.732904\pi$$
0.744047 + 0.668128i $$0.232904\pi$$
$$314$$ 22.9706 1.29630
$$315$$ −0.686292 5.51472i −0.0386681 0.310719i
$$316$$ −12.4853 −0.702352
$$317$$ 1.65685 1.65685i 0.0930582 0.0930582i −0.659045 0.752103i $$-0.729039\pi$$
0.752103 + 0.659045i $$0.229039\pi$$
$$318$$ −0.828427 1.17157i −0.0464559 0.0656985i
$$319$$ 24.0000i 1.34374i
$$320$$ −2.12132 0.707107i −0.118585 0.0395285i
$$321$$ −29.1421 5.00000i −1.62656 0.279073i
$$322$$ 2.34315 + 2.34315i 0.130578 + 0.130578i
$$323$$ −20.4853 20.4853i −1.13983 1.13983i
$$324$$ −5.65685 + 7.00000i −0.314270 + 0.388889i
$$325$$ 4.94975 0.707107i 0.274563 0.0392232i
$$326$$ 3.31371i 0.183529i
$$327$$ −6.97056 + 4.92893i −0.385473 + 0.272571i
$$328$$ 1.41421 1.41421i 0.0780869 0.0780869i
$$329$$ 2.62742 0.144854
$$330$$ −13.6569 7.31371i −0.751785 0.402606i
$$331$$ −32.2843 −1.77450 −0.887252 0.461285i $$-0.847389\pi$$
−0.887252 + 0.461285i $$0.847389\pi$$
$$332$$ 6.82843 6.82843i 0.374759 0.374759i
$$333$$ 9.89949 4.72792i 0.542489 0.259089i
$$334$$ 4.82843i 0.264200i
$$335$$ 2.34315 1.17157i 0.128020 0.0640099i
$$336$$ 0.242641 1.41421i 0.0132371 0.0771517i
$$337$$ −23.0000 23.0000i −1.25289 1.25289i −0.954419 0.298471i $$-0.903523\pi$$
−0.298471 0.954419i $$-0.596477\pi$$
$$338$$ −0.707107 0.707107i −0.0384615 0.0384615i
$$339$$ 2.89949 16.8995i 0.157479 0.917855i
$$340$$ 8.48528 4.24264i 0.460179 0.230089i
$$341$$ 13.6569i 0.739560i
$$342$$ 18.4853 8.82843i 0.999570 0.477387i
$$343$$ 7.79899 7.79899i 0.421106 0.421106i
$$344$$ −1.75736 −0.0947505
$$345$$ −13.6569 7.31371i −0.735260 0.393757i
$$346$$ 24.1421 1.29789
$$347$$ −10.5563 + 10.5563i −0.566695 + 0.566695i −0.931201 0.364506i $$-0.881238\pi$$
0.364506 + 0.931201i $$0.381238\pi$$
$$348$$ 8.48528 6.00000i 0.454859 0.321634i
$$349$$ 32.7279i 1.75189i 0.482415 + 0.875943i $$0.339760\pi$$
−0.482415 + 0.875943i $$0.660240\pi$$
$$350$$ −3.31371 2.48528i −0.177125 0.132844i
$$351$$ 2.53553 4.53553i 0.135337 0.242089i
$$352$$ −2.82843 2.82843i −0.150756 0.150756i
$$353$$ −25.5563 25.5563i −1.36023 1.36023i −0.873622 0.486605i $$-0.838235\pi$$
−0.486605 0.873622i $$-0.661765\pi$$
$$354$$ −7.65685 1.31371i −0.406957 0.0698228i
$$355$$ 30.2132 + 10.0711i 1.60355 + 0.534517i
$$356$$ 11.1716i 0.592092i
$$357$$ 3.51472 + 4.97056i 0.186019 + 0.263070i
$$358$$ 12.4853 12.4853i 0.659868 0.659868i
$$359$$ −23.4142 −1.23575 −0.617877 0.786274i $$-0.712007\pi$$
−0.617877 + 0.786274i $$0.712007\pi$$
$$360$$ 0.828427 + 6.65685i 0.0436619 + 0.350847i
$$361$$ −27.6274 −1.45407
$$362$$ 4.24264 4.24264i 0.222988 0.222988i
$$363$$ −5.00000 7.07107i −0.262432 0.371135i
$$364$$ 0.828427i 0.0434214i
$$365$$ −15.6569 31.3137i −0.819517 1.63903i
$$366$$ 8.24264 + 1.41421i 0.430850 + 0.0739221i
$$367$$ 14.1421 + 14.1421i 0.738213 + 0.738213i 0.972232 0.234019i $$-0.0751877\pi$$
−0.234019 + 0.972232i $$0.575188\pi$$
$$368$$ −2.82843 2.82843i −0.147442 0.147442i
$$369$$ −5.65685 2.00000i −0.294484 0.104116i
$$370$$ 2.58579 7.75736i 0.134429 0.403286i
$$371$$ 0.686292i 0.0356305i
$$372$$ 4.82843 3.41421i 0.250342 0.177019i
$$373$$ 4.92893 4.92893i 0.255210 0.255210i −0.567892 0.823103i $$-0.692241\pi$$
0.823103 + 0.567892i $$0.192241\pi$$
$$374$$ 16.9706 0.877527
$$375$$ 18.1924 + 6.63604i 0.939451 + 0.342684i
$$376$$ −3.17157 −0.163561
$$377$$ −4.24264 + 4.24264i −0.218507 + 0.218507i
$$378$$ −4.14214 + 1.17157i −0.213048 + 0.0602592i
$$379$$ 38.1421i 1.95923i −0.200884 0.979615i $$-0.564382\pi$$
0.200884 0.979615i $$-0.435618\pi$$
$$380$$ 4.82843 14.4853i 0.247693 0.743079i
$$381$$ 1.31371 7.65685i 0.0673033 0.392273i
$$382$$ −2.00000 2.00000i −0.102329 0.102329i
$$383$$ −1.65685 1.65685i −0.0846613 0.0846613i 0.663508 0.748169i $$-0.269067\pi$$
−0.748169 + 0.663508i $$0.769067\pi$$
$$384$$ −0.292893 + 1.70711i −0.0149466 + 0.0871154i
$$385$$ −3.31371 6.62742i −0.168882 0.337764i
$$386$$ 16.1421i 0.821613i
$$387$$ 2.27208 + 4.75736i 0.115496 + 0.241830i
$$388$$ 9.07107 9.07107i 0.460514 0.460514i
$$389$$ 2.00000 0.101404 0.0507020 0.998714i $$-0.483854\pi$$
0.0507020 + 0.998714i $$0.483854\pi$$
$$390$$ −1.12132 3.70711i −0.0567803 0.187717i
$$391$$ 16.9706 0.858238
$$392$$ −4.46447 + 4.46447i −0.225490 + 0.225490i
$$393$$ 18.3431 12.9706i 0.925289 0.654278i
$$394$$ 5.31371i 0.267701i
$$395$$ 26.4853 + 8.82843i 1.33262 + 0.444206i
$$396$$ −4.00000 + 11.3137i −0.201008 + 0.568535i
$$397$$ −9.17157 9.17157i −0.460308 0.460308i 0.438448 0.898756i $$-0.355528\pi$$
−0.898756 + 0.438448i $$0.855528\pi$$
$$398$$ −15.6569 15.6569i −0.784807 0.784807i
$$399$$ 9.65685 + 1.65685i 0.483447 + 0.0829465i
$$400$$ 4.00000 + 3.00000i 0.200000 + 0.150000i
$$401$$ 1.79899i 0.0898373i 0.998991 + 0.0449186i $$0.0143029\pi$$
−0.998991 + 0.0449186i $$0.985697\pi$$
$$402$$ −1.17157 1.65685i −0.0584327 0.0826364i
$$403$$ −2.41421 + 2.41421i −0.120261 + 0.120261i
$$404$$ 3.17157 0.157792
$$405$$ 16.9497 10.8492i 0.842240 0.539103i
$$406$$ 4.97056 0.246685
$$407$$ 10.3431 10.3431i 0.512691 0.512691i
$$408$$ −4.24264 6.00000i −0.210042 0.297044i
$$409$$ 3.17157i 0.156824i −0.996921 0.0784121i $$-0.975015\pi$$
0.996921 0.0784121i $$-0.0249850\pi$$
$$410$$ −4.00000 + 2.00000i −0.197546 + 0.0987730i
$$411$$ −36.3848 6.24264i −1.79473 0.307927i
$$412$$ −12.4853 12.4853i −0.615106 0.615106i
$$413$$ −2.62742 2.62742i −0.129287 0.129287i
$$414$$ −4.00000 + 11.3137i −0.196589 + 0.556038i
$$415$$ −19.3137 + 9.65685i −0.948073 + 0.474036i
$$416$$ 1.00000i 0.0490290i
$$417$$ −2.34315 + 1.65685i −0.114744 + 0.0811365i
$$418$$ 19.3137 19.3137i 0.944664 0.944664i
$$419$$ 5.51472 0.269412 0.134706 0.990886i $$-0.456991\pi$$
0.134706 + 0.990886i $$0.456991\pi$$
$$420$$ −1.51472 + 2.82843i −0.0739107 + 0.138013i
$$421$$ 27.0711 1.31936 0.659682 0.751545i $$-0.270691\pi$$
0.659682 + 0.751545i $$0.270691\pi$$
$$422$$ 1.17157 1.17157i 0.0570313 0.0570313i
$$423$$ 4.10051 + 8.58579i 0.199373 + 0.417455i
$$424$$ 0.828427i 0.0402320i
$$425$$ −21.0000 + 3.00000i −1.01865 + 0.145521i
$$426$$ 4.17157 24.3137i 0.202113 1.17800i
$$427$$ 2.82843 + 2.82843i 0.136877 + 0.136877i
$$428$$ 12.0711 + 12.0711i 0.583477 + 0.583477i
$$429$$ 1.17157 6.82843i 0.0565641 0.329680i
$$430$$ 3.72792 + 1.24264i 0.179776 + 0.0599255i
$$431$$ 10.9289i 0.526428i 0.964737 + 0.263214i $$0.0847826\pi$$
−0.964737 + 0.263214i $$0.915217\pi$$
$$432$$ 5.00000 1.41421i 0.240563 0.0680414i
$$433$$ −16.3137 + 16.3137i −0.783987 + 0.783987i −0.980501 0.196514i $$-0.937038\pi$$
0.196514 + 0.980501i $$0.437038\pi$$
$$434$$ 2.82843 0.135769
$$435$$ −22.2426 + 6.72792i −1.06645 + 0.322579i
$$436$$ 4.92893 0.236053
$$437$$ 19.3137 19.3137i 0.923900 0.923900i
$$438$$ −22.1421 + 15.6569i −1.05799 + 0.748113i
$$439$$ 18.3431i 0.875471i 0.899104 + 0.437735i $$0.144219\pi$$
−0.899104 + 0.437735i $$0.855781\pi$$
$$440$$ 4.00000 + 8.00000i 0.190693 + 0.381385i
$$441$$ 17.8579 + 6.31371i 0.850374 + 0.300653i
$$442$$ 3.00000 + 3.00000i 0.142695 + 0.142695i
$$443$$ 0.899495 + 0.899495i 0.0427363 + 0.0427363i 0.728152 0.685416i $$-0.240379\pi$$
−0.685416 + 0.728152i $$0.740379\pi$$
$$444$$ −6.24264 1.07107i −0.296263 0.0508306i
$$445$$ 7.89949 23.6985i 0.374472 1.12342i
$$446$$ 13.6569i 0.646671i
$$447$$ −22.3848 31.6569i −1.05876 1.49732i
$$448$$ −0.585786 + 0.585786i −0.0276758 + 0.0276758i
$$449$$ −17.7990 −0.839986 −0.419993 0.907527i $$-0.637968\pi$$
−0.419993 + 0.907527i $$0.637968\pi$$
$$450$$ 2.94975 14.7071i 0.139052 0.693300i
$$451$$ −8.00000 −0.376705
$$452$$ −7.00000 + 7.00000i −0.329252 + 0.329252i
$$453$$ 1.07107 + 1.51472i 0.0503232 + 0.0711677i
$$454$$ 2.82843i 0.132745i
$$455$$ 0.585786 1.75736i 0.0274621 0.0823863i
$$456$$ −11.6569 2.00000i −0.545882 0.0936586i
$$457$$ −21.0711 21.0711i −0.985663 0.985663i 0.0142357 0.999899i $$-0.495468\pi$$
−0.999899 + 0.0142357i $$0.995468\pi$$
$$458$$ 12.6569 + 12.6569i 0.591416 + 0.591416i
$$459$$ −10.7574 + 19.2426i −0.502111 + 0.898170i
$$460$$ 4.00000 + 8.00000i 0.186501 + 0.373002i
$$461$$ 21.6985i 1.01060i −0.862944 0.505300i $$-0.831382\pi$$
0.862944 0.505300i $$-0.168618\pi$$
$$462$$ −4.68629 + 3.31371i −0.218026 + 0.154168i
$$463$$ 5.65685 5.65685i 0.262896 0.262896i −0.563333 0.826230i $$-0.690481\pi$$
0.826230 + 0.563333i $$0.190481\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ −12.6569 + 3.82843i −0.586948 + 0.177539i
$$466$$ 12.2426 0.567129
$$467$$ −16.8995 + 16.8995i −0.782015 + 0.782015i −0.980171 0.198155i $$-0.936505\pi$$
0.198155 + 0.980171i $$0.436505\pi$$
$$468$$ −2.70711 + 1.29289i −0.125136 + 0.0597640i
$$469$$ 0.970563i 0.0448164i
$$470$$ 6.72792 + 2.24264i 0.310336 + 0.103445i
$$471$$ −6.72792 + 39.2132i −0.310006 + 1.80685i
$$472$$ 3.17157 + 3.17157i 0.145983 + 0.145983i
$$473$$ 4.97056 + 4.97056i 0.228547 + 0.228547i
$$474$$ 3.65685 21.3137i 0.167965 0.978971i
$$475$$ −20.4853 + 27.3137i −0.939929 + 1.25324i
$$476$$ 3.51472i 0.161097i
$$477$$ 2.24264 1.07107i 0.102683 0.0490408i
$$478$$ 14.0711 14.0711i 0.643596 0.643596i
$$479$$ 24.3848 1.11417 0.557084 0.830456i $$-0.311920\pi$$
0.557084 + 0.830456i $$0.311920\pi$$
$$480$$ 1.82843 3.41421i 0.0834559 0.155837i
$$481$$ 3.65685 0.166738
$$482$$ −2.58579 + 2.58579i −0.117779 + 0.117779i
$$483$$ −4.68629 + 3.31371i −0.213234 + 0.150779i
$$484$$ 5.00000i 0.227273i
$$485$$ −25.6569 + 12.8284i −1.16502 + 0.582509i
$$486$$ −10.2929 11.7071i −0.466895 0.531045i
$$487$$ 2.92893 + 2.92893i 0.132723 + 0.132723i 0.770347 0.637625i $$-0.220083\pi$$
−0.637625 + 0.770347i $$0.720083\pi$$
$$488$$ −3.41421 3.41421i −0.154554 0.154554i
$$489$$ 5.65685 + 0.970563i 0.255812 + 0.0438904i
$$490$$ 12.6274 6.31371i 0.570449 0.285224i
$$491$$ 13.7990i 0.622740i 0.950289 + 0.311370i $$0.100788\pi$$
−0.950289 + 0.311370i $$0.899212\pi$$
$$492$$ 2.00000 + 2.82843i 0.0901670 + 0.127515i
$$493$$ 18.0000 18.0000i 0.810679 0.810679i
$$494$$ 6.82843 0.307225
$$495$$ 16.4853 21.1716i 0.740958 0.951591i
$$496$$ −3.41421 −0.153303
$$497$$ 8.34315 8.34315i 0.374241 0.374241i
$$498$$ 9.65685 + 13.6569i 0.432734 + 0.611978i
$$499$$ 8.00000i 0.358129i −0.983837 0.179065i $$-0.942693\pi$$
0.983837 0.179065i $$-0.0573071\pi$$
$$500$$ −6.36396 9.19239i −0.284605 0.411096i
$$501$$ −8.24264 1.41421i −0.368254 0.0631824i
$$502$$ −10.1421 10.1421i −0.452666 0.452666i
$$503$$ 16.1421 + 16.1421i 0.719742 + 0.719742i 0.968552 0.248810i $$-0.0800395\pi$$
−0.248810 + 0.968552i $$0.580039\pi$$
$$504$$ 2.34315 + 0.828427i 0.104372 + 0.0369011i
$$505$$ −6.72792 2.24264i −0.299389 0.0997962i
$$506$$ 16.0000i 0.711287i
$$507$$ 1.41421 1.00000i 0.0628074 0.0444116i
$$508$$ −3.17157 + 3.17157i −0.140716 + 0.140716i
$$509$$ −41.2132 −1.82674 −0.913372 0.407127i $$-0.866531\pi$$
−0.913372 + 0.407127i $$0.866531\pi$$
$$510$$ 4.75736 + 15.7279i 0.210659 + 0.696444i
$$511$$ −12.9706 −0.573784
$$512$$ 0.707107 0.707107i 0.0312500 0.0312500i
$$513$$ 9.65685 + 34.1421i 0.426361 + 1.50741i
$$514$$ 9.89949i 0.436648i
$$515$$ 17.6569 + 35.3137i 0.778054 + 1.55611i
$$516$$ 0.514719 3.00000i 0.0226592 0.132068i
$$517$$ 8.97056 + 8.97056i 0.394525 + 0.394525i
$$518$$ −2.14214 2.14214i −0.0941200 0.0941200i
$$519$$ −7.07107 + 41.2132i −0.310385 + 1.80906i
$$520$$ −0.707107 + 2.12132i −0.0310087 + 0.0930261i
$$521$$ 24.9706i 1.09398i 0.837139 + 0.546990i $$0.184226\pi$$
−0.837139 + 0.546990i $$0.815774\pi$$
$$522$$ 7.75736 + 16.2426i 0.339530 + 0.710921i
$$523$$ −6.07107 + 6.07107i −0.265469 + 0.265469i −0.827272 0.561802i $$-0.810108\pi$$
0.561802 + 0.827272i $$0.310108\pi$$
$$524$$ −12.9706 −0.566622
$$525$$ 5.21320 4.92893i 0.227523 0.215116i
$$526$$ −22.6274 −0.986602
$$527$$ 10.2426 10.2426i 0.446176 0.446176i
$$528$$ 5.65685 4.00000i 0.246183 0.174078i
$$529$$ 7.00000i 0.304348i
$$530$$ 0.585786 1.75736i 0.0254449 0.0763348i
$$531$$ 4.48528 12.6863i 0.194645 0.550538i
$$532$$ −4.00000 4.00000i −0.173422 0.173422i
$$533$$ −1.41421 1.41421i −0.0612564 0.0612564i
$$534$$ −19.0711 3.27208i −0.825286 0.141597i
$$535$$ −17.0711 34.1421i −0.738047 1.47609i
$$536$$ 1.17157i 0.0506042i
$$537$$ 17.6569 + 24.9706i 0.761950 + 1.07756i
$$538$$ −10.7279 + 10.7279i −0.462514 + 0.462514i
$$539$$ 25.2548 1.08780
$$540$$ −11.6066 0.535534i −0.499469 0.0230457i
$$541$$ −4.24264 −0.182405 −0.0912027 0.995832i $$-0.529071\pi$$
−0.0912027 + 0.995832i $$0.529071\pi$$
$$542$$ −1.58579 + 1.58579i −0.0681154 + 0.0681154i
$$543$$ 6.00000 + 8.48528i 0.257485 + 0.364138i
$$544$$ 4.24264i 0.181902i
$$545$$ −10.4558 3.48528i −0.447879 0.149293i
$$546$$ −1.41421 0.242641i −0.0605228 0.0103841i
$$547$$ −20.4142 20.4142i −0.872849 0.872849i 0.119933 0.992782i $$-0.461732\pi$$
−0.992782 + 0.119933i $$0.961732\pi$$
$$548$$ 15.0711 + 15.0711i 0.643804 + 0.643804i
$$549$$ −4.82843 + 13.6569i −0.206072 + 0.582860i
$$550$$ −2.82843 19.7990i −0.120605 0.844232i
$$551$$ 40.9706i 1.74540i
$$552$$ 5.65685 4.00000i 0.240772 0.170251i
$$553$$ 7.31371 7.31371i 0.311011 0.311011i
$$554$$ −22.4853 −0.955308
$$555$$ 12.4853 + 6.68629i 0.529971 + 0.283817i
$$556$$ 1.65685 0.0702663
$$557$$ −0.928932 + 0.928932i −0.0393601 + 0.0393601i −0.726513 0.687153i $$-0.758860\pi$$
0.687153 + 0.726513i $$0.258860\pi$$
$$558$$ 4.41421 + 9.24264i 0.186869 + 0.391272i
$$559$$ 1.75736i 0.0743284i
$$560$$ 1.65685 0.828427i 0.0700149 0.0350074i
$$561$$ −4.97056 + 28.9706i −0.209857 + 1.22314i
$$562$$ 0.585786 + 0.585786i 0.0247099 + 0.0247099i
$$563$$ 19.2426 + 19.2426i 0.810981 + 0.810981i 0.984781 0.173800i $$-0.0556047\pi$$
−0.173800 + 0.984781i $$0.555605\pi$$
$$564$$ 0.928932 5.41421i 0.0391151 0.227980i
$$565$$ 19.7990 9.89949i 0.832950 0.416475i
$$566$$ 24.3848i 1.02497i
$$567$$ −0.786797 7.41421i −0.0330423 0.311368i
$$568$$ −10.0711 + 10.0711i −0.422573 + 0.422573i
$$569$$ 18.3431 0.768985 0.384492 0.923128i $$-0.374377\pi$$
0.384492 + 0.923128i $$0.374377\pi$$
$$570$$ 23.3137 + 12.4853i 0.976504 + 0.522951i
$$571$$ 34.4853 1.44316 0.721582 0.692329i $$-0.243415\pi$$
0.721582 + 0.692329i $$0.243415\pi$$
$$572$$ −2.82843 + 2.82843i −0.118262 + 0.118262i
$$573$$ 4.00000 2.82843i 0.167102 0.118159i
$$574$$ 1.65685i 0.0691558i
$$575$$ −2.82843 19.7990i −0.117954 0.825675i
$$576$$ −2.82843 1.00000i −0.117851 0.0416667i
$$577$$ −16.0416 16.0416i −0.667822 0.667822i 0.289390 0.957211i $$-0.406548\pi$$
−0.957211 + 0.289390i $$0.906548\pi$$
$$578$$ −0.707107 0.707107i −0.0294118 0.0294118i
$$579$$ 27.5563 + 4.72792i 1.14520 + 0.196486i
$$580$$ 12.7279 + 4.24264i 0.528498 + 0.176166i
$$581$$ 8.00000i 0.331896i
$$582$$ 12.8284 + 18.1421i 0.531755 + 0.752016i
$$583$$ 2.34315 2.34315i 0.0970432 0.0970432i
$$584$$ 15.6569 0.647885
$$585$$ 6.65685 0.828427i 0.275227 0.0342512i
$$586$$ 6.34315 0.262033
$$587$$ 7.79899 7.79899i 0.321899 0.321899i −0.527596 0.849495i $$-0.676907\pi$$
0.849495 + 0.527596i $$0.176907\pi$$
$$588$$ −6.31371 8.92893i −0.260373 0.368223i
$$589$$ 23.3137i 0.960625i
$$590$$ −4.48528 8.97056i −0.184656 0.369312i
$$591$$ −9.07107 1.55635i −0.373134 0.0640197i
$$592$$ 2.58579 + 2.58579i 0.106275 + 0.106275i
$$593$$ −7.41421 7.41421i −0.304465 0.304465i 0.538293 0.842758i $$-0.319069\pi$$
−0.842758 + 0.538293i $$0.819069\pi$$
$$594$$ −18.1421 10.1421i −0.744381 0.416137i
$$595$$ −2.48528 + 7.45584i −0.101887 + 0.305660i
$$596$$ 22.3848i 0.916916i
$$597$$ 31.3137 22.1421i 1.28158 0.906217i
$$598$$ −2.82843 + 2.82843i −0.115663 + 0.115663i
$$599$$ −16.4853 −0.673570 −0.336785 0.941582i $$-0.609340\pi$$
−0.336785 + 0.941582i $$0.609340\pi$$
$$600$$ −6.29289 + 5.94975i −0.256906 + 0.242897i
$$601$$ −17.6569 −0.720238 −0.360119 0.932906i $$-0.617264\pi$$
−0.360119 + 0.932906i $$0.617264\pi$$
$$602$$ 1.02944 1.02944i 0.0419567 0.0419567i
$$603$$ 3.17157 1.51472i 0.129156 0.0616841i
$$604$$ 1.07107i 0.0435811i
$$605$$ 3.53553 10.6066i 0.143740 0.431220i
$$606$$ −0.928932 + 5.41421i −0.0377353 + 0.219937i
$$607$$ 14.4853 + 14.4853i 0.587939 + 0.587939i 0.937073 0.349134i $$-0.113524\pi$$
−0.349134 + 0.937073i $$0.613524\pi$$
$$608$$ 4.82843 + 4.82843i 0.195819 + 0.195819i
$$609$$ −1.45584 + 8.48528i −0.0589938 + 0.343841i
$$610$$ 4.82843 + 9.65685i 0.195497 + 0.390995i
$$611$$ 3.17157i 0.128308i
$$612$$ 11.4853 5.48528i 0.464265 0.221729i
$$613$$ 10.3431 10.3431i 0.417756 0.417756i −0.466674 0.884430i $$-0.654548\pi$$
0.884430 + 0.466674i $$0.154548\pi$$
$$614$$ 10.1421 0.409303
$$615$$ −2.24264 7.41421i −0.0904320 0.298970i
$$616$$ 3.31371 0.133513
$$617$$ 10.9289 10.9289i 0.439982 0.439982i −0.452024 0.892006i $$-0.649298\pi$$
0.892006 + 0.452024i $$0.149298\pi$$
$$618$$ 24.9706 17.6569i 1.00446 0.710263i
$$619$$ 26.6274i 1.07025i 0.844774 + 0.535123i $$0.179735\pi$$
−0.844774 + 0.535123i $$0.820265\pi$$
$$620$$ 7.24264 + 2.41421i 0.290871 + 0.0969571i
$$621$$ −18.1421 10.1421i −0.728019 0.406990i
$$622$$ −19.7990 19.7990i −0.793867 0.793867i
$$623$$ −6.54416 6.54416i −0.262186 0.262186i
$$624$$ 1.70711 + 0.292893i 0.0683390 + 0.0117251i
$$625$$ 7.00000 + 24.0000i 0.280000 + 0.960000i
$$626$$ 1.89949i 0.0759191i
$$627$$ 27.3137 + 38.6274i 1.09080 + 1.54263i
$$628$$ 16.2426 16.2426i 0.648152 0.648152i
$$629$$ −15.5147 −0.618612
$$630$$ −4.38478 3.41421i −0.174694 0.136026i
$$631$$ 23.8995 0.951424 0.475712 0.879601i $$-0.342190\pi$$
0.475712 + 0.879601i $$0.342190\pi$$
$$632$$ −8.82843 + 8.82843i −0.351176 + 0.351176i
$$633$$ 1.65685 + 2.34315i 0.0658540 + 0.0931317i
$$634$$ 2.34315i 0.0930582i
$$635$$ 8.97056 4.48528i 0.355986 0.177993i
$$636$$ −1.41421 0.242641i −0.0560772 0.00962133i
$$637$$ 4.46447 + 4.46447i 0.176889 + 0.176889i
$$638$$ 16.9706 + 16.9706i 0.671871 + 0.671871i
$$639$$ 40.2843 + 14.2426i 1.59362 + 0.563430i
$$640$$ −2.00000 + 1.00000i −0.0790569 + 0.0395285i
$$641$$ 10.6863i 0.422083i 0.977477 + 0.211042i $$0.0676855\pi$$
−0.977477 + 0.211042i $$0.932314\pi$$
$$642$$ −24.1421 + 17.0711i −0.952814 + 0.673741i
$$643$$ 22.1421 22.1421i 0.873201 0.873201i −0.119619 0.992820i $$-0.538167\pi$$
0.992820 + 0.119619i $$0.0381674\pi$$
$$644$$ 3.31371 0.130578
$$645$$ −3.21320 + 6.00000i −0.126520 + 0.236250i
$$646$$ −28.9706 −1.13983
$$647$$ −29.3137 + 29.3137i −1.15244 + 1.15244i −0.166379 + 0.986062i $$0.553207\pi$$
−0.986062 + 0.166379i $$0.946793\pi$$
$$648$$ 0.949747 + 8.94975i 0.0373096 + 0.351579i
$$649$$ 17.9411i 0.704251i
$$650$$ 3.00000 4.00000i 0.117670 0.156893i
$$651$$ −0.828427 + 4.82843i −0.0324686 + 0.189241i
$$652$$ −2.34315 2.34315i −0.0917647 0.0917647i
$$653$$ 4.24264 + 4.24264i 0.166027 + 0.166027i 0.785231 0.619203i $$-0.212544\pi$$
−0.619203 + 0.785231i $$0.712544\pi$$
$$654$$ −1.44365 + 8.41421i −0.0564512 + 0.329022i
$$655$$ 27.5147 + 9.17157i 1.07509 + 0.358363i
$$656$$ 2.00000i 0.0780869i
$$657$$ −20.2426 42.3848i −0.789741 1.65359i
$$658$$ 1.85786 1.85786i 0.0724271 0.0724271i
$$659$$ 25.5147 0.993912 0.496956 0.867776i $$-0.334451\pi$$
0.496956 + 0.867776i $$0.334451\pi$$
$$660$$ −14.8284 + 4.48528i −0.577196 + 0.174589i
$$661$$ 48.5269 1.88748 0.943739 0.330691i $$-0.107282\pi$$
0.943739 + 0.330691i $$0.107282\pi$$
$$662$$ −22.8284 + 22.8284i −0.887252 + 0.887252i
$$663$$ −6.00000 + 4.24264i −0.233021 + 0.164771i
$$664$$ 9.65685i 0.374759i
$$665$$ 5.65685 + 11.3137i 0.219363 + 0.438727i
$$666$$ 3.65685 10.3431i 0.141700 0.400789i
$$667$$ 16.9706 + 16.9706i 0.657103 + 0.657103i
$$668$$ 3.41421 + 3.41421i 0.132100 + 0.132100i
$$669$$ −23.3137 4.00000i −0.901360 0.154649i
$$670$$ 0.828427 2.48528i 0.0320049 0.0960148i
$$671$$ 19.3137i 0.745597i
$$672$$ −0.828427 1.17157i −0.0319573 0.0451944i
$$673$$ −2.85786 + 2.85786i −0.110163 + 0.110163i −0.760039 0.649877i $$-0.774820\pi$$
0.649877 + 0.760039i $$0.274820\pi$$
$$674$$ −32.5269 −1.25289
$$675$$ 24.2426 + 9.34315i 0.933100 + 0.359618i
$$676$$ −1.00000 −0.0384615
$$677$$ −10.3848 + 10.3848i −0.399119 + 0.399119i −0.877922 0.478803i $$-0.841071\pi$$
0.478803 + 0.877922i $$0.341071\pi$$
$$678$$ −9.89949 14.0000i −0.380188 0.537667i
$$679$$ 10.6274i 0.407843i
$$680$$ 3.00000 9.00000i 0.115045 0.345134i
$$681$$ −4.82843 0.828427i −0.185026 0.0317454i
$$682$$ 9.65685 + 9.65685i 0.369780 + 0.369780i
$$683$$ −8.82843 8.82843i −0.337810 0.337810i 0.517732 0.855543i $$-0.326776\pi$$
−0.855543 + 0.517732i $$0.826776\pi$$
$$684$$ 6.82843 19.3137i 0.261091 0.738478i
$$685$$ −21.3137 42.6274i −0.814355 1.62871i
$$686$$ 11.0294i 0.421106i
$$687$$ −25.3137 + 17.8995i −0.965778 + 0.682908i
$$688$$ −1.24264 + 1.24264i −0.0473752 + 0.0473752i
$$689$$ 0.828427 0.0315606
$$690$$ −14.8284 + 4.48528i −0.564509 + 0.170752i
$$691$$ −37.6569 −1.43253 −0.716267 0.697826i $$-0.754151\pi$$
−0.716267 + 0.697826i $$0.754151\pi$$
$$692$$ 17.0711 17.0711i 0.648945 0.648945i
$$693$$ −4.28427 8.97056i −0.162746 0.340764i
$$694$$ 14.9289i 0.566695i
$$695$$ −3.51472 1.17157i −0.133321 0.0444403i
$$696$$ 1.75736 10.2426i 0.0666125 0.388246i
$$697$$ 6.00000 + 6.00000i 0.227266 + 0.227266i
$$698$$ 23.1421 + 23.1421i 0.875943 + 0.875943i
$$699$$ −3.58579 + 20.8995i −0.135627 + 0.790491i
$$700$$ −4.10051 + 0.585786i −0.154985 + 0.0221406i
$$701$$ 35.4558i 1.33915i −0.742745 0.669574i $$-0.766477\pi$$
0.742745 0.669574i $$-0.233523\pi$$
$$702$$ −1.41421 5.00000i −0.0533761 0.188713i
$$703$$ −17.6569 + 17.6569i −0.665941 + 0.665941i
$$704$$ −4.00000 −0.150756
$$705$$ −5.79899 + 10.8284i −0.218403 + 0.407822i
$$706$$ −36.1421 −1.36023
$$707$$ −1.85786 + 1.85786i −0.0698722 + 0.0698722i
$$708$$ −6.34315 + 4.48528i −0.238390 + 0.168567i
$$709$$ 3.27208i 0.122885i 0.998111 + 0.0614427i $$0.0195702\pi$$
−0.998111 + 0.0614427i $$0.980430\pi$$
$$710$$ 28.4853 14.2426i 1.06903 0.534517i
$$711$$ 35.3137 + 12.4853i 1.32437 + 0.468235i
$$712$$ 7.89949 + 7.89949i 0.296046 + 0.296046i
$$713$$ 9.65685 + 9.65685i 0.361652 + 0.361652i
$$714$$ 6.00000 + 1.02944i 0.224544 + 0.0385257i
$$715$$ 8.00000 4.00000i 0.299183 0.149592i
$$716$$ 17.6569i 0.659868i
$$717$$ 19.8995 + 28.1421i 0.743160 + 1.05099i
$$718$$ −16.5563 + 16.5563i −0.617877 + 0.617877i
$$719$$ −12.4853 −0.465622 −0.232811 0.972522i $$-0.574792\pi$$
−0.232811 + 0.972522i $$0.574792\pi$$
$$720$$ 5.29289 + 4.12132i 0.197254 + 0.153593i
$$721$$ 14.6274 0.544753
$$722$$ −19.5355 + 19.5355i −0.727037 + 0.727037i
$$723$$ −3.65685 5.17157i −0.136000 0.192333i
$$724$$ 6.00000i 0.222988i
$$725$$ −24.0000 18.0000i −0.891338 0.668503i
$$726$$ −8.53553 1.46447i −0.316783 0.0543514i
$$727$$ −25.3137 25.3137i −0.938833 0.938833i 0.0594007 0.998234i $$-0.481081\pi$$
−0.998234 + 0.0594007i $$0.981081\pi$$
$$728$$ 0.585786 + 0.585786i 0.0217107 + 0.0217107i
$$729$$ 23.0000 14.1421i 0.851852 0.523783i
$$730$$ −33.2132 11.0711i −1.22928 0.409759i
$$731$$ 7.45584i 0.275764i
$$732$$ 6.82843 4.82843i 0.252386 0.178464i
$$733$$ −15.5563 + 15.5563i −0.574587 + 0.574587i −0.933407 0.358820i $$-0.883179\pi$$
0.358820 + 0.933407i $$0.383179\pi$$
$$734$$ 20.0000 0.738213
$$735$$ 7.07969 + 23.4056i 0.261138 + 0.863328i
$$736$$ −4.00000 −0.147442
$$737$$ 3.31371 3.31371i 0.122062 0.122062i
$$738$$ −5.41421 + 2.58579i −0.199300 + 0.0951841i
$$739$$ 10.1421i 0.373084i −0.982447 0.186542i $$-0.940272\pi$$
0.982447 0.186542i $$-0.0597281\pi$$
$$740$$ −3.65685 7.31371i −0.134429 0.268857i
$$741$$ −2.00000 + 11.6569i −0.0734718 + 0.428225i
$$742$$ −0.485281 0.485281i −0.0178152 0.0178152i
$$743$$ −10.6274 10.6274i −0.389882 0.389882i 0.484763 0.874645i $$-0.338906\pi$$
−0.874645 + 0.484763i $$0.838906\pi$$
$$744$$ 1.00000 5.82843i 0.0366618 0.213681i
$$745$$ 15.8284 47.4853i 0.579909 1.73973i
$$746$$ 6.97056i 0.255210i
$$747$$ −26.1421 + 12.4853i −0.956491 + 0.456813i
$$748$$ 12.0000 12.0000i 0.438763 0.438763i
$$749$$ −14.1421 −0.516742
$$750$$ 17.5563 8.17157i 0.641067 0.298384i
$$751$$ 36.2843 1.32403 0.662016 0.749490i $$-0.269701\pi$$
0.662016 + 0.749490i $$0.269701\pi$$
$$752$$ −2.24264 + 2.24264i −0.0817807 + 0.0817807i
$$753$$ 20.2843 14.3431i 0.739200 0.522693i
$$754$$ 6.00000i 0.218507i
$$755$$ −0.757359 + 2.27208i −0.0275631 + 0.0826894i
$$756$$ −2.10051 + 3.75736i −0.0763946 + 0.136654i
$$757$$ 3.41421 + 3.41421i 0.124092 + 0.124092i 0.766425 0.642334i $$-0.222034\pi$$
−0.642334 + 0.766425i $$0.722034\pi$$
$$758$$ −26.9706 26.9706i −0.979615 0.979615i
$$759$$ −27.3137 4.68629i −0.991425 0.170102i
$$760$$ −6.82843 13.6569i −0.247693 0.495386i
$$761$$ 26.4853i 0.960091i 0.877244 + 0.480045i $$0.159380\pi$$
−0.877244 + 0.480045i $$0.840620\pi$$
$$762$$ −4.48528 6.34315i −0.162485 0.229788i
$$763$$ −2.88730 + 2.88730i −0.104527 + 0.104527i
$$764$$ −2.82843 −0.102329
$$765$$ −28.2426 + 3.51472i −1.02111 + 0.127075i
$$766$$ −2.34315 −0.0846613
$$767$$ 3.17157 3.17157i 0.114519 0.114519i
$$768$$ 1.00000 + 1.41421i 0.0360844 + 0.0510310i
$$769$$ 8.62742i 0.311113i 0.987827 + 0.155556i $$0.0497170\pi$$
−0.987827 + 0.155556i $$0.950283\pi$$
$$770$$ −7.02944 2.34315i −0.253323 0.0844411i
$$771$$ −16.8995 2.89949i −0.608620 0.104423i
$$772$$ −11.4142 11.4142i −0.410807 0.410807i
$$773$$ 16.2426 + 16.2426i 0.584207