# Properties

 Label 546.2.e.f.545.3 Level $546$ Weight $2$ Character 546.545 Analytic conductor $4.360$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.10070523904.11 Defining polynomial: $$x^{8} - 10 x^{4} + 81$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 545.3 Root $$-0.420861 + 1.68014i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.545 Dual form 546.2.e.f.545.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +(-0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +3.36028i q^{5} +(0.420861 + 1.68014i) q^{6} +(2.37608 + 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +(-0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +3.36028i q^{5} +(0.420861 + 1.68014i) q^{6} +(2.37608 + 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} -3.36028i q^{10} +(-0.420861 - 1.68014i) q^{12} +(-2.79694 + 2.27533i) q^{13} +(-2.37608 - 1.16372i) q^{14} +(5.64575 - 1.41421i) q^{15} +1.00000 q^{16} -7.82087 q^{17} +(2.64575 - 1.41421i) q^{18} -5.59388 q^{19} +3.36028i q^{20} +(0.955218 - 4.48191i) q^{21} -0.500983i q^{23} +(0.420861 + 1.68014i) q^{24} -6.29150 q^{25} +(2.79694 - 2.27533i) q^{26} +(3.48957 + 3.85005i) q^{27} +(2.37608 + 1.16372i) q^{28} -5.15587i q^{29} +(-5.64575 + 1.41421i) q^{30} -3.06871 q^{31} -1.00000 q^{32} +7.82087 q^{34} +(-3.91044 + 7.98430i) q^{35} +(-2.64575 + 1.41421i) q^{36} +2.32744i q^{37} +5.59388 q^{38} +(5.00000 + 3.74166i) q^{39} -3.36028i q^{40} +9.87000i q^{41} +(-0.955218 + 4.48191i) q^{42} +8.00000 q^{43} +(-4.75216 - 8.89047i) q^{45} +0.500983i q^{46} +4.33981i q^{47} +(-0.420861 - 1.68014i) q^{48} +(4.29150 + 5.53019i) q^{49} +6.29150 q^{50} +(3.29150 + 13.1402i) q^{51} +(-2.79694 + 2.27533i) q^{52} -0.500983i q^{53} +(-3.48957 - 3.85005i) q^{54} +(-2.37608 - 1.16372i) q^{56} +(2.35425 + 9.39851i) q^{57} +5.15587i q^{58} -2.16991i q^{59} +(5.64575 - 1.41421i) q^{60} -4.55066i q^{61} +3.06871 q^{62} +(-7.93227 + 0.281364i) q^{63} +1.00000 q^{64} +(-7.64575 - 9.39851i) q^{65} +13.1402i q^{67} -7.82087 q^{68} +(-0.841723 + 0.210845i) q^{69} +(3.91044 - 7.98430i) q^{70} -6.58301 q^{71} +(2.64575 - 1.41421i) q^{72} +12.5730 q^{73} -2.32744i q^{74} +(2.64785 + 10.5706i) q^{75} -5.59388 q^{76} +(-5.00000 - 3.74166i) q^{78} -0.708497 q^{79} +3.36028i q^{80} +(5.00000 - 7.48331i) q^{81} -9.87000i q^{82} -11.2712i q^{83} +(0.955218 - 4.48191i) q^{84} -26.2803i q^{85} -8.00000 q^{86} +(-8.66259 + 2.16991i) q^{87} -3.14944i q^{89} +(4.75216 + 8.89047i) q^{90} +(-9.29360 + 2.15150i) q^{91} -0.500983i q^{92} +(1.29150 + 5.15587i) q^{93} -4.33981i q^{94} -18.7970i q^{95} +(0.420861 + 1.68014i) q^{96} -10.8896 q^{97} +(-4.29150 - 5.53019i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 8q^{2} + 8q^{4} - 8q^{8} + O(q^{10})$$ $$8q - 8q^{2} + 8q^{4} - 8q^{8} + 24q^{15} + 8q^{16} - 8q^{21} - 8q^{25} - 24q^{30} - 8q^{32} + 40q^{39} + 8q^{42} + 64q^{43} - 8q^{49} + 8q^{50} - 16q^{51} + 40q^{57} + 24q^{60} + 8q^{63} + 8q^{64} - 40q^{65} + 32q^{71} - 40q^{78} - 48q^{79} + 40q^{81} - 8q^{84} - 64q^{86} - 32q^{91} - 32q^{93} + 8q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ −0.420861 1.68014i −0.242984 0.970030i
$$4$$ 1.00000 0.500000
$$5$$ 3.36028i 1.50276i 0.659867 + 0.751382i $$0.270612\pi$$
−0.659867 + 0.751382i $$0.729388\pi$$
$$6$$ 0.420861 + 1.68014i 0.171816 + 0.685915i
$$7$$ 2.37608 + 1.16372i 0.898073 + 0.439846i
$$8$$ −1.00000 −0.353553
$$9$$ −2.64575 + 1.41421i −0.881917 + 0.471405i
$$10$$ 3.36028i 1.06261i
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ −0.420861 1.68014i −0.121492 0.485015i
$$13$$ −2.79694 + 2.27533i −0.775732 + 0.631063i
$$14$$ −2.37608 1.16372i −0.635034 0.311018i
$$15$$ 5.64575 1.41421i 1.45773 0.365148i
$$16$$ 1.00000 0.250000
$$17$$ −7.82087 −1.89684 −0.948420 0.317017i $$-0.897319\pi$$
−0.948420 + 0.317017i $$0.897319\pi$$
$$18$$ 2.64575 1.41421i 0.623610 0.333333i
$$19$$ −5.59388 −1.28332 −0.641662 0.766987i $$-0.721755\pi$$
−0.641662 + 0.766987i $$0.721755\pi$$
$$20$$ 3.36028i 0.751382i
$$21$$ 0.955218 4.48191i 0.208446 0.978034i
$$22$$ 0 0
$$23$$ 0.500983i 0.104462i −0.998635 0.0522311i $$-0.983367\pi$$
0.998635 0.0522311i $$-0.0166333\pi$$
$$24$$ 0.420861 + 1.68014i 0.0859080 + 0.342957i
$$25$$ −6.29150 −1.25830
$$26$$ 2.79694 2.27533i 0.548525 0.446229i
$$27$$ 3.48957 + 3.85005i 0.671569 + 0.740942i
$$28$$ 2.37608 + 1.16372i 0.449037 + 0.219923i
$$29$$ 5.15587i 0.957421i −0.877973 0.478711i $$-0.841104\pi$$
0.877973 0.478711i $$-0.158896\pi$$
$$30$$ −5.64575 + 1.41421i −1.03077 + 0.258199i
$$31$$ −3.06871 −0.551157 −0.275578 0.961279i $$-0.588869\pi$$
−0.275578 + 0.961279i $$0.588869\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 7.82087 1.34127
$$35$$ −3.91044 + 7.98430i −0.660984 + 1.34959i
$$36$$ −2.64575 + 1.41421i −0.440959 + 0.235702i
$$37$$ 2.32744i 0.382629i 0.981529 + 0.191315i $$0.0612751\pi$$
−0.981529 + 0.191315i $$0.938725\pi$$
$$38$$ 5.59388 0.907447
$$39$$ 5.00000 + 3.74166i 0.800641 + 0.599145i
$$40$$ 3.36028i 0.531307i
$$41$$ 9.87000i 1.54144i 0.637177 + 0.770718i $$0.280102\pi$$
−0.637177 + 0.770718i $$0.719898\pi$$
$$42$$ −0.955218 + 4.48191i −0.147393 + 0.691574i
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0 0
$$45$$ −4.75216 8.89047i −0.708410 1.32531i
$$46$$ 0.500983i 0.0738660i
$$47$$ 4.33981i 0.633027i 0.948588 + 0.316513i $$0.102512\pi$$
−0.948588 + 0.316513i $$0.897488\pi$$
$$48$$ −0.420861 1.68014i −0.0607461 0.242508i
$$49$$ 4.29150 + 5.53019i 0.613072 + 0.790027i
$$50$$ 6.29150 0.889753
$$51$$ 3.29150 + 13.1402i 0.460903 + 1.83999i
$$52$$ −2.79694 + 2.27533i −0.387866 + 0.315531i
$$53$$ 0.500983i 0.0688153i −0.999408 0.0344077i $$-0.989046\pi$$
0.999408 0.0344077i $$-0.0109545\pi$$
$$54$$ −3.48957 3.85005i −0.474871 0.523925i
$$55$$ 0 0
$$56$$ −2.37608 1.16372i −0.317517 0.155509i
$$57$$ 2.35425 + 9.39851i 0.311828 + 1.24486i
$$58$$ 5.15587i 0.676999i
$$59$$ 2.16991i 0.282498i −0.989974 0.141249i $$-0.954888\pi$$
0.989974 0.141249i $$-0.0451118\pi$$
$$60$$ 5.64575 1.41421i 0.728863 0.182574i
$$61$$ 4.55066i 0.582652i −0.956624 0.291326i $$-0.905904\pi$$
0.956624 0.291326i $$-0.0940965\pi$$
$$62$$ 3.06871 0.389727
$$63$$ −7.93227 + 0.281364i −0.999372 + 0.0354486i
$$64$$ 1.00000 0.125000
$$65$$ −7.64575 9.39851i −0.948339 1.16574i
$$66$$ 0 0
$$67$$ 13.1402i 1.60533i 0.596432 + 0.802664i $$0.296585\pi$$
−0.596432 + 0.802664i $$0.703415\pi$$
$$68$$ −7.82087 −0.948420
$$69$$ −0.841723 + 0.210845i −0.101332 + 0.0253827i
$$70$$ 3.91044 7.98430i 0.467386 0.954306i
$$71$$ −6.58301 −0.781259 −0.390629 0.920548i $$-0.627743\pi$$
−0.390629 + 0.920548i $$0.627743\pi$$
$$72$$ 2.64575 1.41421i 0.311805 0.166667i
$$73$$ 12.5730 1.47156 0.735781 0.677220i $$-0.236815\pi$$
0.735781 + 0.677220i $$0.236815\pi$$
$$74$$ 2.32744i 0.270560i
$$75$$ 2.64785 + 10.5706i 0.305747 + 1.22059i
$$76$$ −5.59388 −0.641662
$$77$$ 0 0
$$78$$ −5.00000 3.74166i −0.566139 0.423659i
$$79$$ −0.708497 −0.0797122 −0.0398561 0.999205i $$-0.512690\pi$$
−0.0398561 + 0.999205i $$0.512690\pi$$
$$80$$ 3.36028i 0.375691i
$$81$$ 5.00000 7.48331i 0.555556 0.831479i
$$82$$ 9.87000i 1.08996i
$$83$$ 11.2712i 1.23718i −0.785715 0.618589i $$-0.787705\pi$$
0.785715 0.618589i $$-0.212295\pi$$
$$84$$ 0.955218 4.48191i 0.104223 0.489017i
$$85$$ 26.2803i 2.85050i
$$86$$ −8.00000 −0.862662
$$87$$ −8.66259 + 2.16991i −0.928727 + 0.232638i
$$88$$ 0 0
$$89$$ 3.14944i 0.333840i −0.985970 0.166920i $$-0.946618\pi$$
0.985970 0.166920i $$-0.0533821\pi$$
$$90$$ 4.75216 + 8.89047i 0.500921 + 0.937138i
$$91$$ −9.29360 + 2.15150i −0.974234 + 0.225539i
$$92$$ 0.500983i 0.0522311i
$$93$$ 1.29150 + 5.15587i 0.133923 + 0.534639i
$$94$$ 4.33981i 0.447618i
$$95$$ 18.7970i 1.92853i
$$96$$ 0.420861 + 1.68014i 0.0429540 + 0.171479i
$$97$$ −10.8896 −1.10567 −0.552835 0.833291i $$-0.686454\pi$$
−0.552835 + 0.833291i $$0.686454\pi$$
$$98$$ −4.29150 5.53019i −0.433507 0.558634i
$$99$$ 0 0
$$100$$ −6.29150 −0.629150
$$101$$ 10.3460 1.02947 0.514735 0.857350i $$-0.327890\pi$$
0.514735 + 0.857350i $$0.327890\pi$$
$$102$$ −3.29150 13.1402i −0.325907 1.30107i
$$103$$ 16.5906i 1.63472i 0.576129 + 0.817359i $$0.304563\pi$$
−0.576129 + 0.817359i $$0.695437\pi$$
$$104$$ 2.79694 2.27533i 0.274263 0.223114i
$$105$$ 15.0605 + 3.20980i 1.46975 + 0.313245i
$$106$$ 0.500983i 0.0486598i
$$107$$ 5.65685i 0.546869i 0.961891 + 0.273434i $$0.0881596\pi$$
−0.961891 + 0.273434i $$0.911840\pi$$
$$108$$ 3.48957 + 3.85005i 0.335784 + 0.370471i
$$109$$ 6.98233i 0.668786i −0.942434 0.334393i $$-0.891469\pi$$
0.942434 0.334393i $$-0.108531\pi$$
$$110$$ 0 0
$$111$$ 3.91044 0.979531i 0.371162 0.0929730i
$$112$$ 2.37608 + 1.16372i 0.224518 + 0.109961i
$$113$$ 14.1421i 1.33038i 0.746674 + 0.665190i $$0.231650\pi$$
−0.746674 + 0.665190i $$0.768350\pi$$
$$114$$ −2.35425 9.39851i −0.220496 0.880251i
$$115$$ 1.68345 0.156982
$$116$$ 5.15587i 0.478711i
$$117$$ 4.18221 9.97543i 0.386645 0.922229i
$$118$$ 2.16991i 0.199756i
$$119$$ −18.5830 9.10132i −1.70350 0.834316i
$$120$$ −5.64575 + 1.41421i −0.515384 + 0.129099i
$$121$$ −11.0000 −1.00000
$$122$$ 4.55066i 0.411997i
$$123$$ 16.5830 4.15390i 1.49524 0.374545i
$$124$$ −3.06871 −0.275578
$$125$$ 4.33981i 0.388165i
$$126$$ 7.93227 0.281364i 0.706662 0.0250659i
$$127$$ 14.5830 1.29403 0.647016 0.762476i $$-0.276017\pi$$
0.647016 + 0.762476i $$0.276017\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −3.36689 13.4411i −0.296438 1.18343i
$$130$$ 7.64575 + 9.39851i 0.670577 + 0.824304i
$$131$$ 18.1669 1.58725 0.793625 0.608407i $$-0.208191\pi$$
0.793625 + 0.608407i $$0.208191\pi$$
$$132$$ 0 0
$$133$$ −13.2915 6.50972i −1.15252 0.564464i
$$134$$ 13.1402i 1.13514i
$$135$$ −12.9373 + 11.7260i −1.11346 + 1.00921i
$$136$$ 7.82087 0.670634
$$137$$ 9.29150 0.793827 0.396913 0.917856i $$-0.370081\pi$$
0.396913 + 0.917856i $$0.370081\pi$$
$$138$$ 0.841723 0.210845i 0.0716522 0.0179483i
$$139$$ 0.979531i 0.0830828i 0.999137 + 0.0415414i $$0.0132268\pi$$
−0.999137 + 0.0415414i $$0.986773\pi$$
$$140$$ −3.91044 + 7.98430i −0.330492 + 0.674796i
$$141$$ 7.29150 1.82646i 0.614055 0.153816i
$$142$$ 6.58301 0.552434
$$143$$ 0 0
$$144$$ −2.64575 + 1.41421i −0.220479 + 0.117851i
$$145$$ 17.3252 1.43878
$$146$$ −12.5730 −1.04055
$$147$$ 7.48537 9.53778i 0.617383 0.786662i
$$148$$ 2.32744i 0.191315i
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ −2.64785 10.5706i −0.216196 0.863087i
$$151$$ 6.15784i 0.501118i 0.968101 + 0.250559i $$0.0806144\pi$$
−0.968101 + 0.250559i $$0.919386\pi$$
$$152$$ 5.59388 0.453724
$$153$$ 20.6921 11.0604i 1.67286 0.894179i
$$154$$ 0 0
$$155$$ 10.3117i 0.828259i
$$156$$ 5.00000 + 3.74166i 0.400320 + 0.299572i
$$157$$ 17.5701i 1.40225i 0.713040 + 0.701123i $$0.247318\pi$$
−0.713040 + 0.701123i $$0.752682\pi$$
$$158$$ 0.708497 0.0563650
$$159$$ −0.841723 + 0.210845i −0.0667530 + 0.0167211i
$$160$$ 3.36028i 0.265654i
$$161$$ 0.583005 1.19038i 0.0459472 0.0938148i
$$162$$ −5.00000 + 7.48331i −0.392837 + 0.587945i
$$163$$ 8.48528i 0.664619i −0.943170 0.332309i $$-0.892172\pi$$
0.943170 0.332309i $$-0.107828\pi$$
$$164$$ 9.87000i 0.770718i
$$165$$ 0 0
$$166$$ 11.2712i 0.874817i
$$167$$ 6.72057i 0.520053i −0.965601 0.260027i $$-0.916269\pi$$
0.965601 0.260027i $$-0.0837313\pi$$
$$168$$ −0.955218 + 4.48191i −0.0736966 + 0.345787i
$$169$$ 2.64575 12.7279i 0.203519 0.979071i
$$170$$ 26.2803i 2.01561i
$$171$$ 14.8000 7.91094i 1.13179 0.604965i
$$172$$ 8.00000 0.609994
$$173$$ −5.29570 −0.402625 −0.201312 0.979527i $$-0.564521\pi$$
−0.201312 + 0.979527i $$0.564521\pi$$
$$174$$ 8.66259 2.16991i 0.656709 0.164500i
$$175$$ −14.9491 7.32156i −1.13005 0.553458i
$$176$$ 0 0
$$177$$ −3.64575 + 0.913230i −0.274031 + 0.0686426i
$$178$$ 3.14944i 0.236060i
$$179$$ 11.3137i 0.845626i −0.906217 0.422813i $$-0.861043\pi$$
0.906217 0.422813i $$-0.138957\pi$$
$$180$$ −4.75216 8.89047i −0.354205 0.662657i
$$181$$ 24.7124i 1.83686i −0.395589 0.918428i $$-0.629460\pi$$
0.395589 0.918428i $$-0.370540\pi$$
$$182$$ 9.29360 2.15150i 0.688888 0.159480i
$$183$$ −7.64575 + 1.91520i −0.565190 + 0.141575i
$$184$$ 0.500983i 0.0369330i
$$185$$ −7.82087 −0.575002
$$186$$ −1.29150 5.15587i −0.0946976 0.378047i
$$187$$ 0 0
$$188$$ 4.33981i 0.316513i
$$189$$ 3.81112 + 13.2089i 0.277218 + 0.960807i
$$190$$ 18.7970i 1.36368i
$$191$$ 7.98430i 0.577724i 0.957371 + 0.288862i $$0.0932768\pi$$
−0.957371 + 0.288862i $$0.906723\pi$$
$$192$$ −0.420861 1.68014i −0.0303731 0.121254i
$$193$$ 8.48528i 0.610784i 0.952227 + 0.305392i $$0.0987875\pi$$
−0.952227 + 0.305392i $$0.901213\pi$$
$$194$$ 10.8896 0.781826
$$195$$ −12.5730 + 16.8014i −0.900373 + 1.20317i
$$196$$ 4.29150 + 5.53019i 0.306536 + 0.395014i
$$197$$ 12.5830 0.896502 0.448251 0.893908i $$-0.352047\pi$$
0.448251 + 0.893908i $$0.352047\pi$$
$$198$$ 0 0
$$199$$ 12.6724i 0.898326i 0.893450 + 0.449163i $$0.148278\pi$$
−0.893450 + 0.449163i $$0.851722\pi$$
$$200$$ 6.29150 0.444876
$$201$$ 22.0773 5.53019i 1.55722 0.390070i
$$202$$ −10.3460 −0.727945
$$203$$ 6.00000 12.2508i 0.421117 0.859835i
$$204$$ 3.29150 + 13.1402i 0.230451 + 0.919996i
$$205$$ −33.1660 −2.31641
$$206$$ 16.5906i 1.15592i
$$207$$ 0.708497 + 1.32548i 0.0492440 + 0.0921270i
$$208$$ −2.79694 + 2.27533i −0.193933 + 0.157766i
$$209$$ 0 0
$$210$$ −15.0605 3.20980i −1.03927 0.221497i
$$211$$ −10.5830 −0.728564 −0.364282 0.931289i $$-0.618686\pi$$
−0.364282 + 0.931289i $$0.618686\pi$$
$$212$$ 0.500983i 0.0344077i
$$213$$ 2.77053 + 11.0604i 0.189834 + 0.757845i
$$214$$ 5.65685i 0.386695i
$$215$$ 26.8823i 1.83336i
$$216$$ −3.48957 3.85005i −0.237435 0.261963i
$$217$$ −7.29150 3.57113i −0.494979 0.242424i
$$218$$ 6.98233i 0.472903i
$$219$$ −5.29150 21.1245i −0.357567 1.42746i
$$220$$ 0 0
$$221$$ 21.8745 17.7951i 1.47144 1.19703i
$$222$$ −3.91044 + 0.979531i −0.262451 + 0.0657418i
$$223$$ −8.11905 −0.543692 −0.271846 0.962341i $$-0.587634\pi$$
−0.271846 + 0.962341i $$0.587634\pi$$
$$224$$ −2.37608 1.16372i −0.158758 0.0777544i
$$225$$ 16.6458 8.89753i 1.10972 0.593169i
$$226$$ 14.1421i 0.940721i
$$227$$ 17.9918i 1.19416i 0.802183 + 0.597079i $$0.203672\pi$$
−0.802183 + 0.597079i $$0.796328\pi$$
$$228$$ 2.35425 + 9.39851i 0.155914 + 0.622432i
$$229$$ −16.1853 −1.06955 −0.534777 0.844993i $$-0.679604\pi$$
−0.534777 + 0.844993i $$0.679604\pi$$
$$230$$ −1.68345 −0.111003
$$231$$ 0 0
$$232$$ 5.15587i 0.338500i
$$233$$ 22.6274i 1.48237i 0.671300 + 0.741186i $$0.265736\pi$$
−0.671300 + 0.741186i $$0.734264\pi$$
$$234$$ −4.18221 + 9.97543i −0.273399 + 0.652114i
$$235$$ −14.5830 −0.951290
$$236$$ 2.16991i 0.141249i
$$237$$ 0.298179 + 1.19038i 0.0193688 + 0.0773232i
$$238$$ 18.5830 + 9.10132i 1.20456 + 0.589951i
$$239$$ −9.87451 −0.638729 −0.319364 0.947632i $$-0.603469\pi$$
−0.319364 + 0.947632i $$0.603469\pi$$
$$240$$ 5.64575 1.41421i 0.364432 0.0912871i
$$241$$ 1.98162 0.127648 0.0638238 0.997961i $$-0.479670\pi$$
0.0638238 + 0.997961i $$0.479670\pi$$
$$242$$ 11.0000 0.707107
$$243$$ −14.6773 5.25127i −0.941551 0.336869i
$$244$$ 4.55066i 0.291326i
$$245$$ −18.5830 + 14.4207i −1.18722 + 0.921302i
$$246$$ −16.5830 + 4.15390i −1.05729 + 0.264843i
$$247$$ 15.6458 12.7279i 0.995515 0.809858i
$$248$$ 3.06871 0.194863
$$249$$ −18.9373 + 4.74362i −1.20010 + 0.300615i
$$250$$ 4.33981i 0.274474i
$$251$$ −10.3460 −0.653036 −0.326518 0.945191i $$-0.605875\pi$$
−0.326518 + 0.945191i $$0.605875\pi$$
$$252$$ −7.93227 + 0.281364i −0.499686 + 0.0177243i
$$253$$ 0 0
$$254$$ −14.5830 −0.915019
$$255$$ −44.1547 + 11.0604i −2.76507 + 0.692628i
$$256$$ 1.00000 0.0625000
$$257$$ −12.8712 −0.802884 −0.401442 0.915884i $$-0.631491\pi$$
−0.401442 + 0.915884i $$0.631491\pi$$
$$258$$ 3.36689 + 13.4411i 0.209614 + 0.836808i
$$259$$ −2.70850 + 5.53019i −0.168298 + 0.343629i
$$260$$ −7.64575 9.39851i −0.474169 0.582871i
$$261$$ 7.29150 + 13.6412i 0.451333 + 0.844366i
$$262$$ −18.1669 −1.12236
$$263$$ 8.98626i 0.554117i −0.960853 0.277058i $$-0.910640\pi$$
0.960853 0.277058i $$-0.0893596\pi$$
$$264$$ 0 0
$$265$$ 1.68345 0.103413
$$266$$ 13.2915 + 6.50972i 0.814954 + 0.399137i
$$267$$ −5.29150 + 1.32548i −0.323835 + 0.0811179i
$$268$$ 13.1402i 0.802664i
$$269$$ 20.9374 1.27658 0.638289 0.769797i $$-0.279642\pi$$
0.638289 + 0.769797i $$0.279642\pi$$
$$270$$ 12.9373 11.7260i 0.787336 0.713619i
$$271$$ 7.52269 0.456971 0.228485 0.973547i $$-0.426623\pi$$
0.228485 + 0.973547i $$0.426623\pi$$
$$272$$ −7.82087 −0.474210
$$273$$ 7.52615 + 14.7091i 0.455503 + 0.890234i
$$274$$ −9.29150 −0.561320
$$275$$ 0 0
$$276$$ −0.841723 + 0.210845i −0.0506658 + 0.0126914i
$$277$$ −11.1660 −0.670901 −0.335450 0.942058i $$-0.608888\pi$$
−0.335450 + 0.942058i $$0.608888\pi$$
$$278$$ 0.979531i 0.0587484i
$$279$$ 8.11905 4.33981i 0.486075 0.259818i
$$280$$ 3.91044 7.98430i 0.233693 0.477153i
$$281$$ −2.70850 −0.161575 −0.0807877 0.996731i $$-0.525744\pi$$
−0.0807877 + 0.996731i $$0.525744\pi$$
$$282$$ −7.29150 + 1.82646i −0.434203 + 0.108764i
$$283$$ 12.0399i 0.715698i −0.933779 0.357849i $$-0.883510\pi$$
0.933779 0.357849i $$-0.116490\pi$$
$$284$$ −6.58301 −0.390629
$$285$$ −31.5817 + 7.91094i −1.87074 + 0.468604i
$$286$$ 0 0
$$287$$ −11.4859 + 23.4519i −0.677994 + 1.38432i
$$288$$ 2.64575 1.41421i 0.155902 0.0833333i
$$289$$ 44.1660 2.59800
$$290$$ −17.3252 −1.01737
$$291$$ 4.58301 + 18.2960i 0.268661 + 1.07253i
$$292$$ 12.5730 0.735781
$$293$$ 18.7605i 1.09600i −0.836479 0.547999i $$-0.815390\pi$$
0.836479 0.547999i $$-0.184610\pi$$
$$294$$ −7.48537 + 9.53778i −0.436556 + 0.556254i
$$295$$ 7.29150 0.424528
$$296$$ 2.32744i 0.135280i
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 1.13990 + 1.40122i 0.0659222 + 0.0810347i
$$300$$ 2.64785 + 10.5706i 0.152874 + 0.610295i
$$301$$ 19.0086 + 9.30978i 1.09564 + 0.536607i
$$302$$ 6.15784i 0.354344i
$$303$$ −4.35425 17.3828i −0.250145 0.998616i
$$304$$ −5.59388 −0.320831
$$305$$ 15.2915 0.875589
$$306$$ −20.6921 + 11.0604i −1.18289 + 0.632280i
$$307$$ 2.22699 0.127101 0.0635505 0.997979i $$-0.479758\pi$$
0.0635505 + 0.997979i $$0.479758\pi$$
$$308$$ 0 0
$$309$$ 27.8745 6.98233i 1.58573 0.397211i
$$310$$ 10.3117i 0.585668i
$$311$$ 28.5129 1.61682 0.808410 0.588619i $$-0.200328\pi$$
0.808410 + 0.588619i $$0.200328\pi$$
$$312$$ −5.00000 3.74166i −0.283069 0.211830i
$$313$$ 27.3040i 1.54331i −0.636041 0.771655i $$-0.719429\pi$$
0.636041 0.771655i $$-0.280571\pi$$
$$314$$ 17.5701i 0.991538i
$$315$$ −0.945464 26.6547i −0.0532709 1.50182i
$$316$$ −0.708497 −0.0398561
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 0.841723 0.210845i 0.0472015 0.0118236i
$$319$$ 0 0
$$320$$ 3.36028i 0.187846i
$$321$$ 9.50432 2.38075i 0.530479 0.132881i
$$322$$ −0.583005 + 1.19038i −0.0324896 + 0.0663371i
$$323$$ 43.7490 2.43426
$$324$$ 5.00000 7.48331i 0.277778 0.415740i
$$325$$ 17.5970 14.3152i 0.976104 0.794067i
$$326$$ 8.48528i 0.469956i
$$327$$ −11.7313 + 2.93859i −0.648743 + 0.162505i
$$328$$ 9.87000i 0.544980i
$$329$$ −5.05034 + 10.3117i −0.278434 + 0.568505i
$$330$$ 0 0
$$331$$ 8.48528i 0.466393i −0.972430 0.233197i $$-0.925081\pi$$
0.972430 0.233197i $$-0.0749186\pi$$
$$332$$ 11.2712i 0.618589i
$$333$$ −3.29150 6.15784i −0.180373 0.337447i
$$334$$ 6.72057i 0.367733i
$$335$$ −44.1547 −2.41243
$$336$$ 0.955218 4.48191i 0.0521114 0.244508i
$$337$$ −19.8745 −1.08263 −0.541317 0.840819i $$-0.682074\pi$$
−0.541317 + 0.840819i $$0.682074\pi$$
$$338$$ −2.64575 + 12.7279i −0.143910 + 0.692308i
$$339$$ 23.7608 5.95188i 1.29051 0.323262i
$$340$$ 26.2803i 1.42525i
$$341$$ 0 0
$$342$$ −14.8000 + 7.91094i −0.800293 + 0.427775i
$$343$$ 3.76135 + 18.1343i 0.203094 + 0.979159i
$$344$$ −8.00000 −0.431331
$$345$$ −0.708497 2.82843i −0.0381442 0.152277i
$$346$$ 5.29570 0.284699
$$347$$ 31.9372i 1.71448i 0.514918 + 0.857239i $$0.327822\pi$$
−0.514918 + 0.857239i $$0.672178\pi$$
$$348$$ −8.66259 + 2.16991i −0.464364 + 0.116319i
$$349$$ −0.543544 −0.0290952 −0.0145476 0.999894i $$-0.504631\pi$$
−0.0145476 + 0.999894i $$0.504631\pi$$
$$350$$ 14.9491 + 7.32156i 0.799063 + 0.391354i
$$351$$ −18.5203 2.82843i −0.988538 0.150970i
$$352$$ 0 0
$$353$$ 30.0317i 1.59843i 0.601048 + 0.799213i $$0.294750\pi$$
−0.601048 + 0.799213i $$0.705250\pi$$
$$354$$ 3.64575 0.913230i 0.193769 0.0485376i
$$355$$ 22.1208i 1.17405i
$$356$$ 3.14944i 0.166920i
$$357$$ −7.47063 + 35.0525i −0.395388 + 1.85517i
$$358$$ 11.3137i 0.597948i
$$359$$ 27.2915 1.44039 0.720195 0.693771i $$-0.244052\pi$$
0.720195 + 0.693771i $$0.244052\pi$$
$$360$$ 4.75216 + 8.89047i 0.250461 + 0.468569i
$$361$$ 12.2915 0.646921
$$362$$ 24.7124i 1.29885i
$$363$$ 4.62948 + 18.4816i 0.242984 + 0.970030i
$$364$$ −9.29360 + 2.15150i −0.487117 + 0.112769i
$$365$$ 42.2489i 2.21141i
$$366$$ 7.64575 1.91520i 0.399650 0.100109i
$$367$$ 14.6315i 0.763759i 0.924212 + 0.381879i $$0.124723\pi$$
−0.924212 + 0.381879i $$0.875277\pi$$
$$368$$ 0.500983i 0.0261156i
$$369$$ −13.9583 26.1136i −0.726640 1.35942i
$$370$$ 7.82087 0.406588
$$371$$ 0.583005 1.19038i 0.0302681 0.0618012i
$$372$$ 1.29150 + 5.15587i 0.0669613 + 0.267319i
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ 0 0
$$375$$ −7.29150 + 1.82646i −0.376532 + 0.0943180i
$$376$$ 4.33981i 0.223809i
$$377$$ 11.7313 + 14.4207i 0.604193 + 0.742702i
$$378$$ −3.81112 13.2089i −0.196023 0.679393i
$$379$$ 30.1107i 1.54668i 0.633989 + 0.773342i $$0.281417\pi$$
−0.633989 + 0.773342i $$0.718583\pi$$
$$380$$ 18.7970i 0.964267i
$$381$$ −6.13742 24.5015i −0.314430 1.25525i
$$382$$ 7.98430i 0.408512i
$$383$$ 21.6991i 1.10877i −0.832260 0.554385i $$-0.812953\pi$$
0.832260 0.554385i $$-0.187047\pi$$
$$384$$ 0.420861 + 1.68014i 0.0214770 + 0.0857394i
$$385$$ 0 0
$$386$$ 8.48528i 0.431889i
$$387$$ −21.1660 + 11.3137i −1.07593 + 0.575108i
$$388$$ −10.8896 −0.552835
$$389$$ 9.81076i 0.497425i −0.968577 0.248713i $$-0.919993\pi$$
0.968577 0.248713i $$-0.0800075\pi$$
$$390$$ 12.5730 16.8014i 0.636660 0.850773i
$$391$$ 3.91813i 0.198148i
$$392$$ −4.29150 5.53019i −0.216754 0.279317i
$$393$$ −7.64575 30.5230i −0.385677 1.53968i
$$394$$ −12.5830 −0.633923
$$395$$ 2.38075i 0.119789i
$$396$$ 0 0
$$397$$ −26.2860 −1.31925 −0.659627 0.751593i $$-0.729286\pi$$
−0.659627 + 0.751593i $$0.729286\pi$$
$$398$$ 12.6724i 0.635212i
$$399$$ −5.34337 + 25.0713i −0.267503 + 1.25513i
$$400$$ −6.29150 −0.314575
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ −22.0773 + 5.53019i −1.10112 + 0.275821i
$$403$$ 8.58301 6.98233i 0.427550 0.347815i
$$404$$ 10.3460 0.514735
$$405$$ 25.1461 + 16.8014i 1.24952 + 0.834869i
$$406$$ −6.00000 + 12.2508i −0.297775 + 0.607995i
$$407$$ 0 0
$$408$$ −3.29150 13.1402i −0.162954 0.650535i
$$409$$ 4.75216 0.234979 0.117490 0.993074i $$-0.462515\pi$$
0.117490 + 0.993074i $$0.462515\pi$$
$$410$$ 33.1660 1.63795
$$411$$ −3.91044 15.6110i −0.192888 0.770036i
$$412$$ 16.5906i 0.817359i
$$413$$ 2.52517 5.15587i 0.124255 0.253704i
$$414$$ −0.708497 1.32548i −0.0348207 0.0651437i
$$415$$ 37.8745 1.85919
$$416$$ 2.79694 2.27533i 0.137131 0.111557i
$$417$$ 1.64575 0.412247i 0.0805928 0.0201878i
$$418$$ 0 0
$$419$$ −15.3964 −0.752162 −0.376081 0.926587i $$-0.622729\pi$$
−0.376081 + 0.926587i $$0.622729\pi$$
$$420$$ 15.0605 + 3.20980i 0.734877 + 0.156622i
$$421$$ 19.2980i 0.940527i −0.882526 0.470264i $$-0.844159\pi$$
0.882526 0.470264i $$-0.155841\pi$$
$$422$$ 10.5830 0.515173
$$423$$ −6.13742 11.4821i −0.298412 0.558277i
$$424$$ 0.500983i 0.0243299i
$$425$$ 49.2050 2.38679
$$426$$ −2.77053 11.0604i −0.134233 0.535877i
$$427$$ 5.29570 10.8127i 0.256277 0.523264i
$$428$$ 5.65685i 0.273434i
$$429$$ 0 0
$$430$$ 26.8823i 1.29638i
$$431$$ 3.29150 0.158546 0.0792731 0.996853i $$-0.474740\pi$$
0.0792731 + 0.996853i $$0.474740\pi$$
$$432$$ 3.48957 + 3.85005i 0.167892 + 0.185236i
$$433$$ 1.95906i 0.0941465i −0.998891 0.0470733i $$-0.985011\pi$$
0.998891 0.0470733i $$-0.0149894\pi$$
$$434$$ 7.29150 + 3.57113i 0.350003 + 0.171420i
$$435$$ −7.29150 29.1088i −0.349601 1.39566i
$$436$$ 6.98233i 0.334393i
$$437$$ 2.80244i 0.134059i
$$438$$ 5.29150 + 21.1245i 0.252838 + 1.00937i
$$439$$ 14.6315i 0.698324i 0.937062 + 0.349162i $$0.113534\pi$$
−0.937062 + 0.349162i $$0.886466\pi$$
$$440$$ 0 0
$$441$$ −19.1751 8.56241i −0.913101 0.407734i
$$442$$ −21.8745 + 17.7951i −1.04046 + 0.846425i
$$443$$ 5.65685i 0.268765i 0.990930 + 0.134383i $$0.0429051\pi$$
−0.990930 + 0.134383i $$0.957095\pi$$
$$444$$ 3.91044 0.979531i 0.185581 0.0464865i
$$445$$ 10.5830 0.501683
$$446$$ 8.11905 0.384448
$$447$$ 2.52517 + 10.0808i 0.119436 + 0.476808i
$$448$$ 2.37608 + 1.16372i 0.112259 + 0.0549807i
$$449$$ −22.4575 −1.05984 −0.529918 0.848049i $$-0.677777\pi$$
−0.529918 + 0.848049i $$0.677777\pi$$
$$450$$ −16.6458 + 8.89753i −0.784688 + 0.419434i
$$451$$ 0 0
$$452$$ 14.1421i 0.665190i
$$453$$ 10.3460 2.59160i 0.486099 0.121764i
$$454$$ 17.9918i 0.844397i
$$455$$ −7.22966 31.2291i −0.338931 1.46404i
$$456$$ −2.35425 9.39851i −0.110248 0.440126i
$$457$$ 17.7951i 0.832418i 0.909269 + 0.416209i $$0.136641\pi$$
−0.909269 + 0.416209i $$0.863359\pi$$
$$458$$ 16.1853 0.756289
$$459$$ −27.2915 30.1107i −1.27386 1.40545i
$$460$$ 1.68345 0.0784911
$$461$$ 25.9027i 1.20641i −0.797586 0.603205i $$-0.793890\pi$$
0.797586 0.603205i $$-0.206110\pi$$
$$462$$ 0 0
$$463$$ 11.6372i 0.540827i −0.962744 0.270414i $$-0.912840\pi$$
0.962744 0.270414i $$-0.0871605\pi$$
$$464$$ 5.15587i 0.239355i
$$465$$ −17.3252 + 4.33981i −0.803436 + 0.201254i
$$466$$ 22.6274i 1.04819i
$$467$$ 33.8086 1.56448 0.782239 0.622979i $$-0.214078\pi$$
0.782239 + 0.622979i $$0.214078\pi$$
$$468$$ 4.18221 9.97543i 0.193323 0.461114i
$$469$$ −15.2915 + 31.2221i −0.706096 + 1.44170i
$$470$$ 14.5830 0.672664
$$471$$ 29.5203 7.39458i 1.36022 0.340724i
$$472$$ 2.16991i 0.0998781i
$$473$$ 0 0
$$474$$ −0.298179 1.19038i −0.0136958 0.0546758i
$$475$$ 35.1939 1.61481
$$476$$ −18.5830 9.10132i −0.851751 0.417158i
$$477$$ 0.708497 + 1.32548i 0.0324399 + 0.0606894i
$$478$$ 9.87451 0.451649
$$479$$ 35.9836i 1.64413i −0.569392 0.822066i $$-0.692821\pi$$
0.569392 0.822066i $$-0.307179\pi$$
$$480$$ −5.64575 + 1.41421i −0.257692 + 0.0645497i
$$481$$ −5.29570 6.50972i −0.241463 0.296818i
$$482$$ −1.98162 −0.0902605
$$483$$ −2.24536 0.478548i −0.102168 0.0217747i
$$484$$ −11.0000 −0.500000
$$485$$ 36.5921i 1.66156i
$$486$$ 14.6773 + 5.25127i 0.665777 + 0.238202i
$$487$$ 20.1225i 0.911838i 0.890021 + 0.455919i $$0.150689\pi$$
−0.890021 + 0.455919i $$0.849311\pi$$
$$488$$ 4.55066i 0.205999i
$$489$$ −14.2565 + 3.57113i −0.644700 + 0.161492i
$$490$$ 18.5830 14.4207i 0.839495 0.651459i
$$491$$ 3.65292i 0.164854i −0.996597 0.0824270i $$-0.973733\pi$$
0.996597 0.0824270i $$-0.0262671\pi$$
$$492$$ 16.5830 4.15390i 0.747620 0.187272i
$$493$$ 40.3234i 1.81607i
$$494$$ −15.6458 + 12.7279i −0.703936 + 0.572656i
$$495$$ 0 0
$$496$$ −3.06871 −0.137789
$$497$$ −15.6417 7.66079i −0.701628 0.343633i
$$498$$ 18.9373 4.74362i 0.848599 0.212567i
$$499$$ 3.83039i 0.171472i 0.996318 + 0.0857360i $$0.0273242\pi$$
−0.996318 + 0.0857360i $$0.972676\pi$$
$$500$$ 4.33981i 0.194082i
$$501$$ −11.2915 + 2.82843i −0.504467 + 0.126365i
$$502$$ 10.3460 0.461766
$$503$$ 15.6417 0.697431 0.348715 0.937229i $$-0.386618\pi$$
0.348715 + 0.937229i $$0.386618\pi$$
$$504$$ 7.93227 0.281364i 0.353331 0.0125330i
$$505$$ 34.7656i 1.54705i
$$506$$ 0 0
$$507$$ −22.4982 + 0.911455i −0.999180 + 0.0404791i
$$508$$ 14.5830 0.647016
$$509$$ 25.9027i 1.14812i −0.818814 0.574059i $$-0.805368\pi$$
0.818814 0.574059i $$-0.194632\pi$$
$$510$$ 44.1547 11.0604i 1.95520 0.489762i
$$511$$ 29.8745 + 14.6315i 1.32157 + 0.647260i
$$512$$ −1.00000 −0.0441942
$$513$$ −19.5203 21.5367i −0.861840 0.950869i
$$514$$ 12.8712 0.567725
$$515$$ −55.7490 −2.45660
$$516$$ −3.36689 13.4411i −0.148219 0.591713i
$$517$$ 0 0
$$518$$ 2.70850 5.53019i 0.119005 0.242983i
$$519$$ 2.22876 + 8.89753i 0.0978316 + 0.390558i
$$520$$ 7.64575 + 9.39851i 0.335288 + 0.412152i
$$521$$ −36.3338 −1.59181 −0.795907 0.605419i $$-0.793005\pi$$
−0.795907 + 0.605419i $$0.793005\pi$$
$$522$$ −7.29150 13.6412i −0.319140 0.597057i
$$523$$ 13.9990i 0.612132i −0.952010 0.306066i $$-0.900987\pi$$
0.952010 0.306066i $$-0.0990129\pi$$
$$524$$ 18.1669 0.793625
$$525$$ −6.00975 + 28.1980i −0.262287 + 1.23066i
$$526$$ 8.98626i 0.391820i
$$527$$ 24.0000 1.04546
$$528$$ 0 0
$$529$$ 22.7490 0.989088
$$530$$ −1.68345 −0.0731242
$$531$$ 3.06871 + 5.74103i 0.133171 + 0.249140i
$$532$$ −13.2915 6.50972i −0.576260 0.282232i
$$533$$ −22.4575 27.6058i −0.972743 1.19574i
$$534$$ 5.29150 1.32548i 0.228986 0.0573590i
$$535$$ −19.0086 −0.821815
$$536$$ 13.1402i 0.567569i
$$537$$ −19.0086 + 4.76150i −0.820283 + 0.205474i
$$538$$ −20.9374 −0.902677
$$539$$ 0 0
$$540$$ −12.9373 + 11.7260i −0.556731 + 0.504605i
$$541$$ 37.9176i 1.63020i −0.579318 0.815102i $$-0.696681\pi$$
0.579318 0.815102i $$-0.303319\pi$$
$$542$$ −7.52269 −0.323127
$$543$$ −41.5203 + 10.4005i −1.78180 + 0.446327i
$$544$$ 7.82087 0.335317
$$545$$ 23.4626 1.00503
$$546$$ −7.52615 14.7091i −0.322089 0.629491i
$$547$$ 14.5830 0.623524 0.311762 0.950160i $$-0.399081\pi$$
0.311762 + 0.950160i $$0.399081\pi$$
$$548$$ 9.29150 0.396913
$$549$$ 6.43560 + 12.0399i 0.274665 + 0.513851i
$$550$$ 0 0
$$551$$ 28.8413i 1.22868i
$$552$$ 0.841723 0.210845i 0.0358261 0.00897414i
$$553$$ −1.68345 0.824494i −0.0715874 0.0350610i
$$554$$ 11.1660 0.474398
$$555$$ 3.29150 + 13.1402i 0.139717 + 0.557769i
$$556$$ 0.979531i 0.0415414i
$$557$$ −19.1660 −0.812090 −0.406045 0.913853i $$-0.633092\pi$$
−0.406045 + 0.913853i $$0.633092\pi$$
$$558$$ −8.11905 + 4.33981i −0.343707 + 0.183719i
$$559$$ −22.3755 + 18.2026i −0.946384 + 0.769889i
$$560$$ −3.91044 + 7.98430i −0.165246 + 0.337398i
$$561$$ 0 0
$$562$$ 2.70850 0.114251
$$563$$ 33.8086 1.42486 0.712432 0.701741i $$-0.247594\pi$$
0.712432 + 0.701741i $$0.247594\pi$$
$$564$$ 7.29150 1.82646i 0.307028 0.0769079i
$$565$$ −47.5216 −1.99925
$$566$$ 12.0399i 0.506075i
$$567$$ 20.5889 11.9623i 0.864652 0.502371i
$$568$$ 6.58301 0.276217
$$569$$ 15.1441i 0.634874i −0.948279 0.317437i $$-0.897178\pi$$
0.948279 0.317437i $$-0.102822\pi$$
$$570$$ 31.5817 7.91094i 1.32281 0.331353i
$$571$$ −22.5830 −0.945069 −0.472535 0.881312i $$-0.656661\pi$$
−0.472535 + 0.881312i $$0.656661\pi$$
$$572$$ 0 0
$$573$$ 13.4148 3.36028i 0.560409 0.140378i
$$574$$ 11.4859 23.4519i 0.479414 0.978864i
$$575$$ 3.15194i 0.131445i
$$576$$ −2.64575 + 1.41421i −0.110240 + 0.0589256i
$$577$$ −3.06871 −0.127752 −0.0638761 0.997958i $$-0.520346\pi$$
−0.0638761 + 0.997958i $$0.520346\pi$$
$$578$$ −44.1660 −1.83706
$$579$$ 14.2565 3.57113i 0.592479 0.148411i
$$580$$ 17.3252 0.719389
$$581$$ 13.1166 26.7813i 0.544167 1.11108i
$$582$$ −4.58301 18.2960i −0.189972 0.758395i
$$583$$ 0 0
$$584$$ −12.5730 −0.520276
$$585$$ 33.5203 + 14.0534i 1.38589 + 0.581037i
$$586$$ 18.7605i 0.774988i
$$587$$ 19.9509i 0.823460i 0.911306 + 0.411730i $$0.135075\pi$$
−0.911306 + 0.411730i $$0.864925\pi$$
$$588$$ 7.48537 9.53778i 0.308692 0.393331i
$$589$$ 17.1660 0.707313
$$590$$ −7.29150 −0.300186
$$591$$ −5.29570 21.1412i −0.217836 0.869634i
$$592$$ 2.32744i 0.0956574i
$$593$$ 3.99282i 0.163965i 0.996634 + 0.0819827i $$0.0261252\pi$$
−0.996634 + 0.0819827i $$0.973875\pi$$
$$594$$ 0 0
$$595$$ 30.5830 62.4442i 1.25378 2.55996i
$$596$$ −6.00000 −0.245770
$$597$$ 21.2915 5.33334i 0.871403 0.218279i
$$598$$ −1.13990 1.40122i −0.0466141 0.0573002i
$$599$$ 43.5744i 1.78040i 0.455568 + 0.890201i $$0.349436\pi$$
−0.455568 + 0.890201i $$0.650564\pi$$
$$600$$ −2.64785 10.5706i −0.108098 0.431544i
$$601$$ 18.2026i 0.742501i 0.928533 + 0.371251i $$0.121071\pi$$
−0.928533 + 0.371251i $$0.878929\pi$$
$$602$$ −19.0086 9.30978i −0.774734 0.379438i
$$603$$ −18.5830 34.7656i −0.756758 1.41577i
$$604$$ 6.15784i 0.250559i
$$605$$ 36.9631i 1.50276i
$$606$$ 4.35425 + 17.3828i 0.176879 + 0.706128i
$$607$$ 18.5496i 0.752906i 0.926436 + 0.376453i $$0.122856\pi$$
−0.926436 + 0.376453i $$0.877144\pi$$
$$608$$ 5.59388 0.226862
$$609$$ −23.1082 4.92498i −0.936390 0.199570i
$$610$$ −15.2915 −0.619135
$$611$$ −9.87451 12.1382i −0.399480 0.491059i
$$612$$ 20.6921 11.0604i 0.836428 0.447089i
$$613$$ 9.98823i 0.403421i −0.979445 0.201710i $$-0.935350\pi$$
0.979445 0.201710i $$-0.0646500\pi$$
$$614$$ −2.22699 −0.0898740
$$615$$ 13.9583 + 55.7236i 0.562853 + 2.24699i
$$616$$ 0 0
$$617$$ 31.1660 1.25470 0.627348 0.778739i $$-0.284140\pi$$
0.627348 + 0.778739i $$0.284140\pi$$
$$618$$ −27.8745 + 6.98233i −1.12128 + 0.280871i
$$619$$ 33.5105 1.34690 0.673450 0.739233i $$-0.264812\pi$$
0.673450 + 0.739233i $$0.264812\pi$$
$$620$$ 10.3117i 0.414130i
$$621$$ 1.92881 1.74822i 0.0774005 0.0701536i
$$622$$ −28.5129 −1.14327
$$623$$ 3.66507 7.48331i 0.146838 0.299813i
$$624$$ 5.00000 + 3.74166i 0.200160 + 0.149786i
$$625$$ −16.8745 −0.674980
$$626$$ 27.3040i 1.09129i
$$627$$ 0 0
$$628$$ 17.5701i 0.701123i
$$629$$ 18.2026i 0.725787i
$$630$$ 0.945464 + 26.6547i 0.0376682 + 1.06195i
$$631$$ 33.2627i 1.32417i 0.749431 + 0.662083i $$0.230327\pi$$
−0.749431 + 0.662083i $$0.769673\pi$$
$$632$$ 0.708497 0.0281825
$$633$$ 4.45398 + 17.7809i 0.177030 + 0.706729i
$$634$$ −6.00000 −0.238290
$$635$$ 49.0030i 1.94463i
$$636$$ −0.841723 + 0.210845i −0.0333765 + 0.00836053i
$$637$$ −24.5861 5.70303i −0.974136 0.225962i
$$638$$ 0 0
$$639$$ 17.4170 9.30978i 0.689006 0.368289i
$$640$$ 3.36028i 0.132827i
$$641$$ 1.82646i 0.0721409i 0.999349 + 0.0360704i $$0.0114841\pi$$
−0.999349 + 0.0360704i $$0.988516\pi$$
$$642$$ −9.50432 + 2.38075i −0.375105 + 0.0939608i
$$643$$ −5.59388 −0.220601 −0.110301 0.993898i $$-0.535181\pi$$
−0.110301 + 0.993898i $$0.535181\pi$$
$$644$$ 0.583005 1.19038i 0.0229736 0.0469074i
$$645$$ 45.1660 11.3137i 1.77841 0.445477i
$$646$$ −43.7490 −1.72128
$$647$$ −36.3338 −1.42843 −0.714215 0.699926i $$-0.753216\pi$$
−0.714215 + 0.699926i $$0.753216\pi$$
$$648$$ −5.00000 + 7.48331i −0.196419 + 0.293972i
$$649$$ 0 0
$$650$$ −17.5970 + 14.3152i −0.690209 + 0.561490i
$$651$$ −2.93129 + 13.7537i −0.114886 + 0.539050i
$$652$$ 8.48528i 0.332309i
$$653$$ 35.0891i 1.37314i 0.727062 + 0.686572i $$0.240885\pi$$
−0.727062 + 0.686572i $$0.759115\pi$$
$$654$$ 11.7313 2.93859i 0.458730 0.114908i
$$655$$ 61.0460i 2.38526i
$$656$$ 9.87000i 0.385359i
$$657$$ −33.2651 + 17.7809i −1.29780 + 0.693701i
$$658$$ 5.05034 10.3117i 0.196883 0.401994i
$$659$$ 15.9686i 0.622048i −0.950402 0.311024i $$-0.899328\pi$$
0.950402 0.311024i $$-0.100672\pi$$
$$660$$ 0 0
$$661$$ 12.3277 0.479491 0.239745 0.970836i $$-0.422936\pi$$
0.239745 + 0.970836i $$0.422936\pi$$
$$662$$ 8.48528i 0.329790i
$$663$$ −39.1044 29.2630i −1.51869 1.13648i
$$664$$ 11.2712i 0.437408i
$$665$$ 21.8745 44.6632i 0.848257 1.73197i
$$666$$ 3.29150 + 6.15784i 0.127543 + 0.238611i
$$667$$ −2.58301 −0.100014
$$668$$ 6.72057i 0.260027i
$$669$$ 3.41699 + 13.6412i 0.132109 + 0.527397i
$$670$$ 44.1547 1.70584
$$671$$ 0 0
$$672$$ −0.955218 + 4.48191i −0.0368483 + 0.172894i
$$673$$ 2.00000 0.0770943 0.0385472 0.999257i $$-0.487727\pi$$
0.0385472 + 0.999257i $$0.487727\pi$$
$$674$$ 19.8745 0.765537
$$675$$ −21.9547 24.2226i −0.845035 0.932328i
$$676$$ 2.64575 12.7279i 0.101760 0.489535i
$$677$$ −15.8871 −0.610591 −0.305296 0.952258i $$-0.598755\pi$$
−0.305296 + 0.952258i $$0.598755\pi$$
$$678$$ −23.7608 + 5.95188i −0.912528 + 0.228581i
$$679$$ −25.8745 12.6724i −0.992972 0.486324i
$$680$$ 26.2803i 1.00780i
$$681$$ 30.2288 7.57205i 1.15837 0.290162i
$$682$$ 0 0
$$683$$ −29.4170 −1.12561 −0.562805 0.826590i $$-0.690278\pi$$
−0.562805 + 0.826590i $$0.690278\pi$$
$$684$$ 14.8000 7.91094i 0.565893 0.302482i
$$685$$ 31.2221i 1.19293i
$$686$$ −3.76135 18.1343i −0.143609 0.692370i
$$687$$ 6.81176 + 27.1936i 0.259885 + 1.03750i
$$688$$ 8.00000 0.304997
$$689$$ 1.13990 + 1.40122i 0.0434268 + 0.0533822i
$$690$$ 0.708497 + 2.82843i 0.0269720 + 0.107676i
$$691$$ −0.543544 −0.0206774 −0.0103387 0.999947i $$-0.503291\pi$$
−0.0103387 + 0.999947i $$0.503291\pi$$
$$692$$ −5.29570 −0.201312
$$693$$ 0 0
$$694$$ 31.9372i 1.21232i
$$695$$ −3.29150 −0.124854
$$696$$ 8.66259 2.16991i 0.328355 0.0822501i
$$697$$ 77.1920i 2.92386i
$$698$$ 0.543544 0.0205734
$$699$$ 38.0173 9.52301i 1.43794 0.360193i
$$700$$ −14.9491 7.32156i −0.565023 0.276729i
$$701$$ 16.4696i 0.622047i 0.950402 + 0.311024i $$0.100672\pi$$
−0.950402 + 0.311024i $$0.899328\pi$$
$$702$$ 18.5203 + 2.82843i 0.699002 + 0.106752i
$$703$$ 13.0194i 0.491038i
$$704$$ 0 0
$$705$$ 6.13742 + 24.5015i 0.231149 + 0.922780i
$$706$$ 30.0317i 1.13026i
$$707$$ 24.5830 + 12.0399i 0.924539 + 0.452807i
$$708$$ −3.64575 + 0.913230i −0.137016 + 0.0343213i
$$709$$ 36.2686i 1.36209i 0.732239 + 0.681047i $$0.238475\pi$$
−0.732239 + 0.681047i $$0.761525\pi$$
$$710$$ 22.1208i 0.830177i
$$711$$ 1.87451 1.00197i 0.0702995 0.0375767i
$$712$$ 3.14944i 0.118030i
$$713$$ 1.53737i 0.0575751i
$$714$$ 7.47063 35.0525i 0.279581 1.31181i
$$715$$ 0 0
$$716$$ 11.3137i 0.422813i
$$717$$ 4.15580 + 16.5906i 0.155201 + 0.619586i
$$718$$ −27.2915 −1.01851
$$719$$ 33.5633 1.25170 0.625850 0.779944i $$-0.284752\pi$$
0.625850 + 0.779944i $$0.284752\pi$$
$$720$$ −4.75216 8.89047i −0.177102 0.331328i
$$721$$ −19.3068 + 39.4205i −0.719023 + 1.46810i
$$722$$ −12.2915 −0.457442
$$723$$ −0.833990 3.32941i −0.0310164 0.123822i
$$724$$ 24.7124i 0.918428i
$$725$$ 32.4382i 1.20472i
$$726$$ −4.62948 18.4816i −0.171816 0.685915i
$$727$$ 34.7932i 1.29041i −0.764010 0.645204i $$-0.776772\pi$$
0.764010 0.645204i $$-0.223228\pi$$
$$728$$ 9.29360 2.15150i 0.344444 0.0797400i
$$729$$ −2.64575 + 26.8701i −0.0979908 + 0.995187i
$$730$$ 42.2489i 1.56370i
$$731$$ −62.5670 −2.31412
$$732$$ −7.64575 + 1.91520i −0.282595 + 0.0707877i
$$733$$ 46.3817 1.71315 0.856573 0.516026i $$-0.172589\pi$$
0.856573 + 0.516026i $$0.172589\pi$$
$$734$$ 14.6315i 0.540059i
$$735$$ 32.0496 + 25.1530i 1.18217 + 0.927782i
$$736$$ 0.500983i 0.0184665i
$$737$$ 0 0
$$738$$ 13.9583 + 26.1136i 0.513812 + 0.961254i
$$739$$ 3.83039i 0.140903i −0.997515 0.0704517i $$-0.977556\pi$$
0.997515 0.0704517i $$-0.0224441\pi$$
$$740$$ −7.82087 −0.287501
$$741$$ −27.9694 20.9304i −1.02748 0.768897i
$$742$$ −0.583005 + 1.19038i −0.0214028 + 0.0437001i
$$743$$ −3.29150 −0.120754 −0.0603768 0.998176i $$-0.519230\pi$$
−0.0603768 + 0.998176i $$0.519230\pi$$
$$744$$ −1.29150 5.15587i −0.0473488 0.189023i
$$745$$ 20.1617i 0.738667i
$$746$$ 22.0000 0.805477
$$747$$ 15.9399 + 29.8209i 0.583211 + 1.09109i
$$748$$ 0 0
$$749$$ −6.58301 + 13.4411i −0.240538 + 0.491128i
$$750$$ 7.29150 1.82646i 0.266248 0.0666929i
$$751$$ −29.1660 −1.06428 −0.532141 0.846655i $$-0.678613\pi$$
−0.532141 + 0.846655i $$0.678613\pi$$
$$752$$ 4.33981i 0.158257i
$$753$$ 4.35425 + 17.3828i 0.158678 + 0.633465i
$$754$$ −11.7313 14.4207i −0.427229 0.525170i
$$755$$ −20.6921 −0.753062
$$756$$ 3.81112 + 13.2089i 0.138609 + 0.480404i
$$757$$ −16.5830 −0.602720 −0.301360 0.953511i $$-0.597441\pi$$
−0.301360 + 0.953511i $$0.597441\pi$$
$$758$$ 30.1107i 1.09367i
$$759$$ 0 0
$$760$$ 18.7970i 0.681840i
$$761$$ 28.0726i 1.01763i 0.860875 + 0.508816i $$0.169917\pi$$
−0.860875 + 0.508816i $$0.830083\pi$$
$$762$$ 6.13742 + 24.5015i 0.222335 + 0.887596i
$$763$$ 8.12549 16.5906i 0.294163 0.600619i
$$764$$ 7.98430i 0.288862i
$$765$$ 37.1660 + 69.5312i 1.34374 + 2.51391i
$$766$$ 21.6991i 0.784019i
$$767$$ 4.93725 + 6.06910i 0.178274 + 0.219143i
$$768$$ −0.420861 1.68014i −0.0151865 0.0606269i
$$769$$ −36.6320 −1.32098 −0.660492 0.750833i $$-0.729652\pi$$
−0.660492 + 0.750833i $$0.729652\pi$$
$$770$$ 0 0
$$771$$ 5.41699 + 21.6255i 0.195088 + 0.778822i
$$772$$ 8.48528i 0.305392i
$$773$$ 5.74103i 0.206491i −0.994656 0.103245i $$-0.967077\pi$$
0.994656 0.103245i $$-0.0329227\pi$$
$$774$$ 21.1660 11.3137i 0.760797 0.406663i
$$775$$ 19.3068 0.693521
$$776$$ 10.8896 0.390913
$$777$$ 10.4314 + 2.22322i 0.374225 + 0.0797574i
$$778$$ 9.81076i 0.351733i
$$779$$ 55.2116i 1.97816i
$$780$$ −12.5730 + 16.8014i −0.450187 + 0.601587i
$$781$$ 0 0
$$782$$ 3.91813i 0.140112i
$$783$$ 19.8504 17.9918i 0.709394 0.642974i
$$784$$ 4.29150 + 5.53019i 0.153268 + 0.197507i
$$785$$ −59.0405