# Properties

 Label 147.2.e.d.67.2 Level $147$ Weight $2$ Character 147.67 Analytic conductor $1.174$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 147.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.17380090971$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.2 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 147.67 Dual form 147.2.e.d.79.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(-0.292893 - 0.507306i) q^{5} -2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(-0.292893 - 0.507306i) q^{5} -2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.707107 - 1.22474i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.91421 - 3.31552i) q^{12} +5.41421 q^{13} +0.585786 q^{15} +(-1.50000 - 2.59808i) q^{16} +(-3.12132 + 5.40629i) q^{17} +(1.20711 - 2.09077i) q^{18} +(-1.41421 - 2.44949i) q^{19} +2.24264 q^{20} +4.82843 q^{22} +(-1.82843 - 3.16693i) q^{23} +(2.20711 - 3.82282i) q^{24} +(2.32843 - 4.03295i) q^{25} +(6.53553 + 11.3199i) q^{26} +1.00000 q^{27} -1.17157 q^{29} +(0.707107 + 1.22474i) q^{30} +(3.41421 - 5.91359i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(1.00000 + 1.73205i) q^{33} -15.0711 q^{34} +3.82843 q^{36} +(2.00000 + 3.46410i) q^{37} +(3.41421 - 5.91359i) q^{38} +(-2.70711 + 4.68885i) q^{39} +(1.29289 + 2.23936i) q^{40} -2.24264 q^{41} -5.65685 q^{43} +(3.82843 + 6.63103i) q^{44} +(-0.292893 + 0.507306i) q^{45} +(4.41421 - 7.64564i) q^{46} +(-1.41421 - 2.44949i) q^{47} +3.00000 q^{48} +11.2426 q^{50} +(-3.12132 - 5.40629i) q^{51} +(-10.3640 + 17.9509i) q^{52} +(1.00000 - 1.73205i) q^{53} +(1.20711 + 2.09077i) q^{54} -1.17157 q^{55} +2.82843 q^{57} +(-1.41421 - 2.44949i) q^{58} +(3.41421 - 5.91359i) q^{59} +(-1.12132 + 1.94218i) q^{60} +(-1.87868 - 3.25397i) q^{61} +16.4853 q^{62} -9.82843 q^{64} +(-1.58579 - 2.74666i) q^{65} +(-2.41421 + 4.18154i) q^{66} +(-2.82843 + 4.89898i) q^{67} +(-11.9497 - 20.6976i) q^{68} +3.65685 q^{69} -13.3137 q^{71} +(2.20711 + 3.82282i) q^{72} +(2.94975 - 5.10911i) q^{73} +(-4.82843 + 8.36308i) q^{74} +(2.32843 + 4.03295i) q^{75} +10.8284 q^{76} -13.0711 q^{78} +(-1.17157 - 2.02922i) q^{79} +(-0.878680 + 1.52192i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.70711 - 4.68885i) q^{82} -15.3137 q^{83} +3.65685 q^{85} +(-6.82843 - 11.8272i) q^{86} +(0.585786 - 1.01461i) q^{87} +(-4.41421 + 7.64564i) q^{88} +(2.87868 + 4.98602i) q^{89} -1.41421 q^{90} +14.0000 q^{92} +(3.41421 + 5.91359i) q^{93} +(3.41421 - 5.91359i) q^{94} +(-0.828427 + 1.43488i) q^{95} +(-0.792893 - 1.37333i) q^{96} +5.41421 q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} - 4q^{6} - 12q^{8} - 2q^{9} + O(q^{10})$$ $$4q + 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} - 4q^{6} - 12q^{8} - 2q^{9} + 4q^{11} - 2q^{12} + 16q^{13} + 8q^{15} - 6q^{16} - 4q^{17} + 2q^{18} - 8q^{20} + 8q^{22} + 4q^{23} + 6q^{24} - 2q^{25} + 12q^{26} + 4q^{27} - 16q^{29} + 8q^{31} - 6q^{32} + 4q^{33} - 32q^{34} + 4q^{36} + 8q^{37} + 8q^{38} - 8q^{39} + 8q^{40} + 8q^{41} + 4q^{44} - 4q^{45} + 12q^{46} + 12q^{48} + 28q^{50} - 4q^{51} - 16q^{52} + 4q^{53} + 2q^{54} - 16q^{55} + 8q^{59} + 4q^{60} - 16q^{61} + 32q^{62} - 28q^{64} - 12q^{65} - 4q^{66} - 28q^{68} - 8q^{69} - 8q^{71} + 6q^{72} - 8q^{73} - 8q^{74} - 2q^{75} + 32q^{76} - 24q^{78} - 16q^{79} - 12q^{80} - 2q^{81} - 8q^{82} - 16q^{83} - 8q^{85} - 16q^{86} + 8q^{87} - 12q^{88} + 20q^{89} + 56q^{92} + 8q^{93} + 8q^{94} + 8q^{95} - 6q^{96} + 16q^{97} - 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$$.

 $$n$$ $$50$$ $$52$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.20711 + 2.09077i 0.853553 + 1.47840i 0.877981 + 0.478696i $$0.158890\pi$$
−0.0244272 + 0.999702i $$0.507776\pi$$
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ −1.91421 + 3.31552i −0.957107 + 1.65776i
$$5$$ −0.292893 0.507306i −0.130986 0.226874i 0.793071 0.609129i $$-0.208481\pi$$
−0.924057 + 0.382255i $$0.875148\pi$$
$$6$$ −2.41421 −0.985599
$$7$$ 0 0
$$8$$ −4.41421 −1.56066
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0.707107 1.22474i 0.223607 0.387298i
$$11$$ 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i $$-0.735842\pi$$
0.976478 + 0.215615i $$0.0691756\pi$$
$$12$$ −1.91421 3.31552i −0.552586 0.957107i
$$13$$ 5.41421 1.50163 0.750816 0.660511i $$-0.229660\pi$$
0.750816 + 0.660511i $$0.229660\pi$$
$$14$$ 0 0
$$15$$ 0.585786 0.151249
$$16$$ −1.50000 2.59808i −0.375000 0.649519i
$$17$$ −3.12132 + 5.40629i −0.757031 + 1.31122i 0.187327 + 0.982298i $$0.440018\pi$$
−0.944358 + 0.328919i $$0.893316\pi$$
$$18$$ 1.20711 2.09077i 0.284518 0.492799i
$$19$$ −1.41421 2.44949i −0.324443 0.561951i 0.656957 0.753928i $$-0.271843\pi$$
−0.981399 + 0.191977i $$0.938510\pi$$
$$20$$ 2.24264 0.501470
$$21$$ 0 0
$$22$$ 4.82843 1.02942
$$23$$ −1.82843 3.16693i −0.381253 0.660350i 0.609988 0.792410i $$-0.291174\pi$$
−0.991242 + 0.132060i $$0.957841\pi$$
$$24$$ 2.20711 3.82282i 0.450524 0.780330i
$$25$$ 2.32843 4.03295i 0.465685 0.806591i
$$26$$ 6.53553 + 11.3199i 1.28172 + 2.22001i
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −1.17157 −0.217556 −0.108778 0.994066i $$-0.534694\pi$$
−0.108778 + 0.994066i $$0.534694\pi$$
$$30$$ 0.707107 + 1.22474i 0.129099 + 0.223607i
$$31$$ 3.41421 5.91359i 0.613211 1.06211i −0.377485 0.926016i $$-0.623211\pi$$
0.990696 0.136097i $$-0.0434557\pi$$
$$32$$ −0.792893 + 1.37333i −0.140165 + 0.242773i
$$33$$ 1.00000 + 1.73205i 0.174078 + 0.301511i
$$34$$ −15.0711 −2.58467
$$35$$ 0 0
$$36$$ 3.82843 0.638071
$$37$$ 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i $$-0.0600231\pi$$
−0.653476 + 0.756948i $$0.726690\pi$$
$$38$$ 3.41421 5.91359i 0.553859 0.959311i
$$39$$ −2.70711 + 4.68885i −0.433484 + 0.750816i
$$40$$ 1.29289 + 2.23936i 0.204424 + 0.354073i
$$41$$ −2.24264 −0.350242 −0.175121 0.984547i $$-0.556032\pi$$
−0.175121 + 0.984547i $$0.556032\pi$$
$$42$$ 0 0
$$43$$ −5.65685 −0.862662 −0.431331 0.902194i $$-0.641956\pi$$
−0.431331 + 0.902194i $$0.641956\pi$$
$$44$$ 3.82843 + 6.63103i 0.577157 + 0.999665i
$$45$$ −0.292893 + 0.507306i −0.0436619 + 0.0756247i
$$46$$ 4.41421 7.64564i 0.650840 1.12729i
$$47$$ −1.41421 2.44949i −0.206284 0.357295i 0.744257 0.667893i $$-0.232804\pi$$
−0.950541 + 0.310599i $$0.899470\pi$$
$$48$$ 3.00000 0.433013
$$49$$ 0 0
$$50$$ 11.2426 1.58995
$$51$$ −3.12132 5.40629i −0.437072 0.757031i
$$52$$ −10.3640 + 17.9509i −1.43722 + 2.48934i
$$53$$ 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i $$-0.789471\pi$$
0.926497 + 0.376303i $$0.122805\pi$$
$$54$$ 1.20711 + 2.09077i 0.164266 + 0.284518i
$$55$$ −1.17157 −0.157975
$$56$$ 0 0
$$57$$ 2.82843 0.374634
$$58$$ −1.41421 2.44949i −0.185695 0.321634i
$$59$$ 3.41421 5.91359i 0.444493 0.769884i −0.553524 0.832833i $$-0.686717\pi$$
0.998017 + 0.0629492i $$0.0200506\pi$$
$$60$$ −1.12132 + 1.94218i −0.144762 + 0.250735i
$$61$$ −1.87868 3.25397i −0.240540 0.416628i 0.720328 0.693634i $$-0.243991\pi$$
−0.960868 + 0.277006i $$0.910658\pi$$
$$62$$ 16.4853 2.09363
$$63$$ 0 0
$$64$$ −9.82843 −1.22855
$$65$$ −1.58579 2.74666i −0.196693 0.340682i
$$66$$ −2.41421 + 4.18154i −0.297169 + 0.514712i
$$67$$ −2.82843 + 4.89898i −0.345547 + 0.598506i −0.985453 0.169948i $$-0.945640\pi$$
0.639906 + 0.768453i $$0.278973\pi$$
$$68$$ −11.9497 20.6976i −1.44912 2.50995i
$$69$$ 3.65685 0.440234
$$70$$ 0 0
$$71$$ −13.3137 −1.58005 −0.790023 0.613077i $$-0.789932\pi$$
−0.790023 + 0.613077i $$0.789932\pi$$
$$72$$ 2.20711 + 3.82282i 0.260110 + 0.450524i
$$73$$ 2.94975 5.10911i 0.345242 0.597976i −0.640156 0.768245i $$-0.721130\pi$$
0.985398 + 0.170269i $$0.0544636\pi$$
$$74$$ −4.82843 + 8.36308i −0.561293 + 0.972188i
$$75$$ 2.32843 + 4.03295i 0.268864 + 0.465685i
$$76$$ 10.8284 1.24211
$$77$$ 0 0
$$78$$ −13.0711 −1.48001
$$79$$ −1.17157 2.02922i −0.131812 0.228306i 0.792563 0.609790i $$-0.208746\pi$$
−0.924375 + 0.381485i $$0.875413\pi$$
$$80$$ −0.878680 + 1.52192i −0.0982394 + 0.170156i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ −2.70711 4.68885i −0.298950 0.517796i
$$83$$ −15.3137 −1.68090 −0.840449 0.541891i $$-0.817709\pi$$
−0.840449 + 0.541891i $$0.817709\pi$$
$$84$$ 0 0
$$85$$ 3.65685 0.396642
$$86$$ −6.82843 11.8272i −0.736328 1.27536i
$$87$$ 0.585786 1.01461i 0.0628029 0.108778i
$$88$$ −4.41421 + 7.64564i −0.470557 + 0.815028i
$$89$$ 2.87868 + 4.98602i 0.305139 + 0.528517i 0.977292 0.211895i $$-0.0679636\pi$$
−0.672153 + 0.740412i $$0.734630\pi$$
$$90$$ −1.41421 −0.149071
$$91$$ 0 0
$$92$$ 14.0000 1.45960
$$93$$ 3.41421 + 5.91359i 0.354037 + 0.613211i
$$94$$ 3.41421 5.91359i 0.352149 0.609940i
$$95$$ −0.828427 + 1.43488i −0.0849948 + 0.147215i
$$96$$ −0.792893 1.37333i −0.0809243 0.140165i
$$97$$ 5.41421 0.549730 0.274865 0.961483i $$-0.411367\pi$$
0.274865 + 0.961483i $$0.411367\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 8.91421 + 15.4399i 0.891421 + 1.54399i
$$101$$ −8.53553 + 14.7840i −0.849317 + 1.47106i 0.0325010 + 0.999472i $$0.489653\pi$$
−0.881818 + 0.471589i $$0.843681\pi$$
$$102$$ 7.53553 13.0519i 0.746129 1.29233i
$$103$$ 6.24264 + 10.8126i 0.615106 + 1.06539i 0.990366 + 0.138475i $$0.0442200\pi$$
−0.375260 + 0.926919i $$0.622447\pi$$
$$104$$ −23.8995 −2.34354
$$105$$ 0 0
$$106$$ 4.82843 0.468978
$$107$$ 5.82843 + 10.0951i 0.563455 + 0.975933i 0.997192 + 0.0748933i $$0.0238616\pi$$
−0.433736 + 0.901040i $$0.642805\pi$$
$$108$$ −1.91421 + 3.31552i −0.184195 + 0.319036i
$$109$$ −2.82843 + 4.89898i −0.270914 + 0.469237i −0.969096 0.246683i $$-0.920659\pi$$
0.698182 + 0.715920i $$0.253993\pi$$
$$110$$ −1.41421 2.44949i −0.134840 0.233550i
$$111$$ −4.00000 −0.379663
$$112$$ 0 0
$$113$$ 17.3137 1.62874 0.814368 0.580348i $$-0.197084\pi$$
0.814368 + 0.580348i $$0.197084\pi$$
$$114$$ 3.41421 + 5.91359i 0.319770 + 0.553859i
$$115$$ −1.07107 + 1.85514i −0.0998776 + 0.172993i
$$116$$ 2.24264 3.88437i 0.208224 0.360654i
$$117$$ −2.70711 4.68885i −0.250272 0.433484i
$$118$$ 16.4853 1.51759
$$119$$ 0 0
$$120$$ −2.58579 −0.236049
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ 4.53553 7.85578i 0.410628 0.711228i
$$123$$ 1.12132 1.94218i 0.101106 0.175121i
$$124$$ 13.0711 + 22.6398i 1.17382 + 2.03311i
$$125$$ −5.65685 −0.505964
$$126$$ 0 0
$$127$$ 9.65685 0.856907 0.428454 0.903564i $$-0.359059\pi$$
0.428454 + 0.903564i $$0.359059\pi$$
$$128$$ −10.2782 17.8023i −0.908471 1.57352i
$$129$$ 2.82843 4.89898i 0.249029 0.431331i
$$130$$ 3.82843 6.63103i 0.335775 0.581580i
$$131$$ −3.65685 6.33386i −0.319501 0.553392i 0.660883 0.750489i $$-0.270182\pi$$
−0.980384 + 0.197097i $$0.936849\pi$$
$$132$$ −7.65685 −0.666444
$$133$$ 0 0
$$134$$ −13.6569 −1.17977
$$135$$ −0.292893 0.507306i −0.0252082 0.0436619i
$$136$$ 13.7782 23.8645i 1.18147 2.04636i
$$137$$ 7.07107 12.2474i 0.604122 1.04637i −0.388067 0.921631i $$-0.626857\pi$$
0.992190 0.124739i $$-0.0398094\pi$$
$$138$$ 4.41421 + 7.64564i 0.375763 + 0.650840i
$$139$$ −6.34315 −0.538019 −0.269009 0.963138i $$-0.586696\pi$$
−0.269009 + 0.963138i $$0.586696\pi$$
$$140$$ 0 0
$$141$$ 2.82843 0.238197
$$142$$ −16.0711 27.8359i −1.34865 2.33594i
$$143$$ 5.41421 9.37769i 0.452759 0.784202i
$$144$$ −1.50000 + 2.59808i −0.125000 + 0.216506i
$$145$$ 0.343146 + 0.594346i 0.0284967 + 0.0493577i
$$146$$ 14.2426 1.17873
$$147$$ 0 0
$$148$$ −15.3137 −1.25878
$$149$$ 2.65685 + 4.60181i 0.217658 + 0.376995i 0.954092 0.299515i $$-0.0968249\pi$$
−0.736434 + 0.676510i $$0.763492\pi$$
$$150$$ −5.62132 + 9.73641i −0.458979 + 0.794975i
$$151$$ −6.00000 + 10.3923i −0.488273 + 0.845714i −0.999909 0.0134886i $$-0.995706\pi$$
0.511636 + 0.859202i $$0.329040\pi$$
$$152$$ 6.24264 + 10.8126i 0.506345 + 0.877015i
$$153$$ 6.24264 0.504688
$$154$$ 0 0
$$155$$ −4.00000 −0.321288
$$156$$ −10.3640 17.9509i −0.829781 1.43722i
$$157$$ −10.1213 + 17.5306i −0.807769 + 1.39910i 0.106636 + 0.994298i $$0.465992\pi$$
−0.914406 + 0.404799i $$0.867341\pi$$
$$158$$ 2.82843 4.89898i 0.225018 0.389742i
$$159$$ 1.00000 + 1.73205i 0.0793052 + 0.137361i
$$160$$ 0.928932 0.0734385
$$161$$ 0 0
$$162$$ −2.41421 −0.189679
$$163$$ −5.65685 9.79796i −0.443079 0.767435i 0.554837 0.831959i $$-0.312781\pi$$
−0.997916 + 0.0645236i $$0.979447\pi$$
$$164$$ 4.29289 7.43551i 0.335219 0.580616i
$$165$$ 0.585786 1.01461i 0.0456034 0.0789874i
$$166$$ −18.4853 32.0174i −1.43474 2.48504i
$$167$$ 19.7990 1.53209 0.766046 0.642786i $$-0.222221\pi$$
0.766046 + 0.642786i $$0.222221\pi$$
$$168$$ 0 0
$$169$$ 16.3137 1.25490
$$170$$ 4.41421 + 7.64564i 0.338555 + 0.586394i
$$171$$ −1.41421 + 2.44949i −0.108148 + 0.187317i
$$172$$ 10.8284 18.7554i 0.825660 1.43008i
$$173$$ −3.46447 6.00063i −0.263398 0.456220i 0.703744 0.710453i $$-0.251510\pi$$
−0.967143 + 0.254234i $$0.918177\pi$$
$$174$$ 2.82843 0.214423
$$175$$ 0 0
$$176$$ −6.00000 −0.452267
$$177$$ 3.41421 + 5.91359i 0.256628 + 0.444493i
$$178$$ −6.94975 + 12.0373i −0.520906 + 0.902235i
$$179$$ 4.17157 7.22538i 0.311798 0.540050i −0.666954 0.745099i $$-0.732402\pi$$
0.978752 + 0.205049i $$0.0657354\pi$$
$$180$$ −1.12132 1.94218i −0.0835783 0.144762i
$$181$$ −5.41421 −0.402435 −0.201218 0.979547i $$-0.564490\pi$$
−0.201218 + 0.979547i $$0.564490\pi$$
$$182$$ 0 0
$$183$$ 3.75736 0.277752
$$184$$ 8.07107 + 13.9795i 0.595007 + 1.03058i
$$185$$ 1.17157 2.02922i 0.0861358 0.149191i
$$186$$ −8.24264 + 14.2767i −0.604380 + 1.04682i
$$187$$ 6.24264 + 10.8126i 0.456507 + 0.790693i
$$188$$ 10.8284 0.789744
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i $$0.0590746\pi$$
−0.331611 + 0.943416i $$0.607592\pi$$
$$192$$ 4.91421 8.51167i 0.354653 0.614277i
$$193$$ 8.65685 14.9941i 0.623134 1.07930i −0.365765 0.930707i $$-0.619192\pi$$
0.988899 0.148592i $$-0.0474742\pi$$
$$194$$ 6.53553 + 11.3199i 0.469224 + 0.812720i
$$195$$ 3.17157 0.227121
$$196$$ 0 0
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ −2.41421 4.18154i −0.171571 0.297169i
$$199$$ −5.17157 + 8.95743i −0.366603 + 0.634975i −0.989032 0.147701i $$-0.952813\pi$$
0.622429 + 0.782676i $$0.286146\pi$$
$$200$$ −10.2782 + 17.8023i −0.726777 + 1.25881i
$$201$$ −2.82843 4.89898i −0.199502 0.345547i
$$202$$ −41.2132 −2.89975
$$203$$ 0 0
$$204$$ 23.8995 1.67330
$$205$$ 0.656854 + 1.13770i 0.0458767 + 0.0794608i
$$206$$ −15.0711 + 26.1039i −1.05005 + 1.81874i
$$207$$ −1.82843 + 3.16693i −0.127084 + 0.220117i
$$208$$ −8.12132 14.0665i −0.563112 0.975339i
$$209$$ −5.65685 −0.391293
$$210$$ 0 0
$$211$$ −20.9706 −1.44367 −0.721837 0.692064i $$-0.756702\pi$$
−0.721837 + 0.692064i $$0.756702\pi$$
$$212$$ 3.82843 + 6.63103i 0.262937 + 0.455421i
$$213$$ 6.65685 11.5300i 0.456120 0.790023i
$$214$$ −14.0711 + 24.3718i −0.961878 + 1.66602i
$$215$$ 1.65685 + 2.86976i 0.112997 + 0.195716i
$$216$$ −4.41421 −0.300349
$$217$$ 0 0
$$218$$ −13.6569 −0.924959
$$219$$ 2.94975 + 5.10911i 0.199325 + 0.345242i
$$220$$ 2.24264 3.88437i 0.151199 0.261884i
$$221$$ −16.8995 + 29.2708i −1.13678 + 1.96897i
$$222$$ −4.82843 8.36308i −0.324063 0.561293i
$$223$$ −8.97056 −0.600713 −0.300357 0.953827i $$-0.597106\pi$$
−0.300357 + 0.953827i $$0.597106\pi$$
$$224$$ 0 0
$$225$$ −4.65685 −0.310457
$$226$$ 20.8995 + 36.1990i 1.39021 + 2.40792i
$$227$$ 7.89949 13.6823i 0.524308 0.908128i −0.475292 0.879828i $$-0.657657\pi$$
0.999599 0.0282996i $$-0.00900924\pi$$
$$228$$ −5.41421 + 9.37769i −0.358565 + 0.621053i
$$229$$ −4.12132 7.13834i −0.272345 0.471715i 0.697117 0.716957i $$-0.254466\pi$$
−0.969462 + 0.245243i $$0.921132\pi$$
$$230$$ −5.17157 −0.341003
$$231$$ 0 0
$$232$$ 5.17157 0.339530
$$233$$ −11.0711 19.1757i −0.725290 1.25624i −0.958855 0.283898i $$-0.908372\pi$$
0.233565 0.972341i $$-0.424961\pi$$
$$234$$ 6.53553 11.3199i 0.427241 0.740003i
$$235$$ −0.828427 + 1.43488i −0.0540406 + 0.0936011i
$$236$$ 13.0711 + 22.6398i 0.850854 + 1.47372i
$$237$$ 2.34315 0.152204
$$238$$ 0 0
$$239$$ −4.34315 −0.280935 −0.140467 0.990085i $$-0.544861\pi$$
−0.140467 + 0.990085i $$0.544861\pi$$
$$240$$ −0.878680 1.52192i −0.0567185 0.0982394i
$$241$$ 3.87868 6.71807i 0.249848 0.432749i −0.713636 0.700517i $$-0.752953\pi$$
0.963483 + 0.267768i $$0.0862861\pi$$
$$242$$ −8.44975 + 14.6354i −0.543170 + 0.940799i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 14.3848 0.920891
$$245$$ 0 0
$$246$$ 5.41421 0.345198
$$247$$ −7.65685 13.2621i −0.487194 0.843845i
$$248$$ −15.0711 + 26.1039i −0.957014 + 1.65760i
$$249$$ 7.65685 13.2621i 0.485233 0.840449i
$$250$$ −6.82843 11.8272i −0.431868 0.748017i
$$251$$ 4.48528 0.283108 0.141554 0.989931i $$-0.454790\pi$$
0.141554 + 0.989931i $$0.454790\pi$$
$$252$$ 0 0
$$253$$ −7.31371 −0.459809
$$254$$ 11.6569 + 20.1903i 0.731416 + 1.26685i
$$255$$ −1.82843 + 3.16693i −0.114501 + 0.198321i
$$256$$ 14.9853 25.9553i 0.936580 1.62220i
$$257$$ 9.60660 + 16.6391i 0.599243 + 1.03792i 0.992933 + 0.118677i $$0.0378651\pi$$
−0.393690 + 0.919243i $$0.628802\pi$$
$$258$$ 13.6569 0.850239
$$259$$ 0 0
$$260$$ 12.1421 0.753023
$$261$$ 0.585786 + 1.01461i 0.0362593 + 0.0628029i
$$262$$ 8.82843 15.2913i 0.545422 0.944699i
$$263$$ 8.65685 14.9941i 0.533805 0.924577i −0.465416 0.885092i $$-0.654095\pi$$
0.999220 0.0394843i $$-0.0125715\pi$$
$$264$$ −4.41421 7.64564i −0.271676 0.470557i
$$265$$ −1.17157 −0.0719691
$$266$$ 0 0
$$267$$ −5.75736 −0.352345
$$268$$ −10.8284 18.7554i −0.661451 1.14567i
$$269$$ −5.36396 + 9.29065i −0.327046 + 0.566461i −0.981924 0.189274i $$-0.939387\pi$$
0.654878 + 0.755735i $$0.272720\pi$$
$$270$$ 0.707107 1.22474i 0.0430331 0.0745356i
$$271$$ −9.07107 15.7116i −0.551028 0.954409i −0.998201 0.0599610i $$-0.980902\pi$$
0.447173 0.894448i $$-0.352431\pi$$
$$272$$ 18.7279 1.13555
$$273$$ 0 0
$$274$$ 34.1421 2.06260
$$275$$ −4.65685 8.06591i −0.280819 0.486393i
$$276$$ −7.00000 + 12.1244i −0.421350 + 0.729800i
$$277$$ −6.65685 + 11.5300i −0.399972 + 0.692771i −0.993722 0.111878i $$-0.964313\pi$$
0.593750 + 0.804649i $$0.297647\pi$$
$$278$$ −7.65685 13.2621i −0.459228 0.795406i
$$279$$ −6.82843 −0.408807
$$280$$ 0 0
$$281$$ −16.4853 −0.983429 −0.491715 0.870756i $$-0.663630\pi$$
−0.491715 + 0.870756i $$0.663630\pi$$
$$282$$ 3.41421 + 5.91359i 0.203313 + 0.352149i
$$283$$ −4.24264 + 7.34847i −0.252199 + 0.436821i −0.964131 0.265427i $$-0.914487\pi$$
0.711932 + 0.702248i $$0.247820\pi$$
$$284$$ 25.4853 44.1418i 1.51227 2.61933i
$$285$$ −0.828427 1.43488i −0.0490718 0.0849948i
$$286$$ 26.1421 1.54582
$$287$$ 0 0
$$288$$ 1.58579 0.0934434
$$289$$ −10.9853 19.0271i −0.646193 1.11924i
$$290$$ −0.828427 + 1.43488i −0.0486469 + 0.0842589i
$$291$$ −2.70711 + 4.68885i −0.158693 + 0.274865i
$$292$$ 11.2929 + 19.5599i 0.660867 + 1.14465i
$$293$$ 19.4142 1.13419 0.567095 0.823652i $$-0.308067\pi$$
0.567095 + 0.823652i $$0.308067\pi$$
$$294$$ 0 0
$$295$$ −4.00000 −0.232889
$$296$$ −8.82843 15.2913i −0.513142 0.888788i
$$297$$ 1.00000 1.73205i 0.0580259 0.100504i
$$298$$ −6.41421 + 11.1097i −0.371565 + 0.643570i
$$299$$ −9.89949 17.1464i −0.572503 0.991604i
$$300$$ −17.8284 −1.02932
$$301$$ 0 0
$$302$$ −28.9706 −1.66707
$$303$$ −8.53553 14.7840i −0.490354 0.849317i
$$304$$ −4.24264 + 7.34847i −0.243332 + 0.421464i
$$305$$ −1.10051 + 1.90613i −0.0630147 + 0.109145i
$$306$$ 7.53553 + 13.0519i 0.430778 + 0.746129i
$$307$$ 1.85786 0.106034 0.0530170 0.998594i $$-0.483116\pi$$
0.0530170 + 0.998594i $$0.483116\pi$$
$$308$$ 0 0
$$309$$ −12.4853 −0.710263
$$310$$ −4.82843 8.36308i −0.274236 0.474991i
$$311$$ 11.0711 19.1757i 0.627783 1.08735i −0.360213 0.932870i $$-0.617296\pi$$
0.987996 0.154481i $$-0.0493707\pi$$
$$312$$ 11.9497 20.6976i 0.676521 1.17177i
$$313$$ 8.94975 + 15.5014i 0.505870 + 0.876192i 0.999977 + 0.00679098i $$0.00216165\pi$$
−0.494107 + 0.869401i $$0.664505\pi$$
$$314$$ −48.8701 −2.75790
$$315$$ 0 0
$$316$$ 8.97056 0.504634
$$317$$ −5.00000 8.66025i −0.280828 0.486408i 0.690761 0.723083i $$-0.257276\pi$$
−0.971589 + 0.236675i $$0.923942\pi$$
$$318$$ −2.41421 + 4.18154i −0.135382 + 0.234489i
$$319$$ −1.17157 + 2.02922i −0.0655955 + 0.113615i
$$320$$ 2.87868 + 4.98602i 0.160923 + 0.278727i
$$321$$ −11.6569 −0.650622
$$322$$ 0 0
$$323$$ 17.6569 0.982454
$$324$$ −1.91421 3.31552i −0.106345 0.184195i
$$325$$ 12.6066 21.8353i 0.699288 1.21120i
$$326$$ 13.6569 23.6544i 0.756383 1.31009i
$$327$$ −2.82843 4.89898i −0.156412 0.270914i
$$328$$ 9.89949 0.546608
$$329$$ 0 0
$$330$$ 2.82843 0.155700
$$331$$ 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i $$-0.131604\pi$$
−0.805812 + 0.592172i $$0.798271\pi$$
$$332$$ 29.3137 50.7728i 1.60880 2.78652i
$$333$$ 2.00000 3.46410i 0.109599 0.189832i
$$334$$ 23.8995 + 41.3951i 1.30772 + 2.26504i
$$335$$ 3.31371 0.181047
$$336$$ 0 0
$$337$$ −18.3431 −0.999215 −0.499607 0.866252i $$-0.666522\pi$$
−0.499607 + 0.866252i $$0.666522\pi$$
$$338$$ 19.6924 + 34.1082i 1.07112 + 1.85524i
$$339$$ −8.65685 + 14.9941i −0.470176 + 0.814368i
$$340$$ −7.00000 + 12.1244i −0.379628 + 0.657536i
$$341$$ −6.82843 11.8272i −0.369780 0.640478i
$$342$$ −6.82843 −0.369239
$$343$$ 0 0
$$344$$ 24.9706 1.34632
$$345$$ −1.07107 1.85514i −0.0576644 0.0998776i
$$346$$ 8.36396 14.4868i 0.449649 0.778815i
$$347$$ −5.34315 + 9.25460i −0.286835 + 0.496813i −0.973053 0.230584i $$-0.925937\pi$$
0.686217 + 0.727396i $$0.259270\pi$$
$$348$$ 2.24264 + 3.88437i 0.120218 + 0.208224i
$$349$$ 9.89949 0.529908 0.264954 0.964261i $$-0.414643\pi$$
0.264954 + 0.964261i $$0.414643\pi$$
$$350$$ 0 0
$$351$$ 5.41421 0.288989
$$352$$ 1.58579 + 2.74666i 0.0845227 + 0.146398i
$$353$$ −5.36396 + 9.29065i −0.285495 + 0.494492i −0.972729 0.231944i $$-0.925491\pi$$
0.687234 + 0.726436i $$0.258825\pi$$
$$354$$ −8.24264 + 14.2767i −0.438091 + 0.758797i
$$355$$ 3.89949 + 6.75412i 0.206964 + 0.358472i
$$356$$ −22.0416 −1.16820
$$357$$ 0 0
$$358$$ 20.1421 1.06454
$$359$$ 5.82843 + 10.0951i 0.307613 + 0.532801i 0.977840 0.209355i $$-0.0671366\pi$$
−0.670227 + 0.742156i $$0.733803\pi$$
$$360$$ 1.29289 2.23936i 0.0681415 0.118024i
$$361$$ 5.50000 9.52628i 0.289474 0.501383i
$$362$$ −6.53553 11.3199i −0.343500 0.594960i
$$363$$ −7.00000 −0.367405
$$364$$ 0 0
$$365$$ −3.45584 −0.180887
$$366$$ 4.53553 + 7.85578i 0.237076 + 0.410628i
$$367$$ −9.65685 + 16.7262i −0.504084 + 0.873099i 0.495905 + 0.868377i $$0.334836\pi$$
−0.999989 + 0.00472187i $$0.998497\pi$$
$$368$$ −5.48528 + 9.50079i −0.285940 + 0.495263i
$$369$$ 1.12132 + 1.94218i 0.0583736 + 0.101106i
$$370$$ 5.65685 0.294086
$$371$$ 0 0
$$372$$ −26.1421 −1.35541
$$373$$ 16.6569 + 28.8505i 0.862459 + 1.49382i 0.869548 + 0.493848i $$0.164410\pi$$
−0.00708885 + 0.999975i $$0.502256\pi$$
$$374$$ −15.0711 + 26.1039i −0.779306 + 1.34980i
$$375$$ 2.82843 4.89898i 0.146059 0.252982i
$$376$$ 6.24264 + 10.8126i 0.321940 + 0.557616i
$$377$$ −6.34315 −0.326689
$$378$$ 0 0
$$379$$ 31.3137 1.60848 0.804239 0.594307i $$-0.202573\pi$$
0.804239 + 0.594307i $$0.202573\pi$$
$$380$$ −3.17157 5.49333i −0.162698 0.281802i
$$381$$ −4.82843 + 8.36308i −0.247368 + 0.428454i
$$382$$ −21.7279 + 37.6339i −1.11170 + 1.92552i
$$383$$ 14.8284 + 25.6836i 0.757697 + 1.31237i 0.944022 + 0.329882i $$0.107009\pi$$
−0.186325 + 0.982488i $$0.559658\pi$$
$$384$$ 20.5563 1.04901
$$385$$ 0 0
$$386$$ 41.7990 2.12751
$$387$$ 2.82843 + 4.89898i 0.143777 + 0.249029i
$$388$$ −10.3640 + 17.9509i −0.526150 + 0.911319i
$$389$$ −5.07107 + 8.78335i −0.257113 + 0.445333i −0.965467 0.260524i $$-0.916105\pi$$
0.708354 + 0.705857i $$0.249438\pi$$
$$390$$ 3.82843 + 6.63103i 0.193860 + 0.335775i
$$391$$ 22.8284 1.15448
$$392$$ 0 0
$$393$$ 7.31371 0.368928
$$394$$ 2.41421 + 4.18154i 0.121626 + 0.210663i
$$395$$ −0.686292 + 1.18869i −0.0345311 + 0.0598096i
$$396$$ 3.82843 6.63103i 0.192386 0.333222i
$$397$$ −17.1924 29.7781i −0.862861 1.49452i −0.869155 0.494539i $$-0.835337\pi$$
0.00629405 0.999980i $$-0.497997\pi$$
$$398$$ −24.9706 −1.25166
$$399$$ 0 0
$$400$$ −13.9706 −0.698528
$$401$$ −11.0711 19.1757i −0.552863 0.957586i −0.998066 0.0621570i $$-0.980202\pi$$
0.445204 0.895429i $$-0.353131\pi$$
$$402$$ 6.82843 11.8272i 0.340571 0.589886i
$$403$$ 18.4853 32.0174i 0.920817 1.59490i
$$404$$ −32.6777 56.5994i −1.62577 2.81592i
$$405$$ 0.585786 0.0291080
$$406$$ 0 0
$$407$$ 8.00000 0.396545
$$408$$ 13.7782 + 23.8645i 0.682121 + 1.18147i
$$409$$ 9.29289 16.0958i 0.459504 0.795884i −0.539431 0.842030i $$-0.681361\pi$$
0.998935 + 0.0461457i $$0.0146939\pi$$
$$410$$ −1.58579 + 2.74666i −0.0783164 + 0.135648i
$$411$$ 7.07107 + 12.2474i 0.348790 + 0.604122i
$$412$$ −47.7990 −2.35489
$$413$$ 0 0
$$414$$ −8.82843 −0.433894
$$415$$ 4.48528 + 7.76874i 0.220174 + 0.381352i
$$416$$ −4.29289 + 7.43551i −0.210476 + 0.364556i
$$417$$ 3.17157 5.49333i 0.155313 0.269009i
$$418$$ −6.82843 11.8272i −0.333989 0.578486i
$$419$$ 38.8284 1.89689 0.948446 0.316938i $$-0.102655\pi$$
0.948446 + 0.316938i $$0.102655\pi$$
$$420$$ 0 0
$$421$$ −28.6274 −1.39521 −0.697607 0.716480i $$-0.745752\pi$$
−0.697607 + 0.716480i $$0.745752\pi$$
$$422$$ −25.3137 43.8446i −1.23225 2.13432i
$$423$$ −1.41421 + 2.44949i −0.0687614 + 0.119098i
$$424$$ −4.41421 + 7.64564i −0.214373 + 0.371305i
$$425$$ 14.5355 + 25.1763i 0.705077 + 1.22123i
$$426$$ 32.1421 1.55729
$$427$$ 0 0
$$428$$ −44.6274 −2.15715
$$429$$ 5.41421 + 9.37769i 0.261401 + 0.452759i
$$430$$ −4.00000 + 6.92820i −0.192897 + 0.334108i
$$431$$ −3.48528 + 6.03668i −0.167880 + 0.290777i −0.937674 0.347515i $$-0.887025\pi$$
0.769794 + 0.638292i $$0.220359\pi$$
$$432$$ −1.50000 2.59808i −0.0721688 0.125000i
$$433$$ −11.7574 −0.565023 −0.282511 0.959264i $$-0.591167\pi$$
−0.282511 + 0.959264i $$0.591167\pi$$
$$434$$ 0 0
$$435$$ −0.686292 −0.0329052
$$436$$ −10.8284 18.7554i −0.518588 0.898220i
$$437$$ −5.17157 + 8.95743i −0.247390 + 0.428492i
$$438$$ −7.12132 + 12.3345i −0.340270 + 0.589365i
$$439$$ −17.6569 30.5826i −0.842716 1.45963i −0.887590 0.460634i $$-0.847622\pi$$
0.0448746 0.998993i $$-0.485711\pi$$
$$440$$ 5.17157 0.246545
$$441$$ 0 0
$$442$$ −81.5980 −3.88122
$$443$$ −0.514719 0.891519i −0.0244550 0.0423573i 0.853539 0.521029i $$-0.174452\pi$$
−0.877994 + 0.478672i $$0.841118\pi$$
$$444$$ 7.65685 13.2621i 0.363378 0.629390i
$$445$$ 1.68629 2.92074i 0.0799379 0.138456i
$$446$$ −10.8284 18.7554i −0.512741 0.888093i
$$447$$ −5.31371 −0.251330
$$448$$ 0 0
$$449$$ 17.3137 0.817084 0.408542 0.912739i $$-0.366037\pi$$
0.408542 + 0.912739i $$0.366037\pi$$
$$450$$ −5.62132 9.73641i −0.264992 0.458979i
$$451$$ −2.24264 + 3.88437i −0.105602 + 0.182908i
$$452$$ −33.1421 + 57.4039i −1.55887 + 2.70005i
$$453$$ −6.00000 10.3923i −0.281905 0.488273i
$$454$$ 38.1421 1.79010
$$455$$ 0 0
$$456$$ −12.4853 −0.584677
$$457$$ 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i $$-0.0283451\pi$$
−0.575036 + 0.818128i $$0.695012\pi$$
$$458$$ 9.94975 17.2335i 0.464921 0.805267i
$$459$$ −3.12132 + 5.40629i −0.145691 + 0.252344i
$$460$$ −4.10051 7.10228i −0.191187 0.331146i
$$461$$ −19.4142 −0.904210 −0.452105 0.891965i $$-0.649327\pi$$
−0.452105 + 0.891965i $$0.649327\pi$$
$$462$$ 0 0
$$463$$ 18.6274 0.865689 0.432845 0.901468i $$-0.357510\pi$$
0.432845 + 0.901468i $$0.357510\pi$$
$$464$$ 1.75736 + 3.04384i 0.0815834 + 0.141307i
$$465$$ 2.00000 3.46410i 0.0927478 0.160644i
$$466$$ 26.7279 46.2941i 1.23815 2.14453i
$$467$$ −19.8995 34.4669i −0.920839 1.59494i −0.798120 0.602498i $$-0.794172\pi$$
−0.122718 0.992442i $$-0.539161\pi$$
$$468$$ 20.7279 0.958149
$$469$$ 0 0
$$470$$ −4.00000 −0.184506
$$471$$ −10.1213 17.5306i −0.466366 0.807769i
$$472$$ −15.0711 + 26.1039i −0.693702 + 1.20153i
$$473$$ −5.65685 + 9.79796i −0.260102 + 0.450511i
$$474$$ 2.82843 + 4.89898i 0.129914 + 0.225018i
$$475$$ −13.1716 −0.604353
$$476$$ 0 0
$$477$$ −2.00000 −0.0915737
$$478$$ −5.24264 9.08052i −0.239793 0.415333i
$$479$$ −15.0711 + 26.1039i −0.688615 + 1.19272i 0.283671 + 0.958922i $$0.408447\pi$$
−0.972286 + 0.233794i $$0.924886\pi$$
$$480$$ −0.464466 + 0.804479i −0.0211999 + 0.0367193i
$$481$$ 10.8284 + 18.7554i 0.493734 + 0.855172i
$$482$$ 18.7279 0.853033
$$483$$ 0 0
$$484$$ −26.7990 −1.21814
$$485$$ −1.58579 2.74666i −0.0720069 0.124720i
$$486$$ 1.20711 2.09077i 0.0547555 0.0948393i
$$487$$ 9.31371 16.1318i 0.422044 0.731002i −0.574095 0.818789i $$-0.694646\pi$$
0.996139 + 0.0877864i $$0.0279793\pi$$
$$488$$ 8.29289 + 14.3637i 0.375402 + 0.650215i
$$489$$ 11.3137 0.511624
$$490$$ 0 0
$$491$$ 38.9706 1.75872 0.879358 0.476160i $$-0.157972\pi$$
0.879358 + 0.476160i $$0.157972\pi$$
$$492$$ 4.29289 + 7.43551i 0.193539 + 0.335219i
$$493$$ 3.65685 6.33386i 0.164696 0.285263i
$$494$$ 18.4853 32.0174i 0.831692 1.44053i
$$495$$ 0.585786 + 1.01461i 0.0263291 + 0.0456034i
$$496$$ −20.4853 −0.919816
$$497$$ 0 0
$$498$$ 36.9706 1.65669
$$499$$ 9.65685 + 16.7262i 0.432300 + 0.748766i 0.997071 0.0764820i $$-0.0243688\pi$$
−0.564771 + 0.825248i $$0.691035\pi$$
$$500$$ 10.8284 18.7554i 0.484262 0.838766i
$$501$$ −9.89949 + 17.1464i −0.442277 + 0.766046i
$$502$$ 5.41421 + 9.37769i 0.241648 + 0.418547i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ −8.82843 15.2913i −0.392471 0.679781i
$$507$$ −8.15685 + 14.1281i −0.362259 + 0.627450i
$$508$$ −18.4853 + 32.0174i −0.820152 + 1.42054i
$$509$$ 12.7782 + 22.1324i 0.566383 + 0.981003i 0.996920 + 0.0784305i $$0.0249909\pi$$
−0.430537 + 0.902573i $$0.641676\pi$$
$$510$$ −8.82843 −0.390929
$$511$$ 0 0
$$512$$ 31.2426 1.38074
$$513$$ −1.41421 2.44949i −0.0624391 0.108148i
$$514$$ −23.1924 + 40.1704i −1.02297 + 1.77184i
$$515$$ 3.65685 6.33386i 0.161140 0.279103i
$$516$$ 10.8284 + 18.7554i 0.476695 + 0.825660i
$$517$$ −5.65685 −0.248788
$$518$$ 0 0
$$519$$ 6.92893 0.304146
$$520$$ 7.00000 + 12.1244i 0.306970 + 0.531688i
$$521$$ 16.2929 28.2201i 0.713805 1.23635i −0.249614 0.968345i $$-0.580304\pi$$
0.963419 0.268000i $$-0.0863629\pi$$
$$522$$ −1.41421 + 2.44949i −0.0618984 + 0.107211i
$$523$$ 7.17157 + 12.4215i 0.313591 + 0.543156i 0.979137 0.203201i $$-0.0651346\pi$$
−0.665546 + 0.746357i $$0.731801\pi$$
$$524$$ 28.0000 1.22319
$$525$$ 0 0
$$526$$ 41.7990 1.82252
$$527$$ 21.3137 + 36.9164i 0.928440 + 1.60810i
$$528$$ 3.00000 5.19615i 0.130558 0.226134i
$$529$$ 4.81371 8.33759i 0.209292 0.362504i
$$530$$ −1.41421 2.44949i −0.0614295 0.106399i
$$531$$ −6.82843 −0.296328
$$532$$ 0 0
$$533$$ −12.1421 −0.525934
$$534$$ −6.94975 12.0373i −0.300745 0.520906i
$$535$$ 3.41421 5.91359i 0.147609 0.255667i
$$536$$ 12.4853 21.6251i 0.539282 0.934064i
$$537$$ 4.17157 + 7.22538i 0.180017 + 0.311798i
$$538$$ −25.8995 −1.11661
$$539$$ 0 0
$$540$$ 2.24264 0.0965079
$$541$$ 2.65685 + 4.60181i 0.114227 + 0.197847i 0.917471 0.397804i $$-0.130228\pi$$
−0.803243 + 0.595651i $$0.796894\pi$$
$$542$$ 21.8995 37.9310i 0.940664 1.62928i
$$543$$ 2.70711 4.68885i 0.116173 0.201218i
$$544$$ −4.94975 8.57321i −0.212219 0.367574i
$$545$$ 3.31371 0.141944
$$546$$ 0 0
$$547$$ −3.02944 −0.129529 −0.0647647 0.997901i $$-0.520630\pi$$
−0.0647647 + 0.997901i $$0.520630\pi$$
$$548$$ 27.0711 + 46.8885i 1.15642 + 2.00298i
$$549$$ −1.87868 + 3.25397i −0.0801801 + 0.138876i
$$550$$ 11.2426 19.4728i 0.479388 0.830324i
$$551$$ 1.65685 + 2.86976i 0.0705844 + 0.122256i
$$552$$ −16.1421 −0.687055
$$553$$ 0 0
$$554$$ −32.1421 −1.36559
$$555$$ 1.17157 + 2.02922i 0.0497305 + 0.0861358i
$$556$$ 12.1421 21.0308i 0.514941 0.891904i
$$557$$ −13.0000 + 22.5167i −0.550828 + 0.954062i 0.447387 + 0.894340i $$0.352355\pi$$
−0.998215 + 0.0597213i $$0.980979\pi$$
$$558$$ −8.24264 14.2767i −0.348939 0.604380i
$$559$$ −30.6274 −1.29540
$$560$$ 0 0
$$561$$ −12.4853 −0.527129
$$562$$ −19.8995 34.4669i −0.839410 1.45390i
$$563$$ 3.41421 5.91359i 0.143892 0.249228i −0.785067 0.619411i $$-0.787372\pi$$
0.928959 + 0.370183i $$0.120705\pi$$
$$564$$ −5.41421 + 9.37769i −0.227980 + 0.394872i
$$565$$ −5.07107 8.78335i −0.213341 0.369518i
$$566$$ −20.4853 −0.861061
$$567$$ 0 0
$$568$$ 58.7696 2.46592
$$569$$ −0.242641 0.420266i −0.0101720 0.0176185i 0.860895 0.508783i $$-0.169905\pi$$
−0.871067 + 0.491165i $$0.836571\pi$$
$$570$$ 2.00000 3.46410i 0.0837708 0.145095i
$$571$$ −16.8284 + 29.1477i −0.704248 + 1.21979i 0.262715 + 0.964874i $$0.415382\pi$$
−0.966962 + 0.254919i $$0.917951\pi$$
$$572$$ 20.7279 + 35.9018i 0.866678 + 1.50113i
$$573$$ −18.0000 −0.751961
$$574$$ 0 0
$$575$$ −17.0294 −0.710177
$$576$$ 4.91421 + 8.51167i 0.204759 + 0.354653i
$$577$$ 7.05025 12.2114i 0.293506 0.508367i −0.681130 0.732162i $$-0.738511\pi$$
0.974636 + 0.223795i $$0.0718446\pi$$
$$578$$ 26.5208 45.9354i 1.10312 1.91066i
$$579$$ 8.65685 + 14.9941i 0.359767 + 0.623134i
$$580$$ −2.62742 −0.109098
$$581$$ 0 0
$$582$$ −13.0711 −0.541813
$$583$$ −2.00000 3.46410i −0.0828315 0.143468i
$$584$$ −13.0208 + 22.5527i −0.538805 + 0.933238i
$$585$$ −1.58579 + 2.74666i −0.0655642 + 0.113561i
$$586$$ 23.4350 + 40.5907i 0.968092 + 1.67678i
$$587$$ −17.1716 −0.708747 −0.354373 0.935104i $$-0.615306\pi$$
−0.354373 + 0.935104i $$0.615306\pi$$
$$588$$ 0 0
$$589$$ −19.3137 −0.795807
$$590$$ −4.82843 8.36308i −0.198783 0.344303i
$$591$$ −1.00000 + 1.73205i −0.0411345 + 0.0712470i
$$592$$ 6.00000 10.3923i 0.246598 0.427121i
$$593$$ 10.5355 + 18.2481i 0.432643 + 0.749359i 0.997100 0.0761034i $$-0.0242479\pi$$
−0.564457 + 0.825462i $$0.690915\pi$$
$$594$$ 4.82843 0.198113
$$595$$ 0 0
$$596$$ −20.3431 −0.833288
$$597$$ −5.17157 8.95743i −0.211658 0.366603i
$$598$$ 23.8995 41.3951i 0.977323 1.69277i
$$599$$ 1.00000 1.73205i 0.0408589 0.0707697i −0.844873 0.534967i $$-0.820324\pi$$
0.885732 + 0.464198i $$0.153657\pi$$
$$600$$ −10.2782 17.8023i −0.419605 0.726777i
$$601$$ −0.928932 −0.0378919 −0.0189460 0.999821i $$-0.506031\pi$$
−0.0189460 + 0.999821i $$0.506031\pi$$
$$602$$ 0 0
$$603$$ 5.65685 0.230365
$$604$$ −22.9706 39.7862i −0.934659 1.61888i
$$605$$ 2.05025 3.55114i 0.0833546 0.144374i
$$606$$ 20.6066 35.6917i 0.837086 1.44988i
$$607$$ 14.8284 + 25.6836i 0.601867 + 1.04246i 0.992538 + 0.121934i $$0.0389097\pi$$
−0.390671 + 0.920530i $$0.627757\pi$$
$$608$$ 4.48528 0.181902
$$609$$ 0 0
$$610$$ −5.31371 −0.215146
$$611$$ −7.65685 13.2621i −0.309763 0.536526i
$$612$$ −11.9497 + 20.6976i −0.483040 + 0.836650i
$$613$$ −13.6569 + 23.6544i −0.551595 + 0.955391i 0.446565 + 0.894751i $$0.352647\pi$$
−0.998160 + 0.0606394i $$0.980686\pi$$
$$614$$ 2.24264 + 3.88437i 0.0905056 + 0.156760i
$$615$$ −1.31371 −0.0529738
$$616$$ 0 0
$$617$$ −7.51472 −0.302531 −0.151266 0.988493i $$-0.548335\pi$$
−0.151266 + 0.988493i $$0.548335\pi$$
$$618$$ −15.0711 26.1039i −0.606247 1.05005i
$$619$$ 2.48528 4.30463i 0.0998919 0.173018i −0.811748 0.584008i $$-0.801484\pi$$
0.911640 + 0.410990i $$0.134817\pi$$
$$620$$ 7.65685 13.2621i 0.307507 0.532617i
$$621$$ −1.82843 3.16693i −0.0733723 0.127084i
$$622$$ 53.4558 2.14338
$$623$$ 0 0
$$624$$ 16.2426 0.650226
$$625$$ −9.98528 17.2950i −0.399411 0.691801i
$$626$$ −21.6066 + 37.4237i −0.863573 + 1.49575i
$$627$$ 2.82843 4.89898i 0.112956 0.195646i
$$628$$ −38.7487 67.1148i −1.54624 2.67817i
$$629$$ −24.9706 −0.995642
$$630$$ 0 0
$$631$$ 0.686292 0.0273208 0.0136604 0.999907i $$-0.495652\pi$$
0.0136604 + 0.999907i $$0.495652\pi$$
$$632$$ 5.17157 + 8.95743i 0.205714 + 0.356307i
$$633$$ 10.4853 18.1610i 0.416753 0.721837i
$$634$$ 12.0711 20.9077i 0.479403 0.830351i
$$635$$ −2.82843 4.89898i −0.112243 0.194410i
$$636$$ −7.65685 −0.303614
$$637$$ 0 0
$$638$$ −5.65685 −0.223957
$$639$$ 6.65685 + 11.5300i 0.263341 + 0.456120i
$$640$$ −6.02082 + 10.4284i −0.237994 + 0.412217i
$$641$$ 2.58579 4.47871i 0.102132 0.176899i −0.810431 0.585835i $$-0.800767\pi$$
0.912563 + 0.408936i $$0.134100\pi$$
$$642$$ −14.0711 24.3718i −0.555341 0.961878i
$$643$$ 50.4264 1.98862 0.994312 0.106510i $$-0.0339675\pi$$
0.994312 + 0.106510i $$0.0339675\pi$$
$$644$$ 0 0
$$645$$ −3.31371 −0.130477
$$646$$ 21.3137 + 36.9164i 0.838577 + 1.45246i
$$647$$ −10.5858 + 18.3351i −0.416170 + 0.720828i −0.995551 0.0942294i $$-0.969961\pi$$
0.579380 + 0.815057i $$0.303295\pi$$
$$648$$ 2.20711 3.82282i 0.0867033 0.150175i
$$649$$ −6.82843 11.8272i −0.268039 0.464258i
$$650$$ 60.8701 2.38752
$$651$$ 0 0
$$652$$ 43.3137 1.69630
$$653$$ −9.75736 16.9002i −0.381835 0.661358i 0.609490 0.792794i $$-0.291374\pi$$
−0.991325 + 0.131436i $$0.958041\pi$$
$$654$$ 6.82843 11.8272i 0.267013 0.462479i
$$655$$ −2.14214 + 3.71029i −0.0837002 + 0.144973i
$$656$$ 3.36396 + 5.82655i 0.131341 + 0.227489i
$$657$$ −5.89949 −0.230161
$$658$$ 0 0
$$659$$ −13.3137 −0.518628 −0.259314 0.965793i $$-0.583497\pi$$
−0.259314 + 0.965793i $$0.583497\pi$$
$$660$$ 2.24264 + 3.88437i 0.0872947 + 0.151199i
$$661$$ −3.77817 + 6.54399i −0.146954 + 0.254532i −0.930100 0.367306i $$-0.880280\pi$$
0.783146 + 0.621838i $$0.213614\pi$$
$$662$$ −4.82843 + 8.36308i −0.187662 + 0.325040i
$$663$$ −16.8995 29.2708i −0.656322 1.13678i
$$664$$ 67.5980 2.62331
$$665$$ 0 0
$$666$$ 9.65685 0.374196
$$667$$ 2.14214 + 3.71029i 0.0829438 + 0.143663i
$$668$$ −37.8995 + 65.6439i −1.46638 + 2.53984i
$$669$$ 4.48528 7.76874i 0.173411 0.300357i
$$670$$ 4.00000 + 6.92820i 0.154533 + 0.267660i
$$671$$ −7.51472 −0.290102
$$672$$ 0 0
$$673$$ 0.686292 0.0264546 0.0132273 0.999913i $$-0.495789\pi$$
0.0132273 + 0.999913i $$0.495789\pi$$
$$674$$ −22.1421 38.3513i −0.852883 1.47724i
$$675$$ 2.32843 4.03295i 0.0896212 0.155228i
$$676$$ −31.2279 + 54.0883i −1.20107 + 2.08032i
$$677$$ −14.2929 24.7560i −0.549321 0.951451i −0.998321 0.0579196i $$-0.981553\pi$$
0.449001 0.893531i $$-0.351780\pi$$
$$678$$ −41.7990 −1.60528
$$679$$ 0 0
$$680$$ −16.1421 −0.619023
$$681$$ 7.89949 + 13.6823i 0.302709 + 0.524308i
$$682$$ 16.4853 28.5533i 0.631254 1.09336i
$$683$$ 4.17157 7.22538i 0.159621 0.276471i −0.775111 0.631825i $$-0.782306\pi$$
0.934732 + 0.355354i $$0.115640\pi$$
$$684$$ −5.41421 9.37769i −0.207018 0.358565i
$$685$$ −8.28427 −0.316526
$$686$$ 0 0
$$687$$ 8.24264 0.314476
$$688$$ 8.48528 + 14.6969i 0.323498 + 0.560316i
$$689$$ 5.41421 9.37769i 0.206265 0.357262i
$$690$$ 2.58579 4.47871i 0.0984392 0.170502i
$$691$$ 11.6569 + 20.1903i 0.443448 + 0.768074i 0.997943 0.0641132i $$-0.0204219\pi$$
−0.554495 + 0.832187i $$0.687089\pi$$
$$692$$ 26.5269 1.00840
$$693$$ 0 0
$$694$$ −25.7990 −0.979316
$$695$$ 1.85786 + 3.21792i 0.0704728 + 0.122062i
$$696$$ −2.58579 + 4.47871i −0.0980140 + 0.169765i
$$697$$ 7.00000 12.1244i 0.265144 0.459243i
$$698$$ 11.9497 + 20.6976i 0.452305 + 0.783415i
$$699$$ 22.1421 0.837492
$$700$$ 0 0
$$701$$ −22.8284 −0.862218 −0.431109 0.902300i $$-0.641878\pi$$
−0.431109 + 0.902300i $$0.641878\pi$$
$$702$$ 6.53553 + 11.3199i 0.246668 + 0.427241i
$$703$$ 5.65685 9.79796i 0.213352 0.369537i
$$704$$ −9.82843 + 17.0233i −0.370423 + 0.641591i
$$705$$ −0.828427 1.43488i −0.0312004 0.0540406i
$$706$$ −25.8995 −0.974740
$$707$$ 0 0
$$708$$ −26.1421 −0.982482
$$709$$ −10.1421 17.5667i −0.380896 0.659731i 0.610295 0.792174i $$-0.291051\pi$$
−0.991191 + 0.132443i $$0.957718\pi$$
$$710$$ −9.41421 + 16.3059i −0.353309 + 0.611949i
$$711$$ −1.17157 + 2.02922i −0.0439374 + 0.0761018i
$$712$$ −12.7071 22.0094i −0.476219 0.824835i
$$713$$ −24.9706 −0.935155
$$714$$ 0 0
$$715$$ −6.34315 −0.237220
$$716$$ 15.9706 + 27.6618i 0.596848 + 1.03377i
$$717$$ 2.17157 3.76127i 0.0810989 0.140467i
$$718$$ −14.0711 + 24.3718i −0.525128 + 0.909548i
$$719$$ 12.9706 + 22.4657i 0.483720 + 0.837828i 0.999825 0.0186972i $$-0.00595184\pi$$
−0.516105 + 0.856525i $$0.672619\pi$$
$$720$$ 1.75736 0.0654929
$$721$$ 0 0
$$722$$ 26.5563 0.988325
$$723$$ 3.87868 + 6.71807i 0.144250 + 0.249848i
$$724$$ 10.3640 17.9509i 0.385174 0.667140i
$$725$$ −2.72792 + 4.72490i −0.101312 + 0.175478i
$$726$$ −8.44975 14.6354i −0.313600 0.543170i
$$727$$ −4.48528 −0.166350 −0.0831749 0.996535i $$-0.526506\pi$$
−0.0831749 + 0.996535i $$0.526506\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ −4.17157 7.22538i −0.154397 0.267423i
$$731$$ 17.6569 30.5826i 0.653062 1.13114i
$$732$$ −7.19239 + 12.4576i −0.265838 + 0.460445i
$$733$$ 4.84924 + 8.39913i 0.179111 + 0.310229i 0.941576 0.336800i $$-0.109345\pi$$
−0.762465 + 0.647029i $$0.776011\pi$$
$$734$$ −46.6274 −1.72105
$$735$$ 0 0
$$736$$ 5.79899 0.213754
$$737$$ 5.65685 + 9.79796i 0.208373 + 0.360912i
$$738$$ −2.70711 + 4.68885i −0.0996500 + 0.172599i
$$739$$ −13.6569 + 23.6544i −0.502376 + 0.870140i 0.497621 + 0.867395i $$0.334207\pi$$
−0.999996 + 0.00274517i $$0.999126\pi$$
$$740$$ 4.48528 + 7.76874i 0.164882 + 0.285584i
$$741$$ 15.3137 0.562563
$$742$$ 0 0
$$743$$ −17.0294 −0.624749 −0.312375 0.949959i $$-0.601124\pi$$
−0.312375 + 0.949959i $$0.601124\pi$$
$$744$$ −15.0711 26.1039i −0.552532 0.957014i
$$745$$ 1.55635 2.69568i 0.0570202 0.0987619i
$$746$$ −40.2132 + 69.6513i −1.47231 + 2.55012i
$$747$$ 7.65685 + 13.2621i 0.280150 + 0.485233i
$$748$$ −47.7990 −1.74770
$$749$$ 0 0
$$750$$ 13.6569 0.498678
$$751$$ −1.17157 2.02922i −0.0427513 0.0740474i 0.843858 0.536567i $$-0.180279\pi$$
−0.886609 + 0.462519i $$0.846946\pi$$
$$752$$ −4.24264 + 7.34847i −0.154713 + 0.267971i
$$753$$ −2.24264 + 3.88437i −0.0817264 + 0.141554i
$$754$$ −7.65685 13.2621i −0.278846 0.482976i
$$755$$ 7.02944 0.255827
$$756$$ 0 0
$$757$$ 37.6569 1.36866 0.684331 0.729172i $$-0.260094\pi$$
0.684331 + 0.729172i $$0.260094\pi$$
$$758$$ 37.7990 + 65.4698i 1.37292 + 2.37797i
$$759$$ 3.65685 6.33386i 0.132735 0.229904i
$$760$$ 3.65685 6.33386i 0.132648 0.229753i
$$761$$ −23.2635 40.2935i −0.843300 1.46064i −0.887090 0.461597i $$-0.847277\pi$$
0.0437901 0.999041i $$-0.486057\pi$$
$$762$$ −23.3137 −0.844567
$$763$$ 0 0
$$764$$ −68.9117 −2.49314
$$765$$ −1.82843 3.16693i −0.0661069 0.114501i
$$766$$ −35.7990 + 62.0057i −1.29347 + 2.24036i
$$767$$ 18.4853 32.0174i 0.667465 1.15608i
$$768$$ 14.9853 + 25.9553i 0.540735 + 0.936580i
$$769$$ −29.6985 −1.07095 −0.535477 0.844550i $$-0.679868\pi$$
−0.535477 + 0.844550i $$0.679868\pi$$
$$770$$ 0 0
$$771$$ −19.2132 −0.691947
$$772$$ 33.1421 + 57.4039i 1.19281 + 2.06601i
$$773$$ −10.7782 + 18.6683i −0.387664 + 0.671454i −0.992135 0.125174i $$-0.960051\pi$$
0.604471 + 0.796627i $$0.293385\pi$$
$$774$$ −6.82843 + 11.8272i −0.245443 + 0.425119i
$$775$$ −15.8995 27.5387i −0.571127 0.989220i
$$776$$ −23.8995 −0.857942
$$777$$ 0 0
$$778$$ −24.4853 −0.877840
$$779$$ 3.17157 + 5.49333i 0.113633 + 0.196819i
$$780$$ −6.07107 + 10.5154i −0.217379 + 0.376512i
$$781$$ −13.3137 + 23.0600i −0.476402 + 0.825152i
$$782$$ 27.5563 + 47.7290i 0.985413 + 1.70679i
$$783$$ −1.17157 −0.0418686