# Properties

 Label 105.3.k.a.62.1 Level 105 Weight 3 Character 105.62 Analytic conductor 2.861 Analytic rank 0 Dimension 4 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.86104277578$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 62.1 Root $$-0.707107 + 0.707107i$$ of $$x^{4} + 1$$ Character $$\chi$$ $$=$$ 105.62 Dual form 105.3.k.a.83.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 0.707107i) q^{2} +(-1.29289 - 2.70711i) q^{3} +3.00000i q^{4} +(0.707107 - 4.94975i) q^{5} +(2.82843 + 1.00000i) q^{6} -7.00000 q^{7} +(-4.94975 - 4.94975i) q^{8} +(-5.65685 + 7.00000i) q^{9} +O(q^{10})$$ $$q+(-0.707107 + 0.707107i) q^{2} +(-1.29289 - 2.70711i) q^{3} +3.00000i q^{4} +(0.707107 - 4.94975i) q^{5} +(2.82843 + 1.00000i) q^{6} -7.00000 q^{7} +(-4.94975 - 4.94975i) q^{8} +(-5.65685 + 7.00000i) q^{9} +(3.00000 + 4.00000i) q^{10} -9.89949i q^{11} +(8.12132 - 3.87868i) q^{12} +(-8.00000 - 8.00000i) q^{13} +(4.94975 - 4.94975i) q^{14} +(-14.3137 + 4.48528i) q^{15} -5.00000 q^{16} +(-18.3848 - 18.3848i) q^{17} +(-0.949747 - 8.94975i) q^{18} +10.0000 q^{19} +(14.8492 + 2.12132i) q^{20} +(9.05025 + 18.9497i) q^{21} +(7.00000 + 7.00000i) q^{22} +(24.0416 + 24.0416i) q^{23} +(-7.00000 + 19.7990i) q^{24} +(-24.0000 - 7.00000i) q^{25} +11.3137 q^{26} +(26.2635 + 6.26346i) q^{27} -21.0000i q^{28} +4.24264 q^{29} +(6.94975 - 13.2929i) q^{30} +14.0000i q^{31} +(23.3345 - 23.3345i) q^{32} +(-26.7990 + 12.7990i) q^{33} +26.0000 q^{34} +(-4.94975 + 34.6482i) q^{35} +(-21.0000 - 16.9706i) q^{36} +(30.0000 + 30.0000i) q^{37} +(-7.07107 + 7.07107i) q^{38} +(-11.3137 + 32.0000i) q^{39} +(-28.0000 + 21.0000i) q^{40} -33.9411 q^{41} +(-19.7990 - 7.00000i) q^{42} +(36.0000 - 36.0000i) q^{43} +29.6985 q^{44} +(30.6482 + 32.9497i) q^{45} -34.0000 q^{46} +(-4.24264 - 4.24264i) q^{47} +(6.46447 + 13.5355i) q^{48} +49.0000 q^{49} +(21.9203 - 12.0208i) q^{50} +(-26.0000 + 73.5391i) q^{51} +(24.0000 - 24.0000i) q^{52} +(-70.7107 - 70.7107i) q^{53} +(-23.0000 + 14.1421i) q^{54} +(-49.0000 - 7.00000i) q^{55} +(34.6482 + 34.6482i) q^{56} +(-12.9289 - 27.0711i) q^{57} +(-3.00000 + 3.00000i) q^{58} -29.6985i q^{59} +(-13.4558 - 42.9411i) q^{60} -14.0000i q^{61} +(-9.89949 - 9.89949i) q^{62} +(39.5980 - 49.0000i) q^{63} +13.0000i q^{64} +(-45.2548 + 33.9411i) q^{65} +(9.89949 - 28.0000i) q^{66} +(32.0000 + 32.0000i) q^{67} +(55.1543 - 55.1543i) q^{68} +(34.0000 - 96.1665i) q^{69} +(-21.0000 - 28.0000i) q^{70} -59.3970i q^{71} +(62.6482 - 6.64823i) q^{72} +(-39.0000 - 39.0000i) q^{73} -42.4264 q^{74} +(12.0797 + 74.0208i) q^{75} +30.0000i q^{76} +69.2965i q^{77} +(-14.6274 - 30.6274i) q^{78} -56.0000i q^{79} +(-3.53553 + 24.7487i) q^{80} +(-17.0000 - 79.1960i) q^{81} +(24.0000 - 24.0000i) q^{82} +(-36.7696 + 36.7696i) q^{83} +(-56.8492 + 27.1508i) q^{84} +(-104.000 + 78.0000i) q^{85} +50.9117i q^{86} +(-5.48528 - 11.4853i) q^{87} +(-49.0000 + 49.0000i) q^{88} -19.7990i q^{89} +(-44.9706 - 1.62742i) q^{90} +(56.0000 + 56.0000i) q^{91} +(-72.1249 + 72.1249i) q^{92} +(37.8995 - 18.1005i) q^{93} +6.00000 q^{94} +(7.07107 - 49.4975i) q^{95} +(-93.3381 - 33.0000i) q^{96} +(-113.000 + 113.000i) q^{97} +(-34.6482 + 34.6482i) q^{98} +(69.2965 + 56.0000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 8q^{3} - 28q^{7} + O(q^{10})$$ $$4q - 8q^{3} - 28q^{7} + 12q^{10} + 24q^{12} - 32q^{13} - 12q^{15} - 20q^{16} + 16q^{18} + 40q^{19} + 56q^{21} + 28q^{22} - 28q^{24} - 96q^{25} + 40q^{27} + 8q^{30} - 28q^{33} + 104q^{34} - 84q^{36} + 120q^{37} - 112q^{40} + 144q^{43} - 16q^{45} - 136q^{46} + 40q^{48} + 196q^{49} - 104q^{51} + 96q^{52} - 92q^{54} - 196q^{55} - 80q^{57} - 12q^{58} + 48q^{60} + 128q^{67} + 136q^{69} - 84q^{70} + 112q^{72} - 156q^{73} + 136q^{75} + 32q^{78} - 68q^{81} + 96q^{82} - 168q^{84} - 416q^{85} + 12q^{87} - 196q^{88} - 112q^{90} + 224q^{91} + 112q^{93} + 24q^{94} - 452q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$$.

 $$n$$ $$22$$ $$31$$ $$71$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 0.707107i −0.353553 + 0.353553i −0.861430 0.507877i $$-0.830431\pi$$
0.507877 + 0.861430i $$0.330431\pi$$
$$3$$ −1.29289 2.70711i −0.430964 0.902369i
$$4$$ 3.00000i 0.750000i
$$5$$ 0.707107 4.94975i 0.141421 0.989949i
$$6$$ 2.82843 + 1.00000i 0.471405 + 0.166667i
$$7$$ −7.00000 −1.00000
$$8$$ −4.94975 4.94975i −0.618718 0.618718i
$$9$$ −5.65685 + 7.00000i −0.628539 + 0.777778i
$$10$$ 3.00000 + 4.00000i 0.300000 + 0.400000i
$$11$$ 9.89949i 0.899954i −0.893040 0.449977i $$-0.851432\pi$$
0.893040 0.449977i $$-0.148568\pi$$
$$12$$ 8.12132 3.87868i 0.676777 0.323223i
$$13$$ −8.00000 8.00000i −0.615385 0.615385i 0.328959 0.944344i $$-0.393302\pi$$
−0.944344 + 0.328959i $$0.893302\pi$$
$$14$$ 4.94975 4.94975i 0.353553 0.353553i
$$15$$ −14.3137 + 4.48528i −0.954247 + 0.299019i
$$16$$ −5.00000 −0.312500
$$17$$ −18.3848 18.3848i −1.08146 1.08146i −0.996374 0.0850836i $$-0.972884\pi$$
−0.0850836 0.996374i $$-0.527116\pi$$
$$18$$ −0.949747 8.94975i −0.0527637 0.497208i
$$19$$ 10.0000 0.526316 0.263158 0.964753i $$-0.415236\pi$$
0.263158 + 0.964753i $$0.415236\pi$$
$$20$$ 14.8492 + 2.12132i 0.742462 + 0.106066i
$$21$$ 9.05025 + 18.9497i 0.430964 + 0.902369i
$$22$$ 7.00000 + 7.00000i 0.318182 + 0.318182i
$$23$$ 24.0416 + 24.0416i 1.04529 + 1.04529i 0.998925 + 0.0463637i $$0.0147633\pi$$
0.0463637 + 0.998925i $$0.485237\pi$$
$$24$$ −7.00000 + 19.7990i −0.291667 + 0.824958i
$$25$$ −24.0000 7.00000i −0.960000 0.280000i
$$26$$ 11.3137 0.435143
$$27$$ 26.2635 + 6.26346i 0.972721 + 0.231980i
$$28$$ 21.0000i 0.750000i
$$29$$ 4.24264 0.146298 0.0731490 0.997321i $$-0.476695\pi$$
0.0731490 + 0.997321i $$0.476695\pi$$
$$30$$ 6.94975 13.2929i 0.231658 0.443096i
$$31$$ 14.0000i 0.451613i 0.974172 + 0.225806i $$0.0725017\pi$$
−0.974172 + 0.225806i $$0.927498\pi$$
$$32$$ 23.3345 23.3345i 0.729204 0.729204i
$$33$$ −26.7990 + 12.7990i −0.812091 + 0.387848i
$$34$$ 26.0000 0.764706
$$35$$ −4.94975 + 34.6482i −0.141421 + 0.989949i
$$36$$ −21.0000 16.9706i −0.583333 0.471405i
$$37$$ 30.0000 + 30.0000i 0.810811 + 0.810811i 0.984755 0.173945i $$-0.0556514\pi$$
−0.173945 + 0.984755i $$0.555651\pi$$
$$38$$ −7.07107 + 7.07107i −0.186081 + 0.186081i
$$39$$ −11.3137 + 32.0000i −0.290095 + 0.820513i
$$40$$ −28.0000 + 21.0000i −0.700000 + 0.525000i
$$41$$ −33.9411 −0.827832 −0.413916 0.910315i $$-0.635839\pi$$
−0.413916 + 0.910315i $$0.635839\pi$$
$$42$$ −19.7990 7.00000i −0.471405 0.166667i
$$43$$ 36.0000 36.0000i 0.837209 0.837209i −0.151281 0.988491i $$-0.548340\pi$$
0.988491 + 0.151281i $$0.0483400\pi$$
$$44$$ 29.6985 0.674966
$$45$$ 30.6482 + 32.9497i 0.681072 + 0.732217i
$$46$$ −34.0000 −0.739130
$$47$$ −4.24264 4.24264i −0.0902690 0.0902690i 0.660530 0.750799i $$-0.270331\pi$$
−0.750799 + 0.660530i $$0.770331\pi$$
$$48$$ 6.46447 + 13.5355i 0.134676 + 0.281990i
$$49$$ 49.0000 1.00000
$$50$$ 21.9203 12.0208i 0.438406 0.240416i
$$51$$ −26.0000 + 73.5391i −0.509804 + 1.44194i
$$52$$ 24.0000 24.0000i 0.461538 0.461538i
$$53$$ −70.7107 70.7107i −1.33416 1.33416i −0.901606 0.432557i $$-0.857611\pi$$
−0.432557 0.901606i $$-0.642389\pi$$
$$54$$ −23.0000 + 14.1421i −0.425926 + 0.261891i
$$55$$ −49.0000 7.00000i −0.890909 0.127273i
$$56$$ 34.6482 + 34.6482i 0.618718 + 0.618718i
$$57$$ −12.9289 27.0711i −0.226823 0.474931i
$$58$$ −3.00000 + 3.00000i −0.0517241 + 0.0517241i
$$59$$ 29.6985i 0.503364i −0.967810 0.251682i $$-0.919016\pi$$
0.967810 0.251682i $$-0.0809837\pi$$
$$60$$ −13.4558 42.9411i −0.224264 0.715685i
$$61$$ 14.0000i 0.229508i −0.993394 0.114754i $$-0.963392\pi$$
0.993394 0.114754i $$-0.0366080\pi$$
$$62$$ −9.89949 9.89949i −0.159669 0.159669i
$$63$$ 39.5980 49.0000i 0.628539 0.777778i
$$64$$ 13.0000i 0.203125i
$$65$$ −45.2548 + 33.9411i −0.696228 + 0.522171i
$$66$$ 9.89949 28.0000i 0.149992 0.424242i
$$67$$ 32.0000 + 32.0000i 0.477612 + 0.477612i 0.904367 0.426755i $$-0.140343\pi$$
−0.426755 + 0.904367i $$0.640343\pi$$
$$68$$ 55.1543 55.1543i 0.811093 0.811093i
$$69$$ 34.0000 96.1665i 0.492754 1.39372i
$$70$$ −21.0000 28.0000i −0.300000 0.400000i
$$71$$ 59.3970i 0.836577i −0.908314 0.418289i $$-0.862630\pi$$
0.908314 0.418289i $$-0.137370\pi$$
$$72$$ 62.6482 6.64823i 0.870114 0.0923366i
$$73$$ −39.0000 39.0000i −0.534247 0.534247i 0.387587 0.921833i $$-0.373309\pi$$
−0.921833 + 0.387587i $$0.873309\pi$$
$$74$$ −42.4264 −0.573330
$$75$$ 12.0797 + 74.0208i 0.161063 + 0.986944i
$$76$$ 30.0000i 0.394737i
$$77$$ 69.2965i 0.899954i
$$78$$ −14.6274 30.6274i −0.187531 0.392659i
$$79$$ 56.0000i 0.708861i −0.935082 0.354430i $$-0.884675\pi$$
0.935082 0.354430i $$-0.115325\pi$$
$$80$$ −3.53553 + 24.7487i −0.0441942 + 0.309359i
$$81$$ −17.0000 79.1960i −0.209877 0.977728i
$$82$$ 24.0000 24.0000i 0.292683 0.292683i
$$83$$ −36.7696 + 36.7696i −0.443007 + 0.443007i −0.893021 0.450015i $$-0.851419\pi$$
0.450015 + 0.893021i $$0.351419\pi$$
$$84$$ −56.8492 + 27.1508i −0.676777 + 0.323223i
$$85$$ −104.000 + 78.0000i −1.22353 + 0.917647i
$$86$$ 50.9117i 0.591996i
$$87$$ −5.48528 11.4853i −0.0630492 0.132015i
$$88$$ −49.0000 + 49.0000i −0.556818 + 0.556818i
$$89$$ 19.7990i 0.222461i −0.993795 0.111230i $$-0.964521\pi$$
0.993795 0.111230i $$-0.0354791\pi$$
$$90$$ −44.9706 1.62742i −0.499673 0.0180824i
$$91$$ 56.0000 + 56.0000i 0.615385 + 0.615385i
$$92$$ −72.1249 + 72.1249i −0.783966 + 0.783966i
$$93$$ 37.8995 18.1005i 0.407521 0.194629i
$$94$$ 6.00000 0.0638298
$$95$$ 7.07107 49.4975i 0.0744323 0.521026i
$$96$$ −93.3381 33.0000i −0.972272 0.343750i
$$97$$ −113.000 + 113.000i −1.16495 + 1.16495i −0.181571 + 0.983378i $$0.558118\pi$$
−0.983378 + 0.181571i $$0.941882\pi$$
$$98$$ −34.6482 + 34.6482i −0.353553 + 0.353553i
$$99$$ 69.2965 + 56.0000i 0.699964 + 0.565657i
$$100$$ 21.0000 72.0000i 0.210000 0.720000i
$$101$$ 91.9239 0.910137 0.455069 0.890456i $$-0.349615\pi$$
0.455069 + 0.890456i $$0.349615\pi$$
$$102$$ −33.6152 70.3848i −0.329561 0.690047i
$$103$$ 5.00000 + 5.00000i 0.0485437 + 0.0485437i 0.730962 0.682418i $$-0.239072\pi$$
−0.682418 + 0.730962i $$0.739072\pi$$
$$104$$ 79.1960i 0.761500i
$$105$$ 100.196 31.3970i 0.954247 0.299019i
$$106$$ 100.000 0.943396
$$107$$ 4.24264 4.24264i 0.0396508 0.0396508i −0.687003 0.726654i $$-0.741074\pi$$
0.726654 + 0.687003i $$0.241074\pi$$
$$108$$ −18.7904 + 78.7904i −0.173985 + 0.729540i
$$109$$ 70.0000i 0.642202i −0.947045 0.321101i $$-0.895947\pi$$
0.947045 0.321101i $$-0.104053\pi$$
$$110$$ 39.5980 29.6985i 0.359982 0.269986i
$$111$$ 42.4264 120.000i 0.382220 1.08108i
$$112$$ 35.0000 0.312500
$$113$$ −12.7279 12.7279i −0.112636 0.112636i 0.648542 0.761179i $$-0.275379\pi$$
−0.761179 + 0.648542i $$0.775379\pi$$
$$114$$ 28.2843 + 10.0000i 0.248108 + 0.0877193i
$$115$$ 136.000 102.000i 1.18261 0.886957i
$$116$$ 12.7279i 0.109723i
$$117$$ 101.255 10.7452i 0.865426 0.0918390i
$$118$$ 21.0000 + 21.0000i 0.177966 + 0.177966i
$$119$$ 128.693 + 128.693i 1.08146 + 1.08146i
$$120$$ 93.0503 + 48.6482i 0.775419 + 0.405402i
$$121$$ 23.0000 0.190083
$$122$$ 9.89949 + 9.89949i 0.0811434 + 0.0811434i
$$123$$ 43.8823 + 91.8823i 0.356766 + 0.747010i
$$124$$ −42.0000 −0.338710
$$125$$ −51.6188 + 113.844i −0.412950 + 0.910754i
$$126$$ 6.64823 + 62.6482i 0.0527637 + 0.497208i
$$127$$ −111.000 111.000i −0.874016 0.874016i 0.118892 0.992907i $$-0.462066\pi$$
−0.992907 + 0.118892i $$0.962066\pi$$
$$128$$ 84.1457 + 84.1457i 0.657388 + 0.657388i
$$129$$ −144.000 50.9117i −1.11628 0.394664i
$$130$$ 8.00000 56.0000i 0.0615385 0.430769i
$$131$$ −38.1838 −0.291479 −0.145740 0.989323i $$-0.546556\pi$$
−0.145740 + 0.989323i $$0.546556\pi$$
$$132$$ −38.3970 80.3970i −0.290886 0.609068i
$$133$$ −70.0000 −0.526316
$$134$$ −45.2548 −0.337723
$$135$$ 49.5736 125.569i 0.367212 0.930137i
$$136$$ 182.000i 1.33824i
$$137$$ 18.3848 18.3848i 0.134195 0.134195i −0.636818 0.771014i $$-0.719750\pi$$
0.771014 + 0.636818i $$0.219750\pi$$
$$138$$ 43.9584 + 92.0416i 0.318539 + 0.666968i
$$139$$ 138.000 0.992806 0.496403 0.868092i $$-0.334654\pi$$
0.496403 + 0.868092i $$0.334654\pi$$
$$140$$ −103.945 14.8492i −0.742462 0.106066i
$$141$$ −6.00000 + 16.9706i −0.0425532 + 0.120359i
$$142$$ 42.0000 + 42.0000i 0.295775 + 0.295775i
$$143$$ −79.1960 + 79.1960i −0.553818 + 0.553818i
$$144$$ 28.2843 35.0000i 0.196419 0.243056i
$$145$$ 3.00000 21.0000i 0.0206897 0.144828i
$$146$$ 55.1543 0.377769
$$147$$ −63.3518 132.648i −0.430964 0.902369i
$$148$$ −90.0000 + 90.0000i −0.608108 + 0.608108i
$$149$$ −199.404 −1.33828 −0.669141 0.743135i $$-0.733338\pi$$
−0.669141 + 0.743135i $$0.733338\pi$$
$$150$$ −60.8823 43.7990i −0.405882 0.291993i
$$151$$ 78.0000 0.516556 0.258278 0.966071i $$-0.416845\pi$$
0.258278 + 0.966071i $$0.416845\pi$$
$$152$$ −49.4975 49.4975i −0.325641 0.325641i
$$153$$ 232.693 24.6934i 1.52087 0.161395i
$$154$$ −49.0000 49.0000i −0.318182 0.318182i
$$155$$ 69.2965 + 9.89949i 0.447074 + 0.0638677i
$$156$$ −96.0000 33.9411i −0.615385 0.217571i
$$157$$ −46.0000 + 46.0000i −0.292994 + 0.292994i −0.838262 0.545268i $$-0.816428\pi$$
0.545268 + 0.838262i $$0.316428\pi$$
$$158$$ 39.5980 + 39.5980i 0.250620 + 0.250620i
$$159$$ −100.000 + 282.843i −0.628931 + 1.77888i
$$160$$ −99.0000 132.000i −0.618750 0.825000i
$$161$$ −168.291 168.291i −1.04529 1.04529i
$$162$$ 68.0208 + 43.9792i 0.419882 + 0.271476i
$$163$$ −138.000 + 138.000i −0.846626 + 0.846626i −0.989710 0.143085i $$-0.954298\pi$$
0.143085 + 0.989710i $$0.454298\pi$$
$$164$$ 101.823i 0.620874i
$$165$$ 44.4020 + 141.698i 0.269103 + 0.858779i
$$166$$ 52.0000i 0.313253i
$$167$$ 91.9239 + 91.9239i 0.550442 + 0.550442i 0.926568 0.376126i $$-0.122744\pi$$
−0.376126 + 0.926568i $$0.622744\pi$$
$$168$$ 49.0000 138.593i 0.291667 0.824958i
$$169$$ 41.0000i 0.242604i
$$170$$ 18.3848 128.693i 0.108146 0.757020i
$$171$$ −56.5685 + 70.0000i −0.330810 + 0.409357i
$$172$$ 108.000 + 108.000i 0.627907 + 0.627907i
$$173$$ 223.446 223.446i 1.29159 1.29159i 0.357793 0.933801i $$-0.383529\pi$$
0.933801 0.357793i $$-0.116471\pi$$
$$174$$ 12.0000 + 4.24264i 0.0689655 + 0.0243830i
$$175$$ 168.000 + 49.0000i 0.960000 + 0.280000i
$$176$$ 49.4975i 0.281236i
$$177$$ −80.3970 + 38.3970i −0.454220 + 0.216932i
$$178$$ 14.0000 + 14.0000i 0.0786517 + 0.0786517i
$$179$$ −12.7279 −0.0711057 −0.0355529 0.999368i $$-0.511319\pi$$
−0.0355529 + 0.999368i $$0.511319\pi$$
$$180$$ −98.8492 + 91.9447i −0.549162 + 0.510804i
$$181$$ 350.000i 1.93370i −0.255342 0.966851i $$-0.582188\pi$$
0.255342 0.966851i $$-0.417812\pi$$
$$182$$ −79.1960 −0.435143
$$183$$ −37.8995 + 18.1005i −0.207101 + 0.0989099i
$$184$$ 238.000i 1.29348i
$$185$$ 169.706 127.279i 0.917328 0.687996i
$$186$$ −14.0000 + 39.5980i −0.0752688 + 0.212892i
$$187$$ −182.000 + 182.000i −0.973262 + 0.973262i
$$188$$ 12.7279 12.7279i 0.0677017 0.0677017i
$$189$$ −183.844 43.8442i −0.972721 0.231980i
$$190$$ 30.0000 + 40.0000i 0.157895 + 0.210526i
$$191$$ 118.794i 0.621958i −0.950417 0.310979i $$-0.899343\pi$$
0.950417 0.310979i $$-0.100657\pi$$
$$192$$ 35.1924 16.8076i 0.183294 0.0875396i
$$193$$ 67.0000 67.0000i 0.347150 0.347150i −0.511897 0.859047i $$-0.671057\pi$$
0.859047 + 0.511897i $$0.171057\pi$$
$$194$$ 159.806i 0.823743i
$$195$$ 150.392 + 78.6274i 0.771241 + 0.403218i
$$196$$ 147.000i 0.750000i
$$197$$ 56.5685 56.5685i 0.287150 0.287150i −0.548802 0.835952i $$-0.684916\pi$$
0.835952 + 0.548802i $$0.184916\pi$$
$$198$$ −88.5980 + 9.40202i −0.447465 + 0.0474850i
$$199$$ −120.000 −0.603015 −0.301508 0.953464i $$-0.597490\pi$$
−0.301508 + 0.953464i $$0.597490\pi$$
$$200$$ 84.1457 + 153.442i 0.420729 + 0.767211i
$$201$$ 45.2548 128.000i 0.225148 0.636816i
$$202$$ −65.0000 + 65.0000i −0.321782 + 0.321782i
$$203$$ −29.6985 −0.146298
$$204$$ −220.617 78.0000i −1.08146 0.382353i
$$205$$ −24.0000 + 168.000i −0.117073 + 0.819512i
$$206$$ −7.07107 −0.0343256
$$207$$ −304.291 + 32.2914i −1.47001 + 0.155997i
$$208$$ 40.0000 + 40.0000i 0.192308 + 0.192308i
$$209$$ 98.9949i 0.473660i
$$210$$ −48.6482 + 93.0503i −0.231658 + 0.443096i
$$211$$ 86.0000 0.407583 0.203791 0.979014i $$-0.434674\pi$$
0.203791 + 0.979014i $$0.434674\pi$$
$$212$$ 212.132 212.132i 1.00062 1.00062i
$$213$$ −160.794 + 76.7939i −0.754901 + 0.360535i
$$214$$ 6.00000i 0.0280374i
$$215$$ −152.735 203.647i −0.710396 0.947194i
$$216$$ −98.9949 161.000i −0.458310 0.745370i
$$217$$ 98.0000i 0.451613i
$$218$$ 49.4975 + 49.4975i 0.227053 + 0.227053i
$$219$$ −55.1543 + 156.000i −0.251846 + 0.712329i
$$220$$ 21.0000 147.000i 0.0954545 0.668182i
$$221$$ 294.156i 1.33102i
$$222$$ 54.8528 + 114.853i 0.247085 + 0.517355i
$$223$$ 237.000 + 237.000i 1.06278 + 1.06278i 0.997893 + 0.0648877i $$0.0206689\pi$$
0.0648877 + 0.997893i $$0.479331\pi$$
$$224$$ −163.342 + 163.342i −0.729204 + 0.729204i
$$225$$ 184.765 128.402i 0.821176 0.570676i
$$226$$ 18.0000 0.0796460
$$227$$ −117.380 117.380i −0.517091 0.517091i 0.399599 0.916690i $$-0.369149\pi$$
−0.916690 + 0.399599i $$0.869149\pi$$
$$228$$ 81.2132 38.7868i 0.356198 0.170118i
$$229$$ 374.000 1.63319 0.816594 0.577213i $$-0.195860\pi$$
0.816594 + 0.577213i $$0.195860\pi$$
$$230$$ −24.0416 + 168.291i −0.104529 + 0.731702i
$$231$$ 187.593 89.5929i 0.812091 0.387848i
$$232$$ −21.0000 21.0000i −0.0905172 0.0905172i
$$233$$ −173.948 173.948i −0.746559 0.746559i 0.227272 0.973831i $$-0.427019\pi$$
−0.973831 + 0.227272i $$0.927019\pi$$
$$234$$ −64.0000 + 79.1960i −0.273504 + 0.338444i
$$235$$ −24.0000 + 18.0000i −0.102128 + 0.0765957i
$$236$$ 89.0955 0.377523
$$237$$ −151.598 + 72.4020i −0.639654 + 0.305494i
$$238$$ −182.000 −0.764706
$$239$$ 291.328 1.21895 0.609473 0.792807i $$-0.291381\pi$$
0.609473 + 0.792807i $$0.291381\pi$$
$$240$$ 71.5685 22.4264i 0.298202 0.0934434i
$$241$$ 14.0000i 0.0580913i −0.999578 0.0290456i $$-0.990753\pi$$
0.999578 0.0290456i $$-0.00924682\pi$$
$$242$$ −16.2635 + 16.2635i −0.0672044 + 0.0672044i
$$243$$ −192.413 + 148.413i −0.791822 + 0.610752i
$$244$$ 42.0000 0.172131
$$245$$ 34.6482 242.538i 0.141421 0.989949i
$$246$$ −96.0000 33.9411i −0.390244 0.137972i
$$247$$ −80.0000 80.0000i −0.323887 0.323887i
$$248$$ 69.2965 69.2965i 0.279421 0.279421i
$$249$$ 147.078 + 52.0000i 0.590676 + 0.208835i
$$250$$ −44.0000 117.000i −0.176000 0.468000i
$$251$$ −439.820 −1.75227 −0.876136 0.482063i $$-0.839887\pi$$
−0.876136 + 0.482063i $$0.839887\pi$$
$$252$$ 147.000 + 118.794i 0.583333 + 0.471405i
$$253$$ 238.000 238.000i 0.940711 0.940711i
$$254$$ 156.978 0.618022
$$255$$ 345.615 + 180.693i 1.35535 + 0.708602i
$$256$$ −171.000 −0.667969
$$257$$ 35.3553 + 35.3553i 0.137569 + 0.137569i 0.772538 0.634969i $$-0.218987\pi$$
−0.634969 + 0.772538i $$0.718987\pi$$
$$258$$ 137.823 65.8234i 0.534199 0.255129i
$$259$$ −210.000 210.000i −0.810811 0.810811i
$$260$$ −101.823 135.765i −0.391628 0.522171i
$$261$$ −24.0000 + 29.6985i −0.0919540 + 0.113787i
$$262$$ 27.0000 27.0000i 0.103053 0.103053i
$$263$$ 315.370 + 315.370i 1.19912 + 1.19912i 0.974429 + 0.224695i $$0.0721385\pi$$
0.224695 + 0.974429i $$0.427861\pi$$
$$264$$ 196.000 + 69.2965i 0.742424 + 0.262487i
$$265$$ −400.000 + 300.000i −1.50943 + 1.13208i
$$266$$ 49.4975 49.4975i 0.186081 0.186081i
$$267$$ −53.5980 + 25.5980i −0.200741 + 0.0958726i
$$268$$ −96.0000 + 96.0000i −0.358209 + 0.358209i
$$269$$ 267.286i 0.993630i 0.867857 + 0.496815i $$0.165497\pi$$
−0.867857 + 0.496815i $$0.834503\pi$$
$$270$$ 53.7365 + 123.844i 0.199024 + 0.458682i
$$271$$ 112.000i 0.413284i 0.978417 + 0.206642i $$0.0662536\pi$$
−0.978417 + 0.206642i $$0.933746\pi$$
$$272$$ 91.9239 + 91.9239i 0.337955 + 0.337955i
$$273$$ 79.1960 224.000i 0.290095 0.820513i
$$274$$ 26.0000i 0.0948905i
$$275$$ −69.2965 + 237.588i −0.251987 + 0.863956i
$$276$$ 288.500 + 102.000i 1.04529 + 0.369565i
$$277$$ 102.000 + 102.000i 0.368231 + 0.368231i 0.866832 0.498601i $$-0.166153\pi$$
−0.498601 + 0.866832i $$0.666153\pi$$
$$278$$ −97.5807 + 97.5807i −0.351010 + 0.351010i
$$279$$ −98.0000 79.1960i −0.351254 0.283856i
$$280$$ 196.000 147.000i 0.700000 0.525000i
$$281$$ 296.985i 1.05689i 0.848969 + 0.528443i $$0.177224\pi$$
−0.848969 + 0.528443i $$0.822776\pi$$
$$282$$ −7.75736 16.2426i −0.0275084 0.0575980i
$$283$$ −102.000 102.000i −0.360424 0.360424i 0.503545 0.863969i $$-0.332029\pi$$
−0.863969 + 0.503545i $$0.832029\pi$$
$$284$$ 178.191 0.627433
$$285$$ −143.137 + 44.8528i −0.502235 + 0.157378i
$$286$$ 112.000i 0.391608i
$$287$$ 237.588 0.827832
$$288$$ 31.3417 + 295.342i 0.108825 + 1.02549i
$$289$$ 387.000i 1.33910i
$$290$$ 12.7279 + 16.9706i 0.0438894 + 0.0585192i
$$291$$ 452.000 + 159.806i 1.55326 + 0.549162i
$$292$$ 117.000 117.000i 0.400685 0.400685i
$$293$$ −185.262 + 185.262i −0.632293 + 0.632293i −0.948643 0.316349i $$-0.897543\pi$$
0.316349 + 0.948643i $$0.397543\pi$$
$$294$$ 138.593 + 49.0000i 0.471405 + 0.166667i
$$295$$ −147.000 21.0000i −0.498305 0.0711864i
$$296$$ 296.985i 1.00333i
$$297$$ 62.0051 259.995i 0.208771 0.875404i
$$298$$ 141.000 141.000i 0.473154 0.473154i
$$299$$ 384.666i 1.28651i
$$300$$ −222.062 + 36.2391i −0.740208 + 0.120797i
$$301$$ −252.000 + 252.000i −0.837209 + 0.837209i
$$302$$ −55.1543 + 55.1543i −0.182630 + 0.182630i
$$303$$ −118.848 248.848i −0.392237 0.821280i
$$304$$ −50.0000 −0.164474
$$305$$ −69.2965 9.89949i −0.227202 0.0324574i
$$306$$ −147.078 + 182.000i −0.480648 + 0.594771i
$$307$$ 90.0000 90.0000i 0.293160 0.293160i −0.545168 0.838327i $$-0.683534\pi$$
0.838327 + 0.545168i $$0.183534\pi$$
$$308$$ −207.889 −0.674966
$$309$$ 7.07107 20.0000i 0.0228837 0.0647249i
$$310$$ −56.0000 + 42.0000i −0.180645 + 0.135484i
$$311$$ 299.813 0.964030 0.482015 0.876163i $$-0.339905\pi$$
0.482015 + 0.876163i $$0.339905\pi$$
$$312$$ 214.392 102.392i 0.687154 0.328179i
$$313$$ −177.000 177.000i −0.565495 0.565495i 0.365368 0.930863i $$-0.380943\pi$$
−0.930863 + 0.365368i $$0.880943\pi$$
$$314$$ 65.0538i 0.207178i
$$315$$ −214.538 230.648i −0.681072 0.732217i
$$316$$ 168.000 0.531646
$$317$$ −213.546 + 213.546i −0.673647 + 0.673647i −0.958555 0.284908i $$-0.908037\pi$$
0.284908 + 0.958555i $$0.408037\pi$$
$$318$$ −129.289 270.711i −0.406570 0.851291i
$$319$$ 42.0000i 0.131661i
$$320$$ 64.3467 + 9.19239i 0.201083 + 0.0287262i
$$321$$ −16.9706 6.00000i −0.0528678 0.0186916i
$$322$$ 238.000 0.739130
$$323$$ −183.848 183.848i −0.569188 0.569188i
$$324$$ 237.588 51.0000i 0.733296 0.157407i
$$325$$ 136.000 + 248.000i 0.418462 + 0.763077i
$$326$$ 195.161i 0.598655i
$$327$$ −189.497 + 90.5025i −0.579503 + 0.276766i
$$328$$ 168.000 + 168.000i 0.512195 + 0.512195i
$$329$$ 29.6985 + 29.6985i 0.0902690 + 0.0902690i
$$330$$ −131.593 68.7990i −0.398766 0.208482i
$$331$$ 102.000 0.308157 0.154079 0.988059i $$-0.450759\pi$$
0.154079 + 0.988059i $$0.450759\pi$$
$$332$$ −110.309 110.309i −0.332255 0.332255i
$$333$$ −379.706 + 40.2944i −1.14026 + 0.121004i
$$334$$ −130.000 −0.389222
$$335$$ 181.019 135.765i 0.540356 0.405267i
$$336$$ −45.2513 94.7487i −0.134676 0.281990i
$$337$$ 253.000 + 253.000i 0.750742 + 0.750742i 0.974618 0.223876i $$-0.0718710\pi$$
−0.223876 + 0.974618i $$0.571871\pi$$
$$338$$ 28.9914 + 28.9914i 0.0857733 + 0.0857733i
$$339$$ −18.0000 + 50.9117i −0.0530973 + 0.150182i
$$340$$ −234.000 312.000i −0.688235 0.917647i
$$341$$ 138.593 0.406431
$$342$$ −9.49747 89.4975i −0.0277704 0.261689i
$$343$$ −343.000 −1.00000
$$344$$ −356.382 −1.03599
$$345$$ −451.958 236.291i −1.31002 0.684903i
$$346$$ 316.000i 0.913295i
$$347$$ −169.706 + 169.706i −0.489065 + 0.489065i −0.908011 0.418946i $$-0.862400\pi$$
0.418946 + 0.908011i $$0.362400\pi$$
$$348$$ 34.4558 16.4558i 0.0990110 0.0472869i
$$349$$ 446.000 1.27794 0.638968 0.769233i $$-0.279361\pi$$
0.638968 + 0.769233i $$0.279361\pi$$
$$350$$ −153.442 + 84.1457i −0.438406 + 0.240416i
$$351$$ −160.000 260.215i −0.455840 0.741354i
$$352$$ −231.000 231.000i −0.656250 0.656250i
$$353$$ −97.5807 + 97.5807i −0.276433 + 0.276433i −0.831683 0.555250i $$-0.812622\pi$$
0.555250 + 0.831683i $$0.312622\pi$$
$$354$$ 29.6985 84.0000i 0.0838940 0.237288i
$$355$$ −294.000 42.0000i −0.828169 0.118310i
$$356$$ 59.3970 0.166845
$$357$$ 182.000 514.774i 0.509804 1.44194i
$$358$$ 9.00000 9.00000i 0.0251397 0.0251397i
$$359$$ −248.902 −0.693319 −0.346660 0.937991i $$-0.612684\pi$$
−0.346660 + 0.937991i $$0.612684\pi$$
$$360$$ 11.3919 314.794i 0.0316442 0.874428i
$$361$$ −261.000 −0.722992
$$362$$ 247.487 + 247.487i 0.683667 + 0.683667i
$$363$$ −29.7365 62.2635i −0.0819189 0.171525i
$$364$$ −168.000 + 168.000i −0.461538 + 0.461538i
$$365$$ −220.617 + 165.463i −0.604431 + 0.453323i
$$366$$ 14.0000 39.5980i 0.0382514 0.108191i
$$367$$ 185.000 185.000i 0.504087 0.504087i −0.408618 0.912705i $$-0.633989\pi$$
0.912705 + 0.408618i $$0.133989\pi$$
$$368$$ −120.208 120.208i −0.326653 0.326653i
$$369$$ 192.000 237.588i 0.520325 0.643870i
$$370$$ −30.0000 + 210.000i −0.0810811 + 0.567568i
$$371$$ 494.975 + 494.975i 1.33416 + 1.33416i
$$372$$ 54.3015 + 113.698i 0.145972 + 0.305641i
$$373$$ 492.000 492.000i 1.31903 1.31903i 0.404494 0.914540i $$-0.367448\pi$$
0.914540 0.404494i $$-0.132552\pi$$
$$374$$ 257.387i 0.688200i
$$375$$ 374.926 7.45079i 0.999803 0.0198688i
$$376$$ 42.0000i 0.111702i
$$377$$ −33.9411 33.9411i −0.0900295 0.0900295i
$$378$$ 161.000 98.9949i 0.425926 0.261891i
$$379$$ 266.000i 0.701847i 0.936404 + 0.350923i $$0.114132\pi$$
−0.936404 + 0.350923i $$0.885868\pi$$
$$380$$ 148.492 + 21.2132i 0.390770 + 0.0558242i
$$381$$ −156.978 + 444.000i −0.412015 + 1.16535i
$$382$$ 84.0000 + 84.0000i 0.219895 + 0.219895i
$$383$$ 134.350 134.350i 0.350784 0.350784i −0.509617 0.860401i $$-0.670213\pi$$
0.860401 + 0.509617i $$0.170213\pi$$
$$384$$ 119.000 336.583i 0.309896 0.876518i
$$385$$ 343.000 + 49.0000i 0.890909 + 0.127273i
$$386$$ 94.7523i 0.245472i
$$387$$ 48.3532 + 455.647i 0.124944 + 1.17738i
$$388$$ −339.000 339.000i −0.873711 0.873711i
$$389$$ −329.512 −0.847074 −0.423537 0.905879i $$-0.639212\pi$$
−0.423537 + 0.905879i $$0.639212\pi$$
$$390$$ −161.941 + 50.7452i −0.415234 + 0.130116i
$$391$$ 884.000i 2.26087i
$$392$$ −242.538 242.538i −0.618718 0.618718i
$$393$$ 49.3675 + 103.368i 0.125617 + 0.263022i
$$394$$ 80.0000i 0.203046i
$$395$$ −277.186 39.5980i −0.701736 0.100248i
$$396$$ −168.000 + 207.889i −0.424242 + 0.524973i
$$397$$ −30.0000 + 30.0000i −0.0755668 + 0.0755668i −0.743880 0.668313i $$-0.767017\pi$$
0.668313 + 0.743880i $$0.267017\pi$$
$$398$$ 84.8528 84.8528i 0.213198 0.213198i
$$399$$ 90.5025 + 189.497i 0.226823 + 0.474931i
$$400$$ 120.000 + 35.0000i 0.300000 + 0.0875000i
$$401$$ 79.1960i 0.197496i 0.995112 + 0.0987481i $$0.0314838\pi$$
−0.995112 + 0.0987481i $$0.968516\pi$$
$$402$$ 58.5097 + 122.510i 0.145546 + 0.304750i
$$403$$ 112.000 112.000i 0.277916 0.277916i
$$404$$ 275.772i 0.682603i
$$405$$ −404.021 + 28.1457i −0.997582 + 0.0694956i
$$406$$ 21.0000 21.0000i 0.0517241 0.0517241i
$$407$$ 296.985 296.985i 0.729693 0.729693i
$$408$$ 492.693 235.307i 1.20758 0.576732i
$$409$$ −302.000 −0.738386 −0.369193 0.929353i $$-0.620366\pi$$
−0.369193 + 0.929353i $$0.620366\pi$$
$$410$$ −101.823 135.765i −0.248350 0.331133i
$$411$$ −73.5391 26.0000i −0.178927 0.0632603i
$$412$$ −15.0000 + 15.0000i −0.0364078 + 0.0364078i
$$413$$ 207.889i 0.503364i
$$414$$ 192.333 238.000i 0.464573 0.574879i
$$415$$ 156.000 + 208.000i 0.375904 + 0.501205i
$$416$$ −373.352 −0.897482
$$417$$ −178.419 373.581i −0.427864 0.895877i
$$418$$ 70.0000 + 70.0000i 0.167464 + 0.167464i
$$419$$ 366.281i 0.874180i 0.899418 + 0.437090i $$0.143991\pi$$
−0.899418 + 0.437090i $$0.856009\pi$$
$$420$$ 94.1909 + 300.588i 0.224264 + 0.715685i
$$421$$ −614.000 −1.45843 −0.729216 0.684283i $$-0.760115\pi$$
−0.729216 + 0.684283i $$0.760115\pi$$
$$422$$ −60.8112 + 60.8112i −0.144102 + 0.144102i
$$423$$ 53.6985 5.69848i 0.126947 0.0134716i
$$424$$ 700.000i 1.65094i
$$425$$ 312.541 + 569.928i 0.735391 + 1.34101i
$$426$$ 59.3970 168.000i 0.139430 0.394366i
$$427$$ 98.0000i 0.229508i
$$428$$ 12.7279 + 12.7279i 0.0297381 + 0.0297381i
$$429$$ 316.784 + 112.000i 0.738424 + 0.261072i
$$430$$ 252.000 + 36.0000i 0.586047 + 0.0837209i
$$431$$ 554.372i 1.28625i −0.765763 0.643123i $$-0.777639\pi$$
0.765763 0.643123i $$-0.222361\pi$$
$$432$$ −131.317 31.3173i −0.303975 0.0724937i
$$433$$ 153.000 + 153.000i 0.353349 + 0.353349i 0.861354 0.508005i $$-0.169617\pi$$
−0.508005 + 0.861354i $$0.669617\pi$$
$$434$$ 69.2965 + 69.2965i 0.159669 + 0.159669i
$$435$$ −60.7279 + 19.0294i −0.139604 + 0.0437458i
$$436$$ 210.000 0.481651
$$437$$ 240.416 + 240.416i 0.550152 + 0.550152i
$$438$$ −71.3087 149.309i −0.162805 0.340887i
$$439$$ 248.000 0.564920 0.282460 0.959279i $$-0.408850\pi$$
0.282460 + 0.959279i $$0.408850\pi$$
$$440$$ 207.889 + 277.186i 0.472476 + 0.629968i
$$441$$ −277.186 + 343.000i −0.628539 + 0.777778i
$$442$$ −208.000 208.000i −0.470588 0.470588i
$$443$$ 14.1421 + 14.1421i 0.0319236 + 0.0319236i 0.722888 0.690965i $$-0.242814\pi$$
−0.690965 + 0.722888i $$0.742814\pi$$
$$444$$ 360.000 + 127.279i 0.810811 + 0.286665i
$$445$$ −98.0000 14.0000i −0.220225 0.0314607i
$$446$$ −335.169 −0.751499
$$447$$ 257.808 + 539.808i 0.576752 + 1.20762i
$$448$$ 91.0000i 0.203125i
$$449$$ 647.710 1.44256 0.721280 0.692643i $$-0.243554\pi$$
0.721280 + 0.692643i $$0.243554\pi$$
$$450$$ −39.8543 + 221.442i −0.0885651 + 0.492094i
$$451$$ 336.000i 0.745011i
$$452$$ 38.1838 38.1838i 0.0844774 0.0844774i
$$453$$ −100.846 211.154i −0.222617 0.466124i
$$454$$ 166.000 0.365639
$$455$$ 316.784 237.588i 0.696228 0.522171i
$$456$$ −70.0000 + 197.990i −0.153509 + 0.434188i
$$457$$ −313.000 313.000i −0.684902 0.684902i 0.276199 0.961100i $$-0.410925\pi$$
−0.961100 + 0.276199i $$0.910925\pi$$
$$458$$ −264.458 + 264.458i −0.577419 + 0.577419i
$$459$$ −367.696 598.000i −0.801080 1.30283i
$$460$$ 306.000 + 408.000i 0.665217 + 0.886957i
$$461$$ −142.836 −0.309839 −0.154919 0.987927i $$-0.549512\pi$$
−0.154919 + 0.987927i $$0.549512\pi$$
$$462$$ −69.2965 + 196.000i −0.149992 + 0.424242i
$$463$$ 29.0000 29.0000i 0.0626350 0.0626350i −0.675095 0.737730i $$-0.735898\pi$$
0.737730 + 0.675095i $$0.235898\pi$$
$$464$$ −21.2132 −0.0457181
$$465$$ −62.7939 200.392i −0.135041 0.430950i
$$466$$ 246.000 0.527897
$$467$$ −350.725 350.725i −0.751017 0.751017i 0.223652 0.974669i $$-0.428202\pi$$
−0.974669 + 0.223652i $$0.928202\pi$$
$$468$$ 32.2355 + 303.765i 0.0688793 + 0.649069i
$$469$$ −224.000 224.000i −0.477612 0.477612i
$$470$$ 4.24264 29.6985i 0.00902690 0.0631883i
$$471$$ 184.000 + 65.0538i 0.390658 + 0.138119i
$$472$$ −147.000 + 147.000i −0.311441 + 0.311441i
$$473$$ −356.382 356.382i −0.753450 0.753450i
$$474$$ 56.0000 158.392i 0.118143 0.334160i
$$475$$ −240.000 70.0000i −0.505263 0.147368i
$$476$$ −386.080 + 386.080i −0.811093 + 0.811093i
$$477$$ 894.975 94.9747i 1.87626 0.199108i
$$478$$ −206.000 + 206.000i −0.430962 + 0.430962i
$$479$$ 79.1960i 0.165336i −0.996577 0.0826680i $$-0.973656\pi$$
0.996577 0.0826680i $$-0.0263441\pi$$
$$480$$ −229.342 + 438.665i −0.477795 + 0.913886i
$$481$$ 480.000i 0.997921i
$$482$$ 9.89949 + 9.89949i 0.0205384 + 0.0205384i
$$483$$ −238.000 + 673.166i −0.492754 + 1.39372i
$$484$$ 69.0000i 0.142562i
$$485$$ 479.418 + 639.225i 0.988492 + 1.31799i
$$486$$ 31.1127 241.000i 0.0640179 0.495885i
$$487$$ −101.000 101.000i −0.207392 0.207392i 0.595766 0.803158i $$-0.296849\pi$$
−0.803158 + 0.595766i $$0.796849\pi$$
$$488$$ −69.2965 + 69.2965i −0.142001 + 0.142001i
$$489$$ 552.000 + 195.161i 1.12883 + 0.399103i
$$490$$ 147.000 + 196.000i 0.300000 + 0.400000i
$$491$$ 346.482i 0.705667i −0.935686 0.352833i $$-0.885218\pi$$
0.935686 0.352833i $$-0.114782\pi$$
$$492$$ −275.647 + 131.647i −0.560258 + 0.267575i
$$493$$ −78.0000 78.0000i −0.158215 0.158215i
$$494$$ 113.137 0.229022
$$495$$ 326.186 303.402i 0.658961 0.612933i
$$496$$ 70.0000i 0.141129i
$$497$$ 415.779i 0.836577i
$$498$$ −140.770 + 67.2304i −0.282670 + 0.135001i
$$499$$ 602.000i 1.20641i −0.797585 0.603206i $$-0.793890\pi$$
0.797585 0.603206i $$-0.206110\pi$$
$$500$$ −341.533 154.856i −0.683065 0.309713i
$$501$$ 130.000 367.696i 0.259481 0.733923i
$$502$$ 311.000 311.000i 0.619522 0.619522i
$$503$$ 626.497 626.497i 1.24552 1.24552i 0.287842 0.957678i $$-0.407062\pi$$
0.957678 0.287842i $$-0.0929379\pi$$
$$504$$ −438.538 + 46.5376i −0.870114 + 0.0923366i
$$505$$ 65.0000 455.000i 0.128713 0.900990i
$$506$$ 336.583i 0.665183i
$$507$$ −110.991 + 53.0086i −0.218918 + 0.104553i
$$508$$ 333.000 333.000i 0.655512 0.655512i
$$509$$ 386.080i 0.758507i 0.925293 + 0.379254i $$0.123819\pi$$
−0.925293 + 0.379254i $$0.876181\pi$$
$$510$$ −372.156 + 116.617i −0.729718 + 0.228661i
$$511$$ 273.000 + 273.000i 0.534247 + 0.534247i
$$512$$ −215.668 + 215.668i −0.421226 + 0.421226i
$$513$$ 262.635 + 62.6346i 0.511958 + 0.122095i
$$514$$ −50.0000 −0.0972763
$$515$$ 28.2843 21.2132i 0.0549209 0.0411907i
$$516$$ 152.735 432.000i 0.295998 0.837209i
$$517$$ −42.0000 + 42.0000i −0.0812379 + 0.0812379i
$$518$$ 296.985 0.573330
$$519$$ −893.783 316.000i −1.72213 0.608863i
$$520$$ 392.000 + 56.0000i 0.753846 + 0.107692i
$$521$$ 379.009 0.727465 0.363732 0.931503i $$-0.381502\pi$$
0.363732 + 0.931503i $$0.381502\pi$$
$$522$$ −4.02944 37.9706i −0.00771923 0.0727405i
$$523$$ 642.000 + 642.000i 1.22753 + 1.22753i 0.964894 + 0.262639i $$0.0845930\pi$$
0.262639 + 0.964894i $$0.415407\pi$$
$$524$$ 114.551i 0.218609i
$$525$$ −84.5578 518.146i −0.161063 0.986944i
$$526$$ −446.000 −0.847909
$$527$$ 257.387 257.387i 0.488400 0.488400i
$$528$$ 133.995 63.9949i 0.253778 0.121203i
$$529$$ 627.000i 1.18526i
$$530$$ 70.7107 494.975i 0.133416 0.933915i
$$531$$ 207.889 + 168.000i 0.391505 + 0.316384i
$$532$$ 210.000i 0.394737i
$$533$$ 271.529 + 271.529i 0.509435 + 0.509435i
$$534$$ 19.7990 56.0000i 0.0370768 0.104869i
$$535$$ −18.0000 24.0000i −0.0336449 0.0448598i
$$536$$ 316.784i 0.591015i
$$537$$ 16.4558 + 34.4558i 0.0306440 + 0.0641636i
$$538$$ −189.000 189.000i −0.351301 0.351301i
$$539$$ 485.075i 0.899954i
$$540$$ 376.706 + 148.721i 0.697603 + 0.275409i
$$541$$ 270.000 0.499076 0.249538 0.968365i $$-0.419721\pi$$
0.249538 + 0.968365i $$0.419721\pi$$
$$542$$ −79.1960 79.1960i −0.146118 0.146118i
$$543$$ −947.487 + 452.513i −1.74491 + 0.833357i
$$544$$ −858.000 −1.57721
$$545$$ −346.482 49.4975i −0.635747 0.0908211i
$$546$$ 102.392 + 214.392i 0.187531 + 0.392659i
$$547$$ 176.000 + 176.000i 0.321755 + 0.321755i 0.849440 0.527685i $$-0.176940\pi$$
−0.527685 + 0.849440i $$0.676940\pi$$
$$548$$ 55.1543 + 55.1543i 0.100647 + 0.100647i
$$549$$ 98.0000 + 79.1960i 0.178506 + 0.144255i
$$550$$ −119.000 217.000i −0.216364 0.394545i
$$551$$ 42.4264 0.0769989
$$552$$ −644.291 + 307.709i −1.16719 + 0.557443i
$$553$$ 392.000i 0.708861i
$$554$$ −144.250 −0.260379
$$555$$ −563.970 294.853i −1.01616 0.531266i
$$556$$ 414.000i 0.744604i
$$557$$ 364.867 364.867i 0.655058 0.655058i −0.299149 0.954206i $$-0.596703\pi$$
0.954206 + 0.299149i $$0.0967027\pi$$
$$558$$ 125.296 13.2965i 0.224546 0.0238288i
$$559$$ −576.000 −1.03041
$$560$$ 24.7487 173.241i 0.0441942 0.309359i
$$561$$ 728.000 + 257.387i 1.29768 + 0.458800i
$$562$$ −210.000 210.000i −0.373665 0.373665i
$$563$$ 615.183 615.183i 1.09269 1.09269i 0.0974464 0.995241i $$-0.468933\pi$$
0.995241 0.0974464i $$-0.0310675\pi$$
$$564$$ −50.9117 18.0000i −0.0902690 0.0319149i
$$565$$ −72.0000 + 54.0000i −0.127434 + 0.0955752i
$$566$$ 144.250 0.254858
$$567$$ 119.000 + 554.372i 0.209877 + 0.977728i
$$568$$ −294.000 + 294.000i −0.517606 + 0.517606i
$$569$$ 28.2843 0.0497087 0.0248544 0.999691i $$-0.492088\pi$$
0.0248544 + 0.999691i $$0.492088\pi$$
$$570$$ 69.4975 132.929i 0.121925 0.233209i
$$571$$ −734.000 −1.28546 −0.642732 0.766091i $$-0.722199\pi$$
−0.642732 + 0.766091i $$0.722199\pi$$
$$572$$ −237.588 237.588i −0.415363 0.415363i
$$573$$ −321.588 + 153.588i −0.561235 + 0.268042i
$$574$$ −168.000 + 168.000i −0.292683 + 0.292683i
$$575$$ −408.708 745.291i −0.710796 1.29616i
$$576$$ −91.0000 73.5391i −0.157986 0.127672i
$$577$$ 647.000 647.000i 1.12132 1.12132i 0.129773 0.991544i $$-0.458575\pi$$
0.991544 0.129773i $$-0.0414250\pi$$
$$578$$ −273.650 273.650i −0.473443 0.473443i
$$579$$ −268.000 94.7523i −0.462867 0.163648i
$$580$$ 63.0000 + 9.00000i 0.108621 + 0.0155172i
$$581$$ 257.387 257.387i 0.443007 0.443007i
$$582$$ −432.612 + 206.612i −0.743320 + 0.355004i
$$583$$ −700.000 + 700.000i −1.20069 + 1.20069i
$$584$$ 386.080i 0.661096i
$$585$$ 18.4121 508.784i 0.0314737 0.869716i
$$586$$ 262.000i 0.447099i
$$587$$ −630.739 630.739i −1.07451 1.07451i −0.996991 0.0775226i $$-0.975299\pi$$
−0.0775226 0.996991i $$-0.524701\pi$$
$$588$$ 397.945 190.055i 0.676777 0.323223i
$$589$$ 140.000i 0.237691i
$$590$$ 118.794 89.0955i 0.201346 0.151009i
$$591$$ −226.274 80.0000i −0.382867 0.135364i
$$592$$ −150.000 150.000i −0.253378 0.253378i
$$593$$ −618.011 + 618.011i −1.04218 + 1.04218i −0.0431072 + 0.999070i $$0.513726\pi$$
−0.999070 + 0.0431072i $$0.986274\pi$$
$$594$$ 140.000 + 227.688i 0.235690 + 0.383314i
$$595$$ 728.000 546.000i 1.22353 0.917647i
$$596$$ 598.212i 1.00371i
$$597$$ 155.147 + 324.853i 0.259878 + 0.544142i
$$598$$ 272.000 + 272.000i 0.454849 + 0.454849i
$$599$$ 96.1665 0.160545 0.0802726 0.996773i $$-0.474421\pi$$
0.0802726 + 0.996773i $$0.474421\pi$$
$$600$$ 306.593 426.176i 0.510988 0.710293i
$$601$$ 476.000i 0.792013i 0.918248 + 0.396007i $$0.129604\pi$$
−0.918248 + 0.396007i $$0.870396\pi$$
$$602$$ 356.382i 0.591996i
$$603$$ −405.019 + 42.9807i −0.671674 + 0.0712780i
$$604$$ 234.000i 0.387417i
$$605$$ 16.2635 113.844i 0.0268817 0.188172i
$$606$$ 260.000 + 91.9239i 0.429043 + 0.151690i
$$607$$ −345.000 + 345.000i −0.568369 + 0.568369i −0.931671 0.363302i $$-0.881649\pi$$
0.363302 + 0.931671i $$0.381649\pi$$
$$608$$ 233.345 233.345i 0.383792 0.383792i
$$609$$ 38.3970 + 80.3970i 0.0630492 + 0.132015i
$$610$$ 56.0000 42.0000i 0.0918033 0.0688525i
$$611$$ 67.8823i 0.111100i
$$612$$ 74.0803 + 698.080i 0.121046 + 1.14065i
$$613$$ 116.000 116.000i 0.189233 0.189233i −0.606131 0.795365i $$-0.707279\pi$$
0.795365 + 0.606131i $$0.207279\pi$$
$$614$$ 127.279i 0.207295i
$$615$$ 485.823 152.235i 0.789957 0.247537i
$$616$$ 343.000 343.000i 0.556818 0.556818i
$$617$$ −468.105 + 468.105i −0.758679 + 0.758679i −0.976082 0.217403i $$-0.930241\pi$$
0.217403 + 0.976082i $$0.430241\pi$$
$$618$$ 9.14214 + 19.1421i 0.0147931 + 0.0309743i
$$619$$ −1058.00 −1.70921 −0.854604 0.519280i $$-0.826200\pi$$
−0.854604 + 0.519280i $$0.826200\pi$$
$$620$$ −29.6985 + 207.889i −0.0479008 + 0.335305i
$$621$$ 480.833 + 782.000i 0.774288 + 1.25926i
$$622$$ −212.000 + 212.000i −0.340836 + 0.340836i
$$623$$ 138.593i 0.222461i
$$624$$ 56.5685 160.000i 0.0906547 0.256410i
$$625$$ 527.000 + 336.000i 0.843200 + 0.537600i
$$626$$ 250.316 0.399865
$$627$$ −267.990 + 127.990i −0.427416 + 0.204131i
$$628$$ −138.000 138.000i −0.219745 0.219745i
$$629$$ 1103.09i 1.75371i
$$630$$ 314.794 + 11.3919i 0.499673 + 0.0180824i
$$631$$ 128.000 0.202853 0.101426 0.994843i $$-0.467659\pi$$
0.101426 + 0.994843i $$0.467659\pi$$
$$632$$ −277.186 + 277.186i −0.438585 + 0.438585i
$$633$$ −111.189 232.811i −0.175654 0.367790i
$$634$$ 302.000i 0.476341i
$$635$$ −627.911 + 470.933i −0.988836 + 0.741627i
$$636$$ −848.528 300.000i −1.33416 0.471698i
$$637$$ −392.000 392.000i −0.615385 0.615385i
$$638$$ 29.6985 + 29.6985i 0.0465493 + 0.0465493i
$$639$$ 415.779 + 336.000i 0.650671 + 0.525822i
$$640$$ 476.000 357.000i 0.743750 0.557813i
$$641$$ 277.186i 0.432427i −0.976346 0.216214i $$-0.930629\pi$$
0.976346 0.216214i $$-0.0693708\pi$$
$$642$$ 16.2426 7.75736i 0.0253001 0.0120831i
$$643$$ 636.000 + 636.000i 0.989114 + 0.989114i 0.999941 0.0108278i $$-0.00344668\pi$$
−0.0108278 + 0.999941i $$0.503447\pi$$
$$644$$ 504.874 504.874i 0.783966 0.783966i
$$645$$ −353.823 + 676.764i −0.548563 + 1.04925i
$$646$$ 260.000 0.402477
$$647$$ 535.987 + 535.987i 0.828419 + 0.828419i 0.987298 0.158879i $$-0.0507881\pi$$
−0.158879 + 0.987298i $$0.550788\pi$$
$$648$$ −307.854 + 476.146i −0.475084 + 0.734793i
$$649$$ −294.000 −0.453005
$$650$$ −271.529 79.1960i −0.417737 0.121840i
$$651$$ −265.296 + 126.704i −0.407521 + 0.194629i
$$652$$ −414.000 414.000i −0.634969 0.634969i
$$653$$ 380.423 + 380.423i 0.582578 + 0.582578i 0.935611 0.353033i $$-0.114850\pi$$
−0.353033 + 0.935611i $$0.614850\pi$$
$$654$$ 70.0000 197.990i 0.107034 0.302737i
$$655$$ −27.0000 + 189.000i −0.0412214 + 0.288550i
$$656$$ 169.706 0.258698
$$657$$ 493.617 52.3827i 0.751320 0.0797301i
$$658$$ −42.0000 −0.0638298
$$659$$ −253.144 −0.384134 −0.192067 0.981382i $$-0.561519\pi$$
−0.192067 + 0.981382i $$0.561519\pi$$
$$660$$ −425.095 + 133.206i −0.644084 + 0.201827i
$$661$$ 1106.00i 1.67322i −0.547797 0.836611i $$-0.684533\pi$$
0.547797 0.836611i $$-0.315467\pi$$
$$662$$ −72.1249 + 72.1249i −0.108950 + 0.108950i
$$663$$ 796.313 380.313i 1.20108 0.573624i
$$664$$ 364.000 0.548193
$$665$$ −49.4975 + 346.482i −0.0744323 + 0.521026i
$$666$$ 240.000 296.985i 0.360360 0.445923i
$$667$$ 102.000 + 102.000i 0.152924 + 0.152924i
$$668$$ −275.772 + 275.772i −0.412832 + 0.412832i
$$669$$ 335.169 948.000i 0.500999 1.41704i
$$670$$ −32.0000 + 224.000i −0.0477612 + 0.334328i
$$671$$ −138.593 −0.206547
$$672$$ 653.367 + 231.000i 0.972272 + 0.343750i
$$673$$ 393.000 393.000i 0.583952 0.583952i −0.352035 0.935987i $$-0.614510\pi$$
0.935987 + 0.352035i $$0.114510\pi$$
$$674$$ −357.796 −0.530855
$$675$$ −586.479 334.167i −0.868857 0.495062i
$$676$$ 123.000 0.181953
$$677$$ 144.250 + 144.250i 0.213072 + 0.213072i 0.805571 0.592499i $$-0.201859\pi$$
−0.592499 + 0.805571i $$0.701859\pi$$
$$678$$ −23.2721 48.7279i −0.0343246 0.0718701i
$$679$$ 791.000 791.000i 1.16495 1.16495i
$$680$$ 900.854 + 128.693i 1.32479 + 0.189255i
$$681$$ −166.000 + 469.519i −0.243759 + 0.689455i
$$682$$ −98.0000 + 98.0000i −0.143695 + 0.143695i
$$683$$ 592.555 + 592.555i 0.867578 + 0.867578i 0.992204 0.124626i $$-0.0397732\pi$$
−0.124626 + 0.992204i $$0.539773\pi$$
$$684$$ −210.000 169.706i −0.307018 0.248108i
$$685$$ −78.0000 104.000i −0.113869 0.151825i
$$686$$ 242.538 242.538i 0.353553 0.353553i
$$687$$ −483.542 1012.46i −0.703846 1.47374i
$$688$$ −180.000 + 180.000i −0.261628 + 0.261628i
$$689$$ 1131.37i 1.64205i
$$690$$ 486.666 152.500i 0.705313 0.221014i
$$691$$ 574.000i 0.830680i −0.909666 0.415340i $$-0.863663\pi$$
0.909666 0.415340i $$-0.136337\pi$$
$$692$$ 670.337 + 670.337i 0.968695 + 0.968695i
$$693$$ −485.075 392.000i −0.699964 0.565657i
$$694$$ 240.000i 0.345821i
$$695$$ 97.5807 683.065i 0.140404 0.982828i
$$696$$ −29.6985 + 84.0000i −0.0426702 + 0.120690i
$$697$$ 624.000 + 624.000i 0.895265 + 0.895265i
$$698$$ −315.370 + 315.370i −0.451819 + 0.451819i
$$699$$ −246.000 + 695.793i −0.351931 + 0.995412i
$$700$$ −147.000 + 504.000i −0.210000 + 0.720000i
$$701$$ 1118.64i 1.59578i 0.602802 + 0.797891i $$0.294051\pi$$
−0.602802 + 0.797891i $$0.705949\pi$$
$$702$$ 297.137 + 70.8629i 0.423272 + 0.100944i
$$703$$ 300.000 + 300.000i 0.426743 + 0.426743i
$$704$$ 128.693 0.182803
$$705$$ 79.7574 + 41.6985i 0.113131 + 0.0591468i
$$706$$ 138.000i 0.195467i
$$707$$ −643.467 −0.910137
$$708$$ −115.191 241.191i −0.162699 0.340665i
$$709$$ 546.000i 0.770099i −0.922896 0.385049i $$-0.874184\pi$$
0.922896 0.385049i $$-0.125816\pi$$
$$710$$ 237.588 178.191i 0.334631 0.250973i
$$711$$ 392.000 + 316.784i 0.551336 + 0.445547i
$$712$$ −98.0000 + 98.0000i −0.137640 + 0.137640i
$$713$$ −336.583 + 336.583i −0.472066 + 0.472066i
$$714$$ 235.307 + 492.693i 0.329561 + 0.690047i
$$715$$ 336.000 + 448.000i 0.469930 + 0.626573i
$$716$$ 38.1838i 0.0533293i
$$717$$ −376.656 788.656i −0.525322 1.09994i
$$718$$ 176.000 176.000i 0.245125 0.245125i
$$719$$ 277.186i 0.385516i 0.981246 + 0.192758i $$0.0617432\pi$$
−0.981246 + 0.192758i $$0.938257\pi$$
$$720$$ −153.241 164.749i −0.212835 0.228818i
$$721$$ −35.0000 35.0000i −0.0485437 0.0485437i
$$722$$ 184.555 184.555i 0.255616 0.255616i
$$723$$ −37.8995 + 18.1005i −0.0524198 + 0.0250353i
$$724$$ 1050.00 1.45028
$$725$$ −101.823 29.6985i −0.140446 0.0409634i
$$726$$ 65.0538 + 23.0000i 0.0896058 + 0.0316804i
$$727$$ −225.000 + 225.000i −0.309491 + 0.309491i −0.844712 0.535221i $$-0.820228\pi$$
0.535221 + 0.844712i $$0.320228\pi$$
$$728$$ 554.372i 0.761500i
$$729$$ 650.538 + 329.000i 0.892371 + 0.451303i
$$730$$ 39.0000 273.000i 0.0534247 0.373973i
$$731$$ −1323.70 −1.81081
$$732$$ −54.3015 113.698i −0.0741824 0.155326i
$$733$$ 124.000 + 124.000i 0.169168 + 0.169168i 0.786614 0.617446i $$-0.211832\pi$$
−0.617446 + 0.786614i $$0.711832\pi$$
$$734$$ 261.630i 0.356443i
$$735$$ −701.372 + 219.779i −0.954247 + 0.299019i
$$736$$ 1122.00 1.52446
$$737$$ 316.784 316.784i 0.429829 0.429829i
$$738$$ 32.2355 + 303.765i 0.0436795 + 0.411605i
$$739$$ 350.000i 0.473613i 0.971557 + 0.236806i $$0.0761007\pi$$
−0.971557 + 0.236806i $$0.923899\pi$$
$$740$$ 381.838 + 509.117i 0.515997 + 0.687996i
$$741$$ −113.137 + 320.000i −0.152682 + 0.431849i
$$742$$ −700.000 −0.943396
$$743$$ −666.095 666.095i −0.896493 0.896493i 0.0986307 0.995124i $$-0.468554\pi$$
−0.995124 + 0.0986307i $$0.968554\pi$$
$$744$$ −277.186 98.0000i −0.372562 0.131720i
$$745$$ −141.000 + 987.000i −0.189262 + 1.32483i
$$746$$ 695.793i 0.932698i
$$747$$ −49.3869 465.387i −0.0661136 0.623008i
$$748$$ −546.000 546.000i −0.729947 0.729947i
$$749$$ −29.6985 + 29.6985i −0.0396508 + 0.0396508i
$$750$$ −259.844 + 270.381i −0.346459 + 0.360508i
$$751$$ −1172.00 −1.56059 −0.780293 0.625414i $$-0.784930\pi$$
−0.780293 + 0.625414i $$0.784930\pi$$
$$752$$ 21.2132 + 21.2132i 0.0282090 + 0.0282090i
$$753$$ 568.641 + 1190.64i 0.755167 + 1.58120i
$$754$$ 48.0000 0.0636605
$$755$$ 55.1543 386.080i 0.0730521 0.511365i
$$756$$ 131.533 551.533i 0.173985 0.729540i
$$757$$ 302.000 + 302.000i 0.398943 + 0.398943i 0.877860 0.478917i $$-0.158971\pi$$
−0.478917 + 0.877860i $$0.658971\pi$$
$$758$$ −188.090 188.090i −0.248140 0.248140i
$$759$$ −952.000 336.583i −1.25428 0.443456i
$$760$$ −280.000 + 210.000i −0.368421 + 0.276316i
$$761$$ −701.450 −0.921748 −0.460874 0.887466i $$-0.652464\pi$$
−0.460874 + 0.887466i $$0.652464\pi$$
$$762$$ −202.955 424.955i −0.266346 0.557684i
$$763$$ 490.000i 0.642202i
$$764$$ 356.382 0.466468
$$765$$ 42.3128 1169.23i 0.0553109 1.52841i
$$766$$ 190.000i 0.248042i
$$767$$ −237.588 + 237.588i −0.309763 + 0.309763i
$$768$$ 221.085 + 462.915i 0.287871 + 0.602754i
$$769$$ −436.000 −0.566970 −0.283485 0.958977i $$-0.591491\pi$$
−0.283485 + 0.958977i $$0.591491\pi$$
$$770$$ −277.186 + 207.889i −0.359982 + 0.269986i
$$771$$ 50.0000 141.421i 0.0648508 0.183426i
$$772$$ 201.000 + 201.000i 0.260363 + 0.260363i
$$773$$ 684.479 684.479i 0.885484 0.885484i −0.108601 0.994085i $$-0.534637\pi$$
0.994085 + 0.108601i $$0.0346371\pi$$
$$774$$ −356.382 288.000i −0.460442 0.372093i
$$775$$ 98.0000 336.000i 0.126452 0.433548i
$$776$$ 1118.64 1.44155
$$777$$ −296.985 + 840.000i −0.382220 + 1.08108i
$$778$$ 233.000 233.000i 0.299486 0.299486i
$$779$$ −339.411 −0.435701
$$780$$ −235.882 + 451.176i −0.302413 + 0.578430i
$$781$$