# Properties

 Label 825.2.k.c.518.2 Level $825$ Weight $2$ Character 825.518 Analytic conductor $6.588$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 165) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 518.2 Root $$0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 825.518 Dual form 825.2.k.c.782.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.292893 - 0.292893i) q^{2} +(-1.41421 + 1.00000i) q^{3} -1.82843i q^{4} +(0.707107 + 0.121320i) q^{6} +(3.41421 - 3.41421i) q^{7} +(-1.12132 + 1.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$$ $$q+(-0.292893 - 0.292893i) q^{2} +(-1.41421 + 1.00000i) q^{3} -1.82843i q^{4} +(0.707107 + 0.121320i) q^{6} +(3.41421 - 3.41421i) q^{7} +(-1.12132 + 1.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} -1.00000i q^{11} +(1.82843 + 2.58579i) q^{12} +(2.00000 + 2.00000i) q^{13} -2.00000 q^{14} -3.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} +(-1.12132 + 0.535534i) q^{18} +2.82843i q^{19} +(-1.41421 + 8.24264i) q^{21} +(-0.292893 + 0.292893i) q^{22} +(3.24264 - 3.24264i) q^{23} +(0.464466 - 2.70711i) q^{24} -1.17157i q^{26} +(1.41421 + 5.00000i) q^{27} +(-6.24264 - 6.24264i) q^{28} -0.828427 q^{29} -3.17157 q^{31} +(3.12132 + 3.12132i) q^{32} +(1.00000 + 1.41421i) q^{33} +1.65685i q^{34} +(-5.17157 - 1.82843i) q^{36} +(0.171573 - 0.171573i) q^{37} +(0.828427 - 0.828427i) q^{38} +(-4.82843 - 0.828427i) q^{39} -7.65685i q^{41} +(2.82843 - 2.00000i) q^{42} +(-0.242641 - 0.242641i) q^{43} -1.82843 q^{44} -1.89949 q^{46} +(-7.24264 - 7.24264i) q^{47} +(4.24264 - 3.00000i) q^{48} -16.3137i q^{49} +(6.82843 + 1.17157i) q^{51} +(3.65685 - 3.65685i) q^{52} +(1.00000 - 1.00000i) q^{53} +(1.05025 - 1.87868i) q^{54} +7.65685i q^{56} +(-2.82843 - 4.00000i) q^{57} +(0.242641 + 0.242641i) q^{58} +4.00000 q^{59} -6.48528 q^{61} +(0.928932 + 0.928932i) q^{62} +(-6.24264 - 13.0711i) q^{63} +4.17157i q^{64} +(0.121320 - 0.707107i) q^{66} +(6.41421 - 6.41421i) q^{67} +(-5.17157 + 5.17157i) q^{68} +(-1.34315 + 7.82843i) q^{69} -2.48528i q^{71} +(2.05025 + 4.29289i) q^{72} -0.100505 q^{74} +5.17157 q^{76} +(-3.41421 - 3.41421i) q^{77} +(1.17157 + 1.65685i) q^{78} -10.8284i q^{79} +(-7.00000 - 5.65685i) q^{81} +(-2.24264 + 2.24264i) q^{82} +(-9.07107 + 9.07107i) q^{83} +(15.0711 + 2.58579i) q^{84} +0.142136i q^{86} +(1.17157 - 0.828427i) q^{87} +(1.12132 + 1.12132i) q^{88} +9.65685 q^{89} +13.6569 q^{91} +(-5.92893 - 5.92893i) q^{92} +(4.48528 - 3.17157i) q^{93} +4.24264i q^{94} +(-7.53553 - 1.29289i) q^{96} +(-10.6569 + 10.6569i) q^{97} +(-4.77817 + 4.77817i) q^{98} +(-2.82843 - 1.00000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9} + O(q^{10})$$ $$4 q - 4 q^{2} + 8 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 4 q^{18} - 4 q^{22} - 4 q^{23} + 16 q^{24} - 8 q^{28} + 8 q^{29} - 24 q^{31} + 4 q^{32} + 4 q^{33} - 32 q^{36} + 12 q^{37} - 8 q^{38} - 8 q^{39} + 16 q^{43} + 4 q^{44} + 32 q^{46} - 12 q^{47} + 16 q^{51} - 8 q^{52} + 4 q^{53} + 24 q^{54} - 16 q^{58} + 16 q^{59} + 8 q^{61} + 32 q^{62} - 8 q^{63} - 8 q^{66} + 20 q^{67} - 32 q^{68} - 28 q^{69} + 28 q^{72} - 40 q^{74} + 32 q^{76} - 8 q^{77} + 16 q^{78} - 28 q^{81} + 8 q^{82} - 8 q^{83} + 32 q^{84} + 16 q^{87} - 4 q^{88} + 16 q^{89} + 32 q^{91} - 52 q^{92} - 16 q^{93} - 16 q^{96} - 20 q^{97} + 12 q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$376$$ $$551$$ $$727$$ $$\chi(n)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.292893 0.292893i −0.207107 0.207107i 0.595930 0.803037i $$-0.296784\pi$$
−0.803037 + 0.595930i $$0.796784\pi$$
$$3$$ −1.41421 + 1.00000i −0.816497 + 0.577350i
$$4$$ 1.82843i 0.914214i
$$5$$ 0 0
$$6$$ 0.707107 + 0.121320i 0.288675 + 0.0495288i
$$7$$ 3.41421 3.41421i 1.29045 1.29045i 0.355944 0.934507i $$-0.384159\pi$$
0.934507 0.355944i $$-0.115841\pi$$
$$8$$ −1.12132 + 1.12132i −0.396447 + 0.396447i
$$9$$ 1.00000 2.82843i 0.333333 0.942809i
$$10$$ 0 0
$$11$$ 1.00000i 0.301511i
$$12$$ 1.82843 + 2.58579i 0.527821 + 0.746452i
$$13$$ 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i $$-0.121703\pi$$
−0.373094 + 0.927794i $$0.621703\pi$$
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ −3.00000 −0.750000
$$17$$ −2.82843 2.82843i −0.685994 0.685994i 0.275350 0.961344i $$-0.411206\pi$$
−0.961344 + 0.275350i $$0.911206\pi$$
$$18$$ −1.12132 + 0.535534i −0.264298 + 0.126227i
$$19$$ 2.82843i 0.648886i 0.945905 + 0.324443i $$0.105177\pi$$
−0.945905 + 0.324443i $$0.894823\pi$$
$$20$$ 0 0
$$21$$ −1.41421 + 8.24264i −0.308607 + 1.79869i
$$22$$ −0.292893 + 0.292893i −0.0624450 + 0.0624450i
$$23$$ 3.24264 3.24264i 0.676137 0.676137i −0.282987 0.959124i $$-0.591325\pi$$
0.959124 + 0.282987i $$0.0913252\pi$$
$$24$$ 0.464466 2.70711i 0.0948087 0.552586i
$$25$$ 0 0
$$26$$ 1.17157i 0.229764i
$$27$$ 1.41421 + 5.00000i 0.272166 + 0.962250i
$$28$$ −6.24264 6.24264i −1.17975 1.17975i
$$29$$ −0.828427 −0.153835 −0.0769175 0.997037i $$-0.524508\pi$$
−0.0769175 + 0.997037i $$0.524508\pi$$
$$30$$ 0 0
$$31$$ −3.17157 −0.569631 −0.284816 0.958582i $$-0.591932\pi$$
−0.284816 + 0.958582i $$0.591932\pi$$
$$32$$ 3.12132 + 3.12132i 0.551777 + 0.551777i
$$33$$ 1.00000 + 1.41421i 0.174078 + 0.246183i
$$34$$ 1.65685i 0.284148i
$$35$$ 0 0
$$36$$ −5.17157 1.82843i −0.861929 0.304738i
$$37$$ 0.171573 0.171573i 0.0282064 0.0282064i −0.692863 0.721069i $$-0.743651\pi$$
0.721069 + 0.692863i $$0.243651\pi$$
$$38$$ 0.828427 0.828427i 0.134389 0.134389i
$$39$$ −4.82843 0.828427i −0.773167 0.132655i
$$40$$ 0 0
$$41$$ 7.65685i 1.19580i −0.801571 0.597900i $$-0.796002\pi$$
0.801571 0.597900i $$-0.203998\pi$$
$$42$$ 2.82843 2.00000i 0.436436 0.308607i
$$43$$ −0.242641 0.242641i −0.0370024 0.0370024i 0.688364 0.725366i $$-0.258329\pi$$
−0.725366 + 0.688364i $$0.758329\pi$$
$$44$$ −1.82843 −0.275646
$$45$$ 0 0
$$46$$ −1.89949 −0.280065
$$47$$ −7.24264 7.24264i −1.05645 1.05645i −0.998308 0.0581392i $$-0.981483\pi$$
−0.0581392 0.998308i $$-0.518517\pi$$
$$48$$ 4.24264 3.00000i 0.612372 0.433013i
$$49$$ 16.3137i 2.33053i
$$50$$ 0 0
$$51$$ 6.82843 + 1.17157i 0.956171 + 0.164053i
$$52$$ 3.65685 3.65685i 0.507114 0.507114i
$$53$$ 1.00000 1.00000i 0.137361 0.137361i −0.635083 0.772444i $$-0.719034\pi$$
0.772444 + 0.635083i $$0.219034\pi$$
$$54$$ 1.05025 1.87868i 0.142921 0.255656i
$$55$$ 0 0
$$56$$ 7.65685i 1.02319i
$$57$$ −2.82843 4.00000i −0.374634 0.529813i
$$58$$ 0.242641 + 0.242641i 0.0318603 + 0.0318603i
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −6.48528 −0.830355 −0.415178 0.909740i $$-0.636281\pi$$
−0.415178 + 0.909740i $$0.636281\pi$$
$$62$$ 0.928932 + 0.928932i 0.117975 + 0.117975i
$$63$$ −6.24264 13.0711i −0.786499 1.64680i
$$64$$ 4.17157i 0.521447i
$$65$$ 0 0
$$66$$ 0.121320 0.707107i 0.0149335 0.0870388i
$$67$$ 6.41421 6.41421i 0.783621 0.783621i −0.196819 0.980440i $$-0.563061\pi$$
0.980440 + 0.196819i $$0.0630611\pi$$
$$68$$ −5.17157 + 5.17157i −0.627145 + 0.627145i
$$69$$ −1.34315 + 7.82843i −0.161696 + 0.942432i
$$70$$ 0 0
$$71$$ 2.48528i 0.294949i −0.989066 0.147474i $$-0.952886\pi$$
0.989066 0.147474i $$-0.0471144\pi$$
$$72$$ 2.05025 + 4.29289i 0.241625 + 0.505922i
$$73$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$74$$ −0.100505 −0.0116835
$$75$$ 0 0
$$76$$ 5.17157 0.593220
$$77$$ −3.41421 3.41421i −0.389086 0.389086i
$$78$$ 1.17157 + 1.65685i 0.132655 + 0.187602i
$$79$$ 10.8284i 1.21829i −0.793058 0.609147i $$-0.791512\pi$$
0.793058 0.609147i $$-0.208488\pi$$
$$80$$ 0 0
$$81$$ −7.00000 5.65685i −0.777778 0.628539i
$$82$$ −2.24264 + 2.24264i −0.247658 + 0.247658i
$$83$$ −9.07107 + 9.07107i −0.995679 + 0.995679i −0.999991 0.00431166i $$-0.998628\pi$$
0.00431166 + 0.999991i $$0.498628\pi$$
$$84$$ 15.0711 + 2.58579i 1.64439 + 0.282132i
$$85$$ 0 0
$$86$$ 0.142136i 0.0153269i
$$87$$ 1.17157 0.828427i 0.125606 0.0888167i
$$88$$ 1.12132 + 1.12132i 0.119533 + 0.119533i
$$89$$ 9.65685 1.02362 0.511812 0.859097i $$-0.328974\pi$$
0.511812 + 0.859097i $$0.328974\pi$$
$$90$$ 0 0
$$91$$ 13.6569 1.43163
$$92$$ −5.92893 5.92893i −0.618134 0.618134i
$$93$$ 4.48528 3.17157i 0.465102 0.328877i
$$94$$ 4.24264i 0.437595i
$$95$$ 0 0
$$96$$ −7.53553 1.29289i −0.769092 0.131955i
$$97$$ −10.6569 + 10.6569i −1.08204 + 1.08204i −0.0857204 + 0.996319i $$0.527319\pi$$
−0.996319 + 0.0857204i $$0.972681\pi$$
$$98$$ −4.77817 + 4.77817i −0.482669 + 0.482669i
$$99$$ −2.82843 1.00000i −0.284268 0.100504i
$$100$$ 0 0
$$101$$ 7.17157i 0.713598i −0.934181 0.356799i $$-0.883868\pi$$
0.934181 0.356799i $$-0.116132\pi$$
$$102$$ −1.65685 2.34315i −0.164053 0.232006i
$$103$$ 6.41421 + 6.41421i 0.632011 + 0.632011i 0.948572 0.316561i $$-0.102528\pi$$
−0.316561 + 0.948572i $$0.602528\pi$$
$$104$$ −4.48528 −0.439818
$$105$$ 0 0
$$106$$ −0.585786 −0.0568966
$$107$$ 0.242641 + 0.242641i 0.0234570 + 0.0234570i 0.718738 0.695281i $$-0.244720\pi$$
−0.695281 + 0.718738i $$0.744720\pi$$
$$108$$ 9.14214 2.58579i 0.879702 0.248817i
$$109$$ 3.17157i 0.303782i −0.988397 0.151891i $$-0.951464\pi$$
0.988397 0.151891i $$-0.0485362\pi$$
$$110$$ 0 0
$$111$$ −0.0710678 + 0.414214i −0.00674546 + 0.0393154i
$$112$$ −10.2426 + 10.2426i −0.967839 + 0.967839i
$$113$$ −5.82843 + 5.82843i −0.548292 + 0.548292i −0.925947 0.377654i $$-0.876731\pi$$
0.377654 + 0.925947i $$0.376731\pi$$
$$114$$ −0.343146 + 2.00000i −0.0321385 + 0.187317i
$$115$$ 0 0
$$116$$ 1.51472i 0.140638i
$$117$$ 7.65685 3.65685i 0.707876 0.338076i
$$118$$ −1.17157 1.17157i −0.107852 0.107852i
$$119$$ −19.3137 −1.77048
$$120$$ 0 0
$$121$$ −1.00000 −0.0909091
$$122$$ 1.89949 + 1.89949i 0.171972 + 0.171972i
$$123$$ 7.65685 + 10.8284i 0.690395 + 0.976366i
$$124$$ 5.79899i 0.520765i
$$125$$ 0 0
$$126$$ −2.00000 + 5.65685i −0.178174 + 0.503953i
$$127$$ −1.41421 + 1.41421i −0.125491 + 0.125491i −0.767063 0.641572i $$-0.778283\pi$$
0.641572 + 0.767063i $$0.278283\pi$$
$$128$$ 7.46447 7.46447i 0.659772 0.659772i
$$129$$ 0.585786 + 0.100505i 0.0515756 + 0.00884898i
$$130$$ 0 0
$$131$$ 6.82843i 0.596602i 0.954472 + 0.298301i $$0.0964200\pi$$
−0.954472 + 0.298301i $$0.903580\pi$$
$$132$$ 2.58579 1.82843i 0.225064 0.159144i
$$133$$ 9.65685 + 9.65685i 0.837355 + 0.837355i
$$134$$ −3.75736 −0.324586
$$135$$ 0 0
$$136$$ 6.34315 0.543920
$$137$$ 0.171573 + 0.171573i 0.0146585 + 0.0146585i 0.714398 0.699740i $$-0.246701\pi$$
−0.699740 + 0.714398i $$0.746701\pi$$
$$138$$ 2.68629 1.89949i 0.228672 0.161696i
$$139$$ 17.6569i 1.49763i 0.662776 + 0.748817i $$0.269378\pi$$
−0.662776 + 0.748817i $$0.730622\pi$$
$$140$$ 0 0
$$141$$ 17.4853 + 3.00000i 1.47253 + 0.252646i
$$142$$ −0.727922 + 0.727922i −0.0610859 + 0.0610859i
$$143$$ 2.00000 2.00000i 0.167248 0.167248i
$$144$$ −3.00000 + 8.48528i −0.250000 + 0.707107i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 16.3137 + 23.0711i 1.34553 + 1.90287i
$$148$$ −0.313708 0.313708i −0.0257867 0.0257867i
$$149$$ 10.0000 0.819232 0.409616 0.912258i $$-0.365663\pi$$
0.409616 + 0.912258i $$0.365663\pi$$
$$150$$ 0 0
$$151$$ 10.1421 0.825355 0.412678 0.910877i $$-0.364594\pi$$
0.412678 + 0.910877i $$0.364594\pi$$
$$152$$ −3.17157 3.17157i −0.257249 0.257249i
$$153$$ −10.8284 + 5.17157i −0.875426 + 0.418097i
$$154$$ 2.00000i 0.161165i
$$155$$ 0 0
$$156$$ −1.51472 + 8.82843i −0.121275 + 0.706840i
$$157$$ 9.48528 9.48528i 0.757008 0.757008i −0.218769 0.975777i $$-0.570204\pi$$
0.975777 + 0.218769i $$0.0702041\pi$$
$$158$$ −3.17157 + 3.17157i −0.252317 + 0.252317i
$$159$$ −0.414214 + 2.41421i −0.0328493 + 0.191460i
$$160$$ 0 0
$$161$$ 22.1421i 1.74504i
$$162$$ 0.393398 + 3.70711i 0.0309083 + 0.291258i
$$163$$ −3.58579 3.58579i −0.280860 0.280860i 0.552592 0.833452i $$-0.313639\pi$$
−0.833452 + 0.552592i $$0.813639\pi$$
$$164$$ −14.0000 −1.09322
$$165$$ 0 0
$$166$$ 5.31371 0.412424
$$167$$ 14.7279 + 14.7279i 1.13968 + 1.13968i 0.988507 + 0.151174i $$0.0483052\pi$$
0.151174 + 0.988507i $$0.451695\pi$$
$$168$$ −7.65685 10.8284i −0.590739 0.835431i
$$169$$ 5.00000i 0.384615i
$$170$$ 0 0
$$171$$ 8.00000 + 2.82843i 0.611775 + 0.216295i
$$172$$ −0.443651 + 0.443651i −0.0338281 + 0.0338281i
$$173$$ 8.48528 8.48528i 0.645124 0.645124i −0.306687 0.951811i $$-0.599220\pi$$
0.951811 + 0.306687i $$0.0992203\pi$$
$$174$$ −0.585786 0.100505i −0.0444084 0.00761927i
$$175$$ 0 0
$$176$$ 3.00000i 0.226134i
$$177$$ −5.65685 + 4.00000i −0.425195 + 0.300658i
$$178$$ −2.82843 2.82843i −0.212000 0.212000i
$$179$$ −24.1421 −1.80447 −0.902234 0.431247i $$-0.858074\pi$$
−0.902234 + 0.431247i $$0.858074\pi$$
$$180$$ 0 0
$$181$$ 5.65685 0.420471 0.210235 0.977651i $$-0.432577\pi$$
0.210235 + 0.977651i $$0.432577\pi$$
$$182$$ −4.00000 4.00000i −0.296500 0.296500i
$$183$$ 9.17157 6.48528i 0.677982 0.479406i
$$184$$ 7.27208i 0.536105i
$$185$$ 0 0
$$186$$ −2.24264 0.384776i −0.164438 0.0282132i
$$187$$ −2.82843 + 2.82843i −0.206835 + 0.206835i
$$188$$ −13.2426 + 13.2426i −0.965819 + 0.965819i
$$189$$ 21.8995 + 12.2426i 1.59295 + 0.890521i
$$190$$ 0 0
$$191$$ 11.3137i 0.818631i 0.912393 + 0.409316i $$0.134232\pi$$
−0.912393 + 0.409316i $$0.865768\pi$$
$$192$$ −4.17157 5.89949i −0.301057 0.425759i
$$193$$ −8.00000 8.00000i −0.575853 0.575853i 0.357905 0.933758i $$-0.383491\pi$$
−0.933758 + 0.357905i $$0.883491\pi$$
$$194$$ 6.24264 0.448195
$$195$$ 0 0
$$196$$ −29.8284 −2.13060
$$197$$ −14.1421 14.1421i −1.00759 1.00759i −0.999971 0.00761443i $$-0.997576\pi$$
−0.00761443 0.999971i $$-0.502424\pi$$
$$198$$ 0.535534 + 1.12132i 0.0380587 + 0.0796888i
$$199$$ 14.4853i 1.02683i 0.858139 + 0.513417i $$0.171621\pi$$
−0.858139 + 0.513417i $$0.828379\pi$$
$$200$$ 0 0
$$201$$ −2.65685 + 15.4853i −0.187400 + 1.09225i
$$202$$ −2.10051 + 2.10051i −0.147791 + 0.147791i
$$203$$ −2.82843 + 2.82843i −0.198517 + 0.198517i
$$204$$ 2.14214 12.4853i 0.149979 0.874145i
$$205$$ 0 0
$$206$$ 3.75736i 0.261788i
$$207$$ −5.92893 12.4142i −0.412089 0.862847i
$$208$$ −6.00000 6.00000i −0.416025 0.416025i
$$209$$ 2.82843 0.195646
$$210$$ 0 0
$$211$$ −4.48528 −0.308780 −0.154390 0.988010i $$-0.549341\pi$$
−0.154390 + 0.988010i $$0.549341\pi$$
$$212$$ −1.82843 1.82843i −0.125577 0.125577i
$$213$$ 2.48528 + 3.51472i 0.170289 + 0.240825i
$$214$$ 0.142136i 0.00971619i
$$215$$ 0 0
$$216$$ −7.19239 4.02082i −0.489380 0.273582i
$$217$$ −10.8284 + 10.8284i −0.735082 + 0.735082i
$$218$$ −0.928932 + 0.928932i −0.0629152 + 0.0629152i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 11.3137i 0.761042i
$$222$$ 0.142136 0.100505i 0.00953952 0.00674546i
$$223$$ 16.5563 + 16.5563i 1.10870 + 1.10870i 0.993322 + 0.115373i $$0.0368063\pi$$
0.115373 + 0.993322i $$0.463194\pi$$
$$224$$ 21.3137 1.42408
$$225$$ 0 0
$$226$$ 3.41421 0.227110
$$227$$ 10.2426 + 10.2426i 0.679828 + 0.679828i 0.959961 0.280133i $$-0.0903786\pi$$
−0.280133 + 0.959961i $$0.590379\pi$$
$$228$$ −7.31371 + 5.17157i −0.484362 + 0.342496i
$$229$$ 9.65685i 0.638143i 0.947731 + 0.319071i $$0.103371\pi$$
−0.947731 + 0.319071i $$0.896629\pi$$
$$230$$ 0 0
$$231$$ 8.24264 + 1.41421i 0.542326 + 0.0930484i
$$232$$ 0.928932 0.928932i 0.0609874 0.0609874i
$$233$$ 19.6569 19.6569i 1.28776 1.28776i 0.351621 0.936143i $$-0.385631\pi$$
0.936143 0.351621i $$-0.114369\pi$$
$$234$$ −3.31371 1.17157i −0.216624 0.0765881i
$$235$$ 0 0
$$236$$ 7.31371i 0.476082i
$$237$$ 10.8284 + 15.3137i 0.703382 + 0.994732i
$$238$$ 5.65685 + 5.65685i 0.366679 + 0.366679i
$$239$$ 23.7990 1.53943 0.769714 0.638388i $$-0.220399\pi$$
0.769714 + 0.638388i $$0.220399\pi$$
$$240$$ 0 0
$$241$$ 0.142136 0.00915576 0.00457788 0.999990i $$-0.498543\pi$$
0.00457788 + 0.999990i $$0.498543\pi$$
$$242$$ 0.292893 + 0.292893i 0.0188279 + 0.0188279i
$$243$$ 15.5563 + 1.00000i 0.997940 + 0.0641500i
$$244$$ 11.8579i 0.759122i
$$245$$ 0 0
$$246$$ 0.928932 5.41421i 0.0592266 0.345198i
$$247$$ −5.65685 + 5.65685i −0.359937 + 0.359937i
$$248$$ 3.55635 3.55635i 0.225828 0.225828i
$$249$$ 3.75736 21.8995i 0.238113 1.38782i
$$250$$ 0 0
$$251$$ 16.1421i 1.01888i −0.860505 0.509441i $$-0.829852\pi$$
0.860505 0.509441i $$-0.170148\pi$$
$$252$$ −23.8995 + 11.4142i −1.50553 + 0.719028i
$$253$$ −3.24264 3.24264i −0.203863 0.203863i
$$254$$ 0.828427 0.0519801
$$255$$ 0 0
$$256$$ 3.97056 0.248160
$$257$$ −1.82843 1.82843i −0.114054 0.114054i 0.647776 0.761831i $$-0.275699\pi$$
−0.761831 + 0.647776i $$0.775699\pi$$
$$258$$ −0.142136 0.201010i −0.00884898 0.0125143i
$$259$$ 1.17157i 0.0727980i
$$260$$ 0 0
$$261$$ −0.828427 + 2.34315i −0.0512784 + 0.145037i
$$262$$ 2.00000 2.00000i 0.123560 0.123560i
$$263$$ −1.75736 + 1.75736i −0.108363 + 0.108363i −0.759210 0.650846i $$-0.774414\pi$$
0.650846 + 0.759210i $$0.274414\pi$$
$$264$$ −2.70711 0.464466i −0.166611 0.0285859i
$$265$$ 0 0
$$266$$ 5.65685i 0.346844i
$$267$$ −13.6569 + 9.65685i −0.835786 + 0.590990i
$$268$$ −11.7279 11.7279i −0.716397 0.716397i
$$269$$ 14.0000 0.853595 0.426798 0.904347i $$-0.359642\pi$$
0.426798 + 0.904347i $$0.359642\pi$$
$$270$$ 0 0
$$271$$ 8.48528 0.515444 0.257722 0.966219i $$-0.417028\pi$$
0.257722 + 0.966219i $$0.417028\pi$$
$$272$$ 8.48528 + 8.48528i 0.514496 + 0.514496i
$$273$$ −19.3137 + 13.6569i −1.16892 + 0.826550i
$$274$$ 0.100505i 0.00607173i
$$275$$ 0 0
$$276$$ 14.3137 + 2.45584i 0.861584 + 0.147824i
$$277$$ 18.4853 18.4853i 1.11067 1.11067i 0.117613 0.993059i $$-0.462476\pi$$
0.993059 0.117613i $$-0.0375244\pi$$
$$278$$ 5.17157 5.17157i 0.310170 0.310170i
$$279$$ −3.17157 + 8.97056i −0.189877 + 0.537054i
$$280$$ 0 0
$$281$$ 28.6274i 1.70777i 0.520463 + 0.853884i $$0.325759\pi$$
−0.520463 + 0.853884i $$0.674241\pi$$
$$282$$ −4.24264 6.00000i −0.252646 0.357295i
$$283$$ 15.0711 + 15.0711i 0.895882 + 0.895882i 0.995069 0.0991868i $$-0.0316241\pi$$
−0.0991868 + 0.995069i $$0.531624\pi$$
$$284$$ −4.54416 −0.269646
$$285$$ 0 0
$$286$$ −1.17157 −0.0692766
$$287$$ −26.1421 26.1421i −1.54312 1.54312i
$$288$$ 11.9497 5.70711i 0.704146 0.336294i
$$289$$ 1.00000i 0.0588235i
$$290$$ 0 0
$$291$$ 4.41421 25.7279i 0.258766 1.50820i
$$292$$ 0 0
$$293$$ −3.65685 + 3.65685i −0.213636 + 0.213636i −0.805810 0.592174i $$-0.798270\pi$$
0.592174 + 0.805810i $$0.298270\pi$$
$$294$$ 1.97918 11.5355i 0.115428 0.672766i
$$295$$ 0 0
$$296$$ 0.384776i 0.0223647i
$$297$$ 5.00000 1.41421i 0.290129 0.0820610i
$$298$$ −2.92893 2.92893i −0.169668 0.169668i
$$299$$ 12.9706 0.750107
$$300$$ 0 0
$$301$$ −1.65685 −0.0954995
$$302$$ −2.97056 2.97056i −0.170937 0.170937i
$$303$$ 7.17157 + 10.1421i 0.411996 + 0.582650i
$$304$$ 8.48528i 0.486664i
$$305$$ 0 0
$$306$$ 4.68629 + 1.65685i 0.267897 + 0.0947161i
$$307$$ 11.8995 11.8995i 0.679140 0.679140i −0.280666 0.959806i $$-0.590555\pi$$
0.959806 + 0.280666i $$0.0905552\pi$$
$$308$$ −6.24264 + 6.24264i −0.355707 + 0.355707i
$$309$$ −15.4853 2.65685i −0.880927 0.151143i
$$310$$ 0 0
$$311$$ 28.1421i 1.59579i 0.602794 + 0.797897i $$0.294054\pi$$
−0.602794 + 0.797897i $$0.705946\pi$$
$$312$$ 6.34315 4.48528i 0.359110 0.253929i
$$313$$ −12.6569 12.6569i −0.715408 0.715408i 0.252253 0.967661i $$-0.418828\pi$$
−0.967661 + 0.252253i $$0.918828\pi$$
$$314$$ −5.55635 −0.313563
$$315$$ 0 0
$$316$$ −19.7990 −1.11378
$$317$$ 2.31371 + 2.31371i 0.129951 + 0.129951i 0.769091 0.639140i $$-0.220709\pi$$
−0.639140 + 0.769091i $$0.720709\pi$$
$$318$$ 0.828427 0.585786i 0.0464559 0.0328493i
$$319$$ 0.828427i 0.0463830i
$$320$$ 0 0
$$321$$ −0.585786 0.100505i −0.0326954 0.00560965i
$$322$$ −6.48528 + 6.48528i −0.361411 + 0.361411i
$$323$$ 8.00000 8.00000i 0.445132 0.445132i
$$324$$ −10.3431 + 12.7990i −0.574619 + 0.711055i
$$325$$ 0 0
$$326$$ 2.10051i 0.116336i
$$327$$ 3.17157 + 4.48528i 0.175388 + 0.248037i
$$328$$ 8.58579 + 8.58579i 0.474071 + 0.474071i
$$329$$ −49.4558 −2.72659
$$330$$ 0 0
$$331$$ −6.48528 −0.356463 −0.178232 0.983989i $$-0.557038\pi$$
−0.178232 + 0.983989i $$0.557038\pi$$
$$332$$ 16.5858 + 16.5858i 0.910263 + 0.910263i
$$333$$ −0.313708 0.656854i −0.0171911 0.0359954i
$$334$$ 8.62742i 0.472071i
$$335$$ 0 0
$$336$$ 4.24264 24.7279i 0.231455 1.34902i
$$337$$ 10.8284 10.8284i 0.589862 0.589862i −0.347732 0.937594i $$-0.613048\pi$$
0.937594 + 0.347732i $$0.113048\pi$$
$$338$$ −1.46447 + 1.46447i −0.0796565 + 0.0796565i
$$339$$ 2.41421 14.0711i 0.131122 0.764235i
$$340$$ 0 0
$$341$$ 3.17157i 0.171750i
$$342$$ −1.51472 3.17157i −0.0819066 0.171499i
$$343$$ −31.7990 31.7990i −1.71698 1.71698i
$$344$$ 0.544156 0.0293389
$$345$$ 0 0
$$346$$ −4.97056 −0.267219
$$347$$ 1.89949 + 1.89949i 0.101970 + 0.101970i 0.756251 0.654281i $$-0.227029\pi$$
−0.654281 + 0.756251i $$0.727029\pi$$
$$348$$ −1.51472 2.14214i −0.0811974 0.114831i
$$349$$ 30.0000i 1.60586i −0.596071 0.802932i $$-0.703272\pi$$
0.596071 0.802932i $$-0.296728\pi$$
$$350$$ 0 0
$$351$$ −7.17157 + 12.8284i −0.382790 + 0.684731i
$$352$$ 3.12132 3.12132i 0.166367 0.166367i
$$353$$ 7.82843 7.82843i 0.416665 0.416665i −0.467387 0.884053i $$-0.654805\pi$$
0.884053 + 0.467387i $$0.154805\pi$$
$$354$$ 2.82843 + 0.485281i 0.150329 + 0.0257924i
$$355$$ 0 0
$$356$$ 17.6569i 0.935811i
$$357$$ 27.3137 19.3137i 1.44559 1.02219i
$$358$$ 7.07107 + 7.07107i 0.373718 + 0.373718i
$$359$$ 22.1421 1.16862 0.584309 0.811532i $$-0.301366\pi$$
0.584309 + 0.811532i $$0.301366\pi$$
$$360$$ 0 0
$$361$$ 11.0000 0.578947
$$362$$ −1.65685 1.65685i −0.0870823 0.0870823i
$$363$$ 1.41421 1.00000i 0.0742270 0.0524864i
$$364$$ 24.9706i 1.30881i
$$365$$ 0 0
$$366$$ −4.58579 0.786797i −0.239703 0.0411265i
$$367$$ 1.10051 1.10051i 0.0574459 0.0574459i −0.677800 0.735246i $$-0.737067\pi$$
0.735246 + 0.677800i $$0.237067\pi$$
$$368$$ −9.72792 + 9.72792i −0.507103 + 0.507103i
$$369$$ −21.6569 7.65685i −1.12741 0.398600i
$$370$$ 0 0
$$371$$ 6.82843i 0.354514i
$$372$$ −5.79899 8.20101i −0.300664 0.425203i
$$373$$ −3.51472 3.51472i −0.181985 0.181985i 0.610235 0.792220i $$-0.291075\pi$$
−0.792220 + 0.610235i $$0.791075\pi$$
$$374$$ 1.65685 0.0856739
$$375$$ 0 0
$$376$$ 16.2426 0.837650
$$377$$ −1.65685 1.65685i −0.0853323 0.0853323i
$$378$$ −2.82843 10.0000i −0.145479 0.514344i
$$379$$ 28.1421i 1.44556i 0.691076 + 0.722782i $$0.257137\pi$$
−0.691076 + 0.722782i $$0.742863\pi$$
$$380$$ 0 0
$$381$$ 0.585786 3.41421i 0.0300107 0.174915i
$$382$$ 3.31371 3.31371i 0.169544 0.169544i
$$383$$ −6.07107 + 6.07107i −0.310217 + 0.310217i −0.844994 0.534776i $$-0.820396\pi$$
0.534776 + 0.844994i $$0.320396\pi$$
$$384$$ −3.09188 + 18.0208i −0.157782 + 0.919621i
$$385$$ 0 0
$$386$$ 4.68629i 0.238526i
$$387$$ −0.928932 + 0.443651i −0.0472203 + 0.0225520i
$$388$$ 19.4853 + 19.4853i 0.989215 + 0.989215i
$$389$$ 17.3137 0.877840 0.438920 0.898526i $$-0.355361\pi$$
0.438920 + 0.898526i $$0.355361\pi$$
$$390$$ 0 0
$$391$$ −18.3431 −0.927653
$$392$$ 18.2929 + 18.2929i 0.923931 + 0.923931i
$$393$$ −6.82843 9.65685i −0.344449 0.487124i
$$394$$ 8.28427i 0.417356i
$$395$$ 0 0
$$396$$ −1.82843 + 5.17157i −0.0918819 + 0.259881i
$$397$$ −6.17157 + 6.17157i −0.309742 + 0.309742i −0.844810 0.535067i $$-0.820286\pi$$
0.535067 + 0.844810i $$0.320286\pi$$
$$398$$ 4.24264 4.24264i 0.212664 0.212664i
$$399$$ −23.3137 4.00000i −1.16715 0.200250i
$$400$$ 0 0
$$401$$ 35.6569i 1.78062i 0.455357 + 0.890309i $$0.349512\pi$$
−0.455357 + 0.890309i $$0.650488\pi$$
$$402$$ 5.31371 3.75736i 0.265024 0.187400i
$$403$$ −6.34315 6.34315i −0.315975 0.315975i
$$404$$ −13.1127 −0.652381
$$405$$ 0 0
$$406$$ 1.65685 0.0822283
$$407$$ −0.171573 0.171573i −0.00850455 0.00850455i
$$408$$ −8.97056 + 6.34315i −0.444109 + 0.314033i
$$409$$ 18.4853i 0.914038i −0.889457 0.457019i $$-0.848917\pi$$
0.889457 0.457019i $$-0.151083\pi$$
$$410$$ 0 0
$$411$$ −0.414214 0.0710678i −0.0204316 0.00350552i
$$412$$ 11.7279 11.7279i 0.577793 0.577793i
$$413$$ 13.6569 13.6569i 0.672010 0.672010i
$$414$$ −1.89949 + 5.37258i −0.0933551 + 0.264048i
$$415$$ 0 0
$$416$$ 12.4853i 0.612141i
$$417$$ −17.6569 24.9706i −0.864660 1.22281i
$$418$$ −0.828427 0.828427i −0.0405197 0.0405197i
$$419$$ −15.4558 −0.755067 −0.377534 0.925996i $$-0.623228\pi$$
−0.377534 + 0.925996i $$0.623228\pi$$
$$420$$ 0 0
$$421$$ −4.00000 −0.194948 −0.0974740 0.995238i $$-0.531076\pi$$
−0.0974740 + 0.995238i $$0.531076\pi$$
$$422$$ 1.31371 + 1.31371i 0.0639503 + 0.0639503i
$$423$$ −27.7279 + 13.2426i −1.34818 + 0.643879i
$$424$$ 2.24264i 0.108912i
$$425$$ 0 0
$$426$$ 0.301515 1.75736i 0.0146085 0.0851443i
$$427$$ −22.1421 + 22.1421i −1.07153 + 1.07153i
$$428$$ 0.443651 0.443651i 0.0214447 0.0214447i
$$429$$ −0.828427 + 4.82843i −0.0399968 + 0.233119i
$$430$$ 0 0
$$431$$ 6.34315i 0.305539i −0.988262 0.152769i $$-0.951181\pi$$
0.988262 0.152769i $$-0.0488191\pi$$
$$432$$ −4.24264 15.0000i −0.204124 0.721688i
$$433$$ 0.313708 + 0.313708i 0.0150759 + 0.0150759i 0.714605 0.699529i $$-0.246607\pi$$
−0.699529 + 0.714605i $$0.746607\pi$$
$$434$$ 6.34315 0.304481
$$435$$ 0 0
$$436$$ −5.79899 −0.277721
$$437$$ 9.17157 + 9.17157i 0.438736 + 0.438736i
$$438$$ 0 0
$$439$$ 7.31371i 0.349064i −0.984651 0.174532i $$-0.944159\pi$$
0.984651 0.174532i $$-0.0558413\pi$$
$$440$$ 0 0
$$441$$ −46.1421 16.3137i −2.19724 0.776843i
$$442$$ −3.31371 + 3.31371i −0.157617 + 0.157617i
$$443$$ −20.7574 + 20.7574i −0.986212 + 0.986212i −0.999906 0.0136943i $$-0.995641\pi$$
0.0136943 + 0.999906i $$0.495641\pi$$
$$444$$ 0.757359 + 0.129942i 0.0359427 + 0.00616679i
$$445$$ 0 0
$$446$$ 9.69848i 0.459237i
$$447$$ −14.1421 + 10.0000i −0.668900 + 0.472984i
$$448$$ 14.2426 + 14.2426i 0.672902 + 0.672902i
$$449$$ 3.02944 0.142968 0.0714840 0.997442i $$-0.477227\pi$$
0.0714840 + 0.997442i $$0.477227\pi$$
$$450$$ 0 0
$$451$$ −7.65685 −0.360547
$$452$$ 10.6569 + 10.6569i 0.501256 + 0.501256i
$$453$$ −14.3431 + 10.1421i −0.673900 + 0.476519i
$$454$$ 6.00000i 0.281594i
$$455$$ 0 0
$$456$$ 7.65685 + 1.31371i 0.358565 + 0.0615200i
$$457$$ 6.48528 6.48528i 0.303369 0.303369i −0.538962 0.842330i $$-0.681183\pi$$
0.842330 + 0.538962i $$0.181183\pi$$
$$458$$ 2.82843 2.82843i 0.132164 0.132164i
$$459$$ 10.1421 18.1421i 0.473394 0.846802i
$$460$$ 0 0
$$461$$ 13.5147i 0.629443i −0.949184 0.314722i $$-0.898089\pi$$
0.949184 0.314722i $$-0.101911\pi$$
$$462$$ −2.00000 2.82843i −0.0930484 0.131590i
$$463$$ −11.7279 11.7279i −0.545043 0.545043i 0.379960 0.925003i $$-0.375938\pi$$
−0.925003 + 0.379960i $$0.875938\pi$$
$$464$$ 2.48528 0.115376
$$465$$ 0 0
$$466$$ −11.5147 −0.533409
$$467$$ −0.414214 0.414214i −0.0191675 0.0191675i 0.697458 0.716626i $$-0.254314\pi$$
−0.716626 + 0.697458i $$0.754314\pi$$
$$468$$ −6.68629 14.0000i −0.309074 0.647150i
$$469$$ 43.7990i 2.02245i
$$470$$ 0 0
$$471$$ −3.92893 + 22.8995i −0.181036 + 1.05515i
$$472$$ −4.48528 + 4.48528i −0.206452 + 0.206452i
$$473$$ −0.242641 + 0.242641i −0.0111566 + 0.0111566i
$$474$$ 1.31371 7.65685i 0.0603406 0.351691i
$$475$$ 0 0
$$476$$ 35.3137i 1.61860i
$$477$$ −1.82843 3.82843i −0.0837179 0.175292i
$$478$$ −6.97056 6.97056i −0.318826 0.318826i
$$479$$ 30.1421 1.37723 0.688615 0.725127i $$-0.258219\pi$$
0.688615 + 0.725127i $$0.258219\pi$$
$$480$$ 0 0
$$481$$ 0.686292 0.0312922
$$482$$ −0.0416306 0.0416306i −0.00189622 0.00189622i
$$483$$ 22.1421 + 31.3137i 1.00750 + 1.42482i
$$484$$ 1.82843i 0.0831103i
$$485$$ 0 0
$$486$$ −4.26346 4.84924i −0.193394 0.219966i
$$487$$ −11.7279 + 11.7279i −0.531443 + 0.531443i −0.921002 0.389559i $$-0.872628\pi$$
0.389559 + 0.921002i $$0.372628\pi$$
$$488$$ 7.27208 7.27208i 0.329192 0.329192i
$$489$$ 8.65685 + 1.48528i 0.391476 + 0.0671667i
$$490$$ 0 0
$$491$$ 20.0000i 0.902587i −0.892375 0.451294i $$-0.850963\pi$$
0.892375 0.451294i $$-0.149037\pi$$
$$492$$ 19.7990 14.0000i 0.892607 0.631169i
$$493$$ 2.34315 + 2.34315i 0.105530 + 0.105530i
$$494$$ 3.31371 0.149091
$$495$$ 0 0
$$496$$ 9.51472 0.427223
$$497$$ −8.48528 8.48528i −0.380617 0.380617i
$$498$$ −7.51472 + 5.31371i −0.336743 + 0.238113i
$$499$$ 24.8284i 1.11147i 0.831358 + 0.555737i $$0.187564\pi$$
−0.831358 + 0.555737i $$0.812436\pi$$
$$500$$ 0 0
$$501$$ −35.5563 6.10051i −1.58854 0.272550i
$$502$$ −4.72792 + 4.72792i −0.211017 + 0.211017i
$$503$$ 0.928932 0.928932i 0.0414190 0.0414190i −0.686094 0.727513i $$-0.740676\pi$$
0.727513 + 0.686094i $$0.240676\pi$$
$$504$$ 21.6569 + 7.65685i 0.964673 + 0.341063i
$$505$$ 0 0
$$506$$ 1.89949i 0.0844428i
$$507$$ 5.00000 + 7.07107i 0.222058 + 0.314037i
$$508$$ 2.58579 + 2.58579i 0.114726 + 0.114726i
$$509$$ −35.6569 −1.58046 −0.790231 0.612809i $$-0.790040\pi$$
−0.790231 + 0.612809i $$0.790040\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −16.0919 16.0919i −0.711167 0.711167i
$$513$$ −14.1421 + 4.00000i −0.624391 + 0.176604i
$$514$$ 1.07107i 0.0472428i
$$515$$ 0 0
$$516$$ 0.183766 1.07107i 0.00808986 0.0471511i
$$517$$ −7.24264 + 7.24264i −0.318531 + 0.318531i
$$518$$ −0.343146 + 0.343146i −0.0150770 + 0.0150770i
$$519$$ −3.51472 + 20.4853i −0.154279 + 0.899204i
$$520$$ 0 0
$$521$$ 27.6569i 1.21167i −0.795591 0.605834i $$-0.792839\pi$$
0.795591 0.605834i $$-0.207161\pi$$
$$522$$ 0.928932 0.443651i 0.0406583 0.0194181i
$$523$$ 27.2132 + 27.2132i 1.18995 + 1.18995i 0.977081 + 0.212870i $$0.0682810\pi$$
0.212870 + 0.977081i $$0.431719\pi$$
$$524$$ 12.4853 0.545422
$$525$$ 0 0
$$526$$ 1.02944 0.0448856
$$527$$ 8.97056 + 8.97056i 0.390764 + 0.390764i
$$528$$ −3.00000 4.24264i −0.130558 0.184637i
$$529$$ 1.97056i 0.0856766i
$$530$$ 0 0
$$531$$ 4.00000 11.3137i 0.173585 0.490973i
$$532$$ 17.6569 17.6569i 0.765522 0.765522i
$$533$$ 15.3137 15.3137i 0.663310 0.663310i
$$534$$ 6.82843 + 1.17157i 0.295495 + 0.0506989i
$$535$$ 0 0
$$536$$ 14.3848i 0.621328i
$$537$$ 34.1421 24.1421i 1.47334 1.04181i
$$538$$ −4.10051 4.10051i −0.176785 0.176785i
$$539$$ −16.3137 −0.702681
$$540$$ 0 0
$$541$$ −10.6863 −0.459440 −0.229720 0.973257i $$-0.573781\pi$$
−0.229720 + 0.973257i $$0.573781\pi$$
$$542$$ −2.48528 2.48528i −0.106752 0.106752i
$$543$$ −8.00000 + 5.65685i −0.343313 + 0.242759i
$$544$$ 17.6569i 0.757031i
$$545$$ 0 0
$$546$$ 9.65685 + 1.65685i 0.413275 + 0.0709068i
$$547$$ −2.10051 + 2.10051i −0.0898111 + 0.0898111i −0.750585 0.660774i $$-0.770228\pi$$
0.660774 + 0.750585i $$0.270228\pi$$
$$548$$ 0.313708 0.313708i 0.0134010 0.0134010i
$$549$$ −6.48528 + 18.3431i −0.276785 + 0.782866i
$$550$$ 0 0
$$551$$ 2.34315i 0.0998214i
$$552$$ −7.27208 10.2843i −0.309520 0.437728i
$$553$$ −36.9706 36.9706i −1.57215 1.57215i
$$554$$ −10.8284 −0.460056
$$555$$ 0 0
$$556$$ 32.2843 1.36916
$$557$$ 8.97056 + 8.97056i 0.380095 + 0.380095i 0.871136 0.491041i $$-0.163384\pi$$
−0.491041 + 0.871136i $$0.663384\pi$$
$$558$$ 3.55635 1.69848i 0.150552 0.0719026i
$$559$$ 0.970563i 0.0410504i
$$560$$ 0 0
$$561$$ 1.17157 6.82843i 0.0494638 0.288296i
$$562$$ 8.38478 8.38478i 0.353690 0.353690i
$$563$$ −9.89949 + 9.89949i −0.417214 + 0.417214i −0.884242 0.467028i $$-0.845325\pi$$
0.467028 + 0.884242i $$0.345325\pi$$
$$564$$ 5.48528 31.9706i 0.230972 1.34620i
$$565$$ 0 0
$$566$$ 8.82843i 0.371086i
$$567$$ −43.2132 + 4.58579i −1.81478 + 0.192585i
$$568$$ 2.78680 + 2.78680i 0.116931 + 0.116931i
$$569$$ 28.3431 1.18821 0.594103 0.804389i $$-0.297507\pi$$
0.594103 + 0.804389i $$0.297507\pi$$
$$570$$ 0 0
$$571$$ 29.6569 1.24110 0.620550 0.784167i $$-0.286909\pi$$
0.620550 + 0.784167i $$0.286909\pi$$
$$572$$ −3.65685 3.65685i −0.152901 0.152901i
$$573$$ −11.3137 16.0000i −0.472637 0.668410i
$$574$$ 15.3137i 0.639182i
$$575$$ 0 0
$$576$$ 11.7990 + 4.17157i 0.491625 + 0.173816i
$$577$$ −17.0000 + 17.0000i −0.707719 + 0.707719i −0.966055 0.258336i $$-0.916826\pi$$
0.258336 + 0.966055i $$0.416826\pi$$
$$578$$ −0.292893 + 0.292893i −0.0121828 + 0.0121828i
$$579$$ 19.3137 + 3.31371i 0.802650 + 0.137713i
$$580$$ 0 0
$$581$$ 61.9411i 2.56975i
$$582$$ −8.82843 + 6.24264i −0.365950 + 0.258766i
$$583$$ −1.00000 1.00000i −0.0414158 0.0414158i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 2.14214 0.0884908
$$587$$ −0.414214 0.414214i −0.0170964 0.0170964i 0.698507 0.715603i $$-0.253848\pi$$
−0.715603 + 0.698507i $$0.753848\pi$$
$$588$$ 42.1838 29.8284i 1.73963 1.23010i
$$589$$ 8.97056i 0.369626i
$$590$$ 0 0
$$591$$ 34.1421 + 5.85786i 1.40442 + 0.240960i
$$592$$ −0.514719 + 0.514719i −0.0211548 + 0.0211548i
$$593$$ 5.85786 5.85786i 0.240554 0.240554i −0.576525 0.817079i $$-0.695592\pi$$
0.817079 + 0.576525i $$0.195592\pi$$
$$594$$ −1.87868 1.05025i −0.0770832 0.0430924i
$$595$$ 0 0
$$596$$ 18.2843i 0.748953i
$$597$$ −14.4853 20.4853i −0.592843 0.838407i
$$598$$ −3.79899 3.79899i −0.155352 0.155352i
$$599$$ 3.45584 0.141202 0.0706010 0.997505i $$-0.477508\pi$$
0.0706010 + 0.997505i $$0.477508\pi$$
$$600$$ 0 0
$$601$$ −27.4558 −1.11995 −0.559974 0.828510i $$-0.689189\pi$$
−0.559974 + 0.828510i $$0.689189\pi$$
$$602$$ 0.485281 + 0.485281i 0.0197786 + 0.0197786i
$$603$$ −11.7279 24.5563i −0.477598 1.00001i
$$604$$ 18.5442i 0.754551i
$$605$$ 0 0
$$606$$ 0.870058 5.07107i 0.0353437 0.205998i
$$607$$ 21.8995 21.8995i 0.888873 0.888873i −0.105542 0.994415i $$-0.533658\pi$$
0.994415 + 0.105542i $$0.0336577\pi$$
$$608$$ −8.82843 + 8.82843i −0.358040 + 0.358040i
$$609$$ 1.17157 6.82843i 0.0474745 0.276702i
$$610$$ 0 0
$$611$$ 28.9706i 1.17202i
$$612$$ 9.45584 + 19.7990i 0.382230 + 0.800327i
$$613$$ 16.0000 + 16.0000i 0.646234 + 0.646234i 0.952081 0.305847i $$-0.0989395\pi$$
−0.305847 + 0.952081i $$0.598940\pi$$
$$614$$ −6.97056 −0.281309
$$615$$ 0 0
$$616$$ 7.65685 0.308503
$$617$$ 29.8284 + 29.8284i 1.20085 + 1.20085i 0.973909 + 0.226938i $$0.0728715\pi$$
0.226938 + 0.973909i $$0.427129\pi$$
$$618$$ 3.75736 + 5.31371i 0.151143 + 0.213749i
$$619$$ 0.686292i 0.0275844i −0.999905 0.0137922i $$-0.995610\pi$$
0.999905 0.0137922i $$-0.00439033\pi$$
$$620$$ 0 0
$$621$$ 20.7990 + 11.6274i 0.834635 + 0.466592i
$$622$$ 8.24264 8.24264i 0.330500 0.330500i
$$623$$ 32.9706 32.9706i 1.32094 1.32094i
$$624$$ 14.4853 + 2.48528i 0.579875 + 0.0994909i
$$625$$ 0 0
$$626$$ 7.41421i 0.296332i
$$627$$ −4.00000 + 2.82843i −0.159745 + 0.112956i
$$628$$ −17.3431 17.3431i −0.692067 0.692067i
$$629$$ −0.970563 −0.0386989
$$630$$ 0 0
$$631$$ −16.9706 −0.675587 −0.337794 0.941220i $$-0.609681\pi$$
−0.337794 + 0.941220i $$0.609681\pi$$
$$632$$ 12.1421 + 12.1421i 0.482988 + 0.482988i
$$633$$ 6.34315 4.48528i 0.252117 0.178274i
$$634$$ 1.35534i 0.0538274i
$$635$$ 0 0
$$636$$ 4.41421 + 0.757359i 0.175035 + 0.0300313i
$$637$$ 32.6274 32.6274i 1.29275 1.29275i
$$638$$ 0.242641 0.242641i 0.00960624 0.00960624i
$$639$$ −7.02944 2.48528i −0.278080 0.0983162i
$$640$$ 0 0
$$641$$ 32.6274i 1.28871i −0.764728 0.644353i $$-0.777127\pi$$
0.764728 0.644353i $$-0.222873\pi$$
$$642$$ 0.142136 + 0.201010i 0.00560965 + 0.00793324i
$$643$$ 9.24264 + 9.24264i 0.364494 + 0.364494i 0.865464 0.500970i $$-0.167023\pi$$
−0.500970 + 0.865464i $$0.667023\pi$$
$$644$$ −40.4853 −1.59534
$$645$$ 0 0
$$646$$ −4.68629 −0.184380
$$647$$ 11.7279 + 11.7279i 0.461072 + 0.461072i 0.899007 0.437935i $$-0.144290\pi$$
−0.437935 + 0.899007i $$0.644290\pi$$
$$648$$ 14.1924 1.50610i 0.557530 0.0591651i
$$649$$ 4.00000i 0.157014i
$$650$$ 0 0
$$651$$ 4.48528 26.1421i 0.175792 1.02459i
$$652$$ −6.55635 + 6.55635i −0.256766 + 0.256766i
$$653$$ 8.65685 8.65685i 0.338769 0.338769i −0.517135 0.855904i $$-0.673001\pi$$
0.855904 + 0.517135i $$0.173001\pi$$
$$654$$ 0.384776 2.24264i 0.0150459 0.0876942i
$$655$$ 0 0
$$656$$ 22.9706i 0.896850i
$$657$$ 0 0
$$658$$ 14.4853 + 14.4853i 0.564695 + 0.564695i
$$659$$ 24.9706 0.972715 0.486358 0.873760i $$-0.338325\pi$$
0.486358 + 0.873760i $$0.338325\pi$$
$$660$$ 0 0
$$661$$ 14.0000 0.544537 0.272268 0.962221i $$-0.412226\pi$$
0.272268 + 0.962221i $$0.412226\pi$$
$$662$$ 1.89949 + 1.89949i 0.0738260 + 0.0738260i
$$663$$ 11.3137 + 16.0000i 0.439388 + 0.621389i
$$664$$ 20.3431i 0.789467i
$$665$$ 0 0
$$666$$ −0.100505 + 0.284271i −0.00389449 + 0.0110153i
$$667$$ −2.68629 + 2.68629i −0.104014 + 0.104014i
$$668$$ 26.9289 26.9289i 1.04191 1.04191i
$$669$$ −39.9706 6.85786i −1.54535 0.265140i
$$670$$ 0 0
$$671$$ 6.48528i 0.250362i
$$672$$ −30.1421 + 21.3137i −1.16276 + 0.822194i
$$673$$ 22.3431 + 22.3431i 0.861265 + 0.861265i 0.991485 0.130220i $$-0.0415684\pi$$
−0.130220 + 0.991485i $$0.541568\pi$$
$$674$$ −6.34315 −0.244329
$$675$$ 0 0
$$676$$ −9.14214 −0.351621
$$677$$ 19.6569 + 19.6569i 0.755474 + 0.755474i 0.975495 0.220021i $$-0.0706126\pi$$
−0.220021 + 0.975495i $$0.570613\pi$$
$$678$$ −4.82843 + 3.41421i −0.185435 + 0.131122i
$$679$$ 72.7696i 2.79264i
$$680$$ 0 0
$$681$$ −24.7279 4.24264i −0.947576 0.162578i
$$682$$ 0.928932 0.928932i 0.0355707 0.0355707i
$$683$$ 7.72792 7.72792i 0.295701 0.295701i −0.543627 0.839327i $$-0.682949\pi$$
0.839327 + 0.543627i $$0.182949\pi$$
$$684$$ 5.17157 14.6274i 0.197740 0.559293i
$$685$$ 0 0
$$686$$ 18.6274i 0.711198i
$$687$$ −9.65685 13.6569i −0.368432 0.521041i
$$688$$ 0.727922 + 0.727922i 0.0277518 + 0.0277518i
$$689$$ 4.00000 0.152388
$$690$$ 0 0
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ −15.5147 15.5147i −0.589781 0.589781i
$$693$$ −13.0711 + 6.24264i −0.496529 + 0.237138i
$$694$$ 1.11270i 0.0422375i
$$695$$ 0 0
$$696$$ −0.384776 + 2.24264i −0.0145849 + 0.0850071i
$$697$$ −21.6569 + 21.6569i −0.820312 + 0.820312i
$$698$$ −8.78680 + 8.78680i −0.332585 + 0.332585i
$$699$$ −8.14214 + 47.4558i −0.307964 + 1.79494i
$$700$$ 0 0
$$701$$ 1.31371i 0.0496181i 0.999692 + 0.0248090i $$0.00789777\pi$$
−0.999692 + 0.0248090i $$0.992102\pi$$
$$702$$ 5.85786 1.65685i 0.221091 0.0625339i
$$703$$ 0.485281 + 0.485281i 0.0183027 + 0.0183027i
$$704$$ 4.17157 0.157222
$$705$$ 0 0
$$706$$ −4.58579 −0.172588
$$707$$ −24.4853 24.4853i −0.920864 0.920864i
$$708$$ 7.31371 + 10.3431i 0.274866 + 0.388719i
$$709$$ 29.3137i 1.10090i 0.834868 + 0.550450i $$0.185544\pi$$
−0.834868 + 0.550450i $$0.814456\pi$$
$$710$$ 0 0
$$711$$ −30.6274 10.8284i −1.14862 0.406098i
$$712$$ −10.8284 + 10.8284i −0.405812 + 0.405812i
$$713$$ −10.2843 + 10.2843i −0.385149 + 0.385149i
$$714$$ −13.6569 2.34315i −0.511095 0.0876900i
$$715$$ 0 0
$$716$$ 44.1421i 1.64967i
$$717$$ −33.6569 + 23.7990i −1.25694 + 0.888790i
$$718$$ −6.48528 6.48528i −0.242029 0.242029i
$$719$$ 22.7696 0.849161 0.424581 0.905390i $$-0.360422\pi$$
0.424581 + 0.905390i $$0.360422\pi$$
$$720$$ 0 0
$$721$$ 43.7990 1.63116
$$722$$ −3.22183 3.22183i −0.119904 0.119904i
$$723$$ −0.201010 + 0.142136i −0.00747565 + 0.00528608i
$$724$$ 10.3431i 0.384400i
$$725$$ 0 0
$$726$$ −0.707107 0.121320i −0.0262432 0.00450262i
$$727$$ −20.2132 + 20.2132i −0.749666 + 0.749666i −0.974416 0.224750i $$-0.927843\pi$$
0.224750 + 0.974416i $$0.427843\pi$$
$$728$$ −15.3137 + 15.3137i −0.567564 + 0.567564i
$$729$$ −23.0000 + 14.1421i −0.851852 + 0.523783i
$$730$$ 0 0
$$731$$ 1.37258i 0.0507668i
$$732$$ −11.8579 16.7696i −0.438279 0.619821i
$$733$$ −3.79899 3.79899i −0.140319 0.140319i 0.633458 0.773777i $$-0.281635\pi$$
−0.773777 + 0.633458i $$0.781635\pi$$
$$734$$ −0.644661 −0.0237949
$$735$$ 0 0
$$736$$ 20.2426 0.746154
$$737$$ −6.41421 6.41421i −0.236271 0.236271i
$$738$$ 4.10051 + 8.58579i 0.150942 + 0.316047i
$$739$$ 14.6274i 0.538078i −0.963129 0.269039i $$-0.913294\pi$$
0.963129 0.269039i $$-0.0867061\pi$$
$$740$$ 0 0
$$741$$ 2.34315 13.6569i 0.0860776 0.501697i
$$742$$ −2.00000 + 2.00000i −0.0734223 + 0.0734223i
$$743$$ −26.0416 + 26.0416i −0.955375 + 0.955375i −0.999046 0.0436712i $$-0.986095\pi$$
0.0436712 + 0.999046i $$0.486095\pi$$
$$744$$ −1.47309 + 8.58579i −0.0540060 + 0.314770i
$$745$$ 0 0
$$746$$ 2.05887i 0.0753808i
$$747$$ 16.5858 + 34.7279i 0.606842 + 1.27063i
$$748$$ 5.17157 + 5.17157i 0.189091 + 0.189091i
$$749$$ 1.65685 0.0605401
$$750$$ 0 0
$$751$$ −46.6274 −1.70146 −0.850729 0.525604i $$-0.823839\pi$$
−0.850729 + 0.525604i $$0.823839\pi$$
$$752$$ 21.7279 + 21.7279i 0.792336 + 0.792336i
$$753$$ 16.1421 + 22.8284i 0.588252 + 0.831914i
$$754$$ 0.970563i 0.0353458i
$$755$$ 0 0
$$756$$ 22.3848 40.0416i 0.814126 1.45630i
$$757$$ −0.171573 + 0.171573i −0.00623592 + 0.00623592i −0.710218 0.703982i $$-0.751404\pi$$
0.703982 + 0.710218i $$0.251404\pi$$
$$758$$ 8.24264 8.24264i 0.299386 0.299386i
$$759$$ 7.82843 + 1.34315i 0.284154 + 0.0487531i
$$760$$ 0 0
$$761$$ 1.51472i 0.0549085i 0.999623 + 0.0274543i $$0.00874006\pi$$
−0.999623 + 0.0274543i $$0.991260\pi$$
$$762$$ −1.17157 + 0.828427i −0.0424416 + 0.0300107i
$$763$$ −10.8284 10.8284i −0.392015 0.392015i
$$764$$ 20.6863 0.748404
$$765$$ 0 0
$$766$$ 3.55635 0.128496
$$767$$ 8.00000 + 8.00000i 0.288863 + 0.288863i
$$768$$ −5.61522 + 3.97056i −0.202622 + 0.143275i
$$769$$ 52.6274i 1.89779i 0.315587 + 0.948897i $$0.397799\pi$$
−0.315587 + 0.948897i $$0.602201\pi$$
$$770$$ 0 0
$$771$$ 4.41421 + 0.757359i 0.158974 + 0.0272756i
$$772$$ −14.6274 + 14.6274i −0.526452 + 0.526452i
$$773$$ 10.6569 10.6569i 0.383300 0.383300i −0.488989 0.872290i $$-0.662634\pi$$
0.872290 + 0.488989i $$0.162634\pi$$
$$774$$ 0.402020 + 0.142136i 0.0144503 + 0.00510896i
$$775$$ 0 0
$$776$$ 23.8995i 0.857942i
$$777$$ 1.17157 + 1.65685i 0.0420299 + 0.0594393i
$$778$$ −5.07107 5.07107i −0.181807 0.181807i
$$779$$ 21.6569 0.775937
$$780$$ 0 0
$$781$$ −2.48528 −0.0889304
$$782$$ 5.37258 + 5.37258i 0.192123 + 0.192123i
$$783$$ −1.17157 4.14214i −0.0418686 0.148028i
$$784$$