# Properties

 Label 570.2.c.e.569.3 Level $570$ Weight $2$ Character 570.569 Analytic conductor $4.551$ Analytic rank $0$ Dimension $8$ CM no Inner twists $8$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 569.3 Root $$-0.965926 + 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.569 Dual form 570.2.c.e.569.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.73205 - 1.41421i) q^{5} +(1.00000 - 1.41421i) q^{6} +2.44949i q^{7} +1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.73205 - 1.41421i) q^{5} +(1.00000 - 1.41421i) q^{6} +2.44949i q^{7} +1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +(-1.41421 + 1.73205i) q^{10} -1.41421i q^{11} +(-1.41421 - 1.00000i) q^{12} +4.24264 q^{13} +2.44949 q^{14} +(-1.03528 - 3.73205i) q^{15} +1.00000 q^{16} +6.92820 q^{17} +(2.82843 - 1.00000i) q^{18} +(4.00000 + 1.73205i) q^{19} +(1.73205 + 1.41421i) q^{20} +(-2.44949 + 3.46410i) q^{21} -1.41421 q^{22} +3.46410 q^{23} +(-1.00000 + 1.41421i) q^{24} +(1.00000 + 4.89898i) q^{25} -4.24264i q^{26} +(-1.41421 + 5.00000i) q^{27} -2.44949i q^{28} -2.44949 q^{29} +(-3.73205 + 1.03528i) q^{30} -6.92820i q^{31} -1.00000i q^{32} +(1.41421 - 2.00000i) q^{33} -6.92820i q^{34} +(3.46410 - 4.24264i) q^{35} +(-1.00000 - 2.82843i) q^{36} -4.24264 q^{37} +(1.73205 - 4.00000i) q^{38} +(6.00000 + 4.24264i) q^{39} +(1.41421 - 1.73205i) q^{40} -12.2474 q^{41} +(3.46410 + 2.44949i) q^{42} +7.34847i q^{43} +1.41421i q^{44} +(2.26795 - 6.31319i) q^{45} -3.46410i q^{46} -3.46410 q^{47} +(1.41421 + 1.00000i) q^{48} +1.00000 q^{49} +(4.89898 - 1.00000i) q^{50} +(9.79796 + 6.92820i) q^{51} -4.24264 q^{52} +6.00000i q^{53} +(5.00000 + 1.41421i) q^{54} +(-2.00000 + 2.44949i) q^{55} -2.44949 q^{56} +(3.92480 + 6.44949i) q^{57} +2.44949i q^{58} +4.89898 q^{59} +(1.03528 + 3.73205i) q^{60} -8.00000 q^{61} -6.92820 q^{62} +(-6.92820 + 2.44949i) q^{63} -1.00000 q^{64} +(-7.34847 - 6.00000i) q^{65} +(-2.00000 - 1.41421i) q^{66} -6.92820 q^{68} +(4.89898 + 3.46410i) q^{69} +(-4.24264 - 3.46410i) q^{70} +4.89898 q^{71} +(-2.82843 + 1.00000i) q^{72} -14.6969i q^{73} +4.24264i q^{74} +(-3.48477 + 7.92820i) q^{75} +(-4.00000 - 1.73205i) q^{76} +3.46410 q^{77} +(4.24264 - 6.00000i) q^{78} -10.3923i q^{79} +(-1.73205 - 1.41421i) q^{80} +(-7.00000 + 5.65685i) q^{81} +12.2474i q^{82} +10.3923 q^{83} +(2.44949 - 3.46410i) q^{84} +(-12.0000 - 9.79796i) q^{85} +7.34847 q^{86} +(-3.46410 - 2.44949i) q^{87} +1.41421 q^{88} +2.44949 q^{89} +(-6.31319 - 2.26795i) q^{90} +10.3923i q^{91} -3.46410 q^{92} +(6.92820 - 9.79796i) q^{93} +3.46410i q^{94} +(-4.47871 - 8.65685i) q^{95} +(1.00000 - 1.41421i) q^{96} -12.7279 q^{97} -1.00000i q^{98} +(4.00000 - 1.41421i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 8q^{4} + 8q^{6} + 8q^{9} + O(q^{10})$$ $$8q - 8q^{4} + 8q^{6} + 8q^{9} + 8q^{16} + 32q^{19} - 8q^{24} + 8q^{25} - 16q^{30} - 8q^{36} + 48q^{39} + 32q^{45} + 8q^{49} + 40q^{54} - 16q^{55} - 64q^{61} - 8q^{64} - 16q^{66} - 32q^{76} - 56q^{81} - 96q^{85} + 8q^{96} + 32q^{99} + O(q^{100})$$

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 1.41421 + 1.00000i 0.816497 + 0.577350i
$$4$$ −1.00000 −0.500000
$$5$$ −1.73205 1.41421i −0.774597 0.632456i
$$6$$ 1.00000 1.41421i 0.408248 0.577350i
$$7$$ 2.44949i 0.925820i 0.886405 + 0.462910i $$0.153195\pi$$
−0.886405 + 0.462910i $$0.846805\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000 + 2.82843i 0.333333 + 0.942809i
$$10$$ −1.41421 + 1.73205i −0.447214 + 0.547723i
$$11$$ 1.41421i 0.426401i −0.977008 0.213201i $$-0.931611\pi$$
0.977008 0.213201i $$-0.0683888\pi$$
$$12$$ −1.41421 1.00000i −0.408248 0.288675i
$$13$$ 4.24264 1.17670 0.588348 0.808608i $$-0.299778\pi$$
0.588348 + 0.808608i $$0.299778\pi$$
$$14$$ 2.44949 0.654654
$$15$$ −1.03528 3.73205i −0.267307 0.963611i
$$16$$ 1.00000 0.250000
$$17$$ 6.92820 1.68034 0.840168 0.542326i $$-0.182456\pi$$
0.840168 + 0.542326i $$0.182456\pi$$
$$18$$ 2.82843 1.00000i 0.666667 0.235702i
$$19$$ 4.00000 + 1.73205i 0.917663 + 0.397360i
$$20$$ 1.73205 + 1.41421i 0.387298 + 0.316228i
$$21$$ −2.44949 + 3.46410i −0.534522 + 0.755929i
$$22$$ −1.41421 −0.301511
$$23$$ 3.46410 0.722315 0.361158 0.932505i $$-0.382382\pi$$
0.361158 + 0.932505i $$0.382382\pi$$
$$24$$ −1.00000 + 1.41421i −0.204124 + 0.288675i
$$25$$ 1.00000 + 4.89898i 0.200000 + 0.979796i
$$26$$ 4.24264i 0.832050i
$$27$$ −1.41421 + 5.00000i −0.272166 + 0.962250i
$$28$$ 2.44949i 0.462910i
$$29$$ −2.44949 −0.454859 −0.227429 0.973795i $$-0.573032\pi$$
−0.227429 + 0.973795i $$0.573032\pi$$
$$30$$ −3.73205 + 1.03528i −0.681376 + 0.189015i
$$31$$ 6.92820i 1.24434i −0.782881 0.622171i $$-0.786251\pi$$
0.782881 0.622171i $$-0.213749\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 1.41421 2.00000i 0.246183 0.348155i
$$34$$ 6.92820i 1.18818i
$$35$$ 3.46410 4.24264i 0.585540 0.717137i
$$36$$ −1.00000 2.82843i −0.166667 0.471405i
$$37$$ −4.24264 −0.697486 −0.348743 0.937218i $$-0.613391\pi$$
−0.348743 + 0.937218i $$0.613391\pi$$
$$38$$ 1.73205 4.00000i 0.280976 0.648886i
$$39$$ 6.00000 + 4.24264i 0.960769 + 0.679366i
$$40$$ 1.41421 1.73205i 0.223607 0.273861i
$$41$$ −12.2474 −1.91273 −0.956365 0.292174i $$-0.905621\pi$$
−0.956365 + 0.292174i $$0.905621\pi$$
$$42$$ 3.46410 + 2.44949i 0.534522 + 0.377964i
$$43$$ 7.34847i 1.12063i 0.828279 + 0.560316i $$0.189320\pi$$
−0.828279 + 0.560316i $$0.810680\pi$$
$$44$$ 1.41421i 0.213201i
$$45$$ 2.26795 6.31319i 0.338086 0.941115i
$$46$$ 3.46410i 0.510754i
$$47$$ −3.46410 −0.505291 −0.252646 0.967559i $$-0.581301\pi$$
−0.252646 + 0.967559i $$0.581301\pi$$
$$48$$ 1.41421 + 1.00000i 0.204124 + 0.144338i
$$49$$ 1.00000 0.142857
$$50$$ 4.89898 1.00000i 0.692820 0.141421i
$$51$$ 9.79796 + 6.92820i 1.37199 + 0.970143i
$$52$$ −4.24264 −0.588348
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ 5.00000 + 1.41421i 0.680414 + 0.192450i
$$55$$ −2.00000 + 2.44949i −0.269680 + 0.330289i
$$56$$ −2.44949 −0.327327
$$57$$ 3.92480 + 6.44949i 0.519853 + 0.854256i
$$58$$ 2.44949i 0.321634i
$$59$$ 4.89898 0.637793 0.318896 0.947790i $$-0.396688\pi$$
0.318896 + 0.947790i $$0.396688\pi$$
$$60$$ 1.03528 + 3.73205i 0.133654 + 0.481806i
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ −6.92820 −0.879883
$$63$$ −6.92820 + 2.44949i −0.872872 + 0.308607i
$$64$$ −1.00000 −0.125000
$$65$$ −7.34847 6.00000i −0.911465 0.744208i
$$66$$ −2.00000 1.41421i −0.246183 0.174078i
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ −6.92820 −0.840168
$$69$$ 4.89898 + 3.46410i 0.589768 + 0.417029i
$$70$$ −4.24264 3.46410i −0.507093 0.414039i
$$71$$ 4.89898 0.581402 0.290701 0.956814i $$-0.406112\pi$$
0.290701 + 0.956814i $$0.406112\pi$$
$$72$$ −2.82843 + 1.00000i −0.333333 + 0.117851i
$$73$$ 14.6969i 1.72015i −0.510171 0.860073i $$-0.670418\pi$$
0.510171 0.860073i $$-0.329582\pi$$
$$74$$ 4.24264i 0.493197i
$$75$$ −3.48477 + 7.92820i −0.402386 + 0.915470i
$$76$$ −4.00000 1.73205i −0.458831 0.198680i
$$77$$ 3.46410 0.394771
$$78$$ 4.24264 6.00000i 0.480384 0.679366i
$$79$$ 10.3923i 1.16923i −0.811312 0.584613i $$-0.801246\pi$$
0.811312 0.584613i $$-0.198754\pi$$
$$80$$ −1.73205 1.41421i −0.193649 0.158114i
$$81$$ −7.00000 + 5.65685i −0.777778 + 0.628539i
$$82$$ 12.2474i 1.35250i
$$83$$ 10.3923 1.14070 0.570352 0.821401i $$-0.306807\pi$$
0.570352 + 0.821401i $$0.306807\pi$$
$$84$$ 2.44949 3.46410i 0.267261 0.377964i
$$85$$ −12.0000 9.79796i −1.30158 1.06274i
$$86$$ 7.34847 0.792406
$$87$$ −3.46410 2.44949i −0.371391 0.262613i
$$88$$ 1.41421 0.150756
$$89$$ 2.44949 0.259645 0.129823 0.991537i $$-0.458559\pi$$
0.129823 + 0.991537i $$0.458559\pi$$
$$90$$ −6.31319 2.26795i −0.665469 0.239063i
$$91$$ 10.3923i 1.08941i
$$92$$ −3.46410 −0.361158
$$93$$ 6.92820 9.79796i 0.718421 1.01600i
$$94$$ 3.46410i 0.357295i
$$95$$ −4.47871 8.65685i −0.459506 0.888175i
$$96$$ 1.00000 1.41421i 0.102062 0.144338i
$$97$$ −12.7279 −1.29232 −0.646162 0.763200i $$-0.723627\pi$$
−0.646162 + 0.763200i $$0.723627\pi$$
$$98$$ 1.00000i 0.101015i
$$99$$ 4.00000 1.41421i 0.402015 0.142134i
$$100$$ −1.00000 4.89898i −0.100000 0.489898i
$$101$$ 2.82843i 0.281439i 0.990050 + 0.140720i $$0.0449416\pi$$
−0.990050 + 0.140720i $$0.955058\pi$$
$$102$$ 6.92820 9.79796i 0.685994 0.970143i
$$103$$ −8.48528 −0.836080 −0.418040 0.908429i $$-0.637283\pi$$
−0.418040 + 0.908429i $$0.637283\pi$$
$$104$$ 4.24264i 0.416025i
$$105$$ 9.14162 2.53590i 0.892131 0.247478i
$$106$$ 6.00000 0.582772
$$107$$ 18.0000i 1.74013i −0.492941 0.870063i $$-0.664078\pi$$
0.492941 0.870063i $$-0.335922\pi$$
$$108$$ 1.41421 5.00000i 0.136083 0.481125i
$$109$$ 6.92820i 0.663602i −0.943349 0.331801i $$-0.892344\pi$$
0.943349 0.331801i $$-0.107656\pi$$
$$110$$ 2.44949 + 2.00000i 0.233550 + 0.190693i
$$111$$ −6.00000 4.24264i −0.569495 0.402694i
$$112$$ 2.44949i 0.231455i
$$113$$ 18.0000i 1.69330i 0.532152 + 0.846649i $$0.321383\pi$$
−0.532152 + 0.846649i $$0.678617\pi$$
$$114$$ 6.44949 3.92480i 0.604050 0.367592i
$$115$$ −6.00000 4.89898i −0.559503 0.456832i
$$116$$ 2.44949 0.227429
$$117$$ 4.24264 + 12.0000i 0.392232 + 1.10940i
$$118$$ 4.89898i 0.450988i
$$119$$ 16.9706i 1.55569i
$$120$$ 3.73205 1.03528i 0.340688 0.0945074i
$$121$$ 9.00000 0.818182
$$122$$ 8.00000i 0.724286i
$$123$$ −17.3205 12.2474i −1.56174 1.10432i
$$124$$ 6.92820i 0.622171i
$$125$$ 5.19615 9.89949i 0.464758 0.885438i
$$126$$ 2.44949 + 6.92820i 0.218218 + 0.617213i
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −7.34847 + 10.3923i −0.646997 + 0.914991i
$$130$$ −6.00000 + 7.34847i −0.526235 + 0.644503i
$$131$$ 1.41421i 0.123560i 0.998090 + 0.0617802i $$0.0196778\pi$$
−0.998090 + 0.0617802i $$0.980322\pi$$
$$132$$ −1.41421 + 2.00000i −0.123091 + 0.174078i
$$133$$ −4.24264 + 9.79796i −0.367884 + 0.849591i
$$134$$ 0 0
$$135$$ 9.52056 6.66025i 0.819399 0.573223i
$$136$$ 6.92820i 0.594089i
$$137$$ −17.3205 −1.47979 −0.739895 0.672722i $$-0.765125\pi$$
−0.739895 + 0.672722i $$0.765125\pi$$
$$138$$ 3.46410 4.89898i 0.294884 0.417029i
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ −3.46410 + 4.24264i −0.292770 + 0.358569i
$$141$$ −4.89898 3.46410i −0.412568 0.291730i
$$142$$ 4.89898i 0.411113i
$$143$$ 6.00000i 0.501745i
$$144$$ 1.00000 + 2.82843i 0.0833333 + 0.235702i
$$145$$ 4.24264 + 3.46410i 0.352332 + 0.287678i
$$146$$ −14.6969 −1.21633
$$147$$ 1.41421 + 1.00000i 0.116642 + 0.0824786i
$$148$$ 4.24264 0.348743
$$149$$ 11.3137i 0.926855i 0.886135 + 0.463428i $$0.153381\pi$$
−0.886135 + 0.463428i $$0.846619\pi$$
$$150$$ 7.92820 + 3.48477i 0.647335 + 0.284530i
$$151$$ 13.8564i 1.12762i −0.825905 0.563809i $$-0.809335\pi$$
0.825905 0.563809i $$-0.190665\pi$$
$$152$$ −1.73205 + 4.00000i −0.140488 + 0.324443i
$$153$$ 6.92820 + 19.5959i 0.560112 + 1.58424i
$$154$$ 3.46410i 0.279145i
$$155$$ −9.79796 + 12.0000i −0.786991 + 0.963863i
$$156$$ −6.00000 4.24264i −0.480384 0.339683i
$$157$$ 14.6969i 1.17294i −0.809970 0.586472i $$-0.800517\pi$$
0.809970 0.586472i $$-0.199483\pi$$
$$158$$ −10.3923 −0.826767
$$159$$ −6.00000 + 8.48528i −0.475831 + 0.672927i
$$160$$ −1.41421 + 1.73205i −0.111803 + 0.136931i
$$161$$ 8.48528i 0.668734i
$$162$$ 5.65685 + 7.00000i 0.444444 + 0.549972i
$$163$$ 12.2474i 0.959294i 0.877461 + 0.479647i $$0.159235\pi$$
−0.877461 + 0.479647i $$0.840765\pi$$
$$164$$ 12.2474 0.956365
$$165$$ −5.27792 + 1.46410i −0.410885 + 0.113980i
$$166$$ 10.3923i 0.806599i
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ −3.46410 2.44949i −0.267261 0.188982i
$$169$$ 5.00000 0.384615
$$170$$ −9.79796 + 12.0000i −0.751469 + 0.920358i
$$171$$ −0.898979 + 13.0458i −0.0687467 + 0.997634i
$$172$$ 7.34847i 0.560316i
$$173$$ 6.00000i 0.456172i 0.973641 + 0.228086i $$0.0732467\pi$$
−0.973641 + 0.228086i $$0.926753\pi$$
$$174$$ −2.44949 + 3.46410i −0.185695 + 0.262613i
$$175$$ −12.0000 + 2.44949i −0.907115 + 0.185164i
$$176$$ 1.41421i 0.106600i
$$177$$ 6.92820 + 4.89898i 0.520756 + 0.368230i
$$178$$ 2.44949i 0.183597i
$$179$$ 4.89898 0.366167 0.183083 0.983097i $$-0.441392\pi$$
0.183083 + 0.983097i $$0.441392\pi$$
$$180$$ −2.26795 + 6.31319i −0.169043 + 0.470558i
$$181$$ 13.8564i 1.02994i 0.857209 + 0.514969i $$0.172197\pi$$
−0.857209 + 0.514969i $$0.827803\pi$$
$$182$$ 10.3923 0.770329
$$183$$ −11.3137 8.00000i −0.836333 0.591377i
$$184$$ 3.46410i 0.255377i
$$185$$ 7.34847 + 6.00000i 0.540270 + 0.441129i
$$186$$ −9.79796 6.92820i −0.718421 0.508001i
$$187$$ 9.79796i 0.716498i
$$188$$ 3.46410 0.252646
$$189$$ −12.2474 3.46410i −0.890871 0.251976i
$$190$$ −8.65685 + 4.47871i −0.628034 + 0.324920i
$$191$$ 24.0416i 1.73959i −0.493412 0.869796i $$-0.664251\pi$$
0.493412 0.869796i $$-0.335749\pi$$
$$192$$ −1.41421 1.00000i −0.102062 0.0721688i
$$193$$ −12.7279 −0.916176 −0.458088 0.888907i $$-0.651466\pi$$
−0.458088 + 0.888907i $$0.651466\pi$$
$$194$$ 12.7279i 0.913812i
$$195$$ −4.39230 15.8338i −0.314539 1.13388i
$$196$$ −1.00000 −0.0714286
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ −1.41421 4.00000i −0.100504 0.284268i
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ −4.89898 + 1.00000i −0.346410 + 0.0707107i
$$201$$ 0 0
$$202$$ 2.82843 0.199007
$$203$$ 6.00000i 0.421117i
$$204$$ −9.79796 6.92820i −0.685994 0.485071i
$$205$$ 21.2132 + 17.3205i 1.48159 + 1.20972i
$$206$$ 8.48528i 0.591198i
$$207$$ 3.46410 + 9.79796i 0.240772 + 0.681005i
$$208$$ 4.24264 0.294174
$$209$$ 2.44949 5.65685i 0.169435 0.391293i
$$210$$ −2.53590 9.14162i −0.174994 0.630832i
$$211$$ 3.46410i 0.238479i −0.992866 0.119239i $$-0.961954\pi$$
0.992866 0.119239i $$-0.0380456\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 6.92820 + 4.89898i 0.474713 + 0.335673i
$$214$$ −18.0000 −1.23045
$$215$$ 10.3923 12.7279i 0.708749 0.868037i
$$216$$ −5.00000 1.41421i −0.340207 0.0962250i
$$217$$ 16.9706 1.15204
$$218$$ −6.92820 −0.469237
$$219$$ 14.6969 20.7846i 0.993127 1.40449i
$$220$$ 2.00000 2.44949i 0.134840 0.165145i
$$221$$ 29.3939 1.97725
$$222$$ −4.24264 + 6.00000i −0.284747 + 0.402694i
$$223$$ −25.4558 −1.70465 −0.852325 0.523013i $$-0.824808\pi$$
−0.852325 + 0.523013i $$0.824808\pi$$
$$224$$ 2.44949 0.163663
$$225$$ −12.8564 + 7.72741i −0.857094 + 0.515160i
$$226$$ 18.0000 1.19734
$$227$$ 12.0000i 0.796468i −0.917284 0.398234i $$-0.869623\pi$$
0.917284 0.398234i $$-0.130377\pi$$
$$228$$ −3.92480 6.44949i −0.259926 0.427128i
$$229$$ 28.0000 1.85029 0.925146 0.379611i $$-0.123942\pi$$
0.925146 + 0.379611i $$0.123942\pi$$
$$230$$ −4.89898 + 6.00000i −0.323029 + 0.395628i
$$231$$ 4.89898 + 3.46410i 0.322329 + 0.227921i
$$232$$ 2.44949i 0.160817i
$$233$$ −10.3923 −0.680823 −0.340411 0.940277i $$-0.610566\pi$$
−0.340411 + 0.940277i $$0.610566\pi$$
$$234$$ 12.0000 4.24264i 0.784465 0.277350i
$$235$$ 6.00000 + 4.89898i 0.391397 + 0.319574i
$$236$$ −4.89898 −0.318896
$$237$$ 10.3923 14.6969i 0.675053 0.954669i
$$238$$ 16.9706 1.10004
$$239$$ 1.41421i 0.0914779i 0.998953 + 0.0457389i $$0.0145642\pi$$
−0.998953 + 0.0457389i $$0.985436\pi$$
$$240$$ −1.03528 3.73205i −0.0668268 0.240903i
$$241$$ 13.8564i 0.892570i −0.894891 0.446285i $$-0.852747\pi$$
0.894891 0.446285i $$-0.147253\pi$$
$$242$$ 9.00000i 0.578542i
$$243$$ −15.5563 + 1.00000i −0.997940 + 0.0641500i
$$244$$ 8.00000 0.512148
$$245$$ −1.73205 1.41421i −0.110657 0.0903508i
$$246$$ −12.2474 + 17.3205i −0.780869 + 1.10432i
$$247$$ 16.9706 + 7.34847i 1.07981 + 0.467572i
$$248$$ 6.92820 0.439941
$$249$$ 14.6969 + 10.3923i 0.931381 + 0.658586i
$$250$$ −9.89949 5.19615i −0.626099 0.328634i
$$251$$ 1.41421i 0.0892644i 0.999003 + 0.0446322i $$0.0142116\pi$$
−0.999003 + 0.0446322i $$0.985788\pi$$
$$252$$ 6.92820 2.44949i 0.436436 0.154303i
$$253$$ 4.89898i 0.307996i
$$254$$ 0 0
$$255$$ −7.17260 25.8564i −0.449166 1.61919i
$$256$$ 1.00000 0.0625000
$$257$$ 6.00000i 0.374270i −0.982334 0.187135i $$-0.940080\pi$$
0.982334 0.187135i $$-0.0599201\pi$$
$$258$$ 10.3923 + 7.34847i 0.646997 + 0.457496i
$$259$$ 10.3923i 0.645746i
$$260$$ 7.34847 + 6.00000i 0.455733 + 0.372104i
$$261$$ −2.44949 6.92820i −0.151620 0.428845i
$$262$$ 1.41421 0.0873704
$$263$$ −3.46410 −0.213606 −0.106803 0.994280i $$-0.534061\pi$$
−0.106803 + 0.994280i $$0.534061\pi$$
$$264$$ 2.00000 + 1.41421i 0.123091 + 0.0870388i
$$265$$ 8.48528 10.3923i 0.521247 0.638394i
$$266$$ 9.79796 + 4.24264i 0.600751 + 0.260133i
$$267$$ 3.46410 + 2.44949i 0.212000 + 0.149906i
$$268$$ 0 0
$$269$$ −17.1464 −1.04544 −0.522718 0.852506i $$-0.675082\pi$$
−0.522718 + 0.852506i $$0.675082\pi$$
$$270$$ −6.66025 9.52056i −0.405330 0.579403i
$$271$$ 4.00000 0.242983 0.121491 0.992592i $$-0.461232\pi$$
0.121491 + 0.992592i $$0.461232\pi$$
$$272$$ 6.92820 0.420084
$$273$$ −10.3923 + 14.6969i −0.628971 + 0.889499i
$$274$$ 17.3205i 1.04637i
$$275$$ 6.92820 1.41421i 0.417786 0.0852803i
$$276$$ −4.89898 3.46410i −0.294884 0.208514i
$$277$$ 19.5959i 1.17740i 0.808350 + 0.588702i $$0.200361\pi$$
−0.808350 + 0.588702i $$0.799639\pi$$
$$278$$ 4.00000i 0.239904i
$$279$$ 19.5959 6.92820i 1.17318 0.414781i
$$280$$ 4.24264 + 3.46410i 0.253546 + 0.207020i
$$281$$ −7.34847 −0.438373 −0.219186 0.975683i $$-0.570340\pi$$
−0.219186 + 0.975683i $$0.570340\pi$$
$$282$$ −3.46410 + 4.89898i −0.206284 + 0.291730i
$$283$$ 12.2474i 0.728035i 0.931392 + 0.364018i $$0.118595\pi$$
−0.931392 + 0.364018i $$0.881405\pi$$
$$284$$ −4.89898 −0.290701
$$285$$ 2.32300 16.7214i 0.137602 0.990488i
$$286$$ −6.00000 −0.354787
$$287$$ 30.0000i 1.77084i
$$288$$ 2.82843 1.00000i 0.166667 0.0589256i
$$289$$ 31.0000 1.82353
$$290$$ 3.46410 4.24264i 0.203419 0.249136i
$$291$$ −18.0000 12.7279i −1.05518 0.746124i
$$292$$ 14.6969i 0.860073i
$$293$$ 6.00000i 0.350524i −0.984522 0.175262i $$-0.943923\pi$$
0.984522 0.175262i $$-0.0560772\pi$$
$$294$$ 1.00000 1.41421i 0.0583212 0.0824786i
$$295$$ −8.48528 6.92820i −0.494032 0.403376i
$$296$$ 4.24264i 0.246598i
$$297$$ 7.07107 + 2.00000i 0.410305 + 0.116052i
$$298$$ 11.3137 0.655386
$$299$$ 14.6969 0.849946
$$300$$ 3.48477 7.92820i 0.201193 0.457735i
$$301$$ −18.0000 −1.03750
$$302$$ −13.8564 −0.797347
$$303$$ −2.82843 + 4.00000i −0.162489 + 0.229794i
$$304$$ 4.00000 + 1.73205i 0.229416 + 0.0993399i
$$305$$ 13.8564 + 11.3137i 0.793416 + 0.647821i
$$306$$ 19.5959 6.92820i 1.12022 0.396059i
$$307$$ 25.4558 1.45284 0.726421 0.687250i $$-0.241182\pi$$
0.726421 + 0.687250i $$0.241182\pi$$
$$308$$ −3.46410 −0.197386
$$309$$ −12.0000 8.48528i −0.682656 0.482711i
$$310$$ 12.0000 + 9.79796i 0.681554 + 0.556487i
$$311$$ 26.8701i 1.52366i −0.647776 0.761831i $$-0.724301\pi$$
0.647776 0.761831i $$-0.275699\pi$$
$$312$$ −4.24264 + 6.00000i −0.240192 + 0.339683i
$$313$$ 4.89898i 0.276907i 0.990369 + 0.138453i $$0.0442131\pi$$
−0.990369 + 0.138453i $$0.955787\pi$$
$$314$$ −14.6969 −0.829396
$$315$$ 15.4641 + 5.55532i 0.871303 + 0.313007i
$$316$$ 10.3923i 0.584613i
$$317$$ 18.0000i 1.01098i −0.862832 0.505490i $$-0.831312\pi$$
0.862832 0.505490i $$-0.168688\pi$$
$$318$$ 8.48528 + 6.00000i 0.475831 + 0.336463i
$$319$$ 3.46410i 0.193952i
$$320$$ 1.73205 + 1.41421i 0.0968246 + 0.0790569i
$$321$$ 18.0000 25.4558i 1.00466 1.42081i
$$322$$ 8.48528 0.472866
$$323$$ 27.7128 + 12.0000i 1.54198 + 0.667698i
$$324$$ 7.00000 5.65685i 0.388889 0.314270i
$$325$$ 4.24264 + 20.7846i 0.235339 + 1.15292i
$$326$$ 12.2474 0.678323
$$327$$ 6.92820 9.79796i 0.383131 0.541828i
$$328$$ 12.2474i 0.676252i
$$329$$ 8.48528i 0.467809i
$$330$$ 1.46410 + 5.27792i 0.0805961 + 0.290540i
$$331$$ 6.92820i 0.380808i 0.981706 + 0.190404i $$0.0609799\pi$$
−0.981706 + 0.190404i $$0.939020\pi$$
$$332$$ −10.3923 −0.570352
$$333$$ −4.24264 12.0000i −0.232495 0.657596i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −2.44949 + 3.46410i −0.133631 + 0.188982i
$$337$$ −4.24264 −0.231111 −0.115556 0.993301i $$-0.536865\pi$$
−0.115556 + 0.993301i $$0.536865\pi$$
$$338$$ 5.00000i 0.271964i
$$339$$ −18.0000 + 25.4558i −0.977626 + 1.38257i
$$340$$ 12.0000 + 9.79796i 0.650791 + 0.531369i
$$341$$ −9.79796 −0.530589
$$342$$ 13.0458 + 0.898979i 0.705434 + 0.0486112i
$$343$$ 19.5959i 1.05808i
$$344$$ −7.34847 −0.396203
$$345$$ −3.58630 12.9282i −0.193080 0.696031i
$$346$$ 6.00000 0.322562
$$347$$ −24.2487 −1.30174 −0.650870 0.759190i $$-0.725596\pi$$
−0.650870 + 0.759190i $$0.725596\pi$$
$$348$$ 3.46410 + 2.44949i 0.185695 + 0.131306i
$$349$$ −22.0000 −1.17763 −0.588817 0.808267i $$-0.700406\pi$$
−0.588817 + 0.808267i $$0.700406\pi$$
$$350$$ 2.44949 + 12.0000i 0.130931 + 0.641427i
$$351$$ −6.00000 + 21.2132i −0.320256 + 1.13228i
$$352$$ −1.41421 −0.0753778
$$353$$ 17.3205 0.921878 0.460939 0.887432i $$-0.347513\pi$$
0.460939 + 0.887432i $$0.347513\pi$$
$$354$$ 4.89898 6.92820i 0.260378 0.368230i
$$355$$ −8.48528 6.92820i −0.450352 0.367711i
$$356$$ −2.44949 −0.129823
$$357$$ −16.9706 + 24.0000i −0.898177 + 1.27021i
$$358$$ 4.89898i 0.258919i
$$359$$ 18.3848i 0.970311i −0.874428 0.485156i $$-0.838763\pi$$
0.874428 0.485156i $$-0.161237\pi$$
$$360$$ 6.31319 + 2.26795i 0.332734 + 0.119531i
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ 13.8564 0.728277
$$363$$ 12.7279 + 9.00000i 0.668043 + 0.472377i
$$364$$ 10.3923i 0.544705i
$$365$$ −20.7846 + 25.4558i −1.08792 + 1.33242i
$$366$$ −8.00000 + 11.3137i −0.418167 + 0.591377i
$$367$$ 31.8434i 1.66221i −0.556115 0.831105i $$-0.687709\pi$$
0.556115 0.831105i $$-0.312291\pi$$
$$368$$ 3.46410 0.180579
$$369$$ −12.2474 34.6410i −0.637577 1.80334i
$$370$$ 6.00000 7.34847i 0.311925 0.382029i
$$371$$ −14.6969 −0.763027
$$372$$ −6.92820 + 9.79796i −0.359211 + 0.508001i
$$373$$ −12.7279 −0.659027 −0.329513 0.944151i $$-0.606885\pi$$
−0.329513 + 0.944151i $$0.606885\pi$$
$$374$$ −9.79796 −0.506640
$$375$$ 17.2480 8.80385i 0.890681 0.454629i
$$376$$ 3.46410i 0.178647i
$$377$$ −10.3923 −0.535231
$$378$$ −3.46410 + 12.2474i −0.178174 + 0.629941i
$$379$$ 20.7846i 1.06763i 0.845600 + 0.533817i $$0.179243\pi$$
−0.845600 + 0.533817i $$0.820757\pi$$
$$380$$ 4.47871 + 8.65685i 0.229753 + 0.444087i
$$381$$ 0 0
$$382$$ −24.0416 −1.23008
$$383$$ 6.00000i 0.306586i 0.988181 + 0.153293i $$0.0489878\pi$$
−0.988181 + 0.153293i $$0.951012\pi$$
$$384$$ −1.00000 + 1.41421i −0.0510310 + 0.0721688i
$$385$$ −6.00000 4.89898i −0.305788 0.249675i
$$386$$ 12.7279i 0.647834i
$$387$$ −20.7846 + 7.34847i −1.05654 + 0.373544i
$$388$$ 12.7279 0.646162
$$389$$ 19.7990i 1.00385i −0.864912 0.501924i $$-0.832626\pi$$
0.864912 0.501924i $$-0.167374\pi$$
$$390$$ −15.8338 + 4.39230i −0.801773 + 0.222413i
$$391$$ 24.0000 1.21373
$$392$$ 1.00000i 0.0505076i
$$393$$ −1.41421 + 2.00000i −0.0713376 + 0.100887i
$$394$$ 0 0
$$395$$ −14.6969 + 18.0000i −0.739483 + 0.905678i
$$396$$ −4.00000 + 1.41421i −0.201008 + 0.0710669i
$$397$$ 19.5959i 0.983491i 0.870739 + 0.491745i $$0.163641\pi$$
−0.870739 + 0.491745i $$0.836359\pi$$
$$398$$ 16.0000i 0.802008i
$$399$$ −15.7980 + 9.61377i −0.790887 + 0.481290i
$$400$$ 1.00000 + 4.89898i 0.0500000 + 0.244949i
$$401$$ −22.0454 −1.10090 −0.550448 0.834870i $$-0.685543\pi$$
−0.550448 + 0.834870i $$0.685543\pi$$
$$402$$ 0 0
$$403$$ 29.3939i 1.46421i
$$404$$ 2.82843i 0.140720i
$$405$$ 20.1244 + 0.101536i 0.999987 + 0.00504536i
$$406$$ −6.00000 −0.297775
$$407$$ 6.00000i 0.297409i
$$408$$ −6.92820 + 9.79796i −0.342997 + 0.485071i
$$409$$ 20.7846i 1.02773i 0.857870 + 0.513866i $$0.171787\pi$$
−0.857870 + 0.513866i $$0.828213\pi$$
$$410$$ 17.3205 21.2132i 0.855399 1.04765i
$$411$$ −24.4949 17.3205i −1.20824 0.854358i
$$412$$ 8.48528 0.418040
$$413$$ 12.0000i 0.590481i
$$414$$ 9.79796 3.46410i 0.481543 0.170251i
$$415$$ −18.0000 14.6969i −0.883585 0.721444i
$$416$$ 4.24264i 0.208013i
$$417$$ 5.65685 + 4.00000i 0.277017 + 0.195881i
$$418$$ −5.65685 2.44949i −0.276686 0.119808i
$$419$$ 9.89949i 0.483622i 0.970323 + 0.241811i $$0.0777414\pi$$
−0.970323 + 0.241811i $$0.922259\pi$$
$$420$$ −9.14162 + 2.53590i −0.446065 + 0.123739i
$$421$$ 13.8564i 0.675320i −0.941268 0.337660i $$-0.890365\pi$$
0.941268 0.337660i $$-0.109635\pi$$
$$422$$ −3.46410 −0.168630
$$423$$ −3.46410 9.79796i −0.168430 0.476393i
$$424$$ −6.00000 −0.291386
$$425$$ 6.92820 + 33.9411i 0.336067 + 1.64639i
$$426$$ 4.89898 6.92820i 0.237356 0.335673i
$$427$$ 19.5959i 0.948313i
$$428$$ 18.0000i 0.870063i
$$429$$ 6.00000 8.48528i 0.289683 0.409673i
$$430$$ −12.7279 10.3923i −0.613795 0.501161i
$$431$$ 19.5959 0.943902 0.471951 0.881625i $$-0.343550\pi$$
0.471951 + 0.881625i $$0.343550\pi$$
$$432$$ −1.41421 + 5.00000i −0.0680414 + 0.240563i
$$433$$ 38.1838 1.83499 0.917497 0.397742i $$-0.130206\pi$$
0.917497 + 0.397742i $$0.130206\pi$$
$$434$$ 16.9706i 0.814613i
$$435$$ 2.53590 + 9.14162i 0.121587 + 0.438307i
$$436$$ 6.92820i 0.331801i
$$437$$ 13.8564 + 6.00000i 0.662842 + 0.287019i
$$438$$ −20.7846 14.6969i −0.993127 0.702247i
$$439$$ 3.46410i 0.165333i −0.996577 0.0826663i $$-0.973656\pi$$
0.996577 0.0826663i $$-0.0263436\pi$$
$$440$$ −2.44949 2.00000i −0.116775 0.0953463i
$$441$$ 1.00000 + 2.82843i 0.0476190 + 0.134687i
$$442$$ 29.3939i 1.39812i
$$443$$ 17.3205 0.822922 0.411461 0.911427i $$-0.365019\pi$$
0.411461 + 0.911427i $$0.365019\pi$$
$$444$$ 6.00000 + 4.24264i 0.284747 + 0.201347i
$$445$$ −4.24264 3.46410i −0.201120 0.164214i
$$446$$ 25.4558i 1.20537i
$$447$$ −11.3137 + 16.0000i −0.535120 + 0.756774i
$$448$$ 2.44949i 0.115728i
$$449$$ −12.2474 −0.577993 −0.288996 0.957330i $$-0.593322\pi$$
−0.288996 + 0.957330i $$0.593322\pi$$
$$450$$ 7.72741 + 12.8564i 0.364273 + 0.606057i
$$451$$ 17.3205i 0.815591i
$$452$$ 18.0000i 0.846649i
$$453$$ 13.8564 19.5959i 0.651031 0.920697i
$$454$$ −12.0000 −0.563188
$$455$$ 14.6969 18.0000i 0.689003 0.843853i
$$456$$ −6.44949 + 3.92480i −0.302025 + 0.183796i
$$457$$ 24.4949i 1.14582i 0.819617 + 0.572911i $$0.194186\pi$$
−0.819617 + 0.572911i $$0.805814\pi$$
$$458$$ 28.0000i 1.30835i
$$459$$ −9.79796 + 34.6410i −0.457330 + 1.61690i
$$460$$ 6.00000 + 4.89898i 0.279751 + 0.228416i
$$461$$ 22.6274i 1.05386i 0.849907 + 0.526932i $$0.176658\pi$$
−0.849907 + 0.526932i $$0.823342\pi$$
$$462$$ 3.46410 4.89898i 0.161165 0.227921i
$$463$$ 12.2474i 0.569187i −0.958648 0.284594i $$-0.908141\pi$$
0.958648 0.284594i $$-0.0918587\pi$$
$$464$$ −2.44949 −0.113715
$$465$$ −25.8564 + 7.17260i −1.19906 + 0.332622i
$$466$$ 10.3923i 0.481414i
$$467$$ 24.2487 1.12210 0.561048 0.827783i $$-0.310398\pi$$
0.561048 + 0.827783i $$0.310398\pi$$
$$468$$ −4.24264 12.0000i −0.196116 0.554700i
$$469$$ 0 0
$$470$$ 4.89898 6.00000i 0.225973 0.276759i
$$471$$ 14.6969 20.7846i 0.677199 0.957704i
$$472$$ 4.89898i 0.225494i
$$473$$ 10.3923 0.477839
$$474$$ −14.6969 10.3923i −0.675053 0.477334i
$$475$$ −4.48528 + 21.3280i −0.205799 + 0.978594i
$$476$$ 16.9706i 0.777844i
$$477$$ −16.9706 + 6.00000i −0.777029 + 0.274721i
$$478$$ 1.41421 0.0646846
$$479$$ 9.89949i 0.452319i −0.974090 0.226160i $$-0.927383\pi$$
0.974090 0.226160i $$-0.0726171\pi$$
$$480$$ −3.73205 + 1.03528i −0.170344 + 0.0472537i
$$481$$ −18.0000 −0.820729
$$482$$ −13.8564 −0.631142
$$483$$ −8.48528 + 12.0000i −0.386094 + 0.546019i
$$484$$ −9.00000 −0.409091
$$485$$ 22.0454 + 18.0000i 1.00103 + 0.817338i
$$486$$ 1.00000 + 15.5563i 0.0453609 + 0.705650i
$$487$$ 33.9411 1.53802 0.769010 0.639237i $$-0.220750\pi$$
0.769010 + 0.639237i $$0.220750\pi$$
$$488$$ 8.00000i 0.362143i
$$489$$ −12.2474 + 17.3205i −0.553849 + 0.783260i
$$490$$ −1.41421 + 1.73205i −0.0638877 + 0.0782461i
$$491$$ 7.07107i 0.319113i −0.987189 0.159556i $$-0.948994\pi$$
0.987189 0.159556i $$-0.0510064\pi$$
$$492$$ 17.3205 + 12.2474i 0.780869 + 0.552158i
$$493$$ −16.9706 −0.764316
$$494$$ 7.34847 16.9706i 0.330623 0.763542i
$$495$$ −8.92820 3.20736i −0.401293 0.144160i
$$496$$ 6.92820i 0.311086i
$$497$$ 12.0000i 0.538274i
$$498$$ 10.3923 14.6969i 0.465690 0.658586i
$$499$$ −20.0000 −0.895323 −0.447661 0.894203i $$-0.647743\pi$$
−0.447661 + 0.894203i $$0.647743\pi$$
$$500$$ −5.19615 + 9.89949i −0.232379 + 0.442719i
$$501$$ 0 0
$$502$$ 1.41421 0.0631194
$$503$$ −17.3205 −0.772283 −0.386142 0.922440i $$-0.626192\pi$$
−0.386142 + 0.922440i $$0.626192\pi$$
$$504$$ −2.44949 6.92820i −0.109109 0.308607i
$$505$$ 4.00000 4.89898i 0.177998 0.218002i
$$506$$ −4.89898 −0.217786
$$507$$ 7.07107 + 5.00000i 0.314037 + 0.222058i
$$508$$ 0 0
$$509$$ −22.0454 −0.977146 −0.488573 0.872523i $$-0.662482\pi$$
−0.488573 + 0.872523i $$0.662482\pi$$
$$510$$ −25.8564 + 7.17260i −1.14494 + 0.317608i
$$511$$ 36.0000 1.59255
$$512$$ 1.00000i 0.0441942i
$$513$$ −14.3171 + 17.5505i −0.632116 + 0.774874i
$$514$$ −6.00000 −0.264649
$$515$$ 14.6969 + 12.0000i 0.647624 + 0.528783i
$$516$$ 7.34847 10.3923i 0.323498 0.457496i
$$517$$ 4.89898i 0.215457i
$$518$$ −10.3923 −0.456612
$$519$$ −6.00000 + 8.48528i −0.263371 + 0.372463i
$$520$$ 6.00000 7.34847i 0.263117 0.322252i
$$521$$ 22.0454 0.965827 0.482913 0.875668i $$-0.339579\pi$$
0.482913 + 0.875668i $$0.339579\pi$$
$$522$$ −6.92820 + 2.44949i −0.303239 + 0.107211i
$$523$$ 16.9706 0.742071 0.371035 0.928619i $$-0.379003\pi$$
0.371035 + 0.928619i $$0.379003\pi$$
$$524$$ 1.41421i 0.0617802i
$$525$$ −19.4201 8.53590i −0.847561 0.372537i
$$526$$ 3.46410i 0.151042i
$$527$$ 48.0000i 2.09091i
$$528$$ 1.41421 2.00000i 0.0615457 0.0870388i
$$529$$ −11.0000 −0.478261
$$530$$ −10.3923 8.48528i −0.451413 0.368577i
$$531$$ 4.89898 + 13.8564i 0.212598 + 0.601317i
$$532$$ 4.24264 9.79796i 0.183942 0.424795i
$$533$$ −51.9615 −2.25070
$$534$$ 2.44949 3.46410i 0.106000 0.149906i
$$535$$ −25.4558 + 31.1769i −1.10055 + 1.34790i
$$536$$ 0 0
$$537$$ 6.92820 + 4.89898i 0.298974 + 0.211407i
$$538$$ 17.1464i 0.739235i
$$539$$ 1.41421i 0.0609145i
$$540$$ −9.52056 + 6.66025i −0.409700 + 0.286612i
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 4.00000i 0.171815i
$$543$$ −13.8564 + 19.5959i −0.594635 + 0.840941i
$$544$$ 6.92820i 0.297044i
$$545$$ −9.79796 + 12.0000i −0.419698 + 0.514024i
$$546$$ 14.6969 + 10.3923i 0.628971 + 0.444750i
$$547$$ −25.4558 −1.08841 −0.544207 0.838951i $$-0.683169\pi$$
−0.544207 + 0.838951i $$0.683169\pi$$
$$548$$ 17.3205 0.739895
$$549$$ −8.00000 22.6274i −0.341432 0.965715i
$$550$$ −1.41421 6.92820i −0.0603023 0.295420i
$$551$$ −9.79796 4.24264i −0.417407 0.180743i
$$552$$ −3.46410 + 4.89898i −0.147442 + 0.208514i
$$553$$ 25.4558 1.08249
$$554$$ 19.5959 0.832551
$$555$$ 4.39230 + 15.8338i 0.186443 + 0.672105i
$$556$$ −4.00000 −0.169638
$$557$$ −10.3923 −0.440336 −0.220168 0.975462i $$-0.570661\pi$$
−0.220168 + 0.975462i $$0.570661\pi$$
$$558$$ −6.92820 19.5959i −0.293294 0.829561i
$$559$$ 31.1769i 1.31864i
$$560$$ 3.46410 4.24264i 0.146385 0.179284i
$$561$$ 9.79796 13.8564i 0.413670 0.585018i
$$562$$ 7.34847i 0.309976i
$$563$$ 36.0000i 1.51722i 0.651546 + 0.758610i $$0.274121\pi$$
−0.651546 + 0.758610i $$0.725879\pi$$
$$564$$ 4.89898 + 3.46410i 0.206284 + 0.145865i
$$565$$ 25.4558 31.1769i 1.07094 1.31162i
$$566$$ 12.2474 0.514799
$$567$$ −13.8564 17.1464i −0.581914 0.720082i
$$568$$ 4.89898i 0.205557i
$$569$$ 46.5403 1.95107 0.975536 0.219842i $$-0.0705541\pi$$
0.975536 + 0.219842i $$0.0705541\pi$$
$$570$$ −16.7214 2.32300i −0.700380 0.0972996i
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 6.00000i 0.250873i
$$573$$ 24.0416 34.0000i 1.00435 1.42037i
$$574$$ −30.0000 −1.25218
$$575$$ 3.46410 + 16.9706i 0.144463 + 0.707721i
$$576$$ −1.00000 2.82843i −0.0416667 0.117851i
$$577$$ 24.4949i 1.01974i −0.860253 0.509868i $$-0.829694\pi$$
0.860253 0.509868i $$-0.170306\pi$$
$$578$$ 31.0000i 1.28943i
$$579$$ −18.0000 12.7279i −0.748054 0.528954i
$$580$$ −4.24264 3.46410i −0.176166 0.143839i
$$581$$ 25.4558i 1.05609i
$$582$$ −12.7279 + 18.0000i −0.527589 + 0.746124i
$$583$$ 8.48528 0.351424
$$584$$ 14.6969 0.608164
$$585$$ 9.62209 26.7846i 0.397825 1.10741i
$$586$$ −6.00000 −0.247858
$$587$$ −3.46410 −0.142979 −0.0714894 0.997441i $$-0.522775\pi$$
−0.0714894 + 0.997441i $$0.522775\pi$$
$$588$$ −1.41421 1.00000i −0.0583212 0.0412393i
$$589$$ 12.0000 27.7128i 0.494451 1.14189i
$$590$$ −6.92820 + 8.48528i −0.285230 + 0.349334i
$$591$$ 0 0
$$592$$ −4.24264 −0.174371
$$593$$ −3.46410 −0.142254 −0.0711268 0.997467i $$-0.522659\pi$$
−0.0711268 + 0.997467i $$0.522659\pi$$
$$594$$ 2.00000 7.07107i 0.0820610 0.290129i
$$595$$ 24.0000 29.3939i 0.983904 1.20503i
$$596$$ 11.3137i 0.463428i
$$597$$ −22.6274 16.0000i −0.926079 0.654836i
$$598$$ 14.6969i 0.601003i
$$599$$ 4.89898 0.200167 0.100083 0.994979i $$-0.468089\pi$$
0.100083 + 0.994979i $$0.468089\pi$$
$$600$$ −7.92820 3.48477i −0.323668 0.142265i
$$601$$ 6.92820i 0.282607i 0.989966 + 0.141304i $$0.0451294\pi$$
−0.989966 + 0.141304i $$0.954871\pi$$
$$602$$ 18.0000i 0.733625i
$$603$$ 0 0
$$604$$ 13.8564i 0.563809i
$$605$$ −15.5885 12.7279i −0.633761 0.517464i
$$606$$ 4.00000 + 2.82843i 0.162489 + 0.114897i
$$607$$ −16.9706 −0.688814 −0.344407 0.938820i $$-0.611920\pi$$
−0.344407 + 0.938820i $$0.611920\pi$$
$$608$$ 1.73205 4.00000i 0.0702439 0.162221i
$$609$$ 6.00000 8.48528i 0.243132 0.343841i
$$610$$ 11.3137 13.8564i 0.458079 0.561029i
$$611$$ −14.6969 −0.594574
$$612$$ −6.92820 19.5959i −0.280056 0.792118i
$$613$$ 44.0908i 1.78081i −0.455168 0.890406i $$-0.650421\pi$$
0.455168 0.890406i $$-0.349579\pi$$
$$614$$ 25.4558i 1.02731i
$$615$$ 12.6795 + 45.7081i 0.511286 + 1.84313i
$$616$$ 3.46410i 0.139573i
$$617$$ −20.7846 −0.836757 −0.418378 0.908273i $$-0.637401\pi$$
−0.418378 + 0.908273i $$0.637401\pi$$
$$618$$ −8.48528 + 12.0000i −0.341328 + 0.482711i
$$619$$ 16.0000 0.643094 0.321547 0.946894i $$-0.395797\pi$$
0.321547 + 0.946894i $$0.395797\pi$$
$$620$$ 9.79796 12.0000i 0.393496 0.481932i
$$621$$ −4.89898 + 17.3205i −0.196589 + 0.695048i
$$622$$ −26.8701 −1.07739
$$623$$ 6.00000i 0.240385i
$$624$$ 6.00000 + 4.24264i 0.240192 + 0.169842i
$$625$$ −23.0000 + 9.79796i −0.920000 + 0.391918i
$$626$$ 4.89898 0.195803
$$627$$ 9.12096 5.55051i 0.364256 0.221666i
$$628$$ 14.6969i 0.586472i
$$629$$ −29.3939 −1.17201
$$630$$ 5.55532 15.4641i 0.221329 0.616105i
$$631$$ −44.0000 −1.75161 −0.875806 0.482663i $$-0.839670\pi$$
−0.875806 + 0.482663i $$0.839670\pi$$
$$632$$ 10.3923 0.413384
$$633$$ 3.46410 4.89898i 0.137686 0.194717i
$$634$$ −18.0000 −0.714871
$$635$$ 0 0
$$636$$ 6.00000 8.48528i 0.237915 0.336463i
$$637$$ 4.24264 0.168100
$$638$$ 3.46410 0.137145
$$639$$ 4.89898 + 13.8564i 0.193801 + 0.548151i
$$640$$ 1.41421 1.73205i 0.0559017 0.0684653i
$$641$$ 12.2474 0.483745 0.241873 0.970308i $$-0.422238\pi$$
0.241873 + 0.970308i $$0.422238\pi$$
$$642$$ −25.4558 18.0000i −1.00466 0.710403i
$$643$$ 7.34847i 0.289795i 0.989447 + 0.144898i $$0.0462853\pi$$
−0.989447 + 0.144898i $$0.953715\pi$$
$$644$$ 8.48528i 0.334367i
$$645$$ 27.4249 7.60770i 1.07985 0.299553i
$$646$$ 12.0000 27.7128i 0.472134 1.09035i
$$647$$ −10.3923 −0.408564 −0.204282 0.978912i $$-0.565486\pi$$
−0.204282 + 0.978912i $$0.565486\pi$$
$$648$$ −5.65685 7.00000i −0.222222 0.274986i
$$649$$ 6.92820i 0.271956i
$$650$$ 20.7846 4.24264i 0.815239 0.166410i
$$651$$ 24.0000 + 16.9706i 0.940634 + 0.665129i
$$652$$ 12.2474i 0.479647i
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ −9.79796 6.92820i −0.383131 0.270914i
$$655$$ 2.00000 2.44949i 0.0781465 0.0957095i
$$656$$ −12.2474 −0.478183
$$657$$ 41.5692 14.6969i 1.62177 0.573382i
$$658$$ −8.48528 −0.330791
$$659$$ −44.0908 −1.71753 −0.858767 0.512366i $$-0.828769\pi$$
−0.858767 + 0.512366i $$0.828769\pi$$
$$660$$ 5.27792 1.46410i 0.205443 0.0569901i
$$661$$ 48.4974i 1.88633i 0.332323 + 0.943166i $$0.392168\pi$$
−0.332323 + 0.943166i $$0.607832\pi$$
$$662$$ 6.92820 0.269272
$$663$$ 41.5692 + 29.3939i 1.61441 + 1.14156i
$$664$$ 10.3923i 0.403300i
$$665$$ 21.2049 10.9706i 0.822290 0.425420i
$$666$$ −12.0000 + 4.24264i −0.464991 + 0.164399i
$$667$$ −8.48528 −0.328551
$$668$$ 0 0
$$669$$ −36.0000 25.4558i −1.39184 0.984180i
$$670$$ 0 0
$$671$$ 11.3137i 0.436761i
$$672$$ 3.46410 + 2.44949i 0.133631 + 0.0944911i
$$673$$ 12.7279 0.490625 0.245313 0.969444i $$-0.421109\pi$$
0.245313 + 0.969444i $$0.421109\pi$$
$$674$$ 4.24264i 0.163420i
$$675$$ −25.9091 1.92820i −0.997242 0.0742166i
$$676$$ −5.00000 −0.192308
$$677$$ 30.0000i 1.15299i 0.817099 + 0.576497i $$0.195581\pi$$
−0.817099 + 0.576497i $$0.804419\pi$$
$$678$$ 25.4558 + 18.0000i 0.977626 + 0.691286i
$$679$$ 31.1769i 1.19646i
$$680$$ 9.79796 12.0000i 0.375735 0.460179i
$$681$$ 12.0000 16.9706i 0.459841 0.650313i
$$682$$ 9.79796i 0.375183i
$$683$$ 18.0000i 0.688751i −0.938832 0.344375i $$-0.888091\pi$$
0.938832 0.344375i $$-0.111909\pi$$
$$684$$ 0.898979 13.0458i 0.0343733 0.498817i
$$685$$ 30.0000 + 24.4949i 1.14624 + 0.935902i
$$686$$ 19.5959 0.748176
$$687$$ 39.5980 + 28.0000i 1.51076 + 1.06827i
$$688$$ 7.34847i 0.280158i
$$689$$ 25.4558i 0.969790i
$$690$$ −12.9282 + 3.58630i −0.492168 + 0.136528i
$$691$$ −20.0000 −0.760836 −0.380418 0.924815i $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ 6.00000i 0.228086i
$$693$$ 3.46410 + 9.79796i 0.131590 + 0.372194i
$$694$$ 24.2487i 0.920468i
$$695$$ −6.92820 5.65685i −0.262802 0.214577i
$$696$$ 2.44949 3.46410i 0.0928477 0.131306i
$$697$$ −84.8528 −3.21403
$$698$$ 22.0000i 0.832712i
$$699$$ −14.6969 10.3923i −0.555889 0.393073i
$$700$$ 12.0000 2.44949i 0.453557 0.0925820i
$$701$$ 28.2843i 1.06828i 0.845395 + 0.534141i $$0.179365\pi$$
−0.845395 + 0.534141i $$0.820635\pi$$
$$702$$ 21.2132 + 6.00000i 0.800641 + 0.226455i
$$703$$ −16.9706 7.34847i −0.640057 0.277153i
$$704$$ 1.41421i 0.0533002i
$$705$$ 3.58630 + 12.9282i 0.135068 + 0.486904i
$$706$$ 17.3205i 0.651866i
$$707$$ −6.92820 −0.260562
$$708$$ −6.92820 4.89898i −0.260378 0.184115i
$$709$$ −16.0000 −0.600893 −0.300446 0.953799i $$-0.597136\pi$$
−0.300446 + 0.953799i $$0.597136\pi$$
$$710$$ −6.92820 + 8.48528i −0.260011 + 0.318447i
$$711$$ 29.3939 10.3923i 1.10236 0.389742i
$$712$$ 2.44949i 0.0917985i
$$713$$ 24.0000i 0.898807i
$$714$$ 24.0000 + 16.9706i 0.898177 + 0.635107i
$$715$$ −8.48528 + 10.3923i −0.317332 + 0.388650i
$$716$$ −4.89898 −0.183083
$$717$$ −1.41421 + 2.00000i −0.0528148 + 0.0746914i
$$718$$ −18.3848 −0.686114
$$719$$ 7.07107i 0.263706i 0.991269 + 0.131853i $$0.0420927\pi$$
−0.991269 + 0.131853i $$0.957907\pi$$
$$720$$ 2.26795 6.31319i 0.0845215 0.235279i
$$721$$ 20.7846i 0.774059i
$$722$$ 13.8564 13.0000i 0.515682 0.483810i
$$723$$ 13.8564 19.5959i 0.515325 0.728780i
$$724$$ 13.8564i 0.514969i
$$725$$ −2.44949 12.0000i −0.0909718 0.445669i
$$726$$ 9.00000 12.7279i 0.334021 0.472377i
$$727$$ 31.8434i 1.18101i 0.807036 + 0.590503i $$0.201070\pi$$
−0.807036 + 0.590503i $$0.798930\pi$$
$$728$$ −10.3923 −0.385164
$$729$$ −23.0000 14.1421i −0.851852 0.523783i
$$730$$ 25.4558 + 20.7846i 0.942163 + 0.769273i
$$731$$ 50.9117i 1.88304i
$$732$$ 11.3137 + 8.00000i 0.418167 + 0.295689i
$$733$$ 4.89898i 0.180948i 0.995899 + 0.0904740i $$0.0288382\pi$$
−0.995899 + 0.0904740i $$0.971162\pi$$
$$734$$ −31.8434 −1.17536
$$735$$ −1.03528 3.73205i −0.0381867 0.137659i
$$736$$ 3.46410i 0.127688i
$$737$$ 0 0
$$738$$ −34.6410 + 12.2474i −1.27515 + 0.450835i
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ −7.34847 6.00000i −0.270135 0.220564i
$$741$$ 16.6515 + 27.3629i 0.611709 + 1.00520i
$$742$$ 14.6969i 0.539542i
$$743$$ 30.0000i 1.10059i 0.834969 + 0.550297i $$0.185485\pi$$
−0.834969 + 0.550297i $$0.814515\pi$$
$$744$$ 9.79796 + 6.92820i 0.359211 + 0.254000i
$$745$$ 16.0000 19.5959i 0.586195 0.717939i
$$746$$ 12.7279i 0.466002i
$$747$$ 10.3923 + 29.3939i 0.380235 + 1.07547i
$$748$$ 9.79796i 0.358249i
$$749$$ 44.0908 1.61104
$$750$$ −8.80385 17.2480i −0.321471 0.629807i
$$751$$ 41.5692i 1.51688i −0.651741 0.758441i $$-0.725961\pi$$
0.651741 0.758441i $$-0.274039\pi$$
$$752$$ −3.46410 −0.126323
$$753$$ −1.41421 + 2.00000i −0.0515368 + 0.0728841i
$$754$$ 10.3923i 0.378465i
$$755$$ −19.5959 + 24.0000i −0.713168 + 0.873449i
$$756$$ 12.2474 + 3.46410i 0.445435 + 0.125988i
$$757$$ 9.79796i 0.356113i −0.984020 0.178056i $$-0.943019\pi$$
0.984020 0.178056i $$-0.0569810\pi$$
$$758$$ 20.7846 0.754931
$$759$$ 4.89898 6.92820i 0.177822 0.251478i
$$760$$ 8.65685 4.47871i 0.314017 0.162460i
$$761$$ 14.1421i 0.512652i −0.966590 0.256326i $$-0.917488\pi$$
0.966590 0.256326i $$-0.0825121\pi$$
$$762$$ 0 0
$$763$$ 16.9706 0.614376
$$764$$ 24.0416i 0.869796i
$$765$$ 15.7128 43.7391i 0.568098 1.58139i
$$766$$ 6.00000 0.216789
$$767$$ 20.7846 0.750489
$$768$$ 1.41421 + 1.00000i 0.0510310 + 0.0360844i
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ −4.89898 + 6.00000i −0.176547 + 0.216225i
$$771$$ 6.00000 8.48528i 0.216085 0.305590i
$$772$$ 12.7279 0.458088
$$773$$ 18.0000i 0.647415i −0.946157 0.323708i $$-0.895071\pi$$
0.946157 0.323708i $$-0.104929\pi$$
$$774$$ 7.34847 + 20.7846i 0.264135 + 0.747087i
$$775$$ 33.9411 6.92820i 1.21920 0.248868i
$$776$$ 12.7279i 0.456906i
$$777$$ 10.3923 14.6969i 0.372822 0.527250i
$$778$$ −19.7990 −0.709828
$$779$$ −48.9898 21.2132i −1.75524 0.760042i
$$780$$ 4.39230 + 15.8338i 0.157270 + 0.566939i
$$781$$ 6.92820i 0.247911i
$$782$$ 24.0000i 0.858238i
$$783$$ 3.46410 12.