# Properties

 Label 1950.2.z.n.1849.2 Level $1950$ Weight $2$ Character 1950.1849 Analytic conductor $15.571$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.z (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.1731891456.1 Defining polynomial: $$x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 1849.2 Root $$2.21837 + 1.28078i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.1849 Dual form 1950.2.z.n.1699.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.06155 + 3.57071i) q^{11} -1.00000i q^{12} +(-1.35234 - 3.34233i) q^{13} -3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.43674 + 2.56155i) q^{17} +1.00000i q^{18} +(-1.78078 + 3.08440i) q^{19} +3.56155 q^{21} +(-3.57071 - 2.06155i) q^{22} +(-6.65511 + 3.84233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.84233 + 2.21837i) q^{26} -1.00000i q^{27} +(3.08440 - 1.78078i) q^{28} +(3.28078 + 5.68247i) q^{29} +5.68466 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.57071 + 2.06155i) q^{33} -5.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.57071 + 2.06155i) q^{37} -3.56155i q^{38} +(-2.84233 - 2.21837i) q^{39} +(2.12311 + 3.67733i) q^{41} +(-3.08440 + 1.78078i) q^{42} +(-3.95042 - 2.28078i) q^{43} +4.12311 q^{44} +(3.84233 - 6.65511i) q^{46} -7.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.84233 + 4.92306i) q^{49} +5.12311 q^{51} +(-3.57071 - 0.500000i) q^{52} +4.43845i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.78078 + 3.08440i) q^{56} +3.56155i q^{57} +(-5.68247 - 3.28078i) q^{58} +(5.28078 - 9.14657i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-4.92306 + 2.84233i) q^{62} +(3.08440 - 1.78078i) q^{63} -1.00000 q^{64} -4.12311 q^{66} +(-12.3376 + 7.12311i) q^{67} +(4.43674 - 2.56155i) q^{68} +(-3.84233 + 6.65511i) q^{69} +(2.43845 - 4.22351i) q^{71} +(0.866025 + 0.500000i) q^{72} -15.3693i q^{73} +(2.06155 - 3.57071i) q^{74} +(1.78078 + 3.08440i) q^{76} +14.6847i q^{77} +(3.57071 + 0.500000i) q^{78} -7.43845 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.67733 - 2.12311i) q^{82} +1.12311i q^{83} +(1.78078 - 3.08440i) q^{84} +4.56155 q^{86} +(5.68247 + 3.28078i) q^{87} +(-3.57071 + 2.06155i) q^{88} +(0.903882 + 1.56557i) q^{89} +(1.78078 - 12.7173i) q^{91} +7.68466i q^{92} +(4.92306 - 2.84233i) q^{93} +(3.50000 + 6.06218i) q^{94} +1.00000 q^{96} +(0.972638 + 0.561553i) q^{97} +(-4.92306 - 2.84233i) q^{98} +4.12311 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10})$$ $$8q + 4q^{4} - 4q^{6} + 4q^{9} - 12q^{14} - 4q^{16} - 6q^{19} + 12q^{21} + 4q^{24} - 2q^{26} + 18q^{29} - 4q^{31} - 8q^{34} - 4q^{36} + 2q^{39} - 16q^{41} + 6q^{46} - 2q^{49} + 8q^{51} + 4q^{54} - 6q^{56} + 34q^{59} - 24q^{61} - 8q^{64} - 6q^{69} + 36q^{71} + 6q^{76} - 76q^{79} - 4q^{81} + 6q^{84} + 20q^{86} - 34q^{89} + 6q^{91} + 28q^{94} + 8q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ 0.866025 0.500000i 0.500000 0.288675i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0 0
$$6$$ −0.500000 + 0.866025i −0.204124 + 0.353553i
$$7$$ 3.08440 + 1.78078i 1.16579 + 0.673070i 0.952685 0.303959i $$-0.0983085\pi$$
0.213107 + 0.977029i $$0.431642\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 0.866025i 0.166667 0.288675i
$$10$$ 0 0
$$11$$ 2.06155 + 3.57071i 0.621582 + 1.07661i 0.989191 + 0.146631i $$0.0468429\pi$$
−0.367610 + 0.929980i $$0.619824\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ −1.35234 3.34233i −0.375073 0.926995i
$$14$$ −3.56155 −0.951865
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 4.43674 + 2.56155i 1.07607 + 0.621268i 0.929833 0.367982i $$-0.119951\pi$$
0.146235 + 0.989250i $$0.453285\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ −1.78078 + 3.08440i −0.408538 + 0.707609i −0.994726 0.102566i $$-0.967295\pi$$
0.586188 + 0.810175i $$0.300628\pi$$
$$20$$ 0 0
$$21$$ 3.56155 0.777195
$$22$$ −3.57071 2.06155i −0.761279 0.439525i
$$23$$ −6.65511 + 3.84233i −1.38769 + 0.801181i −0.993054 0.117658i $$-0.962461\pi$$
−0.394632 + 0.918839i $$0.629128\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ 0 0
$$26$$ 2.84233 + 2.21837i 0.557427 + 0.435058i
$$27$$ 1.00000i 0.192450i
$$28$$ 3.08440 1.78078i 0.582896 0.336535i
$$29$$ 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 $$0.329461\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 3.57071 + 2.06155i 0.621582 + 0.358870i
$$34$$ −5.12311 −0.878605
$$35$$ 0 0
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ −3.57071 + 2.06155i −0.587022 + 0.338917i −0.763919 0.645312i $$-0.776727\pi$$
0.176897 + 0.984229i $$0.443394\pi$$
$$38$$ 3.56155i 0.577760i
$$39$$ −2.84233 2.21837i −0.455137 0.355223i
$$40$$ 0 0
$$41$$ 2.12311 + 3.67733i 0.331573 + 0.574302i 0.982821 0.184564i $$-0.0590872\pi$$
−0.651247 + 0.758866i $$0.725754\pi$$
$$42$$ −3.08440 + 1.78078i −0.475933 + 0.274780i
$$43$$ −3.95042 2.28078i −0.602433 0.347815i 0.167565 0.985861i $$-0.446410\pi$$
−0.769998 + 0.638046i $$0.779743\pi$$
$$44$$ 4.12311 0.621582
$$45$$ 0 0
$$46$$ 3.84233 6.65511i 0.566521 0.981242i
$$47$$ 7.00000i 1.02105i −0.859861 0.510527i $$-0.829450\pi$$
0.859861 0.510527i $$-0.170550\pi$$
$$48$$ −0.866025 0.500000i −0.125000 0.0721688i
$$49$$ 2.84233 + 4.92306i 0.406047 + 0.703294i
$$50$$ 0 0
$$51$$ 5.12311 0.717378
$$52$$ −3.57071 0.500000i −0.495169 0.0693375i
$$53$$ 4.43845i 0.609668i 0.952406 + 0.304834i $$0.0986009\pi$$
−0.952406 + 0.304834i $$0.901399\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 0 0
$$56$$ −1.78078 + 3.08440i −0.237966 + 0.412170i
$$57$$ 3.56155i 0.471739i
$$58$$ −5.68247 3.28078i −0.746145 0.430787i
$$59$$ 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 $$0.292159\pi$$
$$62$$ −4.92306 + 2.84233i −0.625229 + 0.360976i
$$63$$ 3.08440 1.78078i 0.388597 0.224357i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ −4.12311 −0.507519
$$67$$ −12.3376 + 7.12311i −1.50728 + 0.870226i −0.507311 + 0.861763i $$0.669361\pi$$
−0.999964 + 0.00846293i $$0.997306\pi$$
$$68$$ 4.43674 2.56155i 0.538034 0.310634i
$$69$$ −3.84233 + 6.65511i −0.462562 + 0.801181i
$$70$$ 0 0
$$71$$ 2.43845 4.22351i 0.289390 0.501239i −0.684274 0.729225i $$-0.739881\pi$$
0.973664 + 0.227986i $$0.0732141\pi$$
$$72$$ 0.866025 + 0.500000i 0.102062 + 0.0589256i
$$73$$ 15.3693i 1.79884i −0.437083 0.899421i $$-0.643988\pi$$
0.437083 0.899421i $$-0.356012\pi$$
$$74$$ 2.06155 3.57071i 0.239651 0.415087i
$$75$$ 0 0
$$76$$ 1.78078 + 3.08440i 0.204269 + 0.353804i
$$77$$ 14.6847i 1.67347i
$$78$$ 3.57071 + 0.500000i 0.404304 + 0.0566139i
$$79$$ −7.43845 −0.836891 −0.418445 0.908242i $$-0.637425\pi$$
−0.418445 + 0.908242i $$0.637425\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −3.67733 2.12311i −0.406093 0.234458i
$$83$$ 1.12311i 0.123277i 0.998099 + 0.0616384i $$0.0196326\pi$$
−0.998099 + 0.0616384i $$0.980367\pi$$
$$84$$ 1.78078 3.08440i 0.194299 0.336535i
$$85$$ 0 0
$$86$$ 4.56155 0.491885
$$87$$ 5.68247 + 3.28078i 0.609225 + 0.351736i
$$88$$ −3.57071 + 2.06155i −0.380639 + 0.219762i
$$89$$ 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
$$92$$ 7.68466i 0.801181i
$$93$$ 4.92306 2.84233i 0.510497 0.294736i
$$94$$ 3.50000 + 6.06218i 0.360997 + 0.625266i
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ 0.972638 + 0.561553i 0.0987564 + 0.0570170i 0.548565 0.836108i $$-0.315174\pi$$
−0.449808 + 0.893125i $$0.648508\pi$$
$$98$$ −4.92306 2.84233i −0.497304 0.287119i
$$99$$ 4.12311 0.414388
$$100$$ 0 0
$$101$$ 8.56155 + 14.8290i 0.851906 + 1.47555i 0.879486 + 0.475925i $$0.157887\pi$$
−0.0275793 + 0.999620i $$0.508780\pi$$
$$102$$ −4.43674 + 2.56155i −0.439303 + 0.253632i
$$103$$ 0.438447i 0.0432015i 0.999767 + 0.0216007i $$0.00687626\pi$$
−0.999767 + 0.0216007i $$0.993124\pi$$
$$104$$ 3.34233 1.35234i 0.327742 0.132608i
$$105$$ 0 0
$$106$$ −2.21922 3.84381i −0.215550 0.373344i
$$107$$ −1.73205 + 1.00000i −0.167444 + 0.0966736i −0.581380 0.813632i $$-0.697487\pi$$
0.413936 + 0.910306i $$0.364154\pi$$
$$108$$ −0.866025 0.500000i −0.0833333 0.0481125i
$$109$$ 20.2462 1.93924 0.969618 0.244625i $$-0.0786650\pi$$
0.969618 + 0.244625i $$0.0786650\pi$$
$$110$$ 0 0
$$111$$ −2.06155 + 3.57071i −0.195674 + 0.338917i
$$112$$ 3.56155i 0.336535i
$$113$$ 3.19101 + 1.84233i 0.300185 + 0.173312i 0.642526 0.766264i $$-0.277887\pi$$
−0.342341 + 0.939576i $$0.611220\pi$$
$$114$$ −1.78078 3.08440i −0.166785 0.288880i
$$115$$ 0 0
$$116$$ 6.56155 0.609225
$$117$$ −3.57071 0.500000i −0.330113 0.0462250i
$$118$$ 10.5616i 0.972270i
$$119$$ 9.12311 + 15.8017i 0.836314 + 1.44854i
$$120$$ 0 0
$$121$$ −3.00000 + 5.19615i −0.272727 + 0.472377i
$$122$$ 6.00000i 0.543214i
$$123$$ 3.67733 + 2.12311i 0.331573 + 0.191434i
$$124$$ 2.84233 4.92306i 0.255249 0.442104i
$$125$$ 0 0
$$126$$ −1.78078 + 3.08440i −0.158644 + 0.274780i
$$127$$ 3.84381 2.21922i 0.341083 0.196924i −0.319668 0.947530i $$-0.603571\pi$$
0.660751 + 0.750605i $$0.270238\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ −4.56155 −0.401622
$$130$$ 0 0
$$131$$ 6.12311 0.534978 0.267489 0.963561i $$-0.413806\pi$$
0.267489 + 0.963561i $$0.413806\pi$$
$$132$$ 3.57071 2.06155i 0.310791 0.179435i
$$133$$ −10.9852 + 6.34233i −0.952541 + 0.549950i
$$134$$ 7.12311 12.3376i 0.615343 1.06580i
$$135$$ 0 0
$$136$$ −2.56155 + 4.43674i −0.219651 + 0.380447i
$$137$$ −7.62775 4.40388i −0.651682 0.376249i 0.137418 0.990513i $$-0.456120\pi$$
−0.789101 + 0.614264i $$0.789453\pi$$
$$138$$ 7.68466i 0.654162i
$$139$$ 4.21922 7.30791i 0.357870 0.619849i −0.629735 0.776810i $$-0.716836\pi$$
0.987605 + 0.156961i $$0.0501698\pi$$
$$140$$ 0 0
$$141$$ −3.50000 6.06218i −0.294753 0.510527i
$$142$$ 4.87689i 0.409260i
$$143$$ 9.14657 11.7192i 0.764875 0.980011i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ 7.68466 + 13.3102i 0.635987 + 1.10156i
$$147$$ 4.92306 + 2.84233i 0.406047 + 0.234431i
$$148$$ 4.12311i 0.338917i
$$149$$ −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 $$0.375500\pi$$
$$152$$ −3.08440 1.78078i −0.250177 0.144440i
$$153$$ 4.43674 2.56155i 0.358689 0.207089i
$$154$$ −7.34233 12.7173i −0.591662 1.02479i
$$155$$ 0 0
$$156$$ −3.34233 + 1.35234i −0.267601 + 0.108274i
$$157$$ 22.1231i 1.76562i −0.469734 0.882808i $$-0.655650\pi$$
0.469734 0.882808i $$-0.344350\pi$$
$$158$$ 6.44188 3.71922i 0.512489 0.295886i
$$159$$ 2.21922 + 3.84381i 0.175996 + 0.304834i
$$160$$ 0 0
$$161$$ −27.3693 −2.15700
$$162$$ 0.866025 + 0.500000i 0.0680414 + 0.0392837i
$$163$$ 16.0748 + 9.28078i 1.25907 + 0.726927i 0.972894 0.231250i $$-0.0742814\pi$$
0.286179 + 0.958176i $$0.407615\pi$$
$$164$$ 4.24621 0.331573
$$165$$ 0 0
$$166$$ −0.561553 0.972638i −0.0435850 0.0754913i
$$167$$ 17.6403 10.1847i 1.36505 0.788113i 0.374760 0.927122i $$-0.377725\pi$$
0.990291 + 0.139009i $$0.0443918\pi$$
$$168$$ 3.56155i 0.274780i
$$169$$ −9.34233 + 9.03996i −0.718641 + 0.695382i
$$170$$ 0 0
$$171$$ 1.78078 + 3.08440i 0.136179 + 0.235870i
$$172$$ −3.95042 + 2.28078i −0.301217 + 0.173908i
$$173$$ 21.8040 + 12.5885i 1.65773 + 0.957089i 0.973760 + 0.227575i $$0.0730798\pi$$
0.683966 + 0.729514i $$0.260254\pi$$
$$174$$ −6.56155 −0.497430
$$175$$ 0 0
$$176$$ 2.06155 3.57071i 0.155395 0.269153i
$$177$$ 10.5616i 0.793855i
$$178$$ −1.56557 0.903882i −0.117344 0.0677488i
$$179$$ −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 $$0.364346\pi$$
$$182$$ 4.81645 + 11.9039i 0.357019 + 0.882374i
$$183$$ 6.00000i 0.443533i
$$184$$ −3.84233 6.65511i −0.283260 0.490621i
$$185$$ 0 0
$$186$$ −2.84233 + 4.92306i −0.208410 + 0.360976i
$$187$$ 21.1231i 1.54467i
$$188$$ −6.06218 3.50000i −0.442130 0.255264i
$$189$$ 1.78078 3.08440i 0.129532 0.224357i
$$190$$ 0 0
$$191$$ −9.56155 + 16.5611i −0.691850 + 1.19832i 0.279381 + 0.960180i $$0.409871\pi$$
−0.971231 + 0.238139i $$0.923463\pi$$
$$192$$ −0.866025 + 0.500000i −0.0625000 + 0.0360844i
$$193$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$194$$ −1.12311 −0.0806343
$$195$$ 0 0
$$196$$ 5.68466 0.406047
$$197$$ 6.76172 3.90388i 0.481753 0.278140i −0.239394 0.970923i $$-0.576949\pi$$
0.721147 + 0.692782i $$0.243615\pi$$
$$198$$ −3.57071 + 2.06155i −0.253760 + 0.146508i
$$199$$ 5.56155 9.63289i 0.394248 0.682858i −0.598757 0.800931i $$-0.704338\pi$$
0.993005 + 0.118073i $$0.0376718\pi$$
$$200$$ 0 0
$$201$$ −7.12311 + 12.3376i −0.502425 + 0.870226i
$$202$$ −14.8290 8.56155i −1.04337 0.602389i
$$203$$ 23.3693i 1.64020i
$$204$$ 2.56155 4.43674i 0.179345 0.310634i
$$205$$ 0 0
$$206$$ −0.219224 0.379706i −0.0152740 0.0264554i
$$207$$ 7.68466i 0.534121i
$$208$$ −2.21837 + 2.84233i −0.153816 + 0.197080i
$$209$$ −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 $$0.910012\pi$$
$$212$$ 3.84381 + 2.21922i 0.263994 + 0.152417i
$$213$$ 4.87689i 0.334159i
$$214$$ 1.00000 1.73205i 0.0683586 0.118401i
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 17.5337 + 10.1231i 1.19027 + 0.687201i
$$218$$ −17.5337 + 10.1231i −1.18753 + 0.685623i
$$219$$ −7.68466 13.3102i −0.519281 0.899421i
$$220$$ 0 0
$$221$$ 2.56155 18.2931i 0.172309 1.23053i
$$222$$ 4.12311i 0.276725i
$$223$$ −22.7766 + 13.1501i −1.52524 + 0.880595i −0.525683 + 0.850680i $$0.676190\pi$$
−0.999552 + 0.0299151i $$0.990476\pi$$
$$224$$ 1.78078 + 3.08440i 0.118983 + 0.206085i
$$225$$ 0 0
$$226$$ −3.68466 −0.245100
$$227$$ −17.3205 10.0000i −1.14960 0.663723i −0.200812 0.979630i $$-0.564358\pi$$
−0.948790 + 0.315906i $$0.897691\pi$$
$$228$$ 3.08440 + 1.78078i 0.204269 + 0.117935i
$$229$$ 7.75379 0.512385 0.256192 0.966626i $$-0.417532\pi$$
0.256192 + 0.966626i $$0.417532\pi$$
$$230$$ 0 0
$$231$$ 7.34233 + 12.7173i 0.483090 + 0.836736i
$$232$$ −5.68247 + 3.28078i −0.373073 + 0.215394i
$$233$$ 17.6847i 1.15856i −0.815128 0.579280i $$-0.803334\pi$$
0.815128 0.579280i $$-0.196666\pi$$
$$234$$ 3.34233 1.35234i 0.218495 0.0884055i
$$235$$ 0 0
$$236$$ −5.28078 9.14657i −0.343749 0.595391i
$$237$$ −6.44188 + 3.71922i −0.418445 + 0.241590i
$$238$$ −15.8017 9.12311i −1.02427 0.591363i
$$239$$ −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 $$-0.0544784\pi$$
$$242$$ 6.00000i 0.385695i
$$243$$ −0.866025 0.500000i −0.0555556 0.0320750i
$$244$$ 3.00000 + 5.19615i 0.192055 + 0.332650i
$$245$$ 0 0
$$246$$ −4.24621 −0.270729
$$247$$ 12.7173 + 1.78078i 0.809182 + 0.113308i
$$248$$ 5.68466i 0.360976i
$$249$$ 0.561553 + 0.972638i 0.0355870 + 0.0616384i
$$250$$ 0 0
$$251$$ −0.0615528 + 0.106613i −0.00388518 + 0.00672933i −0.867961 0.496632i $$-0.834570\pi$$
0.864076 + 0.503361i $$0.167903\pi$$
$$252$$ 3.56155i 0.224357i
$$253$$ −27.4397 15.8423i −1.72512 0.995999i
$$254$$ −2.21922 + 3.84381i −0.139246 + 0.241182i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 1.24573 0.719224i 0.0777066 0.0448639i −0.460643 0.887585i $$-0.652381\pi$$
0.538350 + 0.842721i $$0.319048\pi$$
$$258$$ 3.95042 2.28078i 0.245942 0.141995i
$$259$$ −14.6847 −0.912460
$$260$$ 0 0
$$261$$ 6.56155 0.406150
$$262$$ −5.30277 + 3.06155i −0.327606 + 0.189143i
$$263$$ −11.2583 + 6.50000i −0.694218 + 0.400807i −0.805190 0.593016i $$-0.797937\pi$$
0.110972 + 0.993824i $$0.464604\pi$$
$$264$$ −2.06155 + 3.57071i −0.126880 + 0.219762i
$$265$$ 0 0
$$266$$ 6.34233 10.9852i 0.388873 0.673548i
$$267$$ 1.56557 + 0.903882i 0.0958113 + 0.0553167i
$$268$$ 14.2462i 0.870226i
$$269$$ −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 $$-0.598728\pi$$
$$272$$ 5.12311i 0.310634i
$$273$$ −4.81645 11.9039i −0.291505 0.720456i
$$274$$ 8.80776 0.532096
$$275$$ 0 0
$$276$$ 3.84233 + 6.65511i 0.231281 + 0.400591i
$$277$$ −0.866025 0.500000i −0.0520344 0.0300421i 0.473757 0.880656i $$-0.342897\pi$$
−0.525792 + 0.850613i $$0.676231\pi$$
$$278$$ 8.43845i 0.506104i
$$279$$ 2.84233 4.92306i 0.170166 0.294736i
$$280$$ 0 0
$$281$$ −0.246211 −0.0146877 −0.00734387 0.999973i $$-0.502338\pi$$
−0.00734387 + 0.999973i $$0.502338\pi$$
$$282$$ 6.06218 + 3.50000i 0.360997 + 0.208422i
$$283$$ 9.90599 5.71922i 0.588850 0.339973i −0.175793 0.984427i $$-0.556249\pi$$
0.764643 + 0.644455i $$0.222916\pi$$
$$284$$ −2.43845 4.22351i −0.144695 0.250619i
$$285$$ 0 0
$$286$$ −2.06155 + 14.7224i −0.121902 + 0.870556i
$$287$$ 15.1231i 0.892689i
$$288$$ 0.866025 0.500000i 0.0510310 0.0294628i
$$289$$ 4.62311 + 8.00745i 0.271947 + 0.471027i
$$290$$ 0 0
$$291$$ 1.12311 0.0658376
$$292$$ −13.3102 7.68466i −0.778922 0.449711i
$$293$$ 21.5908 + 12.4654i 1.26135 + 0.728238i 0.973335 0.229389i $$-0.0736727\pi$$
0.288011 + 0.957627i $$0.407006\pi$$
$$294$$ −5.68466 −0.331536
$$295$$ 0 0
$$296$$ −2.06155 3.57071i −0.119825 0.207544i
$$297$$ 3.57071 2.06155i 0.207194 0.119623i
$$298$$ 22.8078i 1.32122i
$$299$$ 21.8423 + 17.0474i 1.26317 + 0.985877i
$$300$$ 0 0
$$301$$ −8.12311 14.0696i −0.468208 0.810960i
$$302$$ −8.11407 + 4.68466i −0.466912 + 0.269572i
$$303$$ 14.8290 + 8.56155i 0.851906 + 0.491848i
$$304$$ 3.56155 0.204269
$$305$$ 0 0
$$306$$ −2.56155 + 4.43674i −0.146434 + 0.253632i
$$307$$ 15.6155i 0.891225i 0.895226 + 0.445613i $$0.147014\pi$$
−0.895226 + 0.445613i $$0.852986\pi$$
$$308$$ 12.7173 + 7.34233i 0.724635 + 0.418368i
$$309$$ 0.219224 + 0.379706i 0.0124712 + 0.0216007i
$$310$$ 0 0
$$311$$ −18.7386 −1.06257 −0.531285 0.847193i $$-0.678291\pi$$
−0.531285 + 0.847193i $$0.678291\pi$$
$$312$$ 2.21837 2.84233i 0.125590 0.160915i
$$313$$ 6.63068i 0.374788i 0.982285 + 0.187394i $$0.0600042\pi$$
−0.982285 + 0.187394i $$0.939996\pi$$
$$314$$ 11.0616 + 19.1592i 0.624240 + 1.08121i
$$315$$ 0 0
$$316$$ −3.71922 + 6.44188i −0.209223 + 0.362384i
$$317$$ 4.19224i 0.235459i 0.993046 + 0.117730i $$0.0375616\pi$$
−0.993046 + 0.117730i $$0.962438\pi$$
$$318$$ −3.84381 2.21922i −0.215550 0.124448i
$$319$$ −13.5270 + 23.4294i −0.757366 + 1.31180i
$$320$$ 0 0
$$321$$ −1.00000 + 1.73205i −0.0558146 + 0.0966736i
$$322$$ 23.7025 13.6847i 1.32089 0.762616i
$$323$$ −15.8017 + 9.12311i −0.879229 + 0.507623i
$$324$$ −1.00000 −0.0555556
$$325$$ 0 0
$$326$$ −18.5616 −1.02803
$$327$$ 17.5337 10.1231i 0.969618 0.559809i
$$328$$ −3.67733 + 2.12311i −0.203046 + 0.117229i
$$329$$ 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 $$-0.00553556\pi$$
$$332$$ 0.972638 + 0.561553i 0.0533804 + 0.0308192i
$$333$$ 4.12311i 0.225945i
$$334$$ −10.1847 + 17.6403i −0.557280 + 0.965237i
$$335$$ 0 0
$$336$$ −1.78078 3.08440i −0.0971493 0.168268i
$$337$$ 6.00000i 0.326841i 0.986557 + 0.163420i $$0.0522527\pi$$
−0.986557 + 0.163420i $$0.947747\pi$$
$$338$$ 3.57071 12.5000i 0.194221 0.679910i
$$339$$ 3.68466 0.200123
$$340$$ 0 0
$$341$$ 11.7192 + 20.2983i 0.634632 + 1.09921i
$$342$$ −3.08440 1.78078i −0.166785 0.0962934i
$$343$$ 4.68466i 0.252948i
$$344$$ 2.28078 3.95042i 0.122971 0.212992i
$$345$$ 0 0
$$346$$ −25.1771 −1.35353
$$347$$ 7.90084 + 4.56155i 0.424139 + 0.244877i 0.696847 0.717220i $$-0.254586\pi$$
−0.272707 + 0.962097i $$0.587919\pi$$
$$348$$ 5.68247 3.28078i 0.304612 0.175868i
$$349$$ −12.2462 21.2111i −0.655525 1.13540i −0.981762 0.190114i $$-0.939114\pi$$
0.326237 0.945288i $$-0.394219\pi$$
$$350$$ 0 0
$$351$$ −3.34233 + 1.35234i −0.178400 + 0.0721828i
$$352$$ 4.12311i 0.219762i
$$353$$ 27.5931 15.9309i 1.46863 0.847915i 0.469249 0.883066i $$-0.344525\pi$$
0.999382 + 0.0351511i $$0.0111913\pi$$
$$354$$ 5.28078 + 9.14657i 0.280670 + 0.486135i
$$355$$ 0 0
$$356$$ 1.80776 0.0958113
$$357$$ 15.8017 + 9.12311i 0.836314 + 0.482846i
$$358$$ 0.273094 + 0.157671i 0.0144335 + 0.00833316i
$$359$$ −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
$$362$$ −9.63289 + 5.56155i −0.506294 + 0.292309i
$$363$$ 6.00000i 0.314918i
$$364$$ −10.1231 7.90084i −0.530595 0.414117i
$$365$$ 0 0
$$366$$ −3.00000 5.19615i −0.156813 0.271607i
$$367$$ 17.7470 10.2462i 0.926384 0.534848i 0.0407177 0.999171i $$-0.487036\pi$$
0.885666 + 0.464323i $$0.153702\pi$$
$$368$$ 6.65511 + 3.84233i 0.346922 + 0.200295i
$$369$$ 4.24621 0.221049
$$370$$ 0 0
$$371$$ −7.90388 + 13.6899i −0.410349 + 0.710746i
$$372$$ 5.68466i 0.294736i
$$373$$ 4.49661 + 2.59612i 0.232826 + 0.134422i 0.611875 0.790955i $$-0.290416\pi$$
−0.379049 + 0.925376i $$0.623749\pi$$
$$374$$ −10.5616 18.2931i −0.546125 0.945916i
$$375$$ 0 0
$$376$$ 7.00000 0.360997
$$377$$ 14.5560 18.6501i 0.749670 0.960529i
$$378$$ 3.56155i 0.183187i
$$379$$ −2.65767 4.60322i −0.136515 0.236452i 0.789660 0.613545i $$-0.210257\pi$$
−0.926175 + 0.377093i $$0.876924\pi$$
$$380$$ 0 0
$$381$$ 2.21922 3.84381i 0.113694 0.196924i
$$382$$ 19.1231i 0.978423i
$$383$$ −18.0201 10.4039i −0.920782 0.531614i −0.0368973 0.999319i $$-0.511747\pi$$
−0.883884 + 0.467706i $$0.845081\pi$$
$$384$$ 0.500000 0.866025i 0.0255155 0.0441942i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −3.95042 + 2.28078i −0.200811 + 0.115938i
$$388$$ 0.972638 0.561553i 0.0493782 0.0285085i
$$389$$ −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
$$392$$ −4.92306 + 2.84233i −0.248652 + 0.143559i
$$393$$ 5.30277 3.06155i 0.267489 0.154435i
$$394$$ −3.90388 + 6.76172i −0.196675 + 0.340651i
$$395$$ 0 0
$$396$$ 2.06155 3.57071i 0.103597 0.179435i
$$397$$ −10.2857 5.93845i −0.516224 0.298042i 0.219164 0.975688i $$-0.429667\pi$$
−0.735388 + 0.677646i $$0.763000\pi$$
$$398$$ 11.1231i 0.557551i
$$399$$ −6.34233 + 10.9852i −0.317514 + 0.549950i
$$400$$ 0 0
$$401$$ −6.34233 10.9852i −0.316721 0.548577i 0.663081 0.748548i $$-0.269248\pi$$
−0.979802 + 0.199971i $$0.935915\pi$$
$$402$$ 14.2462i 0.710536i
$$403$$ −7.68762 19.0000i −0.382947 0.946457i
$$404$$ 17.1231 0.851906
$$405$$ 0 0
$$406$$ −11.6847 20.2384i −0.579900 1.00442i
$$407$$ −14.7224 8.50000i −0.729764 0.421329i
$$408$$ 5.12311i 0.253632i
$$409$$ 0.903882 1.56557i 0.0446941 0.0774124i −0.842813 0.538207i $$-0.819102\pi$$
0.887507 + 0.460794i $$0.152435\pi$$
$$410$$ 0 0
$$411$$ −8.80776 −0.434455
$$412$$ 0.379706 + 0.219224i 0.0187068 + 0.0108004i
$$413$$ 32.5760 18.8078i 1.60296 0.925470i
$$414$$ −3.84233 6.65511i −0.188840 0.327081i
$$415$$ 0 0
$$416$$ 0.500000 3.57071i 0.0245145 0.175069i
$$417$$ 8.43845i 0.413233i
$$418$$ 12.7173 7.34233i 0.622023 0.359125i
$$419$$ −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 $$0.496180\pi$$
$$422$$ 6.00231 + 3.46543i 0.292188 + 0.168695i
$$423$$ −6.06218 3.50000i −0.294753 0.170176i
$$424$$ −4.43845 −0.215550
$$425$$ 0 0
$$426$$ 2.43845 + 4.22351i 0.118143 + 0.204630i
$$427$$ −18.5064 + 10.6847i −0.895586 + 0.517067i
$$428$$ 2.00000i 0.0966736i
$$429$$ 2.06155 14.7224i 0.0995327 0.710806i
$$430$$ 0 0
$$431$$ −13.3693 23.1563i −0.643977 1.11540i −0.984537 0.175178i $$-0.943950\pi$$
0.340559 0.940223i $$-0.389384\pi$$
$$432$$ −0.866025 + 0.500000i −0.0416667 + 0.0240563i
$$433$$ −26.6204 15.3693i −1.27930 0.738602i −0.302578 0.953125i $$-0.597847\pi$$
−0.976719 + 0.214523i $$0.931180\pi$$
$$434$$ −20.2462 −0.971849
$$435$$ 0 0
$$436$$ 10.1231 17.5337i 0.484809 0.839714i
$$437$$ 27.3693i 1.30925i
$$438$$ 13.3102 + 7.68466i 0.635987 + 0.367187i
$$439$$ 8.43845 + 14.6158i 0.402745 + 0.697575i 0.994056 0.108869i $$-0.0347228\pi$$
−0.591311 + 0.806444i $$0.701389\pi$$
$$440$$ 0 0
$$441$$ 5.68466 0.270698
$$442$$ 6.92820 + 17.1231i 0.329541 + 0.814463i
$$443$$ 4.87689i 0.231708i −0.993266 0.115854i $$-0.963039\pi$$
0.993266 0.115854i $$-0.0369605\pi$$
$$444$$ 2.06155 + 3.57071i 0.0978370 + 0.169459i
$$445$$ 0 0
$$446$$ 13.1501 22.7766i 0.622675 1.07850i
$$447$$ 22.8078i 1.07877i
$$448$$ −3.08440 1.78078i −0.145724 0.0841338i
$$449$$ 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
$$452$$ 3.19101 1.84233i 0.150092 0.0866559i
$$453$$ 8.11407 4.68466i 0.381232 0.220104i
$$454$$ 20.0000 0.938647
$$455$$ 0 0
$$456$$ −3.56155 −0.166785
$$457$$ −3.25088 + 1.87689i −0.152070 + 0.0877974i −0.574104 0.818782i $$-0.694649\pi$$
0.422034 + 0.906580i $$0.361316\pi$$
$$458$$ −6.71498 + 3.87689i −0.313770 + 0.181155i
$$459$$ 2.56155 4.43674i 0.119563 0.207089i
$$460$$ 0 0
$$461$$ −3.52699 + 6.10892i −0.164268 + 0.284521i −0.936395 0.350947i $$-0.885860\pi$$
0.772127 + 0.635468i $$0.219193\pi$$
$$462$$ −12.7173 7.34233i −0.591662 0.341596i
$$463$$ 33.6155i 1.56225i 0.624377 + 0.781123i $$0.285353\pi$$
−0.624377 + 0.781123i $$0.714647\pi$$
$$464$$ 3.28078 5.68247i 0.152306 0.263802i
$$465$$ 0 0
$$466$$ 8.84233 + 15.3154i 0.409613 + 0.709471i
$$467$$ 39.8617i 1.84458i −0.386497 0.922291i $$-0.626315\pi$$
0.386497 0.922291i $$-0.373685\pi$$
$$468$$ −2.21837 + 2.84233i −0.102544 + 0.131387i
$$469$$ −50.7386 −2.34289
$$470$$ 0 0
$$471$$ −11.0616 19.1592i −0.509689 0.882808i
$$472$$ 9.14657 + 5.28078i 0.421005 + 0.243067i
$$473$$ 18.8078i 0.864782i
$$474$$ 3.71922 6.44188i 0.170830 0.295886i
$$475$$ 0 0
$$476$$ 18.2462 0.836314
$$477$$ 3.84381 + 2.21922i 0.175996 + 0.101611i
$$478$$ 11.5782 6.68466i 0.529573 0.305749i
$$479$$ −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
$$482$$ 19.8769i 0.905368i
$$483$$ −23.7025 + 13.6847i −1.07850 + 0.622674i
$$484$$ 3.00000 + 5.19615i 0.136364 + 0.236189i
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ −20.8314 12.0270i −0.943959 0.544995i −0.0527597 0.998607i $$-0.516802\pi$$
−0.891199 + 0.453612i $$0.850135\pi$$
$$488$$ −5.19615 3.00000i −0.235219 0.135804i
$$489$$ 18.5616 0.839382
$$490$$ 0 0
$$491$$ 10.7808 + 18.6729i 0.486530 + 0.842694i 0.999880 0.0154850i $$-0.00492923\pi$$
−0.513350 + 0.858179i $$0.671596\pi$$
$$492$$ 3.67733 2.12311i 0.165787 0.0957170i
$$493$$ 33.6155i 1.51397i
$$494$$ −11.9039 + 4.81645i −0.535581 + 0.216702i
$$495$$ 0 0
$$496$$ −2.84233 4.92306i −0.127624 0.221052i
$$497$$ 15.0423 8.68466i 0.674738 0.389560i
$$498$$ −0.972638 0.561553i −0.0435850 0.0251638i
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ 0 0
$$501$$ 10.1847 17.6403i 0.455017 0.788113i
$$502$$ 0.123106i 0.00549447i
$$503$$ 5.14941 + 2.97301i 0.229601 + 0.132560i 0.610388 0.792103i $$-0.291014\pi$$
−0.380787 + 0.924663i $$0.624347\pi$$
$$504$$ 1.78078 + 3.08440i 0.0793221 + 0.137390i
$$505$$ 0 0
$$506$$ 31.6847 1.40855
$$507$$ −3.57071 + 12.5000i −0.158581 + 0.555144i
$$508$$ 4.43845i 0.196924i
$$509$$ −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
$$512$$ 1.00000i 0.0441942i
$$513$$ 3.08440 + 1.78078i 0.136179 + 0.0786232i
$$514$$ −0.719224 + 1.24573i −0.0317236 + 0.0549469i
$$515$$ 0 0
$$516$$ −2.28078 + 3.95042i −0.100406 + 0.173908i
$$517$$ 24.9950 14.4309i 1.09928 0.634669i
$$518$$ 12.7173 7.34233i 0.558766 0.322603i
$$519$$ 25.1771 1.10515
$$520$$ 0 0
$$521$$ −18.6847 −0.818590 −0.409295 0.912402i $$-0.634225\pi$$
−0.409295 + 0.912402i $$0.634225\pi$$
$$522$$ −5.68247 + 3.28078i −0.248715 + 0.143596i
$$523$$ −7.96071 + 4.59612i −0.348098 + 0.200974i −0.663847 0.747868i $$-0.731077\pi$$
0.315749 + 0.948843i $$0.397744\pi$$
$$524$$ 3.06155 5.30277i 0.133745 0.231652i
$$525$$ 0 0
$$526$$ 6.50000 11.2583i 0.283413 0.490887i
$$527$$ 25.2213 + 14.5616i 1.09866 + 0.634311i
$$528$$ 4.12311i 0.179435i
$$529$$ 18.0270 31.2237i 0.783782 1.35755i
$$530$$ 0 0
$$531$$ −5.28078 9.14657i −0.229166 0.396927i
$$532$$ 12.6847i 0.549950i
$$533$$ 9.41967 12.0691i 0.408011 0.522772i
$$534$$ −1.80776 −0.0782296
$$535$$ 0 0
$$536$$ −7.12311 12.3376i −0.307671 0.532902i
$$537$$ −0.273094 0.157671i −0.0117849 0.00680400i
$$538$$ 3.36932i 0.145262i
$$539$$ −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 $$0.518010\pi$$
$$542$$ 27.8662 + 16.0885i 1.19695 + 0.691062i
$$543$$ 9.63289 5.56155i 0.413387 0.238669i
$$544$$ 2.56155 + 4.43674i 0.109826 + 0.190224i
$$545$$ 0 0
$$546$$ 10.1231 + 7.90084i 0.433229 + 0.338125i
$$547$$ 35.6155i 1.52281i −0.648276 0.761405i $$-0.724510\pi$$
0.648276 0.761405i $$-0.275490\pi$$
$$548$$ −7.62775 + 4.40388i −0.325841 + 0.188125i
$$549$$ 3.00000 + 5.19615i 0.128037 + 0.221766i
$$550$$ 0 0
$$551$$ −23.3693 −0.995566
$$552$$ −6.65511 3.84233i −0.283260 0.163540i
$$553$$ −22.9431 13.2462i −0.975640 0.563286i
$$554$$ 1.00000 0.0424859
$$555$$ 0 0
$$556$$ −4.21922 7.30791i −0.178935 0.309924i
$$557$$ 3.84381 2.21922i 0.162867 0.0940315i −0.416351 0.909204i $$-0.636691\pi$$
0.579218 + 0.815172i $$0.303358\pi$$
$$558$$ 5.68466i 0.240651i
$$559$$ −2.28078 + 16.2880i −0.0964666 + 0.688909i
$$560$$ 0 0
$$561$$ 10.5616 + 18.2931i 0.445909 + 0.772337i
$$562$$ 0.213225 0.123106i 0.00899436 0.00519290i
$$563$$ −28.5657 16.4924i −1.20390 0.695073i −0.242481 0.970156i $$-0.577961\pi$$
−0.961420 + 0.275083i $$0.911295\pi$$
$$564$$ −7.00000 −0.294753
$$565$$ 0 0
$$566$$ −5.71922 + 9.90599i −0.240397 + 0.416380i
$$567$$ 3.56155i 0.149571i
$$568$$ 4.22351 + 2.43845i 0.177215 + 0.102315i
$$569$$ −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 $$0.423912\pi$$
$$572$$ −5.57586 13.7808i −0.233138 0.576203i
$$573$$ 19.1231i 0.798879i
$$574$$ −7.56155 13.0970i −0.315613 0.546658i
$$575$$ 0 0
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 8.73863i 0.363794i −0.983318 0.181897i $$-0.941776\pi$$
0.983318 0.181897i $$-0.0582238\pi$$
$$578$$ −8.00745 4.62311i −0.333066 0.192296i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −2.00000 + 3.46410i −0.0829740 + 0.143715i
$$582$$ −0.972638 + 0.561553i −0.0403171 + 0.0232771i
$$583$$ −15.8484 + 9.15009i −0.656375 + 0.378958i
$$584$$ 15.3693 0.635987
$$585$$ 0 0
$$586$$ −24.9309 −1.02988
$$587$$ 20.5714 11.8769i 0.849072 0.490212i −0.0112657 0.999937i $$-0.503586\pi$$
0.860338 + 0.509725i $$0.170253\pi$$
$$588$$ 4.92306 2.84233i 0.203024 0.117216i
$$589$$ −10.1231 + 17.5337i −0.417115 + 0.722465i
$$590$$ 0 0
$$591$$ 3.90388 6.76172i 0.160584 0.278140i
$$592$$ 3.57071 + 2.06155i 0.146755 + 0.0847293i
$$593$$ 12.1771i 0.500053i −0.968239 0.250026i $$-0.919561\pi$$
0.968239 0.250026i $$-0.0804393\pi$$
$$594$$ −2.06155 + 3.57071i −0.0845865 + 0.146508i
$$595$$ 0 0
$$596$$ 11.4039 + 19.7521i 0.467121 + 0.809078i
$$597$$ 11.1231i 0.455238i
$$598$$ −27.4397 3.84233i −1.12209 0.157125i
$$599$$ 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 $$0.571019\pi$$
$$602$$ 14.0696 + 8.12311i 0.573435 + 0.331073i
$$603$$ 14.2462i 0.580151i
$$604$$ 4.68466 8.11407i 0.190616 0.330157i
$$605$$ 0 0
$$606$$ −17.1231 −0.695579
$$607$$ −25.4813 14.7116i −1.03425 0.597127i −0.116054 0.993243i $$-0.537025\pi$$
−0.918201 + 0.396116i $$0.870358\pi$$
$$608$$ −3.08440 + 1.78078i −0.125089 + 0.0722200i
$$609$$ 11.6847 + 20.2384i 0.473486 + 0.820102i
$$610$$ 0 0
$$611$$ −23.3963 + 9.46641i −0.946513 + 0.382970i
$$612$$ 5.12311i 0.207089i
$$613$$ 24.3553 14.0616i 0.983702 0.567941i 0.0803164 0.996769i $$-0.474407\pi$$
0.903386 + 0.428829i $$0.141074\pi$$
$$614$$ −7.80776 13.5234i −0.315096 0.545762i
$$615$$ 0 0
$$616$$ −14.6847 −0.591662
$$617$$ −36.1000 20.8423i −1.45333 0.839081i −0.454662 0.890664i $$-0.650240\pi$$
−0.998669 + 0.0515837i $$0.983573\pi$$
$$618$$ −0.379706 0.219224i −0.0152740 0.00881847i
$$619$$ 16.4384 0.660717 0.330358 0.943856i $$-0.392830\pi$$
0.330358 + 0.943856i $$0.392830\pi$$
$$620$$ 0 0
$$621$$ 3.84233 + 6.65511i 0.154187 + 0.267060i
$$622$$ 16.2281 9.36932i 0.650689 0.375675i
$$623$$ 6.43845i 0.257951i
$$624$$ −0.500000 + 3.57071i −0.0200160 + 0.142943i
$$625$$ 0 0
$$626$$ −3.31534 5.74234i −0.132508 0.229510i
$$627$$ −12.7173 + 7.34233i −0.507880 + 0.293224i
$$628$$ −19.1592 11.0616i −0.764534 0.441404i
$$629$$ −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 $$-0.0389791\pi$$
$$632$$ 7.43845i 0.295886i
$$633$$ −6.00231 3.46543i −0.238570 0.137739i
$$634$$ −2.09612 3.63058i −0.0832475 0.144189i
$$635$$ 0 0
$$636$$ 4.43845 0.175996
$$637$$ 12.6107 16.1577i 0.499653 0.640190i
$$638$$ 27.0540i 1.07108i
$$639$$ −2.43845 4.22351i −0.0964635 0.167080i
$$640$$ 0 0
$$641$$ 7.78078 13.4767i 0.307322 0.532298i −0.670453 0.741952i $$-0.733900\pi$$
0.977776 + 0.209654i $$0.0672337\pi$$
$$642$$ 2.00000i 0.0789337i
$$643$$ −33.1222 19.1231i −1.30621 0.754142i −0.324750 0.945800i $$-0.605280\pi$$
−0.981462 + 0.191658i $$0.938613\pi$$
$$644$$ −13.6847 + 23.7025i −0.539251 + 0.934010i
$$645$$ 0 0
$$646$$ 9.12311 15.8017i 0.358944 0.621709i
$$647$$ 1.77879 1.02699i 0.0699316 0.0403751i −0.464626 0.885507i $$-0.653811\pi$$
0.534558 + 0.845132i $$0.320478\pi$$
$$648$$ 0.866025 0.500000i 0.0340207 0.0196419i
$$649$$ 43.5464 1.70935
$$650$$ 0 0
$$651$$ 20.2462 0.793512
$$652$$ 16.0748 9.28078i 0.629537 0.363463i
$$653$$ −35.0207 + 20.2192i −1.37047 + 0.791239i −0.990987 0.133961i $$-0.957230\pi$$
−0.379480 + 0.925200i $$0.623897\pi$$
$$654$$ −10.1231 + 17.5337i −0.395845 + 0.685623i
$$655$$ 0 0
$$656$$ 2.12311 3.67733i 0.0828933 0.143575i
$$657$$ −13.3102 7.68466i −0.519281 0.299807i
$$658$$ 24.9309i 0.971906i
$$659$$ 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 $$0.760802\pi$$
$$662$$ 18.7386i 0.728298i
$$663$$ −6.92820 17.1231i −0.269069 0.665006i
$$664$$ −1.12311 −0.0435850
$$665$$ 0 0
$$666$$ −2.06155 3.57071i −0.0798835 0.138362i
$$667$$ −43.6679 25.2116i −1.69083 0.976199i
$$668$$ 20.3693i 0.788113i
$$669$$ −13.1501 + 22.7766i −0.508412 + 0.880595i
$$670$$ 0 0
$$671$$ −24.7386 −0.955024
$$672$$ 3.08440 + 1.78078i 0.118983 + 0.0686949i
$$673$$ 36.5863 21.1231i 1.41030 0.814236i 0.414882 0.909875i $$-0.363823\pi$$
0.995416 + 0.0956394i $$0.0304896\pi$$
$$674$$ −3.00000 5.19615i −0.115556 0.200148i
$$675$$ 0 0
$$676$$ 3.15767 + 12.6107i 0.121449 + 0.485026i
$$677$$ 28.8769i 1.10983i 0.831907 + 0.554915i $$0.187249\pi$$
−0.831907 + 0.554915i $$0.812751\pi$$
$$678$$ −3.19101 + 1.84233i −0.122550 + 0.0707542i
$$679$$ 2.00000 + 3.46410i 0.0767530 + 0.132940i
$$680$$ 0 0
$$681$$ −20.0000 −0.766402
$$682$$ −20.2983 11.7192i −0.777262 0.448752i
$$683$$ −7.68762 4.43845i −0.294158 0.169832i 0.345657 0.938361i $$-0.387656\pi$$
−0.639816 + 0.768528i $$0.720989\pi$$
$$684$$ 3.56155 0.136179
$$685$$ 0 0
$$686$$ 2.34233 + 4.05703i 0.0894305 + 0.154898i
$$687$$ 6.71498 3.87689i 0.256192 0.147913i
$$688$$ 4.56155i 0.173908i
$$689$$ 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 $$0.732109\pi$$
$$692$$ 21.8040 12.5885i 0.828863 0.478545i
$$693$$ 12.7173 + 7.34233i 0.483090 + 0.278912i
$$694$$ −9.12311 −0.346308
$$695$$ 0 0
$$696$$ −3.28078 + 5.68247i −0.124358 + 0.215394i
$$697$$ 21.7538i 0.823984i
$$698$$ 21.2111 + 12.2462i 0.802850 + 0.463526i
$$699$$ −8.84233 15.3154i −0.334448 0.579280i
$$700$$ 0 0
$$701$$ 17.3002 0.653419 0.326710 0.945125i $$-0.394060\pi$$
0.326710 + 0.945125i $$0.394060\pi$$
$$702$$ 2.21837 2.84233i 0.0837270 0.107277i
$$703$$ 14.6847i 0.553842i
$$704$$ −2.06155 3.57071i −0.0776977 0.134576i
$$705$$ 0 0
$$706$$ −15.9309 + 27.5931i −0.599566 + 1.03848i
$$707$$ 60.9848i 2.29357i
$$708$$ −9.14657 5.28078i −0.343749 0.198464i
$$709$$ 8.87689 15.3752i 0.333379 0.577429i −0.649793 0.760111i $$-0.725145\pi$$
0.983172 + 0.182682i $$0.0584779\pi$$
$$710$$ 0 0
$$711$$ −3.71922 + 6.44188i −0.139482 + 0.241590i
$$712$$ −1.56557 + 0.903882i −0.0586722 + 0.0338744i
$$713$$ −37.8320 + 21.8423i −1.41682 + 0.818002i
$$714$$ −18.2462 −0.682847
$$715$$ 0 0
$$716$$ −0.315342 −0.0117849
$$717$$ −11.5782 + 6.68466i −0.432395 + 0.249643i
$$718$$ 4.22351 2.43845i 0.157620 0.0910020i
$$719$$ −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
$$722$$ −5.46925 3.15767i −0.203544 0.117516i
$$723$$ 19.8769i 0.739230i
$$724$$ 5.56155 9.63289i 0.206693 0.358004i
$$725$$ 0 0
$$726$$ −3.00000 5.19615i −0.111340 0.192847i
$$727$$ 23.4233i 0.868722i 0.900739 + 0.434361i $$0.143026\pi$$
−0.900739 + 0.434361i $$0.856974\pi$$
$$728$$ 12.7173 + 1.78078i 0.471334 + 0.0660000i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −11.6847 20.2384i −0.432173 0.748545i
$$732$$ 5.19615 + 3.00000i 0.192055 + 0.110883i
$$733$$ 48.9309i 1.80730i 0.428269 + 0.903651i $$0.359124\pi$$
−0.428269 + 0.903651i $$0.640876\pi$$
$$734$$ −10.2462 + 17.7470i −0.378195 + 0.655052i
$$735$$ 0 0
$$736$$ −7.68466 −0.283260
$$737$$ −50.8691 29.3693i −1.87379 1.08183i
$$738$$ −3.67733 + 2.12311i −0.135364 + 0.0781526i
$$739$$ 21.2732 + 36.8463i 0.782547 + 1.35541i 0.930453 + 0.366410i $$0.119413\pi$$
−0.147906 + 0.989001i $$0.547253\pi$$
$$740$$ 0 0
$$741$$ 11.9039 4.81645i 0.437300 0.176937i
$$742$$ 15.8078i 0.580321i
$$743$$ −27.8662 + 16.0885i −1.02231 + 0.590231i −0.914772 0.403970i $$-0.867630\pi$$
−0.107538 + 0.994201i $$0.534297\pi$$
$$744$$ 2.84233 + 4.92306i 0.104205 + 0.180488i
$$745$$ 0 0
$$746$$ −5.19224 −0.190101
$$747$$ 0.972638 + 0.561553i 0.0355870 + 0.0205461i
$$748$$ 18.2931 + 10.5616i 0.668864 + 0.386169i
$$749$$ −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 $$0.814783\pi$$
$$752$$ −6.06218 + 3.50000i −0.221065 + 0.127632i
$$753$$ 0.123106i 0.00448622i
$$754$$ −3.28078 + 23.4294i −0.119479 + 0.853250i
$$755$$ 0 0
$$756$$ −1.78078 3.08440i −0.0647662 0.112178i
$$757$$ −28.9454 + 16.7116i −1.05204 + 0.607395i −0.923220 0.384273i $$-0.874452\pi$$
−0.128820 + 0.991668i $$0.541119\pi$$
$$758$$ 4.60322 + 2.65767i 0.167197 + 0.0965309i
$$759$$ −31.6847 −1.15008
$$760$$ 0 0
$$761$$ −5.46543 + 9.46641i −0.198122 + 0.343157i −0.947919 0.318510i $$-0.896818\pi$$
0.749798 + 0.661667i $$0.230151\pi$$
$$762$$ 4.43845i 0.160788i
$$763$$ 62.4473 + 36.0540i 2.26074 + 1.30524i
$$764$$ 9.56155 + 16.5611i 0.345925 + 0.599159i
$$765$$ 0 0
$$766$$ 20.8078 0.751815
$$767$$ −37.7123 5.28078i −1.36171 0.190678i
$$768$$ 1.00000i 0.0360844i
$$769$$ −22.8423 39.5641i −0.823715 1.42672i −0.902897 0.429857i $$-0.858564\pi$$
0.0791816 0.996860i $$-0.474769\pi$$
$$770$$ 0 0
$$771$$ 0.719224 1.24573i 0.0259022 0.0448639i
$$772$$ 0 0
$$773$$ 18.3399 + 10.5885i 0.659640 + 0.380843i 0.792140 0.610340i $$-0.208967\pi$$
−0.132500 + 0.991183i $$0.542300\pi$$
$$774$$ 2.28078 3.95042i 0.0819808 0.141995i
$$775$$ 0 0
$$776$$ −0.561553 + 0.972638i −0.0201586 + 0.0349157i
$$777$$ −12.7173 + 7.34233i −0.456230 + 0.263405i
$$778$$ 16.5012 9.52699i 0.591598 0.341559i
$$779$$ −15.1231 −0.541841
$$780$$ 0 0
$$781$$ 20.1080 0.719519
$$782$$ 34.0948 19.6847i 1.21923 0.703922i
$$783$$ 5.68247 3.28078i 0.203075 0.117245i
$$784$$ 2.84233 4.92306i 0.101512 0.175824i
$$785$$ 0 0