Properties

 Label 1110.2.x.d.751.2 Level $1110$ Weight $2$ Character 1110.751 Analytic conductor $8.863$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.x (of order $$6$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$8.86339462436$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 751.2 Root $$-0.535537i$$ of defining polynomial Character $$\chi$$ $$=$$ 1110.751 Dual form 1110.2.x.d.841.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-0.267768 + 0.463788i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-0.267768 + 0.463788i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +5.44426 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.556002 + 0.321008i) q^{13} -0.535537i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.402237 + 0.232232i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-7.12118 - 4.11142i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.267768 - 0.463788i) q^{21} +(-4.71487 + 2.72213i) q^{22} -2.37407i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -0.642016 q^{26} +1.00000 q^{27} +(0.267768 + 0.463788i) q^{28} -5.38430i q^{29} +(-0.500000 + 0.866025i) q^{30} +1.32755i q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.72213 + 4.71487i) q^{33} +(0.232232 - 0.402237i) q^{34} +(0.463788 - 0.267768i) q^{35} -1.00000 q^{36} +(6.01205 + 0.924822i) q^{37} +8.22283 q^{38} +(-0.556002 + 0.321008i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.86520 - 8.42677i) q^{41} +(0.463788 + 0.267768i) q^{42} +1.04652i q^{43} +(2.72213 - 4.71487i) q^{44} +1.00000i q^{45} +(1.18703 + 2.05600i) q^{46} +8.14127 q^{47} +1.00000 q^{48} +(3.35660 + 5.81380i) q^{49} +(-0.866025 - 0.500000i) q^{50} -0.464463i q^{51} +(0.556002 - 0.321008i) q^{52} +(2.89110 + 5.00753i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-4.71487 - 2.72213i) q^{55} +(-0.463788 - 0.267768i) q^{56} +(7.12118 - 4.11142i) q^{57} +(2.69215 + 4.66294i) q^{58} +(10.2224 - 5.90190i) q^{59} -1.00000i q^{60} +(2.55109 + 1.47287i) q^{61} +(-0.663773 - 1.14969i) q^{62} +0.535537 q^{63} -1.00000 q^{64} +(-0.321008 - 0.556002i) q^{65} -5.44426i q^{66} +(-2.04849 + 3.54808i) q^{67} +0.464463i q^{68} +(2.05600 + 1.18703i) q^{69} +(-0.267768 + 0.463788i) q^{70} +(2.17408 - 3.76562i) q^{71} +(0.866025 - 0.500000i) q^{72} -1.60237 q^{73} +(-5.66900 + 2.20510i) q^{74} -1.00000 q^{75} +(-7.12118 + 4.11142i) q^{76} +(-1.45780 + 2.52499i) q^{77} +(0.321008 - 0.556002i) q^{78} +(-3.48536 - 2.01228i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +9.73039i q^{82} +(3.61426 + 6.26008i) q^{83} -0.535537 q^{84} +0.464463 q^{85} +(-0.523261 - 0.906314i) q^{86} +(4.66294 + 2.69215i) q^{87} +5.44426i q^{88} +(3.69105 - 2.13103i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-0.297759 + 0.171911i) q^{91} +(-2.05600 - 1.18703i) q^{92} +(-1.14969 - 0.663773i) q^{93} +(-7.05055 + 4.07063i) q^{94} +(4.11142 + 7.12118i) q^{95} +(-0.866025 + 0.500000i) q^{96} -5.43955i q^{97} +(-5.81380 - 3.35660i) q^{98} +(-2.72213 - 4.71487i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10})$$ $$16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$$.

 $$n$$ $$371$$ $$631$$ $$667$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ −0.866025 0.500000i −0.387298 0.223607i
$$6$$ 1.00000i 0.408248i
$$7$$ −0.267768 + 0.463788i −0.101207 + 0.175295i −0.912182 0.409785i $$-0.865604\pi$$
0.810975 + 0.585080i $$0.198937\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 1.00000 0.316228
$$11$$ 5.44426 1.64151 0.820754 0.571282i $$-0.193554\pi$$
0.820754 + 0.571282i $$0.193554\pi$$
$$12$$ 0.500000 + 0.866025i 0.144338 + 0.250000i
$$13$$ 0.556002 + 0.321008i 0.154207 + 0.0890316i 0.575118 0.818070i $$-0.304956\pi$$
−0.420911 + 0.907102i $$0.638289\pi$$
$$14$$ 0.535537i 0.143128i
$$15$$ 0.866025 0.500000i 0.223607 0.129099i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −0.402237 + 0.232232i −0.0975568 + 0.0563245i −0.547985 0.836488i $$-0.684605\pi$$
0.450428 + 0.892813i $$0.351271\pi$$
$$18$$ 0.866025 + 0.500000i 0.204124 + 0.117851i
$$19$$ −7.12118 4.11142i −1.63371 0.943224i −0.982935 0.183955i $$-0.941110\pi$$
−0.650777 0.759269i $$-0.725557\pi$$
$$20$$ −0.866025 + 0.500000i −0.193649 + 0.111803i
$$21$$ −0.267768 0.463788i −0.0584318 0.101207i
$$22$$ −4.71487 + 2.72213i −1.00521 + 0.580360i
$$23$$ 2.37407i 0.495027i −0.968884 0.247514i $$-0.920387\pi$$
0.968884 0.247514i $$-0.0796135\pi$$
$$24$$ −0.866025 0.500000i −0.176777 0.102062i
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ −0.642016 −0.125910
$$27$$ 1.00000 0.192450
$$28$$ 0.267768 + 0.463788i 0.0506034 + 0.0876477i
$$29$$ 5.38430i 0.999840i −0.866072 0.499920i $$-0.833363\pi$$
0.866072 0.499920i $$-0.166637\pi$$
$$30$$ −0.500000 + 0.866025i −0.0912871 + 0.158114i
$$31$$ 1.32755i 0.238434i 0.992868 + 0.119217i $$0.0380385\pi$$
−0.992868 + 0.119217i $$0.961962\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ −2.72213 + 4.71487i −0.473862 + 0.820754i
$$34$$ 0.232232 0.402237i 0.0398274 0.0689831i
$$35$$ 0.463788 0.267768i 0.0783945 0.0452611i
$$36$$ −1.00000 −0.166667
$$37$$ 6.01205 + 0.924822i 0.988374 + 0.152040i
$$38$$ 8.22283 1.33392
$$39$$ −0.556002 + 0.321008i −0.0890316 + 0.0514024i
$$40$$ 0.500000 0.866025i 0.0790569 0.136931i
$$41$$ 4.86520 8.42677i 0.759816 1.31604i −0.183128 0.983089i $$-0.558622\pi$$
0.942944 0.332951i $$-0.108044\pi$$
$$42$$ 0.463788 + 0.267768i 0.0715641 + 0.0413175i
$$43$$ 1.04652i 0.159593i 0.996811 + 0.0797965i $$0.0254270\pi$$
−0.996811 + 0.0797965i $$0.974573\pi$$
$$44$$ 2.72213 4.71487i 0.410377 0.710793i
$$45$$ 1.00000i 0.149071i
$$46$$ 1.18703 + 2.05600i 0.175019 + 0.303141i
$$47$$ 8.14127 1.18753 0.593763 0.804640i $$-0.297642\pi$$
0.593763 + 0.804640i $$0.297642\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 3.35660 + 5.81380i 0.479514 + 0.830543i
$$50$$ −0.866025 0.500000i −0.122474 0.0707107i
$$51$$ 0.464463i 0.0650379i
$$52$$ 0.556002 0.321008i 0.0771036 0.0445158i
$$53$$ 2.89110 + 5.00753i 0.397123 + 0.687837i 0.993370 0.114964i $$-0.0366753\pi$$
−0.596247 + 0.802801i $$0.703342\pi$$
$$54$$ −0.866025 + 0.500000i −0.117851 + 0.0680414i
$$55$$ −4.71487 2.72213i −0.635753 0.367052i
$$56$$ −0.463788 0.267768i −0.0619763 0.0357820i
$$57$$ 7.12118 4.11142i 0.943224 0.544571i
$$58$$ 2.69215 + 4.66294i 0.353497 + 0.612275i
$$59$$ 10.2224 5.90190i 1.33084 0.768362i 0.345414 0.938450i $$-0.387739\pi$$
0.985429 + 0.170088i $$0.0544052\pi$$
$$60$$ 1.00000i 0.129099i
$$61$$ 2.55109 + 1.47287i 0.326633 + 0.188582i 0.654345 0.756196i $$-0.272944\pi$$
−0.327712 + 0.944778i $$0.606278\pi$$
$$62$$ −0.663773 1.14969i −0.0842992 0.146011i
$$63$$ 0.535537 0.0674713
$$64$$ −1.00000 −0.125000
$$65$$ −0.321008 0.556002i −0.0398161 0.0689636i
$$66$$ 5.44426i 0.670142i
$$67$$ −2.04849 + 3.54808i −0.250263 + 0.433468i −0.963598 0.267355i $$-0.913850\pi$$
0.713335 + 0.700823i $$0.247184\pi$$
$$68$$ 0.464463i 0.0563245i
$$69$$ 2.05600 + 1.18703i 0.247514 + 0.142902i
$$70$$ −0.267768 + 0.463788i −0.0320044 + 0.0554333i
$$71$$ 2.17408 3.76562i 0.258016 0.446897i −0.707694 0.706519i $$-0.750265\pi$$
0.965710 + 0.259622i $$0.0835979\pi$$
$$72$$ 0.866025 0.500000i 0.102062 0.0589256i
$$73$$ −1.60237 −0.187543 −0.0937716 0.995594i $$-0.529892\pi$$
−0.0937716 + 0.995594i $$0.529892\pi$$
$$74$$ −5.66900 + 2.20510i −0.659007 + 0.256338i
$$75$$ −1.00000 −0.115470
$$76$$ −7.12118 + 4.11142i −0.816856 + 0.471612i
$$77$$ −1.45780 + 2.52499i −0.166132 + 0.287749i
$$78$$ 0.321008 0.556002i 0.0363470 0.0629548i
$$79$$ −3.48536 2.01228i −0.392134 0.226399i 0.290950 0.956738i $$-0.406029\pi$$
−0.683084 + 0.730339i $$0.739362\pi$$
$$80$$ 1.00000i 0.111803i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 9.73039i 1.07454i
$$83$$ 3.61426 + 6.26008i 0.396716 + 0.687133i 0.993319 0.115404i $$-0.0368164\pi$$
−0.596602 + 0.802537i $$0.703483\pi$$
$$84$$ −0.535537 −0.0584318
$$85$$ 0.464463 0.0503781
$$86$$ −0.523261 0.906314i −0.0564246 0.0977303i
$$87$$ 4.66294 + 2.69215i 0.499920 + 0.288629i
$$88$$ 5.44426i 0.580360i
$$89$$ 3.69105 2.13103i 0.391251 0.225889i −0.291451 0.956586i $$-0.594138\pi$$
0.682702 + 0.730697i $$0.260805\pi$$
$$90$$ −0.500000 0.866025i −0.0527046 0.0912871i
$$91$$ −0.297759 + 0.171911i −0.0312137 + 0.0180212i
$$92$$ −2.05600 1.18703i −0.214353 0.123757i
$$93$$ −1.14969 0.663773i −0.119217 0.0688300i
$$94$$ −7.05055 + 4.07063i −0.727208 + 0.419854i
$$95$$ 4.11142 + 7.12118i 0.421823 + 0.730618i
$$96$$ −0.866025 + 0.500000i −0.0883883 + 0.0510310i
$$97$$ 5.43955i 0.552303i −0.961114 0.276151i $$-0.910941\pi$$
0.961114 0.276151i $$-0.0890591\pi$$
$$98$$ −5.81380 3.35660i −0.587283 0.339068i
$$99$$ −2.72213 4.71487i −0.273585 0.473862i
$$100$$ 1.00000 0.100000
$$101$$ 9.15512 0.910969 0.455484 0.890244i $$-0.349466\pi$$
0.455484 + 0.890244i $$0.349466\pi$$
$$102$$ 0.232232 + 0.402237i 0.0229944 + 0.0398274i
$$103$$ 10.5315i 1.03770i −0.854865 0.518850i $$-0.826360\pi$$
0.854865 0.518850i $$-0.173640\pi$$
$$104$$ −0.321008 + 0.556002i −0.0314774 + 0.0545205i
$$105$$ 0.535537i 0.0522630i
$$106$$ −5.00753 2.89110i −0.486374 0.280808i
$$107$$ −7.54260 + 13.0642i −0.729170 + 1.26296i 0.228064 + 0.973646i $$0.426760\pi$$
−0.957234 + 0.289314i $$0.906573\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ 3.84093 2.21756i 0.367894 0.212404i −0.304644 0.952466i $$-0.598537\pi$$
0.672538 + 0.740063i $$0.265204\pi$$
$$110$$ 5.44426 0.519090
$$111$$ −3.80694 + 4.74417i −0.361339 + 0.450297i
$$112$$ 0.535537 0.0506034
$$113$$ 7.78200 4.49294i 0.732069 0.422660i −0.0871097 0.996199i $$-0.527763\pi$$
0.819179 + 0.573539i $$0.194430\pi$$
$$114$$ −4.11142 + 7.12118i −0.385070 + 0.666960i
$$115$$ −1.18703 + 2.05600i −0.110691 + 0.191723i
$$116$$ −4.66294 2.69215i −0.432944 0.249960i
$$117$$ 0.642016i 0.0593544i
$$118$$ −5.90190 + 10.2224i −0.543314 + 0.941048i
$$119$$ 0.248737i 0.0228017i
$$120$$ 0.500000 + 0.866025i 0.0456435 + 0.0790569i
$$121$$ 18.6400 1.69455
$$122$$ −2.94574 −0.266695
$$123$$ 4.86520 + 8.42677i 0.438680 + 0.759816i
$$124$$ 1.14969 + 0.663773i 0.103245 + 0.0596086i
$$125$$ 1.00000i 0.0894427i
$$126$$ −0.463788 + 0.267768i −0.0413175 + 0.0238547i
$$127$$ 5.95507 + 10.3145i 0.528427 + 0.915262i 0.999451 + 0.0331415i $$0.0105512\pi$$
−0.471024 + 0.882120i $$0.656115\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ −0.906314 0.523261i −0.0797965 0.0460705i
$$130$$ 0.556002 + 0.321008i 0.0487646 + 0.0281543i
$$131$$ 7.32391 4.22846i 0.639893 0.369442i −0.144680 0.989478i $$-0.546215\pi$$
0.784573 + 0.620036i $$0.212882\pi$$
$$132$$ 2.72213 + 4.71487i 0.236931 + 0.410377i
$$133$$ 3.81365 2.20181i 0.330686 0.190922i
$$134$$ 4.09698i 0.353925i
$$135$$ −0.866025 0.500000i −0.0745356 0.0430331i
$$136$$ −0.232232 0.402237i −0.0199137 0.0344916i
$$137$$ 19.7950 1.69120 0.845599 0.533818i $$-0.179243\pi$$
0.845599 + 0.533818i $$0.179243\pi$$
$$138$$ −2.37407 −0.202094
$$139$$ −3.66567 6.34913i −0.310918 0.538526i 0.667643 0.744481i $$-0.267303\pi$$
−0.978561 + 0.205955i $$0.933970\pi$$
$$140$$ 0.535537i 0.0452611i
$$141$$ −4.07063 + 7.05055i −0.342809 + 0.593763i
$$142$$ 4.34816i 0.364890i
$$143$$ 3.02702 + 1.74765i 0.253132 + 0.146146i
$$144$$ −0.500000 + 0.866025i −0.0416667 + 0.0721688i
$$145$$ −2.69215 + 4.66294i −0.223571 + 0.387236i
$$146$$ 1.38769 0.801185i 0.114846 0.0663065i
$$147$$ −6.71320 −0.553695
$$148$$ 3.80694 4.74417i 0.312929 0.389969i
$$149$$ −8.22737 −0.674012 −0.337006 0.941502i $$-0.609414\pi$$
−0.337006 + 0.941502i $$0.609414\pi$$
$$150$$ 0.866025 0.500000i 0.0707107 0.0408248i
$$151$$ −4.98628 + 8.63648i −0.405777 + 0.702827i −0.994412 0.105572i $$-0.966333\pi$$
0.588634 + 0.808400i $$0.299666\pi$$
$$152$$ 4.11142 7.12118i 0.333480 0.577604i
$$153$$ 0.402237 + 0.232232i 0.0325189 + 0.0187748i
$$154$$ 2.91560i 0.234946i
$$155$$ 0.663773 1.14969i 0.0533155 0.0923452i
$$156$$ 0.642016i 0.0514024i
$$157$$ −2.88383 4.99495i −0.230155 0.398640i 0.727699 0.685897i $$-0.240590\pi$$
−0.957854 + 0.287257i $$0.907257\pi$$
$$158$$ 4.02455 0.320176
$$159$$ −5.78220 −0.458558
$$160$$ −0.500000 0.866025i −0.0395285 0.0684653i
$$161$$ 1.10106 + 0.635700i 0.0867760 + 0.0501002i
$$162$$ 1.00000i 0.0785674i
$$163$$ 0.511813 0.295495i 0.0400883 0.0231450i −0.479822 0.877366i $$-0.659299\pi$$
0.519910 + 0.854221i $$0.325965\pi$$
$$164$$ −4.86520 8.42677i −0.379908 0.658020i
$$165$$ 4.71487 2.72213i 0.367052 0.211918i
$$166$$ −6.26008 3.61426i −0.485876 0.280521i
$$167$$ −8.80330 5.08259i −0.681220 0.393302i 0.119095 0.992883i $$-0.462001\pi$$
−0.800314 + 0.599580i $$0.795334\pi$$
$$168$$ 0.463788 0.267768i 0.0357820 0.0206588i
$$169$$ −6.29391 10.9014i −0.484147 0.838567i
$$170$$ −0.402237 + 0.232232i −0.0308502 + 0.0178114i
$$171$$ 8.22283i 0.628816i
$$172$$ 0.906314 + 0.523261i 0.0691058 + 0.0398982i
$$173$$ −7.70420 13.3441i −0.585739 1.01453i −0.994783 0.102015i $$-0.967471\pi$$
0.409043 0.912515i $$-0.365862\pi$$
$$174$$ −5.38430 −0.408183
$$175$$ −0.535537 −0.0404828
$$176$$ −2.72213 4.71487i −0.205188 0.355397i
$$177$$ 11.8038i 0.887228i
$$178$$ −2.13103 + 3.69105i −0.159728 + 0.276656i
$$179$$ 7.91168i 0.591347i 0.955289 + 0.295673i $$0.0955440\pi$$
−0.955289 + 0.295673i $$0.904456\pi$$
$$180$$ 0.866025 + 0.500000i 0.0645497 + 0.0372678i
$$181$$ 4.86182 8.42093i 0.361377 0.625922i −0.626811 0.779171i $$-0.715640\pi$$
0.988188 + 0.153249i $$0.0489736\pi$$
$$182$$ 0.171911 0.297759i 0.0127429 0.0220714i
$$183$$ −2.55109 + 1.47287i −0.188582 + 0.108878i
$$184$$ 2.37407 0.175019
$$185$$ −4.74417 3.80694i −0.348799 0.279892i
$$186$$ 1.32755 0.0973404
$$187$$ −2.18988 + 1.26433i −0.160140 + 0.0924570i
$$188$$ 4.07063 7.05055i 0.296882 0.514214i
$$189$$ −0.267768 + 0.463788i −0.0194773 + 0.0337356i
$$190$$ −7.12118 4.11142i −0.516625 0.298274i
$$191$$ 16.0144i 1.15876i 0.815057 + 0.579380i $$0.196705\pi$$
−0.815057 + 0.579380i $$0.803295\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ 17.2656i 1.24281i 0.783490 + 0.621404i $$0.213437\pi$$
−0.783490 + 0.621404i $$0.786563\pi$$
$$194$$ 2.71977 + 4.71079i 0.195268 + 0.338215i
$$195$$ 0.642016 0.0459757
$$196$$ 6.71320 0.479514
$$197$$ −12.1985 21.1285i −0.869110 1.50534i −0.862907 0.505363i $$-0.831359\pi$$
−0.00620326 0.999981i $$-0.501975\pi$$
$$198$$ 4.71487 + 2.72213i 0.335071 + 0.193453i
$$199$$ 0.826478i 0.0585875i −0.999571 0.0292937i $$-0.990674\pi$$
0.999571 0.0292937i $$-0.00932582\pi$$
$$200$$ −0.866025 + 0.500000i −0.0612372 + 0.0353553i
$$201$$ −2.04849 3.54808i −0.144489 0.250263i
$$202$$ −7.92857 + 4.57756i −0.557852 + 0.322076i
$$203$$ 2.49718 + 1.44175i 0.175267 + 0.101191i
$$204$$ −0.402237 0.232232i −0.0281622 0.0162595i
$$205$$ −8.42677 + 4.86520i −0.588551 + 0.339800i
$$206$$ 5.26575 + 9.12055i 0.366882 + 0.635459i
$$207$$ −2.05600 + 1.18703i −0.142902 + 0.0825045i
$$208$$ 0.642016i 0.0445158i
$$209$$ −38.7696 22.3836i −2.68175 1.54831i
$$210$$ −0.267768 0.463788i −0.0184778 0.0320044i
$$211$$ 4.70749 0.324077 0.162039 0.986784i $$-0.448193\pi$$
0.162039 + 0.986784i $$0.448193\pi$$
$$212$$ 5.78220 0.397123
$$213$$ 2.17408 + 3.76562i 0.148966 + 0.258016i
$$214$$ 15.0852i 1.03120i
$$215$$ 0.523261 0.906314i 0.0356861 0.0618101i
$$216$$ 1.00000i 0.0680414i
$$217$$ −0.615700 0.355475i −0.0417964 0.0241312i
$$218$$ −2.21756 + 3.84093i −0.150192 + 0.260140i
$$219$$ 0.801185 1.38769i 0.0541391 0.0937716i
$$220$$ −4.71487 + 2.72213i −0.317876 + 0.183526i
$$221$$ −0.298193 −0.0200586
$$222$$ 0.924822 6.01205i 0.0620700 0.403502i
$$223$$ −8.14374 −0.545345 −0.272673 0.962107i $$-0.587908\pi$$
−0.272673 + 0.962107i $$0.587908\pi$$
$$224$$ −0.463788 + 0.267768i −0.0309882 + 0.0178910i
$$225$$ 0.500000 0.866025i 0.0333333 0.0577350i
$$226$$ −4.49294 + 7.78200i −0.298866 + 0.517651i
$$227$$ −3.39960 1.96276i −0.225639 0.130273i 0.382919 0.923782i $$-0.374919\pi$$
−0.608559 + 0.793509i $$0.708252\pi$$
$$228$$ 8.22283i 0.544571i
$$229$$ 13.5993 23.5547i 0.898667 1.55654i 0.0694673 0.997584i $$-0.477870\pi$$
0.829200 0.558953i $$-0.188797\pi$$
$$230$$ 2.37407i 0.156541i
$$231$$ −1.45780 2.52499i −0.0959162 0.166132i
$$232$$ 5.38430 0.353497
$$233$$ 11.1032 0.727394 0.363697 0.931517i $$-0.381514\pi$$
0.363697 + 0.931517i $$0.381514\pi$$
$$234$$ 0.321008 + 0.556002i 0.0209849 + 0.0363470i
$$235$$ −7.05055 4.07063i −0.459927 0.265539i
$$236$$ 11.8038i 0.768362i
$$237$$ 3.48536 2.01228i 0.226399 0.130711i
$$238$$ 0.124369 + 0.215413i 0.00806162 + 0.0139631i
$$239$$ −8.61437 + 4.97351i −0.557217 + 0.321710i −0.752028 0.659131i $$-0.770924\pi$$
0.194810 + 0.980841i $$0.437591\pi$$
$$240$$ −0.866025 0.500000i −0.0559017 0.0322749i
$$241$$ −18.7127 10.8038i −1.20539 0.695932i −0.243641 0.969865i $$-0.578342\pi$$
−0.961749 + 0.273933i $$0.911675\pi$$
$$242$$ −16.1427 + 9.32000i −1.03769 + 0.599112i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 2.55109 1.47287i 0.163317 0.0942910i
$$245$$ 6.71320i 0.428891i
$$246$$ −8.42677 4.86520i −0.537271 0.310194i
$$247$$ −2.63960 4.57191i −0.167953 0.290904i
$$248$$ −1.32755 −0.0842992
$$249$$ −7.22851 −0.458088
$$250$$ 0.500000 + 0.866025i 0.0316228 + 0.0547723i
$$251$$ 5.10425i 0.322178i 0.986940 + 0.161089i $$0.0515005\pi$$
−0.986940 + 0.161089i $$0.948499\pi$$
$$252$$ 0.267768 0.463788i 0.0168678 0.0292159i
$$253$$ 12.9250i 0.812590i
$$254$$ −10.3145 5.95507i −0.647188 0.373654i
$$255$$ −0.232232 + 0.402237i −0.0145429 + 0.0251891i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 16.8491 9.72782i 1.05102 0.606805i 0.128083 0.991763i $$-0.459118\pi$$
0.922934 + 0.384959i $$0.125784\pi$$
$$258$$ 1.04652 0.0651536
$$259$$ −2.03876 + 2.54068i −0.126682 + 0.157870i
$$260$$ −0.642016 −0.0398161
$$261$$ −4.66294 + 2.69215i −0.288629 + 0.166640i
$$262$$ −4.22846 + 7.32391i −0.261235 + 0.452473i
$$263$$ −6.04317 + 10.4671i −0.372638 + 0.645428i −0.989970 0.141274i $$-0.954880\pi$$
0.617332 + 0.786702i $$0.288213\pi$$
$$264$$ −4.71487 2.72213i −0.290180 0.167536i
$$265$$ 5.78220i 0.355198i
$$266$$ −2.20181 + 3.81365i −0.135002 + 0.233830i
$$267$$ 4.26206i 0.260834i
$$268$$ 2.04849 + 3.54808i 0.125131 + 0.216734i
$$269$$ −27.8139 −1.69584 −0.847921 0.530123i $$-0.822146\pi$$
−0.847921 + 0.530123i $$0.822146\pi$$
$$270$$ 1.00000 0.0608581
$$271$$ 2.68320 + 4.64744i 0.162993 + 0.282312i 0.935941 0.352158i $$-0.114552\pi$$
−0.772948 + 0.634470i $$0.781219\pi$$
$$272$$ 0.402237 + 0.232232i 0.0243892 + 0.0140811i
$$273$$ 0.343823i 0.0208091i
$$274$$ −17.1430 + 9.89749i −1.03564 + 0.597929i
$$275$$ 2.72213 + 4.71487i 0.164151 + 0.284317i
$$276$$ 2.05600 1.18703i 0.123757 0.0714510i
$$277$$ −9.37602 5.41325i −0.563350 0.325250i 0.191139 0.981563i $$-0.438782\pi$$
−0.754489 + 0.656313i $$0.772115\pi$$
$$278$$ 6.34913 + 3.66567i 0.380795 + 0.219852i
$$279$$ 1.14969 0.663773i 0.0688300 0.0397390i
$$280$$ 0.267768 + 0.463788i 0.0160022 + 0.0277166i
$$281$$ 12.7542 7.36363i 0.760851 0.439277i −0.0687503 0.997634i $$-0.521901\pi$$
0.829601 + 0.558356i $$0.188568\pi$$
$$282$$ 8.14127i 0.484806i
$$283$$ 16.5272 + 9.54199i 0.982440 + 0.567212i 0.903006 0.429628i $$-0.141355\pi$$
0.0794343 + 0.996840i $$0.474689\pi$$
$$284$$ −2.17408 3.76562i −0.129008 0.223448i
$$285$$ −8.22283 −0.487079
$$286$$ −3.49530 −0.206682
$$287$$ 2.60549 + 4.51284i 0.153797 + 0.266385i
$$288$$ 1.00000i 0.0589256i
$$289$$ −8.39214 + 14.5356i −0.493655 + 0.855036i
$$290$$ 5.38430i 0.316177i
$$291$$ 4.71079 + 2.71977i 0.276151 + 0.159436i
$$292$$ −0.801185 + 1.38769i −0.0468858 + 0.0812086i
$$293$$ −1.27637 + 2.21073i −0.0745660 + 0.129152i −0.900897 0.434032i $$-0.857090\pi$$
0.826331 + 0.563184i $$0.190424\pi$$
$$294$$ 5.81380 3.35660i 0.339068 0.195761i
$$295$$ −11.8038 −0.687244
$$296$$ −0.924822 + 6.01205i −0.0537542 + 0.349443i
$$297$$ 5.44426 0.315908
$$298$$ 7.12511 4.11369i 0.412747 0.238299i
$$299$$ 0.762094 1.31999i 0.0440731 0.0763368i
$$300$$ −0.500000 + 0.866025i −0.0288675 + 0.0500000i
$$301$$ −0.485364 0.280225i −0.0279759 0.0161519i
$$302$$ 9.97255i 0.573856i
$$303$$ −4.57756 + 7.92857i −0.262974 + 0.455484i
$$304$$ 8.22283i 0.471612i
$$305$$ −1.47287 2.55109i −0.0843364 0.146075i
$$306$$ −0.464463 −0.0265516
$$307$$ −1.60024 −0.0913305 −0.0456653 0.998957i $$-0.514541\pi$$
−0.0456653 + 0.998957i $$0.514541\pi$$
$$308$$ 1.45780 + 2.52499i 0.0830659 + 0.143874i
$$309$$ 9.12055 + 5.26575i 0.518850 + 0.299558i
$$310$$ 1.32755i 0.0753995i
$$311$$ −4.41158 + 2.54702i −0.250157 + 0.144428i −0.619836 0.784731i $$-0.712801\pi$$
0.369679 + 0.929160i $$0.379468\pi$$
$$312$$ −0.321008 0.556002i −0.0181735 0.0314774i
$$313$$ −2.00909 + 1.15995i −0.113561 + 0.0655642i −0.555704 0.831380i $$-0.687551\pi$$
0.442144 + 0.896944i $$0.354218\pi$$
$$314$$ 4.99495 + 2.88383i 0.281881 + 0.162744i
$$315$$ −0.463788 0.267768i −0.0261315 0.0150870i
$$316$$ −3.48536 + 2.01228i −0.196067 + 0.113199i
$$317$$ 6.42213 + 11.1235i 0.360703 + 0.624756i 0.988077 0.153963i $$-0.0492035\pi$$
−0.627374 + 0.778718i $$0.715870\pi$$
$$318$$ 5.00753 2.89110i 0.280808 0.162125i
$$319$$ 29.3136i 1.64124i
$$320$$ 0.866025 + 0.500000i 0.0484123 + 0.0279508i
$$321$$ −7.54260 13.0642i −0.420987 0.729170i
$$322$$ −1.27140 −0.0708523
$$323$$ 3.81921 0.212506
$$324$$ 0.500000 + 0.866025i 0.0277778 + 0.0481125i
$$325$$ 0.642016i 0.0356126i
$$326$$ −0.295495 + 0.511813i −0.0163660 + 0.0283467i
$$327$$ 4.43512i 0.245263i
$$328$$ 8.42677 + 4.86520i 0.465290 + 0.268636i
$$329$$ −2.17997 + 3.77582i −0.120186 + 0.208168i
$$330$$ −2.72213 + 4.71487i −0.149848 + 0.259545i
$$331$$ −6.20441 + 3.58212i −0.341025 + 0.196891i −0.660725 0.750628i $$-0.729751\pi$$
0.319700 + 0.947519i $$0.396418\pi$$
$$332$$ 7.22851 0.396716
$$333$$ −2.20510 5.66900i −0.120839 0.310659i
$$334$$ 10.1652 0.556214
$$335$$ 3.54808 2.04849i 0.193853 0.111921i
$$336$$ −0.267768 + 0.463788i −0.0146080 + 0.0253017i
$$337$$ −11.4507 + 19.8331i −0.623757 + 1.08038i 0.365023 + 0.930999i $$0.381061\pi$$
−0.988780 + 0.149380i $$0.952272\pi$$
$$338$$ 10.9014 + 6.29391i 0.592956 + 0.342343i
$$339$$ 8.98588i 0.488046i
$$340$$ 0.232232 0.402237i 0.0125945 0.0218144i
$$341$$ 7.22751i 0.391391i
$$342$$ −4.11142 7.12118i −0.222320 0.385070i
$$343$$ −7.34392 −0.396534
$$344$$ −1.04652 −0.0564246
$$345$$ −1.18703 2.05600i −0.0639077 0.110691i
$$346$$ 13.3441 + 7.70420i 0.717381 + 0.414180i
$$347$$ 27.5385i 1.47835i −0.673516 0.739173i $$-0.735217\pi$$
0.673516 0.739173i $$-0.264783\pi$$
$$348$$ 4.66294 2.69215i 0.249960 0.144315i
$$349$$ −11.8294 20.4892i −0.633216 1.09676i −0.986890 0.161393i $$-0.948401\pi$$
0.353675 0.935369i $$-0.384932\pi$$
$$350$$ 0.463788 0.267768i 0.0247905 0.0143128i
$$351$$ 0.556002 + 0.321008i 0.0296772 + 0.0171341i
$$352$$ 4.71487 + 2.72213i 0.251303 + 0.145090i
$$353$$ −4.74750 + 2.74097i −0.252684 + 0.145887i −0.620992 0.783817i $$-0.713270\pi$$
0.368309 + 0.929704i $$0.379937\pi$$
$$354$$ −5.90190 10.2224i −0.313683 0.543314i
$$355$$ −3.76562 + 2.17408i −0.199858 + 0.115388i
$$356$$ 4.26206i 0.225889i
$$357$$ 0.215413 + 0.124369i 0.0114008 + 0.00658228i
$$358$$ −3.95584 6.85171i −0.209073 0.362124i
$$359$$ −20.2538 −1.06895 −0.534477 0.845183i $$-0.679491\pi$$
−0.534477 + 0.845183i $$0.679491\pi$$
$$360$$ −1.00000 −0.0527046
$$361$$ 24.3075 + 42.1018i 1.27934 + 2.21589i
$$362$$ 9.72365i 0.511064i
$$363$$ −9.32000 + 16.1427i −0.489173 + 0.847273i
$$364$$ 0.343823i 0.0180212i
$$365$$ 1.38769 + 0.801185i 0.0726352 + 0.0419359i
$$366$$ 1.47287 2.55109i 0.0769882 0.133348i
$$367$$ −14.5637 + 25.2250i −0.760217 + 1.31673i 0.182522 + 0.983202i $$0.441574\pi$$
−0.942739 + 0.333532i $$0.891759\pi$$
$$368$$ −2.05600 + 1.18703i −0.107177 + 0.0618784i
$$369$$ −9.73039 −0.506544
$$370$$ 6.01205 + 0.924822i 0.312551 + 0.0480792i
$$371$$ −3.09658 −0.160766
$$372$$ −1.14969 + 0.663773i −0.0596086 + 0.0344150i
$$373$$ 18.0747 31.3063i 0.935871 1.62098i 0.162799 0.986659i $$-0.447948\pi$$
0.773073 0.634317i $$-0.218719\pi$$
$$374$$ 1.26433 2.18988i 0.0653770 0.113236i
$$375$$ 0.866025 + 0.500000i 0.0447214 + 0.0258199i
$$376$$ 8.14127i 0.419854i
$$377$$ 1.72840 2.99368i 0.0890174 0.154183i
$$378$$ 0.535537i 0.0275450i
$$379$$ 10.8574 + 18.8055i 0.557706 + 0.965976i 0.997687 + 0.0679687i $$0.0216518\pi$$
−0.439981 + 0.898007i $$0.645015\pi$$
$$380$$ 8.22283 0.421823
$$381$$ −11.9101 −0.610175
$$382$$ −8.00719 13.8689i −0.409684 0.709593i
$$383$$ −27.9465 16.1349i −1.42800 0.824456i −0.431037 0.902334i $$-0.641852\pi$$
−0.996963 + 0.0778783i $$0.975185\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ 2.52499 1.45780i 0.128685 0.0742964i
$$386$$ −8.63282 14.9525i −0.439399 0.761061i
$$387$$ 0.906314 0.523261i 0.0460705 0.0265988i
$$388$$ −4.71079 2.71977i −0.239154 0.138076i
$$389$$ −28.9212 16.6976i −1.46636 0.846604i −0.467069 0.884221i $$-0.654690\pi$$
−0.999292 + 0.0376165i $$0.988023\pi$$
$$390$$ −0.556002 + 0.321008i −0.0281543 + 0.0162549i
$$391$$ 0.551334 + 0.954938i 0.0278821 + 0.0482933i
$$392$$ −5.81380 + 3.35660i −0.293641 + 0.169534i
$$393$$ 8.45692i 0.426595i
$$394$$ 21.1285 + 12.1985i 1.06444 + 0.614554i
$$395$$ 2.01228 + 3.48536i 0.101249 + 0.175368i
$$396$$ −5.44426 −0.273585
$$397$$ −8.82763 −0.443046 −0.221523 0.975155i $$-0.571103\pi$$
−0.221523 + 0.975155i $$0.571103\pi$$
$$398$$ 0.413239 + 0.715751i 0.0207138 + 0.0358774i
$$399$$ 4.40363i 0.220457i
$$400$$ 0.500000 0.866025i 0.0250000 0.0433013i
$$401$$ 35.0800i 1.75181i 0.482482 + 0.875906i $$0.339736\pi$$
−0.482482 + 0.875906i $$0.660264\pi$$
$$402$$ 3.54808 + 2.04849i 0.176962 + 0.102169i
$$403$$ −0.426153 + 0.738118i −0.0212282 + 0.0367683i
$$404$$ 4.57756 7.92857i 0.227742 0.394461i
$$405$$ 0.866025 0.500000i 0.0430331 0.0248452i
$$406$$ −2.88349 −0.143105
$$407$$ 32.7312 + 5.03498i 1.62242 + 0.249575i
$$408$$ 0.464463 0.0229944
$$409$$ 31.4737 18.1714i 1.55627 0.898516i 0.558666 0.829392i $$-0.311313\pi$$
0.997608 0.0691231i $$-0.0220201\pi$$
$$410$$ 4.86520 8.42677i 0.240275 0.416168i
$$411$$ −9.89749 + 17.1430i −0.488207 + 0.845599i
$$412$$ −9.12055 5.26575i −0.449337 0.259425i
$$413$$ 6.32137i 0.311054i
$$414$$ 1.18703 2.05600i 0.0583395 0.101047i
$$415$$ 7.22851i 0.354834i
$$416$$ 0.321008 + 0.556002i 0.0157387 + 0.0272602i
$$417$$ 7.33134 0.359017
$$418$$ 44.7673 2.18964
$$419$$ −6.93685 12.0150i −0.338887 0.586970i 0.645336 0.763898i $$-0.276717\pi$$
−0.984224 + 0.176929i $$0.943384\pi$$
$$420$$ 0.463788 + 0.267768i 0.0226305 + 0.0130658i
$$421$$ 3.08809i 0.150504i −0.997165 0.0752521i $$-0.976024\pi$$
0.997165 0.0752521i $$-0.0239762\pi$$
$$422$$ −4.07681 + 2.35375i −0.198456 + 0.114579i
$$423$$ −4.07063 7.05055i −0.197921 0.342809i
$$424$$ −5.00753 + 2.89110i −0.243187 + 0.140404i
$$425$$ −0.402237 0.232232i −0.0195114 0.0112649i
$$426$$ −3.76562 2.17408i −0.182445 0.105335i
$$427$$ −1.36620 + 0.788777i −0.0661151 + 0.0381716i
$$428$$ 7.54260 + 13.0642i 0.364585 + 0.631480i
$$429$$ −3.02702 + 1.74765i −0.146146 + 0.0843774i
$$430$$ 1.04652i 0.0504677i
$$431$$ 34.4243 + 19.8749i 1.65816 + 0.957341i 0.973562 + 0.228422i $$0.0733565\pi$$
0.684600 + 0.728919i $$0.259977\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ 2.97177 0.142814 0.0714070 0.997447i $$-0.477251\pi$$
0.0714070 + 0.997447i $$0.477251\pi$$
$$434$$ 0.710949 0.0341267
$$435$$ −2.69215 4.66294i −0.129079 0.223571i
$$436$$ 4.43512i 0.212404i
$$437$$ −9.76078 + 16.9062i −0.466921 + 0.808732i
$$438$$ 1.60237i 0.0765642i
$$439$$ 6.90136 + 3.98450i 0.329384 + 0.190170i 0.655568 0.755137i $$-0.272429\pi$$
−0.326184 + 0.945306i $$0.605763\pi$$
$$440$$ 2.72213 4.71487i 0.129773 0.224773i
$$441$$ 3.35660 5.81380i 0.159838 0.276848i
$$442$$ 0.258243 0.149096i 0.0122834 0.00709180i
$$443$$ −34.0828 −1.61932 −0.809662 0.586897i $$-0.800349\pi$$
−0.809662 + 0.586897i $$0.800349\pi$$
$$444$$ 2.20510 + 5.66900i 0.104650 + 0.269039i
$$445$$ −4.26206 −0.202041
$$446$$ 7.05269 4.07187i 0.333955 0.192809i
$$447$$ 4.11369 7.12511i 0.194571 0.337006i
$$448$$ 0.267768 0.463788i 0.0126509 0.0219119i
$$449$$ 24.4617 + 14.1230i 1.15442 + 0.666505i 0.949961 0.312370i $$-0.101123\pi$$
0.204460 + 0.978875i $$0.434456\pi$$
$$450$$ 1.00000i 0.0471405i
$$451$$ 26.4874 45.8775i 1.24724 2.16029i
$$452$$ 8.98588i 0.422660i
$$453$$ −4.98628 8.63648i −0.234276 0.405777i
$$454$$ 3.92552 0.184234
$$455$$ 0.343823 0.0161187
$$456$$ 4.11142 + 7.12118i 0.192535 + 0.333480i
$$457$$ −26.8664 15.5113i −1.25676 0.725588i −0.284313 0.958731i $$-0.591766\pi$$
−0.972442 + 0.233143i $$0.925099\pi$$
$$458$$ 27.1986i 1.27091i
$$459$$ −0.402237 + 0.232232i −0.0187748 + 0.0108396i
$$460$$ 1.18703 + 2.05600i 0.0553457 + 0.0958616i
$$461$$ −3.95564 + 2.28379i −0.184233 + 0.106367i −0.589280 0.807929i $$-0.700588\pi$$
0.405047 + 0.914296i $$0.367255\pi$$
$$462$$ 2.52499 + 1.45780i 0.117473 + 0.0678230i
$$463$$ −5.59102 3.22798i −0.259837 0.150017i 0.364423 0.931233i $$-0.381266\pi$$
−0.624260 + 0.781217i $$0.714599\pi$$
$$464$$ −4.66294 + 2.69215i −0.216472 + 0.124980i
$$465$$ 0.663773 + 1.14969i 0.0307817 + 0.0533155i
$$466$$ −9.61564 + 5.55159i −0.445436 + 0.257173i
$$467$$ 22.5295i 1.04254i −0.853391 0.521271i $$-0.825458\pi$$
0.853391 0.521271i $$-0.174542\pi$$
$$468$$ −0.556002 0.321008i −0.0257012 0.0148386i
$$469$$ −1.09704 1.90013i −0.0506566 0.0877398i
$$470$$ 8.14127 0.375529
$$471$$ 5.76767 0.265760
$$472$$ 5.90190 + 10.2224i 0.271657 + 0.470524i
$$473$$ 5.69754i 0.261973i
$$474$$ −2.01228 + 3.48536i −0.0924269 + 0.160088i
$$475$$ 8.22283i 0.377290i
$$476$$ −0.215413 0.124369i −0.00987342 0.00570042i
$$477$$ 2.89110 5.00753i 0.132374 0.229279i
$$478$$ 4.97351 8.61437i 0.227483 0.394012i
$$479$$ −7.02757 + 4.05737i −0.321098 + 0.185386i −0.651882 0.758321i $$-0.726020\pi$$
0.330784 + 0.943706i $$0.392687\pi$$
$$480$$ 1.00000 0.0456435
$$481$$ 3.04583 + 2.44412i 0.138878 + 0.111442i
$$482$$ 21.6075 0.984196
$$483$$ −1.10106 + 0.635700i −0.0501002 + 0.0289253i
$$484$$ 9.32000 16.1427i 0.423636 0.733760i
$$485$$ −2.71977 + 4.71079i −0.123499 + 0.213906i
$$486$$ 0.866025 + 0.500000i 0.0392837 + 0.0226805i
$$487$$ 5.69618i 0.258118i −0.991637 0.129059i $$-0.958804\pi$$
0.991637 0.129059i $$-0.0411957\pi$$
$$488$$ −1.47287 + 2.55109i −0.0666738 + 0.115482i
$$489$$ 0.590991i 0.0267255i
$$490$$ 3.35660 + 5.81380i 0.151636 + 0.262641i
$$491$$ 26.7699 1.20811 0.604054 0.796943i $$-0.293551\pi$$
0.604054 + 0.796943i $$0.293551\pi$$
$$492$$ 9.73039 0.438680
$$493$$ 1.25041 + 2.16577i 0.0563155 + 0.0975413i
$$494$$ 4.57191 + 2.63960i 0.205700 + 0.118761i
$$495$$ 5.44426i 0.244701i
$$496$$ 1.14969 0.663773i 0.0516225 0.0298043i
$$497$$ 1.16430 + 2.01663i 0.0522260 + 0.0904581i
$$498$$ 6.26008 3.61426i 0.280521 0.161959i
$$499$$ 37.4524 + 21.6232i 1.67660 + 0.967986i 0.963802 + 0.266619i $$0.0859064\pi$$
0.712800 + 0.701368i $$0.247427\pi$$
$$500$$ −0.866025 0.500000i −0.0387298 0.0223607i
$$501$$ 8.80330 5.08259i 0.393302 0.227073i
$$502$$ −2.55213 4.42041i −0.113907 0.197293i
$$503$$ −7.54680 + 4.35715i −0.336495 + 0.194276i −0.658721 0.752387i $$-0.728902\pi$$
0.322226 + 0.946663i $$0.395569\pi$$
$$504$$ 0.535537i 0.0238547i
$$505$$ −7.92857 4.57756i −0.352817 0.203699i
$$506$$ 6.46252 + 11.1934i 0.287294 + 0.497608i
$$507$$ 12.5878 0.559045
$$508$$ 11.9101 0.528427
$$509$$ 21.0800 + 36.5117i 0.934356 + 1.61835i 0.775778 + 0.631007i $$0.217358\pi$$
0.158579 + 0.987346i $$0.449309\pi$$
$$510$$ 0.464463i 0.0205668i
$$511$$ 0.429064 0.743160i 0.0189807 0.0328755i
$$512$$ 1.00000i 0.0441942i
$$513$$ −7.12118 4.11142i −0.314408 0.181524i
$$514$$ −9.72782 + 16.8491i −0.429076 + 0.743181i
$$515$$ −5.26575 + 9.12055i −0.232037 + 0.401900i
$$516$$ −0.906314 + 0.523261i −0.0398982 + 0.0230353i
$$517$$ 44.3232 1.94933
$$518$$ 0.495276 3.21967i 0.0217612 0.141464i
$$519$$ 15.4084 0.676354
$$520$$ 0.556002 0.321008i 0.0243823 0.0140771i
$$521$$ 18.1567 31.4484i 0.795461 1.37778i −0.127086 0.991892i $$-0.540562\pi$$
0.922546 0.385887i $$-0.126104\pi$$
$$522$$ 2.69215 4.66294i 0.117832 0.204092i
$$523$$ −11.5606 6.67449i −0.505508 0.291855i 0.225477 0.974248i $$-0.427606\pi$$
−0.730985 + 0.682393i $$0.760939\pi$$
$$524$$ 8.45692i 0.369442i
$$525$$ 0.267768 0.463788i 0.0116864 0.0202414i
$$526$$ 12.0863i 0.526990i
$$527$$ −0.308298 0.533988i −0.0134297 0.0232609i
$$528$$ 5.44426 0.236931
$$529$$ 17.3638 0.754948
$$530$$ 2.89110 + 5.00753i 0.125581 + 0.217513i
$$531$$ −10.2224 5.90190i −0.443614 0.256121i
$$532$$ 4.40363i 0.190922i
$$533$$ 5.41012 3.12353i 0.234338 0.135295i
$$534$$ −2.13103 3.69105i −0.0922187 0.159728i
$$535$$ 13.0642 7.54260i 0.564813 0.326095i
$$536$$ −3.54808 2.04849i −0.153254 0.0884812i
$$537$$ −6.85171 3.95584i −0.295673 0.170707i
$$538$$ 24.0875 13.9069i 1.03849 0.599570i
$$539$$ 18.2742 + 31.6519i 0.787126 + 1.36334i
$$540$$ −0.866025 + 0.500000i −0.0372678 + 0.0215166i
$$541$$ 28.8021i 1.23830i 0.785273 + 0.619150i $$0.212523\pi$$
−0.785273 + 0.619150i $$0.787477\pi$$
$$542$$ −4.64744 2.68320i −0.199625 0.115253i
$$543$$ 4.86182 + 8.42093i 0.208641 + 0.361377i
$$544$$ −0.464463 −0.0199137
$$545$$ −4.43512 −0.189980
$$546$$ 0.171911 + 0.297759i 0.00735713 + 0.0127429i
$$547$$ 11.5425i 0.493524i −0.969076 0.246762i $$-0.920633\pi$$
0.969076 0.246762i $$-0.0793665\pi$$
$$548$$ 9.89749 17.1430i 0.422800 0.732311i
$$549$$ 2.94574i 0.125721i
$$550$$ −4.71487 2.72213i −0.201043 0.116072i
$$551$$ −22.1371 + 38.3426i −0.943073 + 1.63345i
$$552$$ −1.18703 + 2.05600i −0.0505235 + 0.0875093i
$$553$$ 1.86654 1.07765i 0.0793733 0.0458262i
$$554$$ 10.8265 0.459974
$$555$$ 5.66900 2.20510i 0.240635 0.0936014i
$$556$$ −7.33134 −0.310918
$$557$$ −19.0151 + 10.9784i −0.805694 + 0.465168i −0.845458 0.534041i $$-0.820673\pi$$
0.0397643 + 0.999209i $$0.487339\pi$$
$$558$$ −0.663773 + 1.14969i −0.0280997 + 0.0486702i
$$559$$ −0.335942 + 0.581868i −0.0142088 + 0.0246104i
$$560$$ −0.463788 0.267768i −0.0195986 0.0113153i
$$561$$ 2.52866i 0.106760i
$$562$$ −7.36363 + 12.7542i −0.310616 + 0.538003i
$$563$$ 35.3758i 1.49091i 0.666555 + 0.745456i $$0.267768\pi$$
−0.666555 + 0.745456i $$0.732232\pi$$
$$564$$ 4.07063 + 7.05055i 0.171405 + 0.296882i
$$565$$ −8.98588 −0.378039
$$566$$ −19.0840 −0.802159
$$567$$ −0.267768 0.463788i −0.0112452 0.0194773i
$$568$$ 3.76562 + 2.17408i 0.158002 + 0.0912225i
$$569$$ 0.0883529i 0.00370395i −0.999998 0.00185197i $$-0.999410\pi$$
0.999998 0.00185197i $$-0.000589502\pi$$
$$570$$ 7.12118 4.11142i 0.298274 0.172208i
$$571$$ −21.1519 36.6361i −0.885177 1.53317i −0.845510 0.533959i $$-0.820704\pi$$
−0.0396672 0.999213i $$-0.512630\pi$$
$$572$$ 3.02702 1.74765i 0.126566 0.0730730i
$$573$$ −13.8689 8.00719i −0.579380 0.334505i
$$574$$ −4.51284 2.60549i −0.188362 0.108751i
$$575$$ 2.05600 1.18703i 0.0857412 0.0495027i
$$576$$ 0.500000 + 0.866025i 0.0208333 + 0.0360844i
$$577$$ −21.4986 + 12.4122i −0.895000 + 0.516729i −0.875575 0.483083i $$-0.839517\pi$$
−0.0194254 + 0.999811i $$0.506184\pi$$
$$578$$ 16.7843i 0.698134i
$$579$$ −14.9525 8.63282i −0.621404 0.358768i
$$580$$ 2.69215 + 4.66294i 0.111786 + 0.193618i
$$581$$ −3.87113 −0.160602
$$582$$ −5.43955 −0.225477
$$583$$ 15.7399 + 27.2623i 0.651880 + 1.12909i
$$584$$ 1.60237i 0.0663065i
$$585$$ −0.321008 + 0.556002i −0.0132720 + 0.0229879i
$$586$$ 2.55273i 0.105452i
$$587$$ −27.7557 16.0248i −1.14560 0.661412i −0.197789 0.980245i $$-0.563376\pi$$
−0.947811 + 0.318832i $$0.896709\pi$$
$$588$$ −3.35660 + 5.81380i −0.138424 + 0.239757i
$$589$$ 5.45809 9.45370i 0.224897 0.389533i
$$590$$ 10.2224 5.90190i 0.420849 0.242978i
$$591$$ 24.3971 1.00356
$$592$$ −2.20510 5.66900i −0.0906292 0.232994i
$$593$$ 38.7563 1.59153 0.795765 0.605606i $$-0.207069\pi$$
0.795765 + 0.605606i $$0.207069\pi$$
$$594$$ −4.71487 + 2.72213i −0.193453 + 0.111690i
$$595$$ −0.124369 + 0.215413i −0.00509861 + 0.00883106i
$$596$$ −4.11369 + 7.12511i −0.168503 + 0.291856i
$$597$$ 0.715751 + 0.413239i 0.0292937 + 0.0169127i
$$598$$ 1.52419i 0.0623287i
$$599$$ −11.6301 + 20.1440i −0.475194 + 0.823060i −0.999596 0.0284104i $$-0.990955\pi$$
0.524402 + 0.851471i $$0.324289\pi$$
$$600$$ 1.00000i 0.0408248i
$$601$$ 7.34067 + 12.7144i 0.299432 + 0.518631i 0.976006 0.217743i $$-0.0698695\pi$$
−0.676574 + 0.736375i $$0.736536\pi$$
$$602$$ 0.560450 0.0228422
$$603$$ 4.09698 0.166842
$$604$$ 4.98628 + 8.63648i 0.202889 + 0.351414i
$$605$$ −16.1427 9.32000i −0.656295 0.378912i
$$606$$ 9.15512i 0.371902i
$$607$$ 11.9650 6.90802i 0.485646 0.280388i −0.237121 0.971480i $$-0.576204\pi$$
0.722766 + 0.691093i $$0.242870\pi$$
$$608$$ −4.11142 7.12118i −0.166740 0.288802i
$$609$$ −2.49718 + 1.44175i −0.101191 + 0.0584225i
$$610$$ 2.55109 + 1.47287i 0.103291 + 0.0596348i
$$611$$ 4.52656 + 2.61341i 0.183125 + 0.105727i
$$612$$ 0.402237 0.232232i 0.0162595 0.00938741i
$$613$$ −9.87091 17.0969i −0.398682 0.690538i 0.594881 0.803814i $$-0.297199\pi$$
−0.993564 + 0.113276i $$0.963866\pi$$
$$614$$ 1.38585 0.800120i 0.0559283 0.0322902i
$$615$$ 9.73039i 0.392367i
$$616$$ −2.52499 1.45780i −0.101735 0.0587365i
$$617$$ 7.09744 + 12.2931i 0.285732 + 0.494903i 0.972786 0.231703i $$-0.0744299\pi$$
−0.687054 + 0.726606i $$0.741097\pi$$
$$618$$ −10.5315 −0.423639
$$619$$ −16.2904 −0.654768 −0.327384 0.944891i $$-0.606167\pi$$
−0.327384 + 0.944891i $$0.606167\pi$$
$$620$$ −0.663773 1.14969i −0.0266578 0.0461726i
$$621$$ 2.37407i 0.0952680i
$$622$$ 2.54702 4.41158i 0.102126 0.176888i
$$623$$ 2.28249i 0.0914460i
$$624$$ 0.556002 + 0.321008i 0.0222579 + 0.0128506i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 1.15995 2.00909i 0.0463609 0.0802994i
$$627$$ 38.7696 22.3836i 1.54831 0.893916i
$$628$$ −5.76767 −0.230155
$$629$$ −2.63304 + 1.02419i −0.104986 + 0.0408371i
$$630$$ 0.535537 0.0213363
$$631$$ −24.7908 + 14.3130i −0.986907 + 0.569791i −0.904348 0.426795i $$-0.859643\pi$$
−0.0825589 + 0.996586i $$0.526309\pi$$
$$632$$ 2.01228 3.48536i 0.0800440 0.138640i
$$633$$ −2.35375 + 4.07681i −0.0935530 + 0.162039i
$$634$$ −11.1235 6.42213i −0.441769 0.255055i
$$635$$ 11.9101i 0.472639i
$$636$$ −2.89110 + 5.00753i −0.114640 + 0.198562i
$$637$$ 4.30998i 0.170768i
$$638$$ 14.6568 + 25.3863i 0.580268 + 1.00505i
$$639$$ −4.34816 −0.172011
$$640$$ −1.00000 −0.0395285
$$641$$ −19.3732 33.5553i −0.765194 1.32535i −0.940144 0.340777i $$-0.889310\pi$$
0.174950 0.984577i $$-0.444024\pi$$
$$642$$ 13.0642 + 7.54260i 0.515601 + 0.297683i
$$643$$ 48.8691i 1.92721i 0.267331 + 0.963605i $$0.413858\pi$$
−0.267331 + 0.963605i $$0.586142\pi$$
$$644$$ 1.10106 0.635700i 0.0433880 0.0250501i
$$645$$ 0.523261 + 0.906314i 0.0206034 + 0.0356861i
$$646$$ −3.30753 + 1.90960i −0.130133 + 0.0751323i
$$647$$ 34.6610 + 20.0115i 1.36266 + 0.786734i 0.989978 0.141224i $$-0.0451037\pi$$
0.372685 + 0.927958i $$0.378437\pi$$
$$648$$ −0.866025 0.500000i −0.0340207 0.0196419i
$$649$$ 55.6534 32.1315i 2.18459 1.26127i
$$650$$ −0.321008 0.556002i −0.0125910 0.0218082i
$$651$$ 0.615700 0.355475i 0.0241312 0.0139321i
$$652$$ 0.590991i 0.0231450i
$$653$$ −27.2595 15.7383i −1.06675 0.615886i −0.139456 0.990228i $$-0.544535\pi$$
−0.927291 + 0.374342i $$0.877869\pi$$
$$654$$ −2.21756 3.84093i −0.0867135 0.150192i
$$655$$ −8.45692 −0.330439
$$656$$ −9.73039 −0.379908
$$657$$ 0.801185 + 1.38769i 0.0312572 + 0.0541391i
$$658$$ 4.35995i 0.169968i
$$659$$ −11.9225 + 20.6504i −0.464436 + 0.804426i −0.999176 0.0405905i $$-0.987076\pi$$
0.534740 + 0.845016i $$0.320409\pi$$
$$660$$ 5.44426i 0.211918i
$$661$$ −1.01438 0.585655i −0.0394550 0.0227793i 0.480143 0.877190i $$-0.340585\pi$$
−0.519598 + 0.854411i $$0.673918\pi$$
$$662$$ 3.58212 6.20441i 0.139223 0.241141i
$$663$$ 0.149096 0.258243i 0.00579043 0.0100293i
$$664$$ −6.26008 + 3.61426i −0.242938 + 0.140260i
$$665$$ −4.40363 −0.170765
$$666$$ 4.74417 + 3.80694i 0.183833 + 0.147516i
$$667$$ −12.7827 −0.494948
$$668$$ −8.80330 + 5.08259i −0.340610 + 0.196651i
$$669$$ 4.07187 7.05269i 0.157428 0.272673i
$$670$$ −2.04849 + 3.54808i −0.0791400 + 0.137074i
$$671$$ 13.8888 + 8.01870i 0.536171 + 0.309559i
$$672$$ 0.535537i 0.0206588i
$$673$$ 19.1006 33.0832i 0.736273 1.27526i −0.217890 0.975973i $$-0.569917\pi$$
0.954163 0.299289i $$-0.0967493\pi$$
$$674$$ 22.9013i 0.882126i
$$675$$ 0.500000 + 0.866025i 0.0192450 + 0.0333333i
$$676$$ −12.5878 −0.484147
$$677$$ −27.9347 −1.07362 −0.536808 0.843704i $$-0.680370\pi$$
−0.536808 + 0.843704i $$0.680370\pi$$
$$678$$ −4.49294 7.78200i −0.172550 0.298866i
$$679$$ 2.52280 + 1.45654i 0.0968161 + 0.0558968i
$$680$$ 0.464463i 0.0178114i
$$681$$ 3.39960 1.96276i 0.130273 0.0752131i
$$682$$ −3.61375 6.25920i −0.138378 0.239677i
$$683$$ 17.2614 9.96585i 0.660487 0.381333i −0.131975 0.991253i $$-0.542132\pi$$
0.792463 + 0.609920i $$0.208799\pi$$
$$684$$ 7.12118 + 4.11142i 0.272285 + 0.157204i
$$685$$ −17.1430 9.89749i −0.654999 0.378164i
$$686$$ 6.36002 3.67196i 0.242827 0.140196i
$$687$$ 13.5993 + 23.5547i 0.518846 + 0.898667i
$$688$$ 0.906314 0.523261i 0.0345529 0.0199491i
$$689$$ 3.71226i 0.141426i
$$690$$ 2.05600 + 1.18703i 0.0782707 + 0.0451896i
$$691$$ −6.02368 10.4333i −0.229152 0.396902i 0.728405 0.685147i $$-0.240262\pi$$
−0.957557 + 0.288244i $$0.906929\pi$$
$$692$$ −15.4084 −0.585739
$$693$$ 2.91560 0.110755
$$694$$ 13.7693 + 23.8491i 0.522674 + 0.905298i
$$695$$ 7.33134i 0.278094i
$$696$$ −2.69215 + 4.66294i −0.102046 + 0.176748i
$$697$$ 4.51941i 0.171185i
$$698$$ 20.4892 + 11.8294i 0.775528 + 0.447751i
$$699$$ −5.55159 + 9.61564i −0.209980 + 0.363697i
$$700$$ −0.267768 + 0.463788i −0.0101207 + 0.0175295i
$$701$$ 34.1895 19.7393i 1.29132 0.745543i 0.312430 0.949941i $$-0.398857\pi$$
0.978888 + 0.204398i $$0.0655236\pi$$
$$702$$ −0.642016 −0.0242313
$$703$$ −39.0106 31.3039i −1.47131 1.18065i
$$704$$ −5.44426 −0.205188
$$705$$ 7.05055 4.07063i 0.265539 0.153309i
$$706$$ 2.74097 4.74750i 0.103158 0.178674i
$$707$$ −2.45145 + 4.24604i −0.0921963 + 0.159689i
$$708$$ 10.2224 + 5.90190i 0.384181 + 0.221807i
$$709$$ 14.5551i 0.546630i 0.961925 + 0.273315i $$0.0881202\pi$$
−0.961925 + 0.273315i $$0.911880\pi$$
$$710$$ 2.17408 3.76562i 0.0815918 0.141321i
$$711$$ 4.02455i 0.150932i
$$712$$ 2.13103 + 3.69105i 0.0798638 + 0.138328i
$$713$$ 3.15168 0.118031
$$714$$ −0.248737 −0.00930875
$$715$$ −1.74765 3.02702i −0.0653585 0.113204i
$$716$$ 6.85171 + 3.95584i 0.256061 + 0.147837i
$$717$$ 9.94702i 0.371478i
$$718$$ 17.5403 10.1269i 0.654597 0.377932i
$$719$$ 3.55656 + 6.16015i 0.132637 + 0.229735i 0.924692 0.380715i $$-0.124322\pi$$
−0.792055 + 0.610450i $$0.790989\pi$$
$$720$$ 0.866025 0.500000i 0.0322749 0.0186339i
$$721$$ 4.88439 + 2.82000i 0.181904 + 0.105022i
$$722$$ −42.1018 24.3075i −1.56687 0.904632i
$$723$$ 18.7127 10.8038i 0.695932 0.401797i
$$724$$ −4.86182 8.42093i −0.180688 0.312961i
$$725$$ 4.66294 2.69215i 0.173177 0.0999840i
$$726$$ 18.6400i 0.691795i
$$727$$ 23.4383 + 13.5321i 0.869277 + 0.501877i 0.867108 0.498121i $$-0.165976\pi$$
0.00216883 + 0.999998i $$0.499310\pi$$
$$728$$ −0.171911 0.297759i −0.00637146 0.0110357i
$$729$$ 1.00000 0.0370370
$$730$$ −1.60237 −0.0593064
$$731$$ −0.243035 0.420950i −0.00898899 0.0155694i
$$732$$ 2.94574i 0.108878i
$$733$$ −26.0354 + 45.0947i −0.961641 + 1.66561i −0.243259 + 0.969961i $$0.578217\pi$$
−0.718382 + 0.695649i $$0.755117\pi$$
$$734$$ 29.1273i 1.07511i
$$735$$ 5.81380 + 3.35660i 0.214445 + 0.123810i
$$736$$ 1.18703 2.05600i 0.0437546 0.0757852i
$$737$$ −11.1525 + 19.3167i −0.410808 + 0.711540i
$$738$$ 8.42677 4.86520i 0.310194 0.179090i
$$739$$ 24.0955 0.886369 0.443184 0.896430i $$-0.353849\pi$$
0.443184 + 0.896430i $$0.353849\pi$$
$$740$$ −5.66900 + 2.20510i −0.208396 + 0.0810612i
$$741$$ 5.27919 0.193936
$$742$$ 2.68172 1.54829i 0.0984489 0.0568395i
$$743$$ 5.81888 10.0786i 0.213474 0.369748i −0.739325 0.673348i $$-0.764856\pi$$
0.952799 + 0.303601i $$0.0981888\pi$$
$$744$$ 0.663773 1.14969i 0.0243351 0.0421496i
$$745$$ 7.12511 + 4.11369i 0.261044 + 0.150714i
$$746$$ 36.1494i 1.32352i
$$747$$ 3.61426 6.26008i 0.132239 0.229044i
$$748$$ 2.52866i 0.0924570i
$$749$$ −4.03934 6.99633i −0.147594 0.255641i
$$750$$ −1.00000 −0.0365148
$$751$$ −31.7490 −1.15854 −0.579268 0.815137i $$-0.696662\pi$$
−0.579268 + 0.815137i $$0.696662\pi$$
$$752$$ −4.07063 7.05055i −0.148441 0.257107i
$$753$$ −4.42041 2.55213i −0.161089 0.0930046i
$$754$$ 3.45681i 0.125890i
$$755$$ 8.63648 4.98628i 0.314314 0.181469i
$$756$$ 0.267768 + 0.463788i 0.00973864 + 0.0168678i
$$757$$ 11.4286 6.59830i 0.415379 0.239819i −0.277719 0.960662i $$-0.589578\pi$$
0.693098 + 0.720843i $$0.256245\pi$$
$$758$$ −18.8055 10.8574i −0.683048 0.394358i
$$759$$ 11.1934 + 6.46252i 0.406295 + 0.234575i
$$760$$ −7.12118 + 4.11142i −0.258312 + 0.149137i
$$761$$ 4.53306 + 7.85149i 0.164323 + 0.284616i 0.936415 0.350895i $$-0.114123\pi$$
−0.772091 + 0.635511i $$0.780789\pi$$
$$762$$ 10.3145 5.95507i 0.373654 0.215729i
$$763$$ 2.37517i 0.0859869i
$$764$$ 13.8689 + 8.00719i 0.501758 + 0.289690i
$$765$$ −0.232232 0.402237i −0.00839636 0.0145429i
$$766$$ 32.2698 1.16596
$$767$$ 7.57823 0.273634
$$768$$ −0.500000 0.866025i −0.0180422 0.0312500i
$$769$$ 18.2259i 0.657241i −0.944462 0.328621i $$-0.893416\pi$$
0.944462 0.328621i $$-0.106584\pi$$
$$770$$ −1.45780 + 2.52499i −0.0525355 + 0.0909941i
$$771$$ 19.4556i 0.700678i
$$772$$ 14.9525 + 8.63282i 0.538152 + 0.310702i
$$773$$ 7.27509 12.6008i 0.261667 0.453220i −0.705018 0.709189i $$-0.749061\pi$$
0.966685 + 0.255969i $$0.0823946\pi$$
$$774$$ −0.523261 + 0.906314i −0.0188082 + 0.0325768i
$$775$$ −1.14969 + 0.663773i −0.0412980 + 0.0238434i
$$776$$ 5.43955