# Properties

 Label 1170.2.i.o.991.1 Level $1170$ Weight $2$ Character 1170.991 Analytic conductor $9.342$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.34249703649$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{17})$$ Defining polynomial: $$x^{4} - x^{3} + 5 x^{2} + 4 x + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 991.1 Root $$1.28078 - 2.21837i$$ of defining polynomial Character $$\chi$$ $$=$$ 1170.991 Dual form 1170.2.i.o.451.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 + 3.08440i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.78078 + 3.08440i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-2.06155 - 3.57071i) q^{11} +(-3.34233 + 1.35234i) q^{13} -3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.56155 - 4.43674i) q^{17} +(1.78078 - 3.08440i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.06155 - 3.57071i) q^{22} +(-3.84233 - 6.65511i) q^{23} +1.00000 q^{25} +(-2.84233 - 2.21837i) q^{26} +(-1.78078 - 3.08440i) q^{28} +(3.28078 + 5.68247i) q^{29} +5.68466 q^{31} +(0.500000 - 0.866025i) q^{32} +5.12311 q^{34} +(1.78078 - 3.08440i) q^{35} +(-2.06155 - 3.57071i) q^{37} +3.56155 q^{38} +1.00000 q^{40} +(-2.12311 - 3.67733i) q^{41} +(-2.28078 + 3.95042i) q^{43} +4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} -7.00000 q^{47} +(-2.84233 - 4.92306i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.500000 - 3.57071i) q^{52} -4.43845 q^{53} +(2.06155 + 3.57071i) q^{55} +(1.78078 - 3.08440i) q^{56} +(-3.28078 + 5.68247i) q^{58} +(5.28078 - 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(2.84233 + 4.92306i) q^{62} +1.00000 q^{64} +(3.34233 - 1.35234i) q^{65} +(-7.12311 - 12.3376i) q^{67} +(2.56155 + 4.43674i) q^{68} +3.56155 q^{70} +(-2.43845 + 4.22351i) q^{71} -15.3693 q^{73} +(2.06155 - 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} +14.6847 q^{77} +7.43845 q^{79} +(0.500000 + 0.866025i) q^{80} +(2.12311 - 3.67733i) q^{82} -1.12311 q^{83} +(-2.56155 + 4.43674i) q^{85} -4.56155 q^{86} +(2.06155 + 3.57071i) q^{88} +(0.903882 + 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} +7.68466 q^{92} +(-3.50000 - 6.06218i) q^{94} +(-1.78078 + 3.08440i) q^{95} +(-0.561553 + 0.972638i) q^{97} +(2.84233 - 4.92306i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} - 2q^{4} - 4q^{5} - 3q^{7} - 4q^{8} + O(q^{10})$$ $$4q + 2q^{2} - 2q^{4} - 4q^{5} - 3q^{7} - 4q^{8} - 2q^{10} - q^{13} - 6q^{14} - 2q^{16} + 2q^{17} + 3q^{19} + 2q^{20} - 3q^{23} + 4q^{25} + q^{26} - 3q^{28} + 9q^{29} - 2q^{31} + 2q^{32} + 4q^{34} + 3q^{35} + 6q^{38} + 4q^{40} + 8q^{41} - 5q^{43} + 3q^{46} - 28q^{47} + q^{49} + 2q^{50} + 2q^{52} - 26q^{53} + 3q^{56} - 9q^{58} + 17q^{59} - 12q^{61} - q^{62} + 4q^{64} + q^{65} - 12q^{67} + 2q^{68} + 6q^{70} - 18q^{71} - 12q^{73} + 3q^{76} + 34q^{77} + 38q^{79} + 2q^{80} - 8q^{82} + 12q^{83} - 2q^{85} - 10q^{86} - 17q^{89} + 3q^{91} + 6q^{92} - 14q^{94} - 3q^{95} + 6q^{97} - q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$$.

 $$n$$ $$911$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ −1.78078 + 3.08440i −0.673070 + 1.16579i 0.303959 + 0.952685i $$0.401692\pi$$
−0.977029 + 0.213107i $$0.931642\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ −0.500000 0.866025i −0.158114 0.273861i
$$11$$ −2.06155 3.57071i −0.621582 1.07661i −0.989191 0.146631i $$-0.953157\pi$$
0.367610 0.929980i $$-0.380176\pi$$
$$12$$ 0 0
$$13$$ −3.34233 + 1.35234i −0.926995 + 0.375073i
$$14$$ −3.56155 −0.951865
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.56155 4.43674i 0.621268 1.07607i −0.367982 0.929833i $$-0.619951\pi$$
0.989250 0.146235i $$-0.0467154\pi$$
$$18$$ 0 0
$$19$$ 1.78078 3.08440i 0.408538 0.707609i −0.586188 0.810175i $$-0.699372\pi$$
0.994726 + 0.102566i $$0.0327054\pi$$
$$20$$ 0.500000 0.866025i 0.111803 0.193649i
$$21$$ 0 0
$$22$$ 2.06155 3.57071i 0.439525 0.761279i
$$23$$ −3.84233 6.65511i −0.801181 1.38769i −0.918839 0.394632i $$-0.870872\pi$$
0.117658 0.993054i $$-0.462461\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ −2.84233 2.21837i −0.557427 0.435058i
$$27$$ 0 0
$$28$$ −1.78078 3.08440i −0.336535 0.582896i
$$29$$ 3.28078 + 5.68247i 0.609225 + 1.05521i 0.991368 + 0.131105i $$0.0418527\pi$$
−0.382144 + 0.924103i $$0.624814\pi$$
$$30$$ 0 0
$$31$$ 5.68466 1.02099 0.510497 0.859879i $$-0.329461\pi$$
0.510497 + 0.859879i $$0.329461\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 5.12311 0.878605
$$35$$ 1.78078 3.08440i 0.301006 0.521358i
$$36$$ 0 0
$$37$$ −2.06155 3.57071i −0.338917 0.587022i 0.645312 0.763919i $$-0.276727\pi$$
−0.984229 + 0.176897i $$0.943394\pi$$
$$38$$ 3.56155 0.577760
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ −2.12311 3.67733i −0.331573 0.574302i 0.651247 0.758866i $$-0.274246\pi$$
−0.982821 + 0.184564i $$0.940913\pi$$
$$42$$ 0 0
$$43$$ −2.28078 + 3.95042i −0.347815 + 0.602433i −0.985861 0.167565i $$-0.946410\pi$$
0.638046 + 0.769998i $$0.279743\pi$$
$$44$$ 4.12311 0.621582
$$45$$ 0 0
$$46$$ 3.84233 6.65511i 0.566521 0.981242i
$$47$$ −7.00000 −1.02105 −0.510527 0.859861i $$-0.670550\pi$$
−0.510527 + 0.859861i $$0.670550\pi$$
$$48$$ 0 0
$$49$$ −2.84233 4.92306i −0.406047 0.703294i
$$50$$ 0.500000 + 0.866025i 0.0707107 + 0.122474i
$$51$$ 0 0
$$52$$ 0.500000 3.57071i 0.0693375 0.495169i
$$53$$ −4.43845 −0.609668 −0.304834 0.952406i $$-0.598601\pi$$
−0.304834 + 0.952406i $$0.598601\pi$$
$$54$$ 0 0
$$55$$ 2.06155 + 3.57071i 0.277980 + 0.481475i
$$56$$ 1.78078 3.08440i 0.237966 0.412170i
$$57$$ 0 0
$$58$$ −3.28078 + 5.68247i −0.430787 + 0.746145i
$$59$$ 5.28078 9.14657i 0.687499 1.19078i −0.285146 0.958484i $$-0.592042\pi$$
0.972645 0.232298i $$-0.0746246\pi$$
$$60$$ 0 0
$$61$$ −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i $$-0.958825\pi$$
0.607535 + 0.794293i $$0.292159\pi$$
$$62$$ 2.84233 + 4.92306i 0.360976 + 0.625229i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 3.34233 1.35234i 0.414565 0.167738i
$$66$$ 0 0
$$67$$ −7.12311 12.3376i −0.870226 1.50728i −0.861763 0.507311i $$-0.830639\pi$$
−0.00846293 0.999964i $$-0.502694\pi$$
$$68$$ 2.56155 + 4.43674i 0.310634 + 0.538034i
$$69$$ 0 0
$$70$$ 3.56155 0.425687
$$71$$ −2.43845 + 4.22351i −0.289390 + 0.501239i −0.973664 0.227986i $$-0.926786\pi$$
0.684274 + 0.729225i $$0.260119\pi$$
$$72$$ 0 0
$$73$$ −15.3693 −1.79884 −0.899421 0.437083i $$-0.856012\pi$$
−0.899421 + 0.437083i $$0.856012\pi$$
$$74$$ 2.06155 3.57071i 0.239651 0.415087i
$$75$$ 0 0
$$76$$ 1.78078 + 3.08440i 0.204269 + 0.353804i
$$77$$ 14.6847 1.67347
$$78$$ 0 0
$$79$$ 7.43845 0.836891 0.418445 0.908242i $$-0.362575\pi$$
0.418445 + 0.908242i $$0.362575\pi$$
$$80$$ 0.500000 + 0.866025i 0.0559017 + 0.0968246i
$$81$$ 0 0
$$82$$ 2.12311 3.67733i 0.234458 0.406093i
$$83$$ −1.12311 −0.123277 −0.0616384 0.998099i $$-0.519633\pi$$
−0.0616384 + 0.998099i $$0.519633\pi$$
$$84$$ 0 0
$$85$$ −2.56155 + 4.43674i −0.277839 + 0.481232i
$$86$$ −4.56155 −0.491885
$$87$$ 0 0
$$88$$ 2.06155 + 3.57071i 0.219762 + 0.380639i
$$89$$ 0.903882 + 1.56557i 0.0958113 + 0.165950i 0.909947 0.414725i $$-0.136122\pi$$
−0.814136 + 0.580675i $$0.802789\pi$$
$$90$$ 0 0
$$91$$ 1.78078 12.7173i 0.186676 1.33313i
$$92$$ 7.68466 0.801181
$$93$$ 0 0
$$94$$ −3.50000 6.06218i −0.360997 0.625266i
$$95$$ −1.78078 + 3.08440i −0.182704 + 0.316452i
$$96$$ 0 0
$$97$$ −0.561553 + 0.972638i −0.0570170 + 0.0987564i −0.893125 0.449808i $$-0.851492\pi$$
0.836108 + 0.548565i $$0.184826\pi$$
$$98$$ 2.84233 4.92306i 0.287119 0.497304i
$$99$$ 0 0
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ −8.56155 14.8290i −0.851906 1.47555i −0.879486 0.475925i $$-0.842113\pi$$
0.0275793 0.999620i $$-0.491220\pi$$
$$102$$ 0 0
$$103$$ 0.438447 0.0432015 0.0216007 0.999767i $$-0.493124\pi$$
0.0216007 + 0.999767i $$0.493124\pi$$
$$104$$ 3.34233 1.35234i 0.327742 0.132608i
$$105$$ 0 0
$$106$$ −2.21922 3.84381i −0.215550 0.373344i
$$107$$ 1.00000 + 1.73205i 0.0966736 + 0.167444i 0.910306 0.413936i $$-0.135846\pi$$
−0.813632 + 0.581380i $$0.802513\pi$$
$$108$$ 0 0
$$109$$ −20.2462 −1.93924 −0.969618 0.244625i $$-0.921335\pi$$
−0.969618 + 0.244625i $$0.921335\pi$$
$$110$$ −2.06155 + 3.57071i −0.196561 + 0.340454i
$$111$$ 0 0
$$112$$ 3.56155 0.336535
$$113$$ −1.84233 + 3.19101i −0.173312 + 0.300185i −0.939576 0.342341i $$-0.888780\pi$$
0.766264 + 0.642526i $$0.222113\pi$$
$$114$$ 0 0
$$115$$ 3.84233 + 6.65511i 0.358299 + 0.620592i
$$116$$ −6.56155 −0.609225
$$117$$ 0 0
$$118$$ 10.5616 0.972270
$$119$$ 9.12311 + 15.8017i 0.836314 + 1.44854i
$$120$$ 0 0
$$121$$ −3.00000 + 5.19615i −0.272727 + 0.472377i
$$122$$ −6.00000 −0.543214
$$123$$ 0 0
$$124$$ −2.84233 + 4.92306i −0.255249 + 0.442104i
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 2.21922 + 3.84381i 0.196924 + 0.341083i 0.947530 0.319668i $$-0.103571\pi$$
−0.750605 + 0.660751i $$0.770238\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 2.84233 + 2.21837i 0.249289 + 0.194564i
$$131$$ −6.12311 −0.534978 −0.267489 0.963561i $$-0.586194\pi$$
−0.267489 + 0.963561i $$0.586194\pi$$
$$132$$ 0 0
$$133$$ 6.34233 + 10.9852i 0.549950 + 0.952541i
$$134$$ 7.12311 12.3376i 0.615343 1.06580i
$$135$$ 0 0
$$136$$ −2.56155 + 4.43674i −0.219651 + 0.380447i
$$137$$ −4.40388 + 7.62775i −0.376249 + 0.651682i −0.990513 0.137418i $$-0.956120\pi$$
0.614264 + 0.789101i $$0.289453\pi$$
$$138$$ 0 0
$$139$$ −4.21922 + 7.30791i −0.357870 + 0.619849i −0.987605 0.156961i $$-0.949830\pi$$
0.629735 + 0.776810i $$0.283164\pi$$
$$140$$ 1.78078 + 3.08440i 0.150503 + 0.260679i
$$141$$ 0 0
$$142$$ −4.87689 −0.409260
$$143$$ 11.7192 + 9.14657i 0.980011 + 0.764875i
$$144$$ 0 0
$$145$$ −3.28078 5.68247i −0.272454 0.471904i
$$146$$ −7.68466 13.3102i −0.635987 1.10156i
$$147$$ 0 0
$$148$$ 4.12311 0.338917
$$149$$ −11.4039 + 19.7521i −0.934242 + 1.61816i −0.158263 + 0.987397i $$0.550589\pi$$
−0.775979 + 0.630758i $$0.782744\pi$$
$$150$$ 0 0
$$151$$ 9.36932 0.762464 0.381232 0.924479i $$-0.375500\pi$$
0.381232 + 0.924479i $$0.375500\pi$$
$$152$$ −1.78078 + 3.08440i −0.144440 + 0.250177i
$$153$$ 0 0
$$154$$ 7.34233 + 12.7173i 0.591662 + 1.02479i
$$155$$ −5.68466 −0.456603
$$156$$ 0 0
$$157$$ 22.1231 1.76562 0.882808 0.469734i $$-0.155650\pi$$
0.882808 + 0.469734i $$0.155650\pi$$
$$158$$ 3.71922 + 6.44188i 0.295886 + 0.512489i
$$159$$ 0 0
$$160$$ −0.500000 + 0.866025i −0.0395285 + 0.0684653i
$$161$$ 27.3693 2.15700
$$162$$ 0 0
$$163$$ 9.28078 16.0748i 0.726927 1.25907i −0.231250 0.972894i $$-0.574281\pi$$
0.958176 0.286179i $$-0.0923853\pi$$
$$164$$ 4.24621 0.331573
$$165$$ 0 0
$$166$$ −0.561553 0.972638i −0.0435850 0.0754913i
$$167$$ −10.1847 17.6403i −0.788113 1.36505i −0.927122 0.374760i $$-0.877725\pi$$
0.139009 0.990291i $$-0.455608\pi$$
$$168$$ 0 0
$$169$$ 9.34233 9.03996i 0.718641 0.695382i
$$170$$ −5.12311 −0.392924
$$171$$ 0 0
$$172$$ −2.28078 3.95042i −0.173908 0.301217i
$$173$$ −12.5885 + 21.8040i −0.957089 + 1.65773i −0.227575 + 0.973760i $$0.573080\pi$$
−0.729514 + 0.683966i $$0.760254\pi$$
$$174$$ 0 0
$$175$$ −1.78078 + 3.08440i −0.134614 + 0.233158i
$$176$$ −2.06155 + 3.57071i −0.155395 + 0.269153i
$$177$$ 0 0
$$178$$ −0.903882 + 1.56557i −0.0677488 + 0.117344i
$$179$$ −0.157671 0.273094i −0.0117849 0.0204120i 0.860073 0.510171i $$-0.170418\pi$$
−0.871858 + 0.489759i $$0.837085\pi$$
$$180$$ 0 0
$$181$$ 11.1231 0.826774 0.413387 0.910555i $$-0.364346\pi$$
0.413387 + 0.910555i $$0.364346\pi$$
$$182$$ 11.9039 4.81645i 0.882374 0.357019i
$$183$$ 0 0
$$184$$ 3.84233 + 6.65511i 0.283260 + 0.490621i
$$185$$ 2.06155 + 3.57071i 0.151568 + 0.262524i
$$186$$ 0 0
$$187$$ −21.1231 −1.54467
$$188$$ 3.50000 6.06218i 0.255264 0.442130i
$$189$$ 0 0
$$190$$ −3.56155 −0.258382
$$191$$ 9.56155 16.5611i 0.691850 1.19832i −0.279381 0.960180i $$-0.590129\pi$$
0.971231 0.238139i $$-0.0765373\pi$$
$$192$$ 0 0
$$193$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$194$$ −1.12311 −0.0806343
$$195$$ 0 0
$$196$$ 5.68466 0.406047
$$197$$ −3.90388 6.76172i −0.278140 0.481753i 0.692782 0.721147i $$-0.256385\pi$$
−0.970923 + 0.239394i $$0.923051\pi$$
$$198$$ 0 0
$$199$$ −5.56155 + 9.63289i −0.394248 + 0.682858i −0.993005 0.118073i $$-0.962328\pi$$
0.598757 + 0.800931i $$0.295662\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 0 0
$$202$$ 8.56155 14.8290i 0.602389 1.04337i
$$203$$ −23.3693 −1.64020
$$204$$ 0 0
$$205$$ 2.12311 + 3.67733i 0.148284 + 0.256836i
$$206$$ 0.219224 + 0.379706i 0.0152740 + 0.0264554i
$$207$$ 0 0
$$208$$ 2.84233 + 2.21837i 0.197080 + 0.153816i
$$209$$ −14.6847 −1.01576
$$210$$ 0 0
$$211$$ −3.46543 6.00231i −0.238570 0.413216i 0.721734 0.692171i $$-0.243345\pi$$
−0.960304 + 0.278955i $$0.910012\pi$$
$$212$$ 2.21922 3.84381i 0.152417 0.263994i
$$213$$ 0 0
$$214$$ −1.00000 + 1.73205i −0.0683586 + 0.118401i
$$215$$ 2.28078 3.95042i 0.155548 0.269416i
$$216$$ 0 0
$$217$$ −10.1231 + 17.5337i −0.687201 + 1.19027i
$$218$$ −10.1231 17.5337i −0.685623 1.18753i
$$219$$ 0 0
$$220$$ −4.12311 −0.277980
$$221$$ −2.56155 + 18.2931i −0.172309 + 1.23053i
$$222$$ 0 0
$$223$$ 13.1501 + 22.7766i 0.880595 + 1.52524i 0.850680 + 0.525683i $$0.176190\pi$$
0.0299151 + 0.999552i $$0.490476\pi$$
$$224$$ 1.78078 + 3.08440i 0.118983 + 0.206085i
$$225$$ 0 0
$$226$$ −3.68466 −0.245100
$$227$$ −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i $$0.397691\pi$$
−0.979630 + 0.200812i $$0.935642\pi$$
$$228$$ 0 0
$$229$$ −7.75379 −0.512385 −0.256192 0.966626i $$-0.582468\pi$$
−0.256192 + 0.966626i $$0.582468\pi$$
$$230$$ −3.84233 + 6.65511i −0.253356 + 0.438825i
$$231$$ 0 0
$$232$$ −3.28078 5.68247i −0.215394 0.373073i
$$233$$ 17.6847 1.15856 0.579280 0.815128i $$-0.303334\pi$$
0.579280 + 0.815128i $$0.303334\pi$$
$$234$$ 0 0
$$235$$ 7.00000 0.456630
$$236$$ 5.28078 + 9.14657i 0.343749 + 0.595391i
$$237$$ 0 0
$$238$$ −9.12311 + 15.8017i −0.591363 + 1.02427i
$$239$$ −13.3693 −0.864789 −0.432395 0.901684i $$-0.642331\pi$$
−0.432395 + 0.901684i $$0.642331\pi$$
$$240$$ 0 0
$$241$$ 9.93845 17.2139i 0.640192 1.10884i −0.345198 0.938530i $$-0.612188\pi$$
0.985390 0.170315i $$-0.0544784\pi$$
$$242$$ −6.00000 −0.385695
$$243$$ 0 0
$$244$$ −3.00000 5.19615i −0.192055 0.332650i
$$245$$ 2.84233 + 4.92306i 0.181590 + 0.314523i
$$246$$ 0 0
$$247$$ −1.78078 + 12.7173i −0.113308 + 0.809182i
$$248$$ −5.68466 −0.360976
$$249$$ 0 0
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ 0.0615528 0.106613i 0.00388518 0.00672933i −0.864076 0.503361i $$-0.832097\pi$$
0.867961 + 0.496632i $$0.165430\pi$$
$$252$$ 0 0
$$253$$ −15.8423 + 27.4397i −0.995999 + 1.72512i
$$254$$ −2.21922 + 3.84381i −0.139246 + 0.241182i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −0.719224 1.24573i −0.0448639 0.0777066i 0.842721 0.538350i $$-0.180952\pi$$
−0.887585 + 0.460643i $$0.847619\pi$$
$$258$$ 0 0
$$259$$ 14.6847 0.912460
$$260$$ −0.500000 + 3.57071i −0.0310087 + 0.221446i
$$261$$ 0 0
$$262$$ −3.06155 5.30277i −0.189143 0.327606i
$$263$$ −6.50000 11.2583i −0.400807 0.694218i 0.593016 0.805190i $$-0.297937\pi$$
−0.993824 + 0.110972i $$0.964604\pi$$
$$264$$ 0 0
$$265$$ 4.43845 0.272652
$$266$$ −6.34233 + 10.9852i −0.388873 + 0.673548i
$$267$$ 0 0
$$268$$ 14.2462 0.870226
$$269$$ −1.68466 + 2.91791i −0.102715 + 0.177908i −0.912803 0.408401i $$-0.866086\pi$$
0.810087 + 0.586310i $$0.199420\pi$$
$$270$$ 0 0
$$271$$ −16.0885 27.8662i −0.977309 1.69275i −0.672094 0.740466i $$-0.734605\pi$$
−0.305215 0.952283i $$-0.598728\pi$$
$$272$$ −5.12311 −0.310634
$$273$$ 0 0
$$274$$ −8.80776 −0.532096
$$275$$ −2.06155 3.57071i −0.124316 0.215322i
$$276$$ 0 0
$$277$$ 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i $$-0.823769\pi$$
0.880656 + 0.473757i $$0.157103\pi$$
$$278$$ −8.43845 −0.506104
$$279$$ 0 0
$$280$$ −1.78078 + 3.08440i −0.106422 + 0.184328i
$$281$$ 0.246211 0.0146877 0.00734387 0.999973i $$-0.497662\pi$$
0.00734387 + 0.999973i $$0.497662\pi$$
$$282$$ 0 0
$$283$$ −5.71922 9.90599i −0.339973 0.588850i 0.644455 0.764643i $$-0.277084\pi$$
−0.984427 + 0.175793i $$0.943751\pi$$
$$284$$ −2.43845 4.22351i −0.144695 0.250619i
$$285$$ 0 0
$$286$$ −2.06155 + 14.7224i −0.121902 + 0.870556i
$$287$$ 15.1231 0.892689
$$288$$ 0 0
$$289$$ −4.62311 8.00745i −0.271947 0.471027i
$$290$$ 3.28078 5.68247i 0.192654 0.333686i
$$291$$ 0 0
$$292$$ 7.68466 13.3102i 0.449711 0.778922i
$$293$$ −12.4654 + 21.5908i −0.728238 + 1.26135i 0.229389 + 0.973335i $$0.426327\pi$$
−0.957627 + 0.288011i $$0.907006\pi$$
$$294$$ 0 0
$$295$$ −5.28078 + 9.14657i −0.307459 + 0.532534i
$$296$$ 2.06155 + 3.57071i 0.119825 + 0.207544i
$$297$$ 0 0
$$298$$ −22.8078 −1.32122
$$299$$ 21.8423 + 17.0474i 1.26317 + 0.985877i
$$300$$ 0 0
$$301$$ −8.12311 14.0696i −0.468208 0.810960i
$$302$$ 4.68466 + 8.11407i 0.269572 + 0.466912i
$$303$$ 0 0
$$304$$ −3.56155 −0.204269
$$305$$ 3.00000 5.19615i 0.171780 0.297531i
$$306$$ 0 0
$$307$$ −15.6155 −0.891225 −0.445613 0.895226i $$-0.647014\pi$$
−0.445613 + 0.895226i $$0.647014\pi$$
$$308$$ −7.34233 + 12.7173i −0.418368 + 0.724635i
$$309$$ 0 0
$$310$$ −2.84233 4.92306i −0.161433 0.279611i
$$311$$ 18.7386 1.06257 0.531285 0.847193i $$-0.321709\pi$$
0.531285 + 0.847193i $$0.321709\pi$$
$$312$$ 0 0
$$313$$ 6.63068 0.374788 0.187394 0.982285i $$-0.439996\pi$$
0.187394 + 0.982285i $$0.439996\pi$$
$$314$$ 11.0616 + 19.1592i 0.624240 + 1.08121i
$$315$$ 0 0
$$316$$ −3.71922 + 6.44188i −0.209223 + 0.362384i
$$317$$ 4.19224 0.235459 0.117730 0.993046i $$-0.462438\pi$$
0.117730 + 0.993046i $$0.462438\pi$$
$$318$$ 0 0
$$319$$ 13.5270 23.4294i 0.757366 1.31180i
$$320$$ −1.00000 −0.0559017
$$321$$ 0 0
$$322$$ 13.6847 + 23.7025i 0.762616 + 1.32089i
$$323$$ −9.12311 15.8017i −0.507623 0.879229i
$$324$$ 0 0
$$325$$ −3.34233 + 1.35234i −0.185399 + 0.0750146i
$$326$$ 18.5616 1.02803
$$327$$ 0 0
$$328$$ 2.12311 + 3.67733i 0.117229 + 0.203046i
$$329$$ 12.4654 21.5908i 0.687242 1.19034i
$$330$$ 0 0
$$331$$ 9.36932 16.2281i 0.514984 0.891979i −0.484865 0.874589i $$-0.661131\pi$$
0.999849 0.0173896i $$-0.00553556\pi$$
$$332$$ 0.561553 0.972638i 0.0308192 0.0533804i
$$333$$ 0 0
$$334$$ 10.1847 17.6403i 0.557280 0.965237i
$$335$$ 7.12311 + 12.3376i 0.389177 + 0.674074i
$$336$$ 0 0
$$337$$ −6.00000 −0.326841 −0.163420 0.986557i $$-0.552253\pi$$
−0.163420 + 0.986557i $$0.552253\pi$$
$$338$$ 12.5000 + 3.57071i 0.679910 + 0.194221i
$$339$$ 0 0
$$340$$ −2.56155 4.43674i −0.138920 0.240616i
$$341$$ −11.7192 20.2983i −0.634632 1.09921i
$$342$$ 0 0
$$343$$ −4.68466 −0.252948
$$344$$ 2.28078 3.95042i 0.122971 0.212992i
$$345$$ 0 0
$$346$$ −25.1771 −1.35353
$$347$$ 4.56155 7.90084i 0.244877 0.424139i −0.717220 0.696847i $$-0.754586\pi$$
0.962097 + 0.272707i $$0.0879191\pi$$
$$348$$ 0 0
$$349$$ 12.2462 + 21.2111i 0.655525 + 1.13540i 0.981762 + 0.190114i $$0.0608858\pi$$
−0.326237 + 0.945288i $$0.605781\pi$$
$$350$$ −3.56155 −0.190373
$$351$$ 0 0
$$352$$ −4.12311 −0.219762
$$353$$ 15.9309 + 27.5931i 0.847915 + 1.46863i 0.883066 + 0.469249i $$0.155475\pi$$
−0.0351511 + 0.999382i $$0.511191\pi$$
$$354$$ 0 0
$$355$$ 2.43845 4.22351i 0.129419 0.224161i
$$356$$ −1.80776 −0.0958113
$$357$$ 0 0
$$358$$ 0.157671 0.273094i 0.00833316 0.0144335i
$$359$$ −4.87689 −0.257393 −0.128696 0.991684i $$-0.541079\pi$$
−0.128696 + 0.991684i $$0.541079\pi$$
$$360$$ 0 0
$$361$$ 3.15767 + 5.46925i 0.166193 + 0.287855i
$$362$$ 5.56155 + 9.63289i 0.292309 + 0.506294i
$$363$$ 0 0
$$364$$ 10.1231 + 7.90084i 0.530595 + 0.414117i
$$365$$ 15.3693 0.804467
$$366$$ 0 0
$$367$$ 10.2462 + 17.7470i 0.534848 + 0.926384i 0.999171 + 0.0407177i $$0.0129644\pi$$
−0.464323 + 0.885666i $$0.653702\pi$$
$$368$$ −3.84233 + 6.65511i −0.200295 + 0.346922i
$$369$$ 0 0
$$370$$ −2.06155 + 3.57071i −0.107175 + 0.185633i
$$371$$ 7.90388 13.6899i 0.410349 0.710746i
$$372$$ 0 0
$$373$$ 2.59612 4.49661i 0.134422 0.232826i −0.790955 0.611875i $$-0.790416\pi$$
0.925376 + 0.379049i $$0.123749\pi$$
$$374$$ −10.5616 18.2931i −0.546125 0.945916i
$$375$$ 0 0
$$376$$ 7.00000 0.360997
$$377$$ −18.6501 14.5560i −0.960529 0.749670i
$$378$$ 0 0
$$379$$ 2.65767 + 4.60322i 0.136515 + 0.236452i 0.926175 0.377093i $$-0.123076\pi$$
−0.789660 + 0.613545i $$0.789743\pi$$
$$380$$ −1.78078 3.08440i −0.0913519 0.158226i
$$381$$ 0 0
$$382$$ 19.1231 0.978423
$$383$$ 10.4039 18.0201i 0.531614 0.920782i −0.467706 0.883884i $$-0.654919\pi$$
0.999319 0.0368973i $$-0.0117474\pi$$
$$384$$ 0 0
$$385$$ −14.6847 −0.748399
$$386$$ 0 0
$$387$$ 0 0
$$388$$ −0.561553 0.972638i −0.0285085 0.0493782i
$$389$$ −19.0540 −0.966075 −0.483037 0.875600i $$-0.660467\pi$$
−0.483037 + 0.875600i $$0.660467\pi$$
$$390$$ 0 0
$$391$$ −39.3693 −1.99099
$$392$$ 2.84233 + 4.92306i 0.143559 + 0.248652i
$$393$$ 0 0
$$394$$ 3.90388 6.76172i 0.196675 0.340651i
$$395$$ −7.43845 −0.374269
$$396$$ 0 0
$$397$$ 5.93845 10.2857i 0.298042 0.516224i −0.677646 0.735388i $$-0.737000\pi$$
0.975688 + 0.219164i $$0.0703331\pi$$
$$398$$ −11.1231 −0.557551
$$399$$ 0 0
$$400$$ −0.500000 0.866025i −0.0250000 0.0433013i
$$401$$ 6.34233 + 10.9852i 0.316721 + 0.548577i 0.979802 0.199971i $$-0.0640848\pi$$
−0.663081 + 0.748548i $$0.730752\pi$$
$$402$$ 0 0
$$403$$ −19.0000 + 7.68762i −0.946457 + 0.382947i
$$404$$ 17.1231 0.851906
$$405$$ 0 0
$$406$$ −11.6847 20.2384i −0.579900 1.00442i
$$407$$ −8.50000 + 14.7224i −0.421329 + 0.729764i
$$408$$ 0 0
$$409$$ −0.903882 + 1.56557i −0.0446941 + 0.0774124i −0.887507 0.460794i $$-0.847565\pi$$
0.842813 + 0.538207i $$0.180898\pi$$
$$410$$ −2.12311 + 3.67733i −0.104853 + 0.181610i
$$411$$ 0 0
$$412$$ −0.219224 + 0.379706i −0.0108004 + 0.0187068i
$$413$$ 18.8078 + 32.5760i 0.925470 + 1.60296i
$$414$$ 0 0
$$415$$ 1.12311 0.0551311
$$416$$ −0.500000 + 3.57071i −0.0245145 + 0.175069i
$$417$$ 0 0
$$418$$ −7.34233 12.7173i −0.359125 0.622023i
$$419$$ −0.246211 0.426450i −0.0120282 0.0208335i 0.859949 0.510381i $$-0.170495\pi$$
−0.871977 + 0.489547i $$0.837162\pi$$
$$420$$ 0 0
$$421$$ 0.492423 0.0239992 0.0119996 0.999928i $$-0.496180\pi$$
0.0119996 + 0.999928i $$0.496180\pi$$
$$422$$ 3.46543 6.00231i 0.168695 0.292188i
$$423$$ 0 0
$$424$$ 4.43845 0.215550
$$425$$ 2.56155 4.43674i 0.124254 0.215213i
$$426$$ 0 0
$$427$$ −10.6847 18.5064i −0.517067 0.895586i
$$428$$ −2.00000 −0.0966736
$$429$$ 0 0
$$430$$ 4.56155 0.219978
$$431$$ 13.3693 + 23.1563i 0.643977 + 1.11540i 0.984537 + 0.175178i $$0.0560502\pi$$
−0.340559 + 0.940223i $$0.610616\pi$$
$$432$$ 0 0
$$433$$ −15.3693 + 26.6204i −0.738602 + 1.27930i 0.214523 + 0.976719i $$0.431180\pi$$
−0.953125 + 0.302578i $$0.902153\pi$$
$$434$$ −20.2462 −0.971849
$$435$$ 0 0
$$436$$ 10.1231 17.5337i 0.484809 0.839714i
$$437$$ −27.3693 −1.30925
$$438$$ 0 0
$$439$$ −8.43845 14.6158i −0.402745 0.697575i 0.591311 0.806444i $$-0.298611\pi$$
−0.994056 + 0.108869i $$0.965277\pi$$
$$440$$ −2.06155 3.57071i −0.0982807 0.170227i
$$441$$ 0 0
$$442$$ −17.1231 + 6.92820i −0.814463 + 0.329541i
$$443$$ 4.87689 0.231708 0.115854 0.993266i $$-0.463039\pi$$
0.115854 + 0.993266i $$0.463039\pi$$
$$444$$ 0 0
$$445$$ −0.903882 1.56557i −0.0428481 0.0742151i
$$446$$ −13.1501 + 22.7766i −0.622675 + 1.07850i
$$447$$ 0 0
$$448$$ −1.78078 + 3.08440i −0.0841338 + 0.145724i
$$449$$ 12.5885 21.8040i 0.594090 1.02899i −0.399585 0.916696i $$-0.630846\pi$$
0.993675 0.112298i $$-0.0358210\pi$$
$$450$$ 0 0
$$451$$ −8.75379 + 15.1620i −0.412200 + 0.713951i
$$452$$ −1.84233 3.19101i −0.0866559 0.150092i
$$453$$ 0 0
$$454$$ −20.0000 −0.938647
$$455$$ −1.78078 + 12.7173i −0.0834841 + 0.596196i
$$456$$ 0 0
$$457$$ −1.87689 3.25088i −0.0877974 0.152070i 0.818782 0.574104i $$-0.194649\pi$$
−0.906580 + 0.422034i $$0.861316\pi$$
$$458$$ −3.87689 6.71498i −0.181155 0.313770i
$$459$$ 0 0
$$460$$ −7.68466 −0.358299
$$461$$ 3.52699 6.10892i 0.164268 0.284521i −0.772127 0.635468i $$-0.780807\pi$$
0.936395 + 0.350947i $$0.114140\pi$$
$$462$$ 0 0
$$463$$ 33.6155 1.56225 0.781123 0.624377i $$-0.214647\pi$$
0.781123 + 0.624377i $$0.214647\pi$$
$$464$$ 3.28078 5.68247i 0.152306 0.263802i
$$465$$ 0 0
$$466$$ 8.84233 + 15.3154i 0.409613 + 0.709471i
$$467$$ −39.8617 −1.84458 −0.922291 0.386497i $$-0.873685\pi$$
−0.922291 + 0.386497i $$0.873685\pi$$
$$468$$ 0 0
$$469$$ 50.7386 2.34289
$$470$$ 3.50000 + 6.06218i 0.161443 + 0.279627i
$$471$$ 0 0
$$472$$ −5.28078 + 9.14657i −0.243067 + 0.421005i
$$473$$ 18.8078 0.864782
$$474$$ 0 0
$$475$$ 1.78078 3.08440i 0.0817076 0.141522i
$$476$$ −18.2462 −0.836314
$$477$$ 0 0
$$478$$ −6.68466 11.5782i −0.305749 0.529573i
$$479$$ −10.8769 18.8393i −0.496978 0.860791i 0.503016 0.864277i $$-0.332224\pi$$
−0.999994 + 0.00348601i $$0.998890\pi$$
$$480$$ 0 0
$$481$$ 11.7192 + 9.14657i 0.534351 + 0.417048i
$$482$$ 19.8769 0.905368
$$483$$ 0 0
$$484$$ −3.00000 5.19615i −0.136364 0.236189i
$$485$$ 0.561553 0.972638i 0.0254988 0.0441652i
$$486$$ 0 0
$$487$$ 12.0270 20.8314i 0.544995 0.943959i −0.453612 0.891199i $$-0.649865\pi$$
0.998607 0.0527597i $$-0.0168017\pi$$
$$488$$ 3.00000 5.19615i 0.135804 0.235219i
$$489$$ 0 0
$$490$$ −2.84233 + 4.92306i −0.128403 + 0.222401i
$$491$$ −10.7808 18.6729i −0.486530 0.842694i 0.513350 0.858179i $$-0.328404\pi$$
−0.999880 + 0.0154850i $$0.995071\pi$$
$$492$$ 0 0
$$493$$ 33.6155 1.51397
$$494$$ −11.9039 + 4.81645i −0.535581 + 0.216702i
$$495$$ 0 0
$$496$$ −2.84233 4.92306i −0.127624 0.221052i
$$497$$ −8.68466 15.0423i −0.389560 0.674738i
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 0.500000 0.866025i 0.0223607 0.0387298i
$$501$$ 0 0
$$502$$ 0.123106 0.00549447
$$503$$ −2.97301 + 5.14941i −0.132560 + 0.229601i −0.924663 0.380787i $$-0.875653\pi$$
0.792103 + 0.610388i $$0.208986\pi$$
$$504$$ 0 0
$$505$$ 8.56155 + 14.8290i 0.380984 + 0.659884i
$$506$$ −31.6847 −1.40855
$$507$$ 0 0
$$508$$ −4.43845 −0.196924
$$509$$ −14.7732 25.5879i −0.654811 1.13417i −0.981941 0.189186i $$-0.939415\pi$$
0.327131 0.944979i $$-0.393918\pi$$
$$510$$ 0 0
$$511$$ 27.3693 47.4050i 1.21075 2.09708i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 0.719224 1.24573i 0.0317236 0.0549469i
$$515$$ −0.438447 −0.0193203
$$516$$ 0 0
$$517$$ 14.4309 + 24.9950i 0.634669 + 1.09928i
$$518$$ 7.34233 + 12.7173i 0.322603 + 0.558766i
$$519$$ 0 0
$$520$$ −3.34233 + 1.35234i −0.146571 + 0.0593042i
$$521$$ 18.6847 0.818590 0.409295 0.912402i $$-0.365775\pi$$
0.409295 + 0.912402i $$0.365775\pi$$
$$522$$ 0 0
$$523$$ 4.59612 + 7.96071i 0.200974 + 0.348098i 0.948843 0.315749i $$-0.102256\pi$$
−0.747868 + 0.663847i $$0.768923\pi$$
$$524$$ 3.06155 5.30277i 0.133745 0.231652i
$$525$$ 0 0
$$526$$ 6.50000 11.2583i 0.283413 0.490887i
$$527$$ 14.5616 25.2213i 0.634311 1.09866i
$$528$$ 0 0
$$529$$ −18.0270 + 31.2237i −0.783782 + 1.35755i
$$530$$ 2.21922 + 3.84381i 0.0963969 + 0.166964i
$$531$$ 0 0
$$532$$ −12.6847 −0.549950
$$533$$ 12.0691 + 9.41967i 0.522772 + 0.408011i
$$534$$ 0 0
$$535$$ −1.00000 1.73205i −0.0432338 0.0748831i
$$536$$ 7.12311 + 12.3376i 0.307671 + 0.532902i
$$537$$ 0 0
$$538$$ −3.36932 −0.145262
$$539$$ −11.7192 + 20.2983i −0.504783 + 0.874309i
$$540$$ 0 0
$$541$$ −2.63068 −0.113102 −0.0565510 0.998400i $$-0.518010\pi$$
−0.0565510 + 0.998400i $$0.518010\pi$$
$$542$$ 16.0885 27.8662i 0.691062 1.19695i
$$543$$ 0 0
$$544$$ −2.56155 4.43674i −0.109826 0.190224i
$$545$$ 20.2462 0.867252
$$546$$ 0 0
$$547$$ 35.6155 1.52281 0.761405 0.648276i $$-0.224510\pi$$
0.761405 + 0.648276i $$0.224510\pi$$
$$548$$ −4.40388 7.62775i −0.188125 0.325841i
$$549$$ 0 0
$$550$$ 2.06155 3.57071i 0.0879049 0.152256i
$$551$$ 23.3693 0.995566
$$552$$ 0 0
$$553$$ −13.2462 + 22.9431i −0.563286 + 0.975640i
$$554$$ 1.00000 0.0424859
$$555$$ 0 0
$$556$$ −4.21922 7.30791i −0.178935 0.309924i
$$557$$ −2.21922 3.84381i −0.0940315 0.162867i 0.815172 0.579218i $$-0.196642\pi$$
−0.909204 + 0.416351i $$0.863309\pi$$
$$558$$ 0 0
$$559$$ 2.28078 16.2880i 0.0964666 0.688909i
$$560$$ −3.56155 −0.150503
$$561$$ 0 0
$$562$$ 0.123106 + 0.213225i 0.00519290 + 0.00899436i
$$563$$ 16.4924 28.5657i 0.695073 1.20390i −0.275083 0.961420i $$-0.588705\pi$$
0.970156 0.242481i $$-0.0779612\pi$$
$$564$$ 0 0
$$565$$ 1.84233 3.19101i 0.0775074 0.134247i
$$566$$ 5.71922 9.90599i 0.240397 0.416380i
$$567$$ 0 0
$$568$$ 2.43845 4.22351i 0.102315 0.177215i
$$569$$ −9.58854 16.6078i −0.401973 0.696237i 0.591991 0.805944i $$-0.298342\pi$$
−0.993964 + 0.109707i $$0.965009\pi$$
$$570$$ 0 0
$$571$$ 11.3153 0.473532 0.236766 0.971567i $$-0.423912\pi$$
0.236766 + 0.971567i $$0.423912\pi$$
$$572$$ −13.7808 + 5.57586i −0.576203 + 0.233138i
$$573$$ 0 0
$$574$$ 7.56155 + 13.0970i 0.315613 + 0.546658i
$$575$$ −3.84233 6.65511i −0.160236 0.277537i
$$576$$ 0 0
$$577$$ 8.73863 0.363794 0.181897 0.983318i $$-0.441776\pi$$
0.181897 + 0.983318i $$0.441776\pi$$
$$578$$ 4.62311 8.00745i 0.192296 0.333066i
$$579$$ 0 0
$$580$$ 6.56155 0.272454
$$581$$ 2.00000 3.46410i 0.0829740 0.143715i
$$582$$ 0 0
$$583$$ 9.15009 + 15.8484i 0.378958 + 0.656375i
$$584$$ 15.3693 0.635987
$$585$$ 0 0
$$586$$ −24.9309 −1.02988
$$587$$ −11.8769 20.5714i −0.490212 0.849072i 0.509725 0.860338i $$-0.329747\pi$$
−0.999937 + 0.0112657i $$0.996414\pi$$
$$588$$ 0 0
$$589$$ 10.1231 17.5337i 0.417115 0.722465i
$$590$$ −10.5616 −0.434812
$$591$$ 0 0
$$592$$ −2.06155 + 3.57071i −0.0847293 + 0.146755i
$$593$$ 12.1771 0.500053 0.250026 0.968239i $$-0.419561\pi$$
0.250026 + 0.968239i $$0.419561\pi$$
$$594$$ 0 0
$$595$$ −9.12311 15.8017i −0.374011 0.647806i
$$596$$ −11.4039 19.7521i −0.467121 0.809078i
$$597$$ 0 0
$$598$$ −3.84233 + 27.4397i −0.157125 + 1.12209i
$$599$$ 14.0000 0.572024 0.286012 0.958226i $$-0.407670\pi$$
0.286012 + 0.958226i $$0.407670\pi$$
$$600$$ 0 0
$$601$$ 17.9924 + 31.1638i 0.733926 + 1.27120i 0.955193 + 0.295984i $$0.0956476\pi$$
−0.221267 + 0.975213i $$0.571019\pi$$
$$602$$ 8.12311 14.0696i 0.331073 0.573435i
$$603$$ 0 0
$$604$$ −4.68466 + 8.11407i −0.190616 + 0.330157i
$$605$$ 3.00000 5.19615i 0.121967 0.211254i
$$606$$ 0 0
$$607$$ 14.7116 25.4813i 0.597127 1.03425i −0.396116 0.918201i $$-0.629642\pi$$
0.993243 0.116054i $$-0.0370246\pi$$
$$608$$ −1.78078 3.08440i −0.0722200 0.125089i
$$609$$ 0 0
$$610$$ 6.00000 0.242933
$$611$$ 23.3963 9.46641i 0.946513 0.382970i
$$612$$ 0 0
$$613$$ −14.0616 24.3553i −0.567941 0.983702i −0.996769 0.0803164i $$-0.974407\pi$$
0.428829 0.903386i $$-0.358926\pi$$
$$614$$ −7.80776 13.5234i −0.315096 0.545762i
$$615$$ 0 0
$$616$$ −14.6847 −0.591662
$$617$$ −20.8423 + 36.1000i −0.839081 + 1.45333i 0.0515837 + 0.998669i $$0.483573\pi$$
−0.890664 + 0.454662i $$0.849760\pi$$
$$618$$ 0 0
$$619$$ −16.4384 −0.660717 −0.330358 0.943856i $$-0.607170\pi$$
−0.330358 + 0.943856i $$0.607170\pi$$
$$620$$ 2.84233 4.92306i 0.114151 0.197715i
$$621$$ 0 0
$$622$$ 9.36932 + 16.2281i 0.375675 + 0.650689i
$$623$$ −6.43845 −0.257951
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 3.31534 + 5.74234i 0.132508 + 0.229510i
$$627$$ 0 0
$$628$$ −11.0616 + 19.1592i −0.441404 + 0.764534i
$$629$$ −21.1231 −0.842233
$$630$$ 0 0
$$631$$ 15.1231 26.1940i 0.602041 1.04277i −0.390470 0.920616i $$-0.627688\pi$$
0.992512 0.122151i $$-0.0389791\pi$$
$$632$$ −7.43845 −0.295886
$$633$$ 0 0
$$634$$ 2.09612 + 3.63058i 0.0832475 + 0.144189i
$$635$$ −2.21922 3.84381i −0.0880672 0.152537i
$$636$$ 0 0
$$637$$ 16.1577 + 12.6107i 0.640190 + 0.499653i
$$638$$ 27.0540 1.07108
$$639$$ 0 0
$$640$$ −0.500000 0.866025i −0.0197642 0.0342327i
$$641$$ −7.78078 + 13.4767i −0.307322 + 0.532298i −0.977776 0.209654i $$-0.932766\pi$$
0.670453 + 0.741952i $$0.266100\pi$$
$$642$$ 0 0
$$643$$ −19.1231 + 33.1222i −0.754142 + 1.30621i 0.191658 + 0.981462i $$0.438613\pi$$
−0.945800 + 0.324750i $$0.894720\pi$$
$$644$$ −13.6847 + 23.7025i −0.539251 + 0.934010i
$$645$$ 0 0
$$646$$ 9.12311 15.8017i 0.358944 0.621709i
$$647$$ −1.02699 1.77879i −0.0403751 0.0699316i 0.845132 0.534558i $$-0.179522\pi$$
−0.885507 + 0.464626i $$0.846189\pi$$
$$648$$ 0 0
$$649$$ −43.5464 −1.70935
$$650$$ −2.84233 2.21837i −0.111485 0.0870116i
$$651$$ 0 0
$$652$$ 9.28078 + 16.0748i 0.363463 + 0.629537i
$$653$$ −20.2192 35.0207i −0.791239 1.37047i −0.925200 0.379480i $$-0.876103\pi$$
0.133961 0.990987i $$-0.457230\pi$$
$$654$$ 0 0
$$655$$ 6.12311 0.239250
$$656$$ −2.12311 + 3.67733i −0.0828933 + 0.143575i
$$657$$ 0 0
$$658$$ 24.9309 0.971906
$$659$$ 15.5270 26.8935i 0.604846 1.04762i −0.387230 0.921983i $$-0.626568\pi$$
0.992076 0.125640i $$-0.0400985\pi$$
$$660$$ 0 0
$$661$$ 5.80776 + 10.0593i 0.225896 + 0.391263i 0.956588 0.291444i $$-0.0941358\pi$$
−0.730692 + 0.682707i $$0.760802\pi$$
$$662$$ 18.7386 0.728298
$$663$$ 0 0
$$664$$ 1.12311 0.0435850
$$665$$ −6.34233 10.9852i −0.245945 0.425989i
$$666$$ 0 0
$$667$$ 25.2116 43.6679i 0.976199 1.69083i
$$668$$ 20.3693 0.788113
$$669$$ 0 0
$$670$$ −7.12311 + 12.3376i −0.275190 + 0.476642i
$$671$$ 24.7386 0.955024
$$672$$ 0 0
$$673$$ −21.1231 36.5863i −0.814236 1.41030i −0.909875 0.414882i $$-0.863823\pi$$
0.0956394 0.995416i $$-0.469510\pi$$
$$674$$ −3.00000 5.19615i −0.115556 0.200148i
$$675$$ 0 0
$$676$$ 3.15767 + 12.6107i 0.121449 + 0.485026i
$$677$$ 28.8769 1.10983 0.554915 0.831907i $$-0.312751\pi$$
0.554915 + 0.831907i $$0.312751\pi$$
$$678$$ 0 0
$$679$$ −2.00000 3.46410i −0.0767530 0.132940i
$$680$$ 2.56155 4.43674i 0.0982311 0.170141i
$$681$$ 0 0
$$682$$ 11.7192 20.2983i 0.448752 0.777262i
$$683$$ 4.43845 7.68762i 0.169832 0.294158i −0.768528 0.639816i $$-0.779011\pi$$
0.938361 + 0.345657i $$0.112344\pi$$
$$684$$ 0 0
$$685$$ 4.40388 7.62775i 0.168264 0.291441i
$$686$$ −2.34233 4.05703i −0.0894305 0.154898i
$$687$$ 0 0
$$688$$ 4.56155 0.173908
$$689$$ 14.8348 6.00231i 0.565159 0.228670i
$$690$$ 0 0
$$691$$ 8.21922 + 14.2361i 0.312674 + 0.541567i 0.978940 0.204147i $$-0.0654419\pi$$
−0.666266 + 0.745714i $$0.732109\pi$$
$$692$$ −12.5885 21.8040i −0.478545 0.828863i
$$693$$ 0 0
$$694$$ 9.12311 0.346308
$$695$$ 4.21922 7.30791i 0.160044 0.277205i
$$696$$ 0 0
$$697$$ −21.7538 −0.823984
$$698$$ −12.2462 + 21.2111i −0.463526 + 0.802850i
$$699$$ 0 0
$$700$$ −1.78078 3.08440i −0.0673070 0.116579i
$$701$$ −17.3002 −0.653419 −0.326710 0.945125i $$-0.605940\pi$$
−0.326710 + 0.945125i $$0.605940\pi$$
$$702$$ 0 0
$$703$$ −14.6847 −0.553842
$$704$$ −2.06155 3.57071i −0.0776977 0.134576i
$$705$$ 0 0
$$706$$ −15.9309 + 27.5931i −0.599566 + 1.03848i
$$707$$ 60.9848 2.29357
$$708$$ 0 0
$$709$$ −8.87689 + 15.3752i −0.333379 + 0.577429i −0.983172 0.182682i $$-0.941522\pi$$
0.649793 + 0.760111i $$0.274855\pi$$
$$710$$ 4.87689 0.183027
$$711$$ 0 0
$$712$$ −0.903882 1.56557i −0.0338744 0.0586722i
$$713$$ −21.8423 37.8320i −0.818002 1.41682i
$$714$$ 0 0
$$715$$ −11.7192 9.14657i −0.438274 0.342062i
$$716$$ 0.315342 0.0117849
$$717$$ 0 0
$$718$$ −2.43845 4.22351i −0.0910020 0.157620i
$$719$$ −10.4924 + 18.1734i −0.391301 + 0.677754i −0.992621 0.121254i $$-0.961308\pi$$
0.601320 + 0.799008i $$0.294642\pi$$
$$720$$ 0 0
$$721$$ −0.780776 + 1.35234i −0.0290776 + 0.0503639i
$$722$$ −3.15767 + 5.46925i −0.117516 + 0.203544i
$$723$$ 0 0
$$724$$ −5.56155 + 9.63289i −0.206693 + 0.358004i
$$725$$ 3.28078 + 5.68247i 0.121845 + 0.211042i
$$726$$ 0 0
$$727$$ −23.4233 −0.868722 −0.434361 0.900739i $$-0.643026\pi$$
−0.434361 + 0.900739i $$0.643026\pi$$
$$728$$ −1.78078 + 12.7173i −0.0660000 + 0.471334i
$$729$$ 0 0
$$730$$ 7.68466 + 13.3102i 0.284422 + 0.492633i
$$731$$ 11.6847 + 20.2384i 0.432173 + 0.748545i
$$732$$ 0 0
$$733$$ 48.9309 1.80730 0.903651 0.428269i $$-0.140876\pi$$
0.903651 + 0.428269i $$0.140876\pi$$
$$734$$ −10.2462 + 17.7470i −0.378195 + 0.655052i
$$735$$ 0 0
$$736$$ −7.68466 −0.283260
$$737$$ −29.3693 + 50.8691i −1.08183 + 1.87379i
$$738$$ 0 0
$$739$$ −21.2732 36.8463i −0.782547 1.35541i −0.930453 0.366410i $$-0.880587\pi$$
0.147906 0.989001i $$-0.452747\pi$$
$$740$$ −4.12311 −0.151568
$$741$$ 0 0
$$742$$ 15.8078 0.580321
$$743$$ −16.0885 27.8662i −0.590231 1.02231i −0.994201 0.107538i $$-0.965703\pi$$
0.403970 0.914772i $$-0.367630\pi$$
$$744$$ 0 0
$$745$$ 11.4039 19.7521i 0.417806 0.723661i
$$746$$ 5.19224 0.190101
$$747$$ 0 0
$$748$$ 10.5616 18.2931i 0.386169 0.668864i
$$749$$ −7.12311 −0.260273
$$750$$ 0 0
$$751$$ 1.59612 + 2.76456i 0.0582432 + 0.100880i 0.893677 0.448711i $$-0.148117\pi$$
−0.835434 + 0.549591i $$0.814783\pi$$
$$752$$ 3.50000 + 6.06218i 0.127632 + 0.221065i
$$753$$ 0 0
$$754$$ 3.28078 23.4294i 0.119479 0.853250i
$$755$$ −9.36932 −0.340984
$$756$$ 0 0
$$757$$ −16.7116 28.9454i −0.607395 1.05204i −0.991668 0.128820i $$-0.958881\pi$$
0.384273 0.923220i $$-0.374452\pi$$
$$758$$ −2.65767 + 4.60322i −0.0965309 + 0.167197i
$$759$$ 0 0
$$760$$ 1.78078 3.08440i 0.0645955 0.111883i
$$761$$ 5.46543 9.46641i 0.198122 0.343157i −0.749798 0.661667i $$-0.769849\pi$$
0.947919 + 0.318510i $$0.103182\pi$$
$$762$$ 0 0
$$763$$ 36.0540 62.4473i 1.30524 2.26074i
$$764$$ 9.56155 + 16.5611i 0.345925 + 0.599159i
$$765$$ 0 0
$$766$$ 20.8078 0.751815
$$767$$ −5.28078 + 37.7123i −0.190678 + 1.36171i
$$768$$ 0 0
$$769$$ 22.8423 + 39.5641i 0.823715 + 1.42672i 0.902897 + 0.429857i $$0.141436\pi$$
−0.0791816 + 0.996860i $$0.525231\pi$$
$$770$$ −7.34233 12.7173i −0.264599 0.458299i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −10.5885 + 18.3399i −0.380843 + 0.659640i −0.991183 0.132500i $$-0.957700\pi$$
0.610340 + 0.792140i $$0.291033\pi$$
$$774$$ 0 0
$$775$$ 5.68466 0.204199
$$776$$ 0.561553 0.972638i 0.0201586 0.0349157i
$$777$$ 0 0
$$778$$ −9.52699 16.5012i −0.341559 0.591598i
$$779$$ −15.1231 −0.541841
$$780$$ 0 0
$$781$$ 20.1080 0.719519
$$782$$ −19.6847 34.0948i −0.703922 1.21923i
$$783$$ 0 0
$$784$$ −2.84233 + 4.92306i −0.101512 + 0.175824i
$$785$$ −22.1231 −0.789607
$$786$$ 0 0
$$787$$ −21.8423 + 37.8320i −0.778595 + 1.34857i 0.154157 + 0.988046i $$0.450734\pi$$
−0.932752 + 0.360520i $$0.882599\pi$$
$$788$$ 7.80776 0.278140
$$789$$ 0 0
$$790$$ −3.71922 6.44188i