# Properties

 Label 825.2.k.h.782.2 Level $825$ Weight $2$ Character 825.782 Analytic conductor $6.588$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 825.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.58765816676$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 782.2 Root $$0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 825.782 Dual form 825.2.k.h.518.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.70711 - 1.70711i) q^{2} +(0.292893 + 1.70711i) q^{3} -3.82843i q^{4} +(3.41421 + 2.41421i) q^{6} +(3.41421 + 3.41421i) q^{7} +(-3.12132 - 3.12132i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$$ $$q+(1.70711 - 1.70711i) q^{2} +(0.292893 + 1.70711i) q^{3} -3.82843i q^{4} +(3.41421 + 2.41421i) q^{6} +(3.41421 + 3.41421i) q^{7} +(-3.12132 - 3.12132i) q^{8} +(-2.82843 + 1.00000i) q^{9} +1.00000i q^{11} +(6.53553 - 1.12132i) q^{12} +(0.585786 - 0.585786i) q^{13} +11.6569 q^{14} -3.00000 q^{16} +(-2.00000 + 2.00000i) q^{17} +(-3.12132 + 6.53553i) q^{18} -4.82843i q^{19} +(-4.82843 + 6.82843i) q^{21} +(1.70711 + 1.70711i) q^{22} +(4.82843 + 4.82843i) q^{23} +(4.41421 - 6.24264i) q^{24} -2.00000i q^{26} +(-2.53553 - 4.53553i) q^{27} +(13.0711 - 13.0711i) q^{28} -3.17157 q^{29} +4.00000 q^{31} +(1.12132 - 1.12132i) q^{32} +(-1.70711 + 0.292893i) q^{33} +6.82843i q^{34} +(3.82843 + 10.8284i) q^{36} +(-5.65685 - 5.65685i) q^{37} +(-8.24264 - 8.24264i) q^{38} +(1.17157 + 0.828427i) q^{39} +0.828427i q^{41} +(3.41421 + 19.8995i) q^{42} +(7.41421 - 7.41421i) q^{43} +3.82843 q^{44} +16.4853 q^{46} +(0.828427 - 0.828427i) q^{47} +(-0.878680 - 5.12132i) q^{48} +16.3137i q^{49} +(-4.00000 - 2.82843i) q^{51} +(-2.24264 - 2.24264i) q^{52} +(-8.48528 - 8.48528i) q^{53} +(-12.0711 - 3.41421i) q^{54} -21.3137i q^{56} +(8.24264 - 1.41421i) q^{57} +(-5.41421 + 5.41421i) q^{58} -13.6569 q^{59} -6.00000 q^{61} +(6.82843 - 6.82843i) q^{62} +(-13.0711 - 6.24264i) q^{63} -9.82843i q^{64} +(-2.41421 + 3.41421i) q^{66} +(-5.41421 - 5.41421i) q^{67} +(7.65685 + 7.65685i) q^{68} +(-6.82843 + 9.65685i) q^{69} +1.65685i q^{71} +(11.9497 + 5.70711i) q^{72} +(7.41421 - 7.41421i) q^{73} -19.3137 q^{74} -18.4853 q^{76} +(-3.41421 + 3.41421i) q^{77} +(3.41421 - 0.585786i) q^{78} +0.828427i q^{79} +(7.00000 - 5.65685i) q^{81} +(1.41421 + 1.41421i) q^{82} +(4.24264 + 4.24264i) q^{83} +(26.1421 + 18.4853i) q^{84} -25.3137i q^{86} +(-0.928932 - 5.41421i) q^{87} +(3.12132 - 3.12132i) q^{88} +7.31371 q^{89} +4.00000 q^{91} +(18.4853 - 18.4853i) q^{92} +(1.17157 + 6.82843i) q^{93} -2.82843i q^{94} +(2.24264 + 1.58579i) q^{96} +(9.65685 + 9.65685i) q^{97} +(27.8492 + 27.8492i) q^{98} +(-1.00000 - 2.82843i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{2} + 4q^{3} + 8q^{6} + 8q^{7} - 4q^{8} + O(q^{10})$$ $$4q + 4q^{2} + 4q^{3} + 8q^{6} + 8q^{7} - 4q^{8} + 12q^{12} + 8q^{13} + 24q^{14} - 12q^{16} - 8q^{17} - 4q^{18} - 8q^{21} + 4q^{22} + 8q^{23} + 12q^{24} + 4q^{27} + 24q^{28} - 24q^{29} + 16q^{31} - 4q^{32} - 4q^{33} + 4q^{36} - 16q^{38} + 16q^{39} + 8q^{42} + 24q^{43} + 4q^{44} + 32q^{46} - 8q^{47} - 12q^{48} - 16q^{51} + 8q^{52} - 20q^{54} + 16q^{57} - 16q^{58} - 32q^{59} - 24q^{61} + 16q^{62} - 24q^{63} - 4q^{66} - 16q^{67} + 8q^{68} - 16q^{69} + 28q^{72} + 24q^{73} - 32q^{74} - 40q^{76} - 8q^{77} + 8q^{78} + 28q^{81} + 48q^{84} - 32q^{87} + 4q^{88} - 16q^{89} + 16q^{91} + 40q^{92} + 16q^{93} - 8q^{96} + 16q^{97} + 52q^{98} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$$.

 $$n$$ $$376$$ $$551$$ $$727$$ $$\chi(n)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.70711 1.70711i 1.20711 1.20711i 0.235147 0.971960i $$-0.424443\pi$$
0.971960 0.235147i $$-0.0755571\pi$$
$$3$$ 0.292893 + 1.70711i 0.169102 + 0.985599i
$$4$$ 3.82843i 1.91421i
$$5$$ 0 0
$$6$$ 3.41421 + 2.41421i 1.39385 + 0.985599i
$$7$$ 3.41421 + 3.41421i 1.29045 + 1.29045i 0.934507 + 0.355944i $$0.115841\pi$$
0.355944 + 0.934507i $$0.384159\pi$$
$$8$$ −3.12132 3.12132i −1.10355 1.10355i
$$9$$ −2.82843 + 1.00000i −0.942809 + 0.333333i
$$10$$ 0 0
$$11$$ 1.00000i 0.301511i
$$12$$ 6.53553 1.12132i 1.88665 0.323697i
$$13$$ 0.585786 0.585786i 0.162468 0.162468i −0.621191 0.783659i $$-0.713351\pi$$
0.783659 + 0.621191i $$0.213351\pi$$
$$14$$ 11.6569 3.11543
$$15$$ 0 0
$$16$$ −3.00000 −0.750000
$$17$$ −2.00000 + 2.00000i −0.485071 + 0.485071i −0.906747 0.421676i $$-0.861442\pi$$
0.421676 + 0.906747i $$0.361442\pi$$
$$18$$ −3.12132 + 6.53553i −0.735702 + 1.54044i
$$19$$ 4.82843i 1.10772i −0.832611 0.553859i $$-0.813155\pi$$
0.832611 0.553859i $$-0.186845\pi$$
$$20$$ 0 0
$$21$$ −4.82843 + 6.82843i −1.05365 + 1.49008i
$$22$$ 1.70711 + 1.70711i 0.363956 + 0.363956i
$$23$$ 4.82843 + 4.82843i 1.00680 + 1.00680i 0.999977 + 0.00681991i $$0.00217086\pi$$
0.00681991 + 0.999977i $$0.497829\pi$$
$$24$$ 4.41421 6.24264i 0.901048 1.27427i
$$25$$ 0 0
$$26$$ 2.00000i 0.392232i
$$27$$ −2.53553 4.53553i −0.487964 0.872864i
$$28$$ 13.0711 13.0711i 2.47020 2.47020i
$$29$$ −3.17157 −0.588946 −0.294473 0.955660i $$-0.595144\pi$$
−0.294473 + 0.955660i $$0.595144\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 1.12132 1.12132i 0.198223 0.198223i
$$33$$ −1.70711 + 0.292893i −0.297169 + 0.0509862i
$$34$$ 6.82843i 1.17107i
$$35$$ 0 0
$$36$$ 3.82843 + 10.8284i 0.638071 + 1.80474i
$$37$$ −5.65685 5.65685i −0.929981 0.929981i 0.0677230 0.997704i $$-0.478427\pi$$
−0.997704 + 0.0677230i $$0.978427\pi$$
$$38$$ −8.24264 8.24264i −1.33713 1.33713i
$$39$$ 1.17157 + 0.828427i 0.187602 + 0.132655i
$$40$$ 0 0
$$41$$ 0.828427i 0.129379i 0.997905 + 0.0646893i $$0.0206056\pi$$
−0.997905 + 0.0646893i $$0.979394\pi$$
$$42$$ 3.41421 + 19.8995i 0.526825 + 3.07056i
$$43$$ 7.41421 7.41421i 1.13066 1.13066i 0.140589 0.990068i $$-0.455100\pi$$
0.990068 0.140589i $$-0.0448996\pi$$
$$44$$ 3.82843 0.577157
$$45$$ 0 0
$$46$$ 16.4853 2.43062
$$47$$ 0.828427 0.828427i 0.120839 0.120839i −0.644102 0.764940i $$-0.722769\pi$$
0.764940 + 0.644102i $$0.222769\pi$$
$$48$$ −0.878680 5.12132i −0.126826 0.739199i
$$49$$ 16.3137i 2.33053i
$$50$$ 0 0
$$51$$ −4.00000 2.82843i −0.560112 0.396059i
$$52$$ −2.24264 2.24264i −0.310998 0.310998i
$$53$$ −8.48528 8.48528i −1.16554 1.16554i −0.983243 0.182300i $$-0.941646\pi$$
−0.182300 0.983243i $$-0.558354\pi$$
$$54$$ −12.0711 3.41421i −1.64266 0.464616i
$$55$$ 0 0
$$56$$ 21.3137i 2.84816i
$$57$$ 8.24264 1.41421i 1.09176 0.187317i
$$58$$ −5.41421 + 5.41421i −0.710921 + 0.710921i
$$59$$ −13.6569 −1.77797 −0.888985 0.457935i $$-0.848589\pi$$
−0.888985 + 0.457935i $$0.848589\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 6.82843 6.82843i 0.867211 0.867211i
$$63$$ −13.0711 6.24264i −1.64680 0.786499i
$$64$$ 9.82843i 1.22855i
$$65$$ 0 0
$$66$$ −2.41421 + 3.41421i −0.297169 + 0.420261i
$$67$$ −5.41421 5.41421i −0.661451 0.661451i 0.294271 0.955722i $$-0.404923\pi$$
−0.955722 + 0.294271i $$0.904923\pi$$
$$68$$ 7.65685 + 7.65685i 0.928530 + 0.928530i
$$69$$ −6.82843 + 9.65685i −0.822046 + 1.16255i
$$70$$ 0 0
$$71$$ 1.65685i 0.196632i 0.995155 + 0.0983162i $$0.0313457\pi$$
−0.995155 + 0.0983162i $$0.968654\pi$$
$$72$$ 11.9497 + 5.70711i 1.40829 + 0.672589i
$$73$$ 7.41421 7.41421i 0.867768 0.867768i −0.124457 0.992225i $$-0.539719\pi$$
0.992225 + 0.124457i $$0.0397189\pi$$
$$74$$ −19.3137 −2.24517
$$75$$ 0 0
$$76$$ −18.4853 −2.12041
$$77$$ −3.41421 + 3.41421i −0.389086 + 0.389086i
$$78$$ 3.41421 0.585786i 0.386584 0.0663273i
$$79$$ 0.828427i 0.0932053i 0.998914 + 0.0466027i $$0.0148395\pi$$
−0.998914 + 0.0466027i $$0.985161\pi$$
$$80$$ 0 0
$$81$$ 7.00000 5.65685i 0.777778 0.628539i
$$82$$ 1.41421 + 1.41421i 0.156174 + 0.156174i
$$83$$ 4.24264 + 4.24264i 0.465690 + 0.465690i 0.900515 0.434825i $$-0.143190\pi$$
−0.434825 + 0.900515i $$0.643190\pi$$
$$84$$ 26.1421 + 18.4853i 2.85234 + 2.01691i
$$85$$ 0 0
$$86$$ 25.3137i 2.72965i
$$87$$ −0.928932 5.41421i −0.0995920 0.580465i
$$88$$ 3.12132 3.12132i 0.332734 0.332734i
$$89$$ 7.31371 0.775252 0.387626 0.921817i $$-0.373295\pi$$
0.387626 + 0.921817i $$0.373295\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 18.4853 18.4853i 1.92722 1.92722i
$$93$$ 1.17157 + 6.82843i 0.121486 + 0.708075i
$$94$$ 2.82843i 0.291730i
$$95$$ 0 0
$$96$$ 2.24264 + 1.58579i 0.228889 + 0.161849i
$$97$$ 9.65685 + 9.65685i 0.980505 + 0.980505i 0.999814 0.0193086i $$-0.00614649\pi$$
−0.0193086 + 0.999814i $$0.506146\pi$$
$$98$$ 27.8492 + 27.8492i 2.81320 + 2.81320i
$$99$$ −1.00000 2.82843i −0.100504 0.284268i
$$100$$ 0 0
$$101$$ 4.82843i 0.480446i 0.970718 + 0.240223i $$0.0772206\pi$$
−0.970718 + 0.240223i $$0.922779\pi$$
$$102$$ −11.6569 + 2.00000i −1.15420 + 0.198030i
$$103$$ −4.24264 + 4.24264i −0.418040 + 0.418040i −0.884528 0.466488i $$-0.845519\pi$$
0.466488 + 0.884528i $$0.345519\pi$$
$$104$$ −3.65685 −0.358584
$$105$$ 0 0
$$106$$ −28.9706 −2.81387
$$107$$ −5.89949 + 5.89949i −0.570326 + 0.570326i −0.932219 0.361894i $$-0.882130\pi$$
0.361894 + 0.932219i $$0.382130\pi$$
$$108$$ −17.3640 + 9.70711i −1.67085 + 0.934067i
$$109$$ 2.00000i 0.191565i 0.995402 + 0.0957826i $$0.0305354\pi$$
−0.995402 + 0.0957826i $$0.969465\pi$$
$$110$$ 0 0
$$111$$ 8.00000 11.3137i 0.759326 1.07385i
$$112$$ −10.2426 10.2426i −0.967839 0.967839i
$$113$$ −8.48528 8.48528i −0.798228 0.798228i 0.184588 0.982816i $$-0.440905\pi$$
−0.982816 + 0.184588i $$0.940905\pi$$
$$114$$ 11.6569 16.4853i 1.09176 1.54399i
$$115$$ 0 0
$$116$$ 12.1421i 1.12737i
$$117$$ −1.07107 + 2.24264i −0.0990203 + 0.207332i
$$118$$ −23.3137 + 23.3137i −2.14620 + 2.14620i
$$119$$ −13.6569 −1.25192
$$120$$ 0 0
$$121$$ −1.00000 −0.0909091
$$122$$ −10.2426 + 10.2426i −0.927325 + 0.927325i
$$123$$ −1.41421 + 0.242641i −0.127515 + 0.0218782i
$$124$$ 15.3137i 1.37521i
$$125$$ 0 0
$$126$$ −32.9706 + 11.6569i −2.93725 + 1.03848i
$$127$$ −1.75736 1.75736i −0.155940 0.155940i 0.624825 0.780765i $$-0.285170\pi$$
−0.780765 + 0.624825i $$0.785170\pi$$
$$128$$ −14.5355 14.5355i −1.28477 1.28477i
$$129$$ 14.8284 + 10.4853i 1.30557 + 0.923178i
$$130$$ 0 0
$$131$$ 6.34315i 0.554203i −0.960841 0.277102i $$-0.910626\pi$$
0.960841 0.277102i $$-0.0893739\pi$$
$$132$$ 1.12132 + 6.53553i 0.0975984 + 0.568845i
$$133$$ 16.4853 16.4853i 1.42946 1.42946i
$$134$$ −18.4853 −1.59689
$$135$$ 0 0
$$136$$ 12.4853 1.07060
$$137$$ −9.65685 + 9.65685i −0.825041 + 0.825041i −0.986826 0.161785i $$-0.948275\pi$$
0.161785 + 0.986826i $$0.448275\pi$$
$$138$$ 4.82843 + 28.1421i 0.411023 + 2.39562i
$$139$$ 11.1716i 0.947560i 0.880643 + 0.473780i $$0.157111\pi$$
−0.880643 + 0.473780i $$0.842889\pi$$
$$140$$ 0 0
$$141$$ 1.65685 + 1.17157i 0.139532 + 0.0986642i
$$142$$ 2.82843 + 2.82843i 0.237356 + 0.237356i
$$143$$ 0.585786 + 0.585786i 0.0489859 + 0.0489859i
$$144$$ 8.48528 3.00000i 0.707107 0.250000i
$$145$$ 0 0
$$146$$ 25.3137i 2.09498i
$$147$$ −27.8492 + 4.77817i −2.29697 + 0.394097i
$$148$$ −21.6569 + 21.6569i −1.78018 + 1.78018i
$$149$$ −21.7990 −1.78584 −0.892921 0.450213i $$-0.851348\pi$$
−0.892921 + 0.450213i $$0.851348\pi$$
$$150$$ 0 0
$$151$$ −2.48528 −0.202249 −0.101125 0.994874i $$-0.532244\pi$$
−0.101125 + 0.994874i $$0.532244\pi$$
$$152$$ −15.0711 + 15.0711i −1.22243 + 1.22243i
$$153$$ 3.65685 7.65685i 0.295639 0.619020i
$$154$$ 11.6569i 0.939336i
$$155$$ 0 0
$$156$$ 3.17157 4.48528i 0.253929 0.359110i
$$157$$ 7.31371 + 7.31371i 0.583697 + 0.583697i 0.935917 0.352220i $$-0.114573\pi$$
−0.352220 + 0.935917i $$0.614573\pi$$
$$158$$ 1.41421 + 1.41421i 0.112509 + 0.112509i
$$159$$ 12.0000 16.9706i 0.951662 1.34585i
$$160$$ 0 0
$$161$$ 32.9706i 2.59844i
$$162$$ 2.29289 21.6066i 0.180147 1.69757i
$$163$$ 9.89949 9.89949i 0.775388 0.775388i −0.203655 0.979043i $$-0.565282\pi$$
0.979043 + 0.203655i $$0.0652819\pi$$
$$164$$ 3.17157 0.247658
$$165$$ 0 0
$$166$$ 14.4853 1.12428
$$167$$ −0.242641 + 0.242641i −0.0187761 + 0.0187761i −0.716433 0.697656i $$-0.754226\pi$$
0.697656 + 0.716433i $$0.254226\pi$$
$$168$$ 36.3848 6.24264i 2.80715 0.481630i
$$169$$ 12.3137i 0.947208i
$$170$$ 0 0
$$171$$ 4.82843 + 13.6569i 0.369239 + 1.04437i
$$172$$ −28.3848 28.3848i −2.16432 2.16432i
$$173$$ 0.828427 + 0.828427i 0.0629841 + 0.0629841i 0.737897 0.674913i $$-0.235819\pi$$
−0.674913 + 0.737897i $$0.735819\pi$$
$$174$$ −10.8284 7.65685i −0.820901 0.580465i
$$175$$ 0 0
$$176$$ 3.00000i 0.226134i
$$177$$ −4.00000 23.3137i −0.300658 1.75237i
$$178$$ 12.4853 12.4853i 0.935811 0.935811i
$$179$$ 3.31371 0.247678 0.123839 0.992302i $$-0.460479\pi$$
0.123839 + 0.992302i $$0.460479\pi$$
$$180$$ 0 0
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 6.82843 6.82843i 0.506157 0.506157i
$$183$$ −1.75736 10.2426i −0.129908 0.757158i
$$184$$ 30.1421i 2.22211i
$$185$$ 0 0
$$186$$ 13.6569 + 9.65685i 1.00137 + 0.708075i
$$187$$ −2.00000 2.00000i −0.146254 0.146254i
$$188$$ −3.17157 3.17157i −0.231311 0.231311i
$$189$$ 6.82843 24.1421i 0.496695 1.75608i
$$190$$ 0 0
$$191$$ 11.3137i 0.818631i −0.912393 0.409316i $$-0.865768\pi$$
0.912393 0.409316i $$-0.134232\pi$$
$$192$$ 16.7782 2.87868i 1.21086 0.207751i
$$193$$ −5.07107 + 5.07107i −0.365023 + 0.365023i −0.865658 0.500635i $$-0.833100\pi$$
0.500635 + 0.865658i $$0.333100\pi$$
$$194$$ 32.9706 2.36715
$$195$$ 0 0
$$196$$ 62.4558 4.46113
$$197$$ 2.48528 2.48528i 0.177069 0.177069i −0.613008 0.790077i $$-0.710041\pi$$
0.790077 + 0.613008i $$0.210041\pi$$
$$198$$ −6.53553 3.12132i −0.464460 0.221823i
$$199$$ 20.9706i 1.48656i −0.668978 0.743282i $$-0.733268\pi$$
0.668978 0.743282i $$-0.266732\pi$$
$$200$$ 0 0
$$201$$ 7.65685 10.8284i 0.540073 0.763778i
$$202$$ 8.24264 + 8.24264i 0.579950 + 0.579950i
$$203$$ −10.8284 10.8284i −0.760007 0.760007i
$$204$$ −10.8284 + 15.3137i −0.758142 + 1.07217i
$$205$$ 0 0
$$206$$ 14.4853i 1.00924i
$$207$$ −18.4853 8.82843i −1.28482 0.613618i
$$208$$ −1.75736 + 1.75736i −0.121851 + 0.121851i
$$209$$ 4.82843 0.333989
$$210$$ 0 0
$$211$$ 6.48528 0.446465 0.223233 0.974765i $$-0.428339\pi$$
0.223233 + 0.974765i $$0.428339\pi$$
$$212$$ −32.4853 + 32.4853i −2.23110 + 2.23110i
$$213$$ −2.82843 + 0.485281i −0.193801 + 0.0332509i
$$214$$ 20.1421i 1.37689i
$$215$$ 0 0
$$216$$ −6.24264 + 22.0711i −0.424758 + 1.50175i
$$217$$ 13.6569 + 13.6569i 0.927088 + 0.927088i
$$218$$ 3.41421 + 3.41421i 0.231240 + 0.231240i
$$219$$ 14.8284 + 10.4853i 1.00201 + 0.708530i
$$220$$ 0 0
$$221$$ 2.34315i 0.157617i
$$222$$ −5.65685 32.9706i −0.379663 2.21284i
$$223$$ −7.75736 + 7.75736i −0.519471 + 0.519471i −0.917411 0.397940i $$-0.869725\pi$$
0.397940 + 0.917411i $$0.369725\pi$$
$$224$$ 7.65685 0.511595
$$225$$ 0 0
$$226$$ −28.9706 −1.92709
$$227$$ 11.7574 11.7574i 0.780363 0.780363i −0.199529 0.979892i $$-0.563941\pi$$
0.979892 + 0.199529i $$0.0639411\pi$$
$$228$$ −5.41421 31.5563i −0.358565 2.08987i
$$229$$ 18.0000i 1.18947i −0.803921 0.594737i $$-0.797256\pi$$
0.803921 0.594737i $$-0.202744\pi$$
$$230$$ 0 0
$$231$$ −6.82843 4.82843i −0.449278 0.317687i
$$232$$ 9.89949 + 9.89949i 0.649934 + 0.649934i
$$233$$ −10.0000 10.0000i −0.655122 0.655122i 0.299100 0.954222i $$-0.403314\pi$$
−0.954222 + 0.299100i $$0.903314\pi$$
$$234$$ 2.00000 + 5.65685i 0.130744 + 0.369800i
$$235$$ 0 0
$$236$$ 52.2843i 3.40342i
$$237$$ −1.41421 + 0.242641i −0.0918630 + 0.0157612i
$$238$$ −23.3137 + 23.3137i −1.51120 + 1.51120i
$$239$$ 13.6569 0.883388 0.441694 0.897166i $$-0.354378\pi$$
0.441694 + 0.897166i $$0.354378\pi$$
$$240$$ 0 0
$$241$$ 6.97056 0.449013 0.224507 0.974473i $$-0.427923\pi$$
0.224507 + 0.974473i $$0.427923\pi$$
$$242$$ −1.70711 + 1.70711i −0.109737 + 0.109737i
$$243$$ 11.7071 + 10.2929i 0.751011 + 0.660289i
$$244$$ 22.9706i 1.47054i
$$245$$ 0 0
$$246$$ −2.00000 + 2.82843i −0.127515 + 0.180334i
$$247$$ −2.82843 2.82843i −0.179969 0.179969i
$$248$$ −12.4853 12.4853i −0.792816 0.792816i
$$249$$ −6.00000 + 8.48528i −0.380235 + 0.537733i
$$250$$ 0 0
$$251$$ 9.65685i 0.609535i 0.952427 + 0.304768i $$0.0985788\pi$$
−0.952427 + 0.304768i $$0.901421\pi$$
$$252$$ −23.8995 + 50.0416i −1.50553 + 3.15233i
$$253$$ −4.82843 + 4.82843i −0.303561 + 0.303561i
$$254$$ −6.00000 −0.376473
$$255$$ 0 0
$$256$$ −29.9706 −1.87316
$$257$$ 16.0000 16.0000i 0.998053 0.998053i −0.00194553 0.999998i $$-0.500619\pi$$
0.999998 + 0.00194553i $$0.000619281\pi$$
$$258$$ 43.2132 7.41421i 2.69034 0.461589i
$$259$$ 38.6274i 2.40019i
$$260$$ 0 0
$$261$$ 8.97056 3.17157i 0.555264 0.196315i
$$262$$ −10.8284 10.8284i −0.668982 0.668982i
$$263$$ 7.75736 + 7.75736i 0.478339 + 0.478339i 0.904600 0.426261i $$-0.140169\pi$$
−0.426261 + 0.904600i $$0.640169\pi$$
$$264$$ 6.24264 + 4.41421i 0.384208 + 0.271676i
$$265$$ 0 0
$$266$$ 56.2843i 3.45101i
$$267$$ 2.14214 + 12.4853i 0.131097 + 0.764087i
$$268$$ −20.7279 + 20.7279i −1.26616 + 1.26616i
$$269$$ −2.34315 −0.142864 −0.0714321 0.997445i $$-0.522757\pi$$
−0.0714321 + 0.997445i $$0.522757\pi$$
$$270$$ 0 0
$$271$$ −26.4853 −1.60887 −0.804433 0.594043i $$-0.797531\pi$$
−0.804433 + 0.594043i $$0.797531\pi$$
$$272$$ 6.00000 6.00000i 0.363803 0.363803i
$$273$$ 1.17157 + 6.82843i 0.0709068 + 0.413275i
$$274$$ 32.9706i 1.99182i
$$275$$ 0 0
$$276$$ 36.9706 + 26.1421i 2.22537 + 1.57357i
$$277$$ 2.92893 + 2.92893i 0.175982 + 0.175982i 0.789602 0.613619i $$-0.210287\pi$$
−0.613619 + 0.789602i $$0.710287\pi$$
$$278$$ 19.0711 + 19.0711i 1.14381 + 1.14381i
$$279$$ −11.3137 + 4.00000i −0.677334 + 0.239474i
$$280$$ 0 0
$$281$$ 20.1421i 1.20158i −0.799407 0.600790i $$-0.794853\pi$$
0.799407 0.600790i $$-0.205147\pi$$
$$282$$ 4.82843 0.828427i 0.287529 0.0493321i
$$283$$ 7.41421 7.41421i 0.440729 0.440729i −0.451528 0.892257i $$-0.649121\pi$$
0.892257 + 0.451528i $$0.149121\pi$$
$$284$$ 6.34315 0.376396
$$285$$ 0 0
$$286$$ 2.00000 0.118262
$$287$$ −2.82843 + 2.82843i −0.166957 + 0.166957i
$$288$$ −2.05025 + 4.29289i −0.120812 + 0.252961i
$$289$$ 9.00000i 0.529412i
$$290$$ 0 0
$$291$$ −13.6569 + 19.3137i −0.800579 + 1.13219i
$$292$$ −28.3848 28.3848i −1.66109 1.66109i
$$293$$ 14.4853 + 14.4853i 0.846239 + 0.846239i 0.989662 0.143422i $$-0.0458107\pi$$
−0.143422 + 0.989662i $$0.545811\pi$$
$$294$$ −39.3848 + 55.6985i −2.29697 + 3.24840i
$$295$$ 0 0
$$296$$ 35.3137i 2.05257i
$$297$$ 4.53553 2.53553i 0.263178 0.147127i
$$298$$ −37.2132 + 37.2132i −2.15570 + 2.15570i
$$299$$ 5.65685 0.327144
$$300$$ 0 0
$$301$$ 50.6274 2.91812
$$302$$ −4.24264 + 4.24264i −0.244137 + 0.244137i
$$303$$ −8.24264 + 1.41421i −0.473527 + 0.0812444i
$$304$$ 14.4853i 0.830788i
$$305$$ 0 0
$$306$$ −6.82843 19.3137i −0.390355 1.10409i
$$307$$ 6.72792 + 6.72792i 0.383983 + 0.383983i 0.872535 0.488552i $$-0.162475\pi$$
−0.488552 + 0.872535i $$0.662475\pi$$
$$308$$ 13.0711 + 13.0711i 0.744793 + 0.744793i
$$309$$ −8.48528 6.00000i −0.482711 0.341328i
$$310$$ 0 0
$$311$$ 21.6569i 1.22805i 0.789288 + 0.614024i $$0.210450\pi$$
−0.789288 + 0.614024i $$0.789550\pi$$
$$312$$ −1.07107 6.24264i −0.0606373 0.353420i
$$313$$ 13.1716 13.1716i 0.744501 0.744501i −0.228939 0.973441i $$-0.573526\pi$$
0.973441 + 0.228939i $$0.0735258\pi$$
$$314$$ 24.9706 1.40917
$$315$$ 0 0
$$316$$ 3.17157 0.178415
$$317$$ 10.1421 10.1421i 0.569639 0.569639i −0.362388 0.932027i $$-0.618039\pi$$
0.932027 + 0.362388i $$0.118039\pi$$
$$318$$ −8.48528 49.4558i −0.475831 2.77335i
$$319$$ 3.17157i 0.177574i
$$320$$ 0 0
$$321$$ −11.7990 8.34315i −0.658555 0.465669i
$$322$$ 56.2843 + 56.2843i 3.13660 + 3.13660i
$$323$$ 9.65685 + 9.65685i 0.537322 + 0.537322i
$$324$$ −21.6569 26.7990i −1.20316 1.48883i
$$325$$ 0 0
$$326$$ 33.7990i 1.87195i
$$327$$ −3.41421 + 0.585786i −0.188806 + 0.0323941i
$$328$$ 2.58579 2.58579i 0.142776 0.142776i
$$329$$ 5.65685 0.311872
$$330$$ 0 0
$$331$$ −9.65685 −0.530789 −0.265394 0.964140i $$-0.585502\pi$$
−0.265394 + 0.964140i $$0.585502\pi$$
$$332$$ 16.2426 16.2426i 0.891431 0.891431i
$$333$$ 21.6569 + 10.3431i 1.18679 + 0.566801i
$$334$$ 0.828427i 0.0453295i
$$335$$ 0 0
$$336$$ 14.4853 20.4853i 0.790237 1.11756i
$$337$$ −3.89949 3.89949i −0.212419 0.212419i 0.592875 0.805294i $$-0.297993\pi$$
−0.805294 + 0.592875i $$0.797993\pi$$
$$338$$ 21.0208 + 21.0208i 1.14338 + 1.14338i
$$339$$ 12.0000 16.9706i 0.651751 0.921714i
$$340$$ 0 0
$$341$$ 4.00000i 0.216612i
$$342$$ 31.5563 + 15.0711i 1.70637 + 0.814950i
$$343$$ −31.7990 + 31.7990i −1.71698 + 1.71698i
$$344$$ −46.2843 −2.49548
$$345$$ 0 0
$$346$$ 2.82843 0.152057
$$347$$ −16.2426 + 16.2426i −0.871951 + 0.871951i −0.992685 0.120734i $$-0.961475\pi$$
0.120734 + 0.992685i $$0.461475\pi$$
$$348$$ −20.7279 + 3.55635i −1.11113 + 0.190640i
$$349$$ 22.9706i 1.22959i −0.788688 0.614793i $$-0.789240\pi$$
0.788688 0.614793i $$-0.210760\pi$$
$$350$$ 0 0
$$351$$ −4.14214 1.17157i −0.221091 0.0625339i
$$352$$ 1.12132 + 1.12132i 0.0597666 + 0.0597666i
$$353$$ −4.48528 4.48528i −0.238727 0.238727i 0.577596 0.816323i $$-0.303991\pi$$
−0.816323 + 0.577596i $$0.803991\pi$$
$$354$$ −46.6274 32.9706i −2.47822 1.75237i
$$355$$ 0 0
$$356$$ 28.0000i 1.48400i
$$357$$ −4.00000 23.3137i −0.211702 1.23389i
$$358$$ 5.65685 5.65685i 0.298974 0.298974i
$$359$$ 16.9706 0.895672 0.447836 0.894116i $$-0.352195\pi$$
0.447836 + 0.894116i $$0.352195\pi$$
$$360$$ 0 0
$$361$$ −4.31371 −0.227037
$$362$$ −10.2426 + 10.2426i −0.538341 + 0.538341i
$$363$$ −0.292893 1.70711i −0.0153729 0.0895999i
$$364$$ 15.3137i 0.802656i
$$365$$ 0 0
$$366$$ −20.4853 14.4853i −1.07078 0.757158i
$$367$$ 16.2426 + 16.2426i 0.847859 + 0.847859i 0.989866 0.142007i $$-0.0453555\pi$$
−0.142007 + 0.989866i $$0.545355\pi$$
$$368$$ −14.4853 14.4853i −0.755097 0.755097i
$$369$$ −0.828427 2.34315i −0.0431262 0.121979i
$$370$$ 0 0
$$371$$ 57.9411i 3.00815i
$$372$$ 26.1421 4.48528i 1.35541 0.232551i
$$373$$ 3.89949 3.89949i 0.201908 0.201908i −0.598909 0.800817i $$-0.704399\pi$$
0.800817 + 0.598909i $$0.204399\pi$$
$$374$$ −6.82843 −0.353090
$$375$$ 0 0
$$376$$ −5.17157 −0.266704
$$377$$ −1.85786 + 1.85786i −0.0956849 + 0.0956849i
$$378$$ −29.5563 52.8701i −1.52021 2.71934i
$$379$$ 26.6274i 1.36776i 0.729595 + 0.683879i $$0.239709\pi$$
−0.729595 + 0.683879i $$0.760291\pi$$
$$380$$ 0 0
$$381$$ 2.48528 3.51472i 0.127325 0.180064i
$$382$$ −19.3137 19.3137i −0.988175 0.988175i
$$383$$ 13.3137 + 13.3137i 0.680299 + 0.680299i 0.960067 0.279769i $$-0.0902578\pi$$
−0.279769 + 0.960067i $$0.590258\pi$$
$$384$$ 20.5563 29.0711i 1.04901 1.48353i
$$385$$ 0 0
$$386$$ 17.3137i 0.881245i
$$387$$ −13.5563 + 28.3848i −0.689108 + 1.44288i
$$388$$ 36.9706 36.9706i 1.87690 1.87690i
$$389$$ 12.0000 0.608424 0.304212 0.952604i $$-0.401607\pi$$
0.304212 + 0.952604i $$0.401607\pi$$
$$390$$ 0 0
$$391$$ −19.3137 −0.976736
$$392$$ 50.9203 50.9203i 2.57186 2.57186i
$$393$$ 10.8284 1.85786i 0.546222 0.0937169i
$$394$$ 8.48528i 0.427482i
$$395$$ 0 0
$$396$$ −10.8284 + 3.82843i −0.544149 + 0.192386i
$$397$$ 17.1716 + 17.1716i 0.861817 + 0.861817i 0.991549 0.129732i $$-0.0414119\pi$$
−0.129732 + 0.991549i $$0.541412\pi$$
$$398$$ −35.7990 35.7990i −1.79444 1.79444i
$$399$$ 32.9706 + 23.3137i 1.65059 + 1.16715i
$$400$$ 0 0
$$401$$ 36.2843i 1.81195i −0.423331 0.905975i $$-0.639139\pi$$
0.423331 0.905975i $$-0.360861\pi$$
$$402$$ −5.41421 31.5563i −0.270036 1.57389i
$$403$$ 2.34315 2.34315i 0.116720 0.116720i
$$404$$ 18.4853 0.919677
$$405$$ 0 0
$$406$$ −36.9706 −1.83482
$$407$$ 5.65685 5.65685i 0.280400 0.280400i
$$408$$ 3.65685 + 21.3137i 0.181041 + 1.05519i
$$409$$ 27.6569i 1.36754i 0.729696 + 0.683772i $$0.239662\pi$$
−0.729696 + 0.683772i $$0.760338\pi$$
$$410$$ 0 0
$$411$$ −19.3137 13.6569i −0.952675 0.673643i
$$412$$ 16.2426 + 16.2426i 0.800217 + 0.800217i
$$413$$ −46.6274 46.6274i −2.29439 2.29439i
$$414$$ −46.6274 + 16.4853i −2.29161 + 0.810207i
$$415$$ 0 0
$$416$$ 1.31371i 0.0644099i
$$417$$ −19.0711 + 3.27208i −0.933914 + 0.160234i
$$418$$ 8.24264 8.24264i 0.403161 0.403161i
$$419$$ 12.6863 0.619766 0.309883 0.950775i $$-0.399710\pi$$
0.309883 + 0.950775i $$0.399710\pi$$
$$420$$ 0 0
$$421$$ −9.31371 −0.453922 −0.226961 0.973904i $$-0.572879\pi$$
−0.226961 + 0.973904i $$0.572879\pi$$
$$422$$ 11.0711 11.0711i 0.538931 0.538931i
$$423$$ −1.51472 + 3.17157i −0.0736481 + 0.154207i
$$424$$ 52.9706i 2.57248i
$$425$$ 0 0
$$426$$ −4.00000 + 5.65685i −0.193801 + 0.274075i
$$427$$ −20.4853 20.4853i −0.991352 0.991352i
$$428$$ 22.5858 + 22.5858i 1.09173 + 1.09173i
$$429$$ −0.828427 + 1.17157i −0.0399968 + 0.0565641i
$$430$$ 0 0
$$431$$ 5.65685i 0.272481i 0.990676 + 0.136241i $$0.0435020\pi$$
−0.990676 + 0.136241i $$0.956498\pi$$
$$432$$ 7.60660 + 13.6066i 0.365973 + 0.654648i
$$433$$ 15.3137 15.3137i 0.735930 0.735930i −0.235858 0.971788i $$-0.575790\pi$$
0.971788 + 0.235858i $$0.0757899\pi$$
$$434$$ 46.6274 2.23819
$$435$$ 0 0
$$436$$ 7.65685 0.366697
$$437$$ 23.3137 23.3137i 1.11525 1.11525i
$$438$$ 43.2132 7.41421i 2.06481 0.354265i
$$439$$ 4.14214i 0.197693i −0.995103 0.0988467i $$-0.968485\pi$$
0.995103 0.0988467i $$-0.0315153\pi$$
$$440$$ 0 0
$$441$$ −16.3137 46.1421i −0.776843 2.19724i
$$442$$ 4.00000 + 4.00000i 0.190261 + 0.190261i
$$443$$ −9.31371 9.31371i −0.442508 0.442508i 0.450346 0.892854i $$-0.351301\pi$$
−0.892854 + 0.450346i $$0.851301\pi$$
$$444$$ −43.3137 30.6274i −2.05558 1.45351i
$$445$$ 0 0
$$446$$ 26.4853i 1.25411i
$$447$$ −6.38478 37.2132i −0.301990 1.76012i
$$448$$ 33.5563 33.5563i 1.58539 1.58539i
$$449$$ −25.6569 −1.21082 −0.605411 0.795913i $$-0.706991\pi$$
−0.605411 + 0.795913i $$0.706991\pi$$
$$450$$ 0 0
$$451$$ −0.828427 −0.0390091
$$452$$ −32.4853 + 32.4853i −1.52798 + 1.52798i
$$453$$ −0.727922 4.24264i −0.0342008 0.199337i
$$454$$ 40.1421i 1.88396i
$$455$$ 0 0
$$456$$ −30.1421 21.3137i −1.41153 0.998106i
$$457$$ 16.5858 + 16.5858i 0.775850 + 0.775850i 0.979122 0.203272i $$-0.0651576\pi$$
−0.203272 + 0.979122i $$0.565158\pi$$
$$458$$ −30.7279 30.7279i −1.43582 1.43582i
$$459$$ 14.1421 + 4.00000i 0.660098 + 0.186704i
$$460$$ 0 0
$$461$$ 28.8284i 1.34267i 0.741152 + 0.671337i $$0.234280\pi$$
−0.741152 + 0.671337i $$0.765720\pi$$
$$462$$ −19.8995 + 3.41421i −0.925808 + 0.158844i
$$463$$ 14.3848 14.3848i 0.668517 0.668517i −0.288855 0.957373i $$-0.593275\pi$$
0.957373 + 0.288855i $$0.0932747\pi$$
$$464$$ 9.51472 0.441710
$$465$$ 0 0
$$466$$ −34.1421 −1.58160
$$467$$ −7.17157 + 7.17157i −0.331861 + 0.331861i −0.853293 0.521432i $$-0.825398\pi$$
0.521432 + 0.853293i $$0.325398\pi$$
$$468$$ 8.58579 + 4.10051i 0.396878 + 0.189546i
$$469$$ 36.9706i 1.70714i
$$470$$ 0 0
$$471$$ −10.3431 + 14.6274i −0.476587 + 0.673996i
$$472$$ 42.6274 + 42.6274i 1.96209 + 1.96209i
$$473$$ 7.41421 + 7.41421i 0.340906 + 0.340906i
$$474$$ −2.00000 + 2.82843i −0.0918630 + 0.129914i
$$475$$ 0 0
$$476$$ 52.2843i 2.39645i
$$477$$ 32.4853 + 15.5147i 1.48740 + 0.710370i
$$478$$ 23.3137 23.3137i 1.06634 1.06634i
$$479$$ −37.6569 −1.72059 −0.860293 0.509800i $$-0.829719\pi$$
−0.860293 + 0.509800i $$0.829719\pi$$
$$480$$ 0 0
$$481$$ −6.62742 −0.302184
$$482$$ 11.8995 11.8995i 0.542007 0.542007i
$$483$$ −56.2843 + 9.65685i −2.56102 + 0.439402i
$$484$$ 3.82843i 0.174019i
$$485$$ 0 0
$$486$$ 37.5563 2.41421i 1.70359 0.109511i
$$487$$ −13.4142 13.4142i −0.607856 0.607856i 0.334529 0.942385i $$-0.391423\pi$$
−0.942385 + 0.334529i $$0.891423\pi$$
$$488$$ 18.7279 + 18.7279i 0.847773 + 0.847773i
$$489$$ 19.7990 + 14.0000i 0.895341 + 0.633102i
$$490$$ 0 0
$$491$$ 26.6274i 1.20168i 0.799370 + 0.600839i $$0.205167\pi$$
−0.799370 + 0.600839i $$0.794833\pi$$
$$492$$ 0.928932 + 5.41421i 0.0418795 + 0.244092i
$$493$$ 6.34315 6.34315i 0.285681 0.285681i
$$494$$ −9.65685 −0.434482
$$495$$ 0 0
$$496$$ −12.0000 −0.538816
$$497$$ −5.65685 + 5.65685i −0.253745 + 0.253745i
$$498$$ 4.24264 + 24.7279i 0.190117 + 1.10808i
$$499$$ 13.6569i 0.611365i 0.952134 + 0.305682i $$0.0988846\pi$$
−0.952134 + 0.305682i $$0.901115\pi$$
$$500$$ 0 0
$$501$$ −0.485281 0.343146i −0.0216808 0.0153306i
$$502$$ 16.4853 + 16.4853i 0.735774 + 0.735774i
$$503$$ 10.3848 + 10.3848i 0.463034 + 0.463034i 0.899649 0.436614i $$-0.143823\pi$$
−0.436614 + 0.899649i $$0.643823\pi$$
$$504$$ 21.3137 + 60.2843i 0.949388 + 2.68527i
$$505$$ 0 0
$$506$$ 16.4853i 0.732860i
$$507$$ −21.0208 + 3.60660i −0.933567 + 0.160175i
$$508$$ −6.72792 + 6.72792i −0.298503 + 0.298503i
$$509$$ 12.6863 0.562310 0.281155 0.959662i $$-0.409282\pi$$
0.281155 + 0.959662i $$0.409282\pi$$
$$510$$ 0 0
$$511$$ 50.6274 2.23963
$$512$$ −22.0919 + 22.0919i −0.976333 + 0.976333i
$$513$$ −21.8995 + 12.2426i −0.966886 + 0.540526i
$$514$$ 54.6274i 2.40951i
$$515$$ 0 0
$$516$$ 40.1421 56.7696i 1.76716 2.49914i
$$517$$ 0.828427 + 0.828427i 0.0364342 + 0.0364342i
$$518$$ −65.9411 65.9411i −2.89729 2.89729i
$$519$$ −1.17157 + 1.65685i −0.0514263 + 0.0727278i
$$520$$ 0 0
$$521$$ 7.02944i 0.307965i 0.988074 + 0.153983i $$0.0492100\pi$$
−0.988074 + 0.153983i $$0.950790\pi$$
$$522$$ 9.89949 20.7279i 0.433289 0.907237i
$$523$$ −17.0711 + 17.0711i −0.746466 + 0.746466i −0.973814 0.227348i $$-0.926995\pi$$
0.227348 + 0.973814i $$0.426995\pi$$
$$524$$ −24.2843 −1.06086
$$525$$ 0 0
$$526$$ 26.4853 1.15481
$$527$$ −8.00000 + 8.00000i −0.348485 + 0.348485i
$$528$$ 5.12132 0.878680i 0.222877 0.0382396i
$$529$$ 23.6274i 1.02728i
$$530$$ 0 0
$$531$$ 38.6274 13.6569i 1.67629 0.592657i
$$532$$ −63.1127 63.1127i −2.73628 2.73628i
$$533$$ 0.485281 + 0.485281i 0.0210199 + 0.0210199i
$$534$$ 24.9706 + 17.6569i 1.08058 + 0.764087i
$$535$$ 0 0
$$536$$ 33.7990i 1.45989i
$$537$$ 0.970563 + 5.65685i 0.0418829 + 0.244111i
$$538$$ −4.00000 + 4.00000i −0.172452 + 0.172452i
$$539$$ −16.3137 −0.702681
$$540$$ 0 0
$$541$$ −1.02944 −0.0442590 −0.0221295 0.999755i $$-0.507045\pi$$
−0.0221295 + 0.999755i $$0.507045\pi$$
$$542$$ −45.2132 + 45.2132i −1.94207 + 1.94207i
$$543$$ −1.75736 10.2426i −0.0754155 0.439554i
$$544$$ 4.48528i 0.192305i
$$545$$ 0 0
$$546$$ 13.6569 + 9.65685i 0.584459 + 0.413275i
$$547$$ −18.7279 18.7279i −0.800748 0.800748i 0.182464 0.983212i $$-0.441593\pi$$
−0.983212 + 0.182464i $$0.941593\pi$$
$$548$$ 36.9706 + 36.9706i 1.57930 + 1.57930i
$$549$$ 16.9706 6.00000i 0.724286 0.256074i
$$550$$ 0 0
$$551$$ 15.3137i 0.652386i
$$552$$ 51.4558 8.82843i 2.19011 0.375763i
$$553$$ −2.82843 + 2.82843i −0.120277 + 0.120277i
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ 42.7696 1.81383
$$557$$ −31.4558 + 31.4558i −1.33283 + 1.33283i −0.429996 + 0.902831i $$0.641485\pi$$
−0.902831 + 0.429996i $$0.858515\pi$$
$$558$$ −12.4853 + 26.1421i −0.528544 + 1.10668i
$$559$$ 8.68629i 0.367391i
$$560$$ 0 0
$$561$$ 2.82843 4.00000i 0.119416 0.168880i
$$562$$ −34.3848 34.3848i −1.45043 1.45043i
$$563$$ 8.24264 + 8.24264i 0.347386 + 0.347386i 0.859135 0.511749i $$-0.171002\pi$$
−0.511749 + 0.859135i $$0.671002\pi$$
$$564$$ 4.48528 6.34315i 0.188864 0.267095i
$$565$$ 0 0
$$566$$ 25.3137i 1.06401i
$$567$$ 43.2132 + 4.58579i 1.81478 + 0.192585i
$$568$$ 5.17157 5.17157i 0.216994 0.216994i
$$569$$ −7.17157 −0.300648 −0.150324 0.988637i $$-0.548032\pi$$
−0.150324 + 0.988637i $$0.548032\pi$$
$$570$$ 0 0
$$571$$ −38.4853 −1.61056 −0.805279 0.592895i $$-0.797985\pi$$
−0.805279 + 0.592895i $$0.797985\pi$$
$$572$$ 2.24264 2.24264i 0.0937695 0.0937695i
$$573$$ 19.3137 3.31371i 0.806842 0.138432i
$$574$$ 9.65685i 0.403069i
$$575$$ 0 0
$$576$$ 9.82843 + 27.7990i 0.409518 + 1.15829i
$$577$$ 20.4853 + 20.4853i 0.852813 + 0.852813i 0.990479 0.137665i $$-0.0439599\pi$$
−0.137665 + 0.990479i $$0.543960\pi$$
$$578$$ 15.3640 + 15.3640i 0.639057 + 0.639057i
$$579$$ −10.1421 7.17157i −0.421493 0.298040i
$$580$$ 0 0
$$581$$ 28.9706i 1.20190i
$$582$$ 9.65685 + 56.2843i 0.400289 + 2.33306i
$$583$$ 8.48528 8.48528i 0.351424 0.351424i
$$584$$ −46.2843 −1.91526
$$585$$ 0 0
$$586$$ 49.4558 2.04300
$$587$$ 5.51472 5.51472i 0.227617 0.227617i −0.584080 0.811696i $$-0.698544\pi$$
0.811696 + 0.584080i $$0.198544\pi$$
$$588$$ 18.2929 + 106.619i 0.754386 + 4.39689i
$$589$$ 19.3137i 0.795807i
$$590$$ 0 0
$$591$$ 4.97056 + 3.51472i 0.204462 + 0.144576i
$$592$$ 16.9706 + 16.9706i 0.697486 + 0.697486i
$$593$$ 8.34315 + 8.34315i 0.342612 + 0.342612i 0.857348 0.514737i $$-0.172110\pi$$
−0.514737 + 0.857348i $$0.672110\pi$$
$$594$$ 3.41421 12.0711i 0.140087 0.495282i
$$595$$ 0 0
$$596$$ 83.4558i 3.41848i
$$597$$ 35.7990 6.14214i 1.46516 0.251381i
$$598$$ 9.65685 9.65685i 0.394898 0.394898i
$$599$$ 0.686292 0.0280411 0.0140206 0.999902i $$-0.495537\pi$$
0.0140206 + 0.999902i $$0.495537\pi$$
$$600$$ 0 0
$$601$$ −10.9706 −0.447499 −0.223749 0.974647i $$-0.571830\pi$$
−0.223749 + 0.974647i $$0.571830\pi$$
$$602$$ 86.4264 86.4264i 3.52248 3.52248i
$$603$$ 20.7279 + 9.89949i 0.844106 + 0.403139i
$$604$$ 9.51472i 0.387148i
$$605$$ 0 0
$$606$$ −11.6569 + 16.4853i −0.473527 + 0.669669i
$$607$$ −27.8995 27.8995i −1.13241 1.13241i −0.989776 0.142629i $$-0.954444\pi$$
−0.142629 0.989776i $$-0.545556\pi$$
$$608$$ −5.41421 5.41421i −0.219575 0.219575i
$$609$$ 15.3137 21.6569i 0.620543 0.877580i
$$610$$ 0 0
$$611$$ 0.970563i 0.0392648i
$$612$$ −29.3137 14.0000i −1.18494 0.565916i
$$613$$ −30.0416 + 30.0416i −1.21337 + 1.21337i −0.243459 + 0.969911i $$0.578282\pi$$
−0.969911 + 0.243459i $$0.921718\pi$$
$$614$$ 22.9706 0.927016
$$615$$ 0 0
$$616$$ 21.3137 0.858754
$$617$$ 24.4853 24.4853i 0.985740 0.985740i −0.0141594 0.999900i $$-0.504507\pi$$
0.999900 + 0.0141594i $$0.00450724\pi$$
$$618$$ −24.7279 + 4.24264i −0.994703 + 0.170664i
$$619$$ 28.9706i 1.16443i 0.813037 + 0.582213i $$0.197813\pi$$
−0.813037 + 0.582213i $$0.802187\pi$$
$$620$$ 0 0
$$621$$ 9.65685 34.1421i 0.387516 1.37008i
$$622$$ 36.9706 + 36.9706i 1.48238 + 1.48238i
$$623$$ 24.9706 + 24.9706i 1.00042 + 1.00042i
$$624$$ −3.51472 2.48528i −0.140701 0.0994909i
$$625$$ 0 0
$$626$$ 44.9706i 1.79739i
$$627$$ 1.41421 + 8.24264i 0.0564782 + 0.329179i
$$628$$ 28.0000 28.0000i 1.11732 1.11732i
$$629$$ 22.6274 0.902214
$$630$$ 0 0
$$631$$ −9.65685 −0.384433 −0.192217 0.981353i $$-0.561568\pi$$
−0.192217 + 0.981353i $$0.561568\pi$$
$$632$$ 2.58579 2.58579i 0.102857 0.102857i
$$633$$ 1.89949 + 11.0711i 0.0754981 + 0.440035i
$$634$$ 34.6274i 1.37523i
$$635$$ 0 0
$$636$$ −64.9706 45.9411i −2.57625 1.82168i
$$637$$ 9.55635 + 9.55635i 0.378636 + 0.378636i
$$638$$ −5.41421 5.41421i −0.214351 0.214351i
$$639$$ −1.65685 4.68629i −0.0655441 0.185387i
$$640$$ 0 0
$$641$$ 17.6569i 0.697404i −0.937234 0.348702i $$-0.886623\pi$$
0.937234 0.348702i $$-0.113377\pi$$
$$642$$ −34.3848 + 5.89949i −1.35706 + 0.232834i
$$643$$ −1.41421 + 1.41421i −0.0557711 + 0.0557711i −0.734442 0.678671i $$-0.762556\pi$$
0.678671 + 0.734442i $$0.262556\pi$$
$$644$$ 126.225 4.97398
$$645$$ 0 0
$$646$$ 32.9706 1.29721
$$647$$ −6.00000 + 6.00000i −0.235884 + 0.235884i −0.815143 0.579259i $$-0.803342\pi$$
0.579259 + 0.815143i $$0.303342\pi$$
$$648$$ −39.5061 4.19239i −1.55195 0.164693i
$$649$$ 13.6569i 0.536078i
$$650$$ 0 0
$$651$$ −19.3137 + 27.3137i −0.756964 + 1.07051i
$$652$$ −37.8995 37.8995i −1.48426 1.48426i
$$653$$ −4.00000 4.00000i −0.156532 0.156532i 0.624496 0.781028i $$-0.285304\pi$$
−0.781028 + 0.624496i $$0.785304\pi$$
$$654$$ −4.82843 + 6.82843i −0.188806 + 0.267013i
$$655$$ 0 0
$$656$$ 2.48528i 0.0970339i
$$657$$ −13.5563 + 28.3848i −0.528884 + 1.10740i
$$658$$ 9.65685 9.65685i 0.376463 0.376463i
$$659$$ −41.6569 −1.62272 −0.811360 0.584546i $$-0.801273\pi$$
−0.811360 + 0.584546i $$0.801273\pi$$
$$660$$ 0 0
$$661$$ 0.627417 0.0244037 0.0122018 0.999926i $$-0.496116\pi$$
0.0122018 + 0.999926i $$0.496116\pi$$
$$662$$ −16.4853 + 16.4853i −0.640719 + 0.640719i
$$663$$ −4.00000 + 0.686292i −0.155347 + 0.0266534i
$$664$$ 26.4853i 1.02783i
$$665$$ 0 0
$$666$$ 54.6274 19.3137i 2.11677 0.748391i
$$667$$ −15.3137 15.3137i −0.592949 0.592949i
$$668$$ 0.928932 + 0.928932i 0.0359415 + 0.0359415i
$$669$$ −15.5147 10.9706i −0.599834 0.424146i
$$670$$ 0 0
$$671$$ 6.00000i 0.231627i
$$672$$ 2.24264 + 13.0711i 0.0865117 + 0.504227i
$$673$$ −5.27208 + 5.27208i −0.203224 + 0.203224i −0.801380 0.598156i $$-0.795900\pi$$
0.598156 + 0.801380i $$0.295900\pi$$
$$674$$ −13.3137 −0.512825
$$675$$ 0 0
$$676$$ 47.1421 1.81316
$$677$$ 2.48528 2.48528i 0.0955171 0.0955171i −0.657734 0.753251i $$-0.728485\pi$$
0.753251 + 0.657734i $$0.228485\pi$$
$$678$$ −8.48528 49.4558i −0.325875 1.89934i
$$679$$ 65.9411i 2.53059i
$$680$$ 0 0
$$681$$ 23.5147 + 16.6274i 0.901086 + 0.637164i
$$682$$ 6.82843 + 6.82843i 0.261474 + 0.261474i
$$683$$ −6.48528 6.48528i −0.248152 0.248152i 0.572060 0.820212i $$-0.306145\pi$$
−0.820212 + 0.572060i $$0.806145\pi$$
$$684$$ 52.2843 18.4853i 1.99914 0.706802i
$$685$$ 0 0
$$686$$ 108.569i 4.14517i
$$687$$ 30.7279 5.27208i 1.17234 0.201142i
$$688$$ −22.2426 + 22.2426i −0.847993 + 0.847993i
$$689$$ −9.94113 −0.378727
$$690$$ 0 0
$$691$$ −37.9411 −1.44335 −0.721674 0.692233i $$-0.756627\pi$$
−0.721674 + 0.692233i $$0.756627\pi$$
$$692$$ 3.17157 3.17157i 0.120565 0.120565i
$$693$$ 6.24264 13.0711i 0.237138 0.496529i
$$694$$ 55.4558i 2.10508i
$$695$$ 0 0
$$696$$ −14.0000 + 19.7990i −0.530669 + 0.750479i
$$697$$ −1.65685 1.65685i −0.0627578 0.0627578i
$$698$$ −39.2132 39.2132i −1.48424 1.48424i
$$699$$ 14.1421 20.0000i 0.534905 0.756469i
$$700$$ 0 0
$$701$$ 50.4853i 1.90680i 0.301705 + 0.953401i $$0.402444\pi$$
−0.301705 + 0.953401i $$0.597556\pi$$
$$702$$ −9.07107 + 5.07107i −0.342365 + 0.191395i
$$703$$ −27.3137 + 27.3137i −1.03016 + 1.03016i
$$704$$ 9.82843 0.370423
$$705$$ 0 0
$$706$$ −15.3137 −0.576339
$$707$$ −16.4853 + 16.4853i −0.619993 + 0.619993i
$$708$$ −89.2548 + 15.3137i −3.35440 + 0.575524i
$$709$$ 10.0000i 0.375558i 0.982211 + 0.187779i $$0.0601289\pi$$
−0.982211 + 0.187779i $$0.939871\pi$$
$$710$$ 0 0
$$711$$ −0.828427 2.34315i −0.0310684 0.0878748i
$$712$$ −22.8284 22.8284i −0.855531 0.855531i
$$713$$ 19.3137 + 19.3137i 0.723304 + 0.723304i
$$714$$ −46.6274 32.9706i −1.74499 1.23389i
$$715$$ 0 0
$$716$$ 12.6863i 0.474109i
$$717$$ 4.00000 + 23.3137i 0.149383 + 0.870666i
$$718$$ 28.9706 28.9706i 1.08117 1.08117i
$$719$$ −27.3137 −1.01863 −0.509315 0.860580i $$-0.670101\pi$$
−0.509315 + 0.860580i $$0.670101\pi$$
$$720$$ 0 0
$$721$$ −28.9706 −1.07892
$$722$$ −7.36396 + 7.36396i −0.274058 + 0.274058i
$$723$$ 2.04163 + 11.8995i 0.0759291 + 0.442547i
$$724$$ 22.9706i 0.853694i
$$725$$ 0 0
$$726$$ −3.41421 2.41421i −0.126713 0.0895999i
$$727$$ 9.89949 + 9.89949i 0.367152 + 0.367152i 0.866437 0.499286i $$-0.166404\pi$$
−0.499286 + 0.866437i $$0.666404\pi$$
$$728$$ −12.4853 12.4853i −0.462735 0.462735i
$$729$$ −14.1421 + 23.0000i −0.523783 + 0.851852i
$$730$$ 0 0
$$731$$ 29.6569i 1.09690i
$$732$$ −39.2132 + 6.72792i −1.44936 + 0.248671i
$$733$$ 11.8995 11.8995i 0.439518 0.439518i −0.452332 0.891850i $$-0.649408\pi$$
0.891850 + 0.452332i $$0.149408\pi$$
$$734$$ 55.4558 2.04691
$$735$$ 0 0
$$736$$ 10.8284 0.399141
$$737$$ 5.41421 5.41421i 0.199435 0.199435i
$$738$$ −5.41421 2.58579i −0.199300 0.0951841i
$$739$$ 22.4853i 0.827134i −0.910474 0.413567i $$-0.864283\pi$$
0.910474 0.413567i $$-0.135717\pi$$
$$740$$ 0 0
$$741$$ 4.00000 5.65685i 0.146944 0.207810i
$$742$$ −98.9117 98.9117i −3.63116 3.63116i
$$743$$ 8.72792 + 8.72792i 0.320196 + 0.320196i 0.848842 0.528646i $$-0.177300\pi$$
−0.528646 + 0.848842i $$0.677300\pi$$
$$744$$ 17.6569 24.9706i 0.647332 0.915465i
$$745$$ 0 0
$$746$$ 13.3137i 0.487450i
$$747$$ −16.2426 7.75736i −0.594287 0.283827i
$$748$$ −7.65685 + 7.65685i −0.279962 + 0.279962i
$$749$$ −40.2843 −1.47196
$$750$$ 0 0
$$751$$ 24.2843 0.886146 0.443073 0.896486i $$-0.353888\pi$$
0.443073 + 0.896486i $$0.353888\pi$$
$$752$$ −2.48528 + 2.48528i −0.0906289 + 0.0906289i
$$753$$ −16.4853 + 2.82843i −0.600757 + 0.103074i
$$754$$ 6.34315i 0.231004i
$$755$$ 0 0
$$756$$ −92.4264 26.1421i −3.36152 0.950780i
$$757$$ 23.3137 + 23.3137i 0.847351 + 0.847351i 0.989802 0.142451i $$-0.0454983\pi$$
−0.142451 + 0.989802i $$0.545498\pi$$
$$758$$ 45.4558 + 45.4558i 1.65103 + 1.65103i
$$759$$ −9.65685 6.82843i −0.350522 0.247856i
$$760$$ 0 0
$$761$$ 25.7990i 0.935213i 0.883937 + 0.467606i $$0.154883\pi$$
−0.883937 + 0.467606i $$0.845117\pi$$
$$762$$ −1.75736 10.2426i −0.0636624 0.371052i
$$763$$ −6.82843 + 6.82843i −0.247206 + 0.247206i
$$764$$ −43.3137 −1.56703
$$765$$ 0 0
$$766$$ 45.4558 1.64239
$$767$$ −8.00000 + 8.00000i −0.288863 + 0.288863i
$$768$$ −8.77817 51.1630i −0.316755 1.84618i
$$769$$ 21.3137i 0.768592i −0.923210 0.384296i $$-0.874444\pi$$
0.923210 0.384296i $$-0.125556\pi$$
$$770$$ 0 0
$$771$$ 32.0000 + 22.6274i 1.15245 + 0.814907i
$$772$$ 19.4142 + 19.4142i 0.698733 + 0.698733i
$$773$$ 28.9706 + 28.9706i 1.04200 + 1.04200i 0.999079 + 0.0429202i $$0.0136661\pi$$
0.0429202 + 0.999079i $$0.486334\pi$$
$$774$$ 25.3137 + 71.5980i 0.909882 + 2.57354i
$$775$$ 0 0
$$776$$ 60.2843i 2.16408i
$$777$$ 65.9411 11.3137i 2.36562 0.405877i
$$778$$ 20.4853 20.4853i 0.734433 0.734433i
$$779$$ 4.00000 0.143315
$$780$$ 0 0
$$781$$ −1.65685 −0.0592869
$$782$$ −32.9706 + 32.9706i −1.17902 + 1.17902i
$$783$$ 8.04163 + 14.3848i 0.287384 + 0.514070i
$$784$$