# Properties

 Label 462.2.i.g.67.3 Level $462$ Weight $2$ Character 462.67 Analytic conductor $3.689$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$462 = 2 \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 462.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.68908857338$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.21870000.1 Defining polynomial: $$x^{6} - 3 x^{5} + 24 x^{4} - 43 x^{3} + 138 x^{2} - 117 x + 73$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.3 Root $$0.500000 + 0.679547i$$ of defining polynomial Character $$\chi$$ $$=$$ 462.67 Dual form 462.2.i.g.331.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.40280 + 2.42972i) q^{5} -1.00000 q^{6} +(-1.40280 + 2.24325i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.40280 + 2.42972i) q^{5} -1.00000 q^{6} +(-1.40280 + 2.24325i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.40280 - 2.42972i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.64411 + 0.0932392i) q^{14} +2.80560 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.98261 + 6.89809i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.24131 + 5.61411i) q^{19} -2.80560 q^{20} +(1.24131 + 2.33648i) q^{21} -1.00000 q^{22} +(2.64411 + 4.57973i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.43570 + 2.48671i) q^{25} -1.00000 q^{27} +(-1.24131 - 2.33648i) q^{28} +5.12859 q^{29} +(-1.40280 - 2.42972i) q^{30} +(4.48261 - 7.76411i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +7.96523 q^{34} +(-7.41832 - 0.261592i) q^{35} +1.00000 q^{36} +(-5.24131 - 9.07821i) q^{37} +(3.24131 - 5.61411i) q^{38} +(1.40280 + 2.42972i) q^{40} -5.09382 q^{41} +(1.40280 - 2.24325i) q^{42} +11.4478 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.40280 - 2.42972i) q^{45} +(2.64411 - 4.57973i) q^{46} +(-0.161495 - 0.279717i) q^{47} -1.00000 q^{48} +(-3.06430 - 6.29365i) q^{49} +2.87141 q^{50} +(3.98261 + 6.89809i) q^{51} +(-4.00000 + 6.92820i) q^{53} +(0.500000 + 0.866025i) q^{54} +2.80560 q^{55} +(-1.40280 + 2.24325i) q^{56} +6.48261 q^{57} +(-2.56430 - 4.44149i) q^{58} +(0.435704 - 0.754661i) q^{59} +(-1.40280 + 2.42972i) q^{60} +(-1.07981 - 1.87029i) q^{61} -8.96523 q^{62} +(2.64411 + 0.0932392i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(3.54691 - 6.14343i) q^{67} +(-3.98261 - 6.89809i) q^{68} +5.28822 q^{69} +(3.48261 + 6.55525i) q^{70} -7.44784 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-6.28822 + 10.8915i) q^{73} +(-5.24131 + 9.07821i) q^{74} +(1.43570 + 2.48671i) q^{75} -6.48261 q^{76} +(1.24131 + 2.33648i) q^{77} +(-3.40280 - 5.89382i) q^{79} +(1.40280 - 2.42972i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.54691 + 4.41138i) q^{82} +15.0938 q^{83} +(-2.64411 - 0.0932392i) q^{84} -22.3473 q^{85} +(-5.72392 - 9.91412i) q^{86} +(2.56430 - 4.44149i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-0.805603 - 1.39535i) q^{89} -2.80560 q^{90} -5.28822 q^{92} +(-4.48261 - 7.76411i) q^{93} +(-0.161495 + 0.279717i) q^{94} +(-9.09382 + 15.7510i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(-3.91832 + 5.80059i) q^{98} -1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9} + O(q^{10})$$ $$6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9} + 3 q^{11} + 3 q^{12} - 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{21} - 6 q^{22} - 3 q^{23} + 3 q^{24} - 15 q^{25} - 6 q^{27} + 3 q^{28} + 18 q^{29} + 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} - 30 q^{35} + 6 q^{36} - 21 q^{37} + 9 q^{38} + 24 q^{41} + 6 q^{43} + 3 q^{44} - 3 q^{46} - 3 q^{47} - 6 q^{48} - 12 q^{49} + 30 q^{50} + 3 q^{51} - 24 q^{53} + 3 q^{54} + 18 q^{57} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} - 3 q^{63} + 6 q^{64} - 3 q^{66} - 6 q^{67} - 3 q^{68} - 6 q^{69} + 18 q^{71} - 3 q^{72} - 21 q^{74} + 15 q^{75} - 18 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} + 36 q^{83} + 3 q^{84} - 3 q^{86} + 9 q^{87} + 3 q^{88} + 12 q^{89} + 6 q^{92} - 6 q^{93} - 3 q^{94} + 3 q^{96} + 42 q^{97} - 9 q^{98} - 6 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$$.

 $$n$$ $$155$$ $$199$$ $$211$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 1.40280 + 2.42972i 0.627352 + 1.08661i 0.988081 + 0.153935i $$0.0491945\pi$$
−0.360729 + 0.932671i $$0.617472\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ −1.40280 + 2.24325i −0.530209 + 0.847867i
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 1.40280 2.42972i 0.443605 0.768346i
$$11$$ 0.500000 0.866025i 0.150756 0.261116i
$$12$$ 0.500000 + 0.866025i 0.144338 + 0.250000i
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 2.64411 + 0.0932392i 0.706668 + 0.0249192i
$$15$$ 2.80560 0.724404
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −3.98261 + 6.89809i −0.965926 + 1.67303i −0.258818 + 0.965926i $$0.583333\pi$$
−0.707108 + 0.707106i $$0.750000\pi$$
$$18$$ −0.500000 + 0.866025i −0.117851 + 0.204124i
$$19$$ 3.24131 + 5.61411i 0.743607 + 1.28796i 0.950843 + 0.309674i $$0.100220\pi$$
−0.207236 + 0.978291i $$0.566447\pi$$
$$20$$ −2.80560 −0.627352
$$21$$ 1.24131 + 2.33648i 0.270875 + 0.509863i
$$22$$ −1.00000 −0.213201
$$23$$ 2.64411 + 4.57973i 0.551335 + 0.954940i 0.998179 + 0.0603277i $$0.0192146\pi$$
−0.446844 + 0.894612i $$0.647452\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ −1.43570 + 2.48671i −0.287141 + 0.497342i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ −1.24131 2.33648i −0.234585 0.441554i
$$29$$ 5.12859 0.952356 0.476178 0.879349i $$-0.342022\pi$$
0.476178 + 0.879349i $$0.342022\pi$$
$$30$$ −1.40280 2.42972i −0.256115 0.443605i
$$31$$ 4.48261 7.76411i 0.805101 1.39448i −0.111122 0.993807i $$-0.535444\pi$$
0.916223 0.400669i $$-0.131222\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −0.500000 0.866025i −0.0870388 0.150756i
$$34$$ 7.96523 1.36602
$$35$$ −7.41832 0.261592i −1.25392 0.0442171i
$$36$$ 1.00000 0.166667
$$37$$ −5.24131 9.07821i −0.861665 1.49245i −0.870320 0.492486i $$-0.836088\pi$$
0.00865499 0.999963i $$-0.497245\pi$$
$$38$$ 3.24131 5.61411i 0.525809 0.910728i
$$39$$ 0 0
$$40$$ 1.40280 + 2.42972i 0.221802 + 0.384173i
$$41$$ −5.09382 −0.795521 −0.397760 0.917489i $$-0.630212\pi$$
−0.397760 + 0.917489i $$0.630212\pi$$
$$42$$ 1.40280 2.24325i 0.216457 0.346140i
$$43$$ 11.4478 1.74578 0.872890 0.487918i $$-0.162243\pi$$
0.872890 + 0.487918i $$0.162243\pi$$
$$44$$ 0.500000 + 0.866025i 0.0753778 + 0.130558i
$$45$$ 1.40280 2.42972i 0.209117 0.362202i
$$46$$ 2.64411 4.57973i 0.389852 0.675244i
$$47$$ −0.161495 0.279717i −0.0235565 0.0408010i 0.854007 0.520262i $$-0.174166\pi$$
−0.877563 + 0.479461i $$0.840832\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ −3.06430 6.29365i −0.437757 0.899094i
$$50$$ 2.87141 0.406078
$$51$$ 3.98261 + 6.89809i 0.557677 + 0.965926i
$$52$$ 0 0
$$53$$ −4.00000 + 6.92820i −0.549442 + 0.951662i 0.448871 + 0.893597i $$0.351826\pi$$
−0.998313 + 0.0580651i $$0.981507\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 2.80560 0.378307
$$56$$ −1.40280 + 2.24325i −0.187457 + 0.299766i
$$57$$ 6.48261 0.858643
$$58$$ −2.56430 4.44149i −0.336709 0.583196i
$$59$$ 0.435704 0.754661i 0.0567238 0.0982485i −0.836269 0.548319i $$-0.815268\pi$$
0.892993 + 0.450071i $$0.148601\pi$$
$$60$$ −1.40280 + 2.42972i −0.181101 + 0.313676i
$$61$$ −1.07981 1.87029i −0.138256 0.239466i 0.788581 0.614931i $$-0.210816\pi$$
−0.926836 + 0.375465i $$0.877483\pi$$
$$62$$ −8.96523 −1.13858
$$63$$ 2.64411 + 0.0932392i 0.333126 + 0.0117470i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −0.500000 + 0.866025i −0.0615457 + 0.106600i
$$67$$ 3.54691 6.14343i 0.433324 0.750539i −0.563833 0.825889i $$-0.690674\pi$$
0.997157 + 0.0753496i $$0.0240073\pi$$
$$68$$ −3.98261 6.89809i −0.482963 0.836516i
$$69$$ 5.28822 0.636626
$$70$$ 3.48261 + 6.55525i 0.416252 + 0.783502i
$$71$$ −7.44784 −0.883896 −0.441948 0.897041i $$-0.645712\pi$$
−0.441948 + 0.897041i $$0.645712\pi$$
$$72$$ −0.500000 0.866025i −0.0589256 0.102062i
$$73$$ −6.28822 + 10.8915i −0.735980 + 1.27475i 0.218312 + 0.975879i $$0.429945\pi$$
−0.954292 + 0.298876i $$0.903388\pi$$
$$74$$ −5.24131 + 9.07821i −0.609289 + 1.05532i
$$75$$ 1.43570 + 2.48671i 0.165781 + 0.287141i
$$76$$ −6.48261 −0.743607
$$77$$ 1.24131 + 2.33648i 0.141460 + 0.266267i
$$78$$ 0 0
$$79$$ −3.40280 5.89382i −0.382845 0.663107i 0.608623 0.793460i $$-0.291722\pi$$
−0.991468 + 0.130353i $$0.958389\pi$$
$$80$$ 1.40280 2.42972i 0.156838 0.271651i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 2.54691 + 4.41138i 0.281259 + 0.487155i
$$83$$ 15.0938 1.65676 0.828381 0.560165i $$-0.189262\pi$$
0.828381 + 0.560165i $$0.189262\pi$$
$$84$$ −2.64411 0.0932392i −0.288496 0.0101732i
$$85$$ −22.3473 −2.42390
$$86$$ −5.72392 9.91412i −0.617226 1.06907i
$$87$$ 2.56430 4.44149i 0.274921 0.476178i
$$88$$ 0.500000 0.866025i 0.0533002 0.0923186i
$$89$$ −0.805603 1.39535i −0.0853937 0.147906i 0.820165 0.572127i $$-0.193881\pi$$
−0.905559 + 0.424221i $$0.860548\pi$$
$$90$$ −2.80560 −0.295737
$$91$$ 0 0
$$92$$ −5.28822 −0.551335
$$93$$ −4.48261 7.76411i −0.464825 0.805101i
$$94$$ −0.161495 + 0.279717i −0.0166569 + 0.0288507i
$$95$$ −9.09382 + 15.7510i −0.933006 + 1.61601i
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ −3.91832 + 5.80059i −0.395810 + 0.585948i
$$99$$ −1.00000 −0.100504
$$100$$ −1.43570 2.48671i −0.143570 0.248671i
$$101$$ −5.36990 + 9.30094i −0.534325 + 0.925478i 0.464871 + 0.885379i $$0.346101\pi$$
−0.999196 + 0.0400994i $$0.987233\pi$$
$$102$$ 3.98261 6.89809i 0.394337 0.683012i
$$103$$ −1.48261 2.56796i −0.146086 0.253029i 0.783691 0.621150i $$-0.213334\pi$$
−0.929778 + 0.368122i $$0.880001\pi$$
$$104$$ 0 0
$$105$$ −3.93570 + 6.29365i −0.384085 + 0.614198i
$$106$$ 8.00000 0.777029
$$107$$ −2.41832 4.18865i −0.233787 0.404932i 0.725132 0.688610i $$-0.241779\pi$$
−0.958920 + 0.283678i $$0.908445\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ 5.07981 8.79849i 0.486558 0.842743i −0.513323 0.858196i $$-0.671586\pi$$
0.999881 + 0.0154529i $$0.00491901\pi$$
$$110$$ −1.40280 2.42972i −0.133752 0.231665i
$$111$$ −10.4826 −0.994966
$$112$$ 2.64411 + 0.0932392i 0.249845 + 0.00881027i
$$113$$ 10.9652 1.03152 0.515761 0.856733i $$-0.327509\pi$$
0.515761 + 0.856733i $$0.327509\pi$$
$$114$$ −3.24131 5.61411i −0.303576 0.525809i
$$115$$ −7.41832 + 12.8489i −0.691762 + 1.19817i
$$116$$ −2.56430 + 4.44149i −0.238089 + 0.412382i
$$117$$ 0 0
$$118$$ −0.871407 −0.0802195
$$119$$ −9.88729 18.6106i −0.906366 1.70603i
$$120$$ 2.80560 0.256115
$$121$$ −0.500000 0.866025i −0.0454545 0.0787296i
$$122$$ −1.07981 + 1.87029i −0.0977615 + 0.169328i
$$123$$ −2.54691 + 4.41138i −0.229647 + 0.397760i
$$124$$ 4.48261 + 7.76411i 0.402551 + 0.697238i
$$125$$ 5.97199 0.534151
$$126$$ −1.24131 2.33648i −0.110584 0.208151i
$$127$$ −9.28822 −0.824196 −0.412098 0.911140i $$-0.635204\pi$$
−0.412098 + 0.911140i $$0.635204\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 5.72392 9.91412i 0.503963 0.872890i
$$130$$ 0 0
$$131$$ −6.48261 11.2282i −0.566389 0.981014i −0.996919 0.0784377i $$-0.975007\pi$$
0.430530 0.902576i $$-0.358326\pi$$
$$132$$ 1.00000 0.0870388
$$133$$ −17.1407 0.604433i −1.48629 0.0524110i
$$134$$ −7.09382 −0.612813
$$135$$ −1.40280 2.42972i −0.120734 0.209117i
$$136$$ −3.98261 + 6.89809i −0.341506 + 0.591506i
$$137$$ −2.80560 + 4.85945i −0.239699 + 0.415171i −0.960628 0.277838i $$-0.910382\pi$$
0.720929 + 0.693009i $$0.243715\pi$$
$$138$$ −2.64411 4.57973i −0.225081 0.389852i
$$139$$ 13.1286 1.11355 0.556776 0.830662i $$-0.312038\pi$$
0.556776 + 0.830662i $$0.312038\pi$$
$$140$$ 3.93570 6.29365i 0.332628 0.531911i
$$141$$ −0.322990 −0.0272007
$$142$$ 3.72392 + 6.45002i 0.312504 + 0.541273i
$$143$$ 0 0
$$144$$ −0.500000 + 0.866025i −0.0416667 + 0.0721688i
$$145$$ 7.19440 + 12.4611i 0.597462 + 1.03483i
$$146$$ 12.5764 1.04083
$$147$$ −6.98261 0.493069i −0.575916 0.0406676i
$$148$$ 10.4826 0.861665
$$149$$ −8.36990 14.4971i −0.685689 1.18765i −0.973220 0.229877i $$-0.926168\pi$$
0.287531 0.957771i $$-0.407166\pi$$
$$150$$ 1.43570 2.48671i 0.117225 0.203039i
$$151$$ −5.44971 + 9.43918i −0.443491 + 0.768149i −0.997946 0.0640648i $$-0.979594\pi$$
0.554455 + 0.832214i $$0.312927\pi$$
$$152$$ 3.24131 + 5.61411i 0.262905 + 0.455364i
$$153$$ 7.96523 0.643950
$$154$$ 1.40280 2.24325i 0.113041 0.180766i
$$155$$ 25.1529 2.02033
$$156$$ 0 0
$$157$$ −0.887286 + 1.53682i −0.0708132 + 0.122652i −0.899258 0.437419i $$-0.855893\pi$$
0.828445 + 0.560071i $$0.189226\pi$$
$$158$$ −3.40280 + 5.89382i −0.270712 + 0.468888i
$$159$$ 4.00000 + 6.92820i 0.317221 + 0.549442i
$$160$$ −2.80560 −0.221802
$$161$$ −13.9826 0.493069i −1.10198 0.0388593i
$$162$$ 1.00000 0.0785674
$$163$$ 2.02952 + 3.51524i 0.158964 + 0.275335i 0.934496 0.355975i $$-0.115851\pi$$
−0.775531 + 0.631309i $$0.782518\pi$$
$$164$$ 2.54691 4.41138i 0.198880 0.344471i
$$165$$ 1.40280 2.42972i 0.109208 0.189154i
$$166$$ −7.54691 13.0716i −0.585754 1.01456i
$$167$$ 13.8684 1.07317 0.536584 0.843847i $$-0.319714\pi$$
0.536584 + 0.843847i $$0.319714\pi$$
$$168$$ 1.24131 + 2.33648i 0.0957689 + 0.180264i
$$169$$ −13.0000 −1.00000
$$170$$ 11.1736 + 19.3533i 0.856978 + 1.48433i
$$171$$ 3.24131 5.61411i 0.247869 0.429322i
$$172$$ −5.72392 + 9.91412i −0.436445 + 0.755945i
$$173$$ −8.48261 14.6923i −0.644921 1.11704i −0.984320 0.176394i $$-0.943557\pi$$
0.339399 0.940643i $$-0.389776\pi$$
$$174$$ −5.12859 −0.388798
$$175$$ −3.56430 6.70900i −0.269435 0.507153i
$$176$$ −1.00000 −0.0753778
$$177$$ −0.435704 0.754661i −0.0327495 0.0567238i
$$178$$ −0.805603 + 1.39535i −0.0603825 + 0.104586i
$$179$$ 6.33513 10.9728i 0.473509 0.820142i −0.526031 0.850466i $$-0.676320\pi$$
0.999540 + 0.0303231i $$0.00965363\pi$$
$$180$$ 1.40280 + 2.42972i 0.104559 + 0.181101i
$$181$$ −2.57643 −0.191505 −0.0957523 0.995405i $$-0.530526\pi$$
−0.0957523 + 0.995405i $$0.530526\pi$$
$$182$$ 0 0
$$183$$ −2.15962 −0.159644
$$184$$ 2.64411 + 4.57973i 0.194926 + 0.337622i
$$185$$ 14.7050 25.4698i 1.08113 1.87258i
$$186$$ −4.48261 + 7.76411i −0.328681 + 0.569292i
$$187$$ 3.98261 + 6.89809i 0.291238 + 0.504438i
$$188$$ 0.322990 0.0235565
$$189$$ 1.40280 2.24325i 0.102039 0.163172i
$$190$$ 18.1876 1.31947
$$191$$ 1.19440 + 2.06876i 0.0864235 + 0.149690i 0.905997 0.423284i $$-0.139123\pi$$
−0.819573 + 0.572974i $$0.805790\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ 7.28822 12.6236i 0.524617 0.908664i −0.474972 0.880001i $$-0.657542\pi$$
0.999589 0.0286628i $$-0.00912489\pi$$
$$194$$ −3.50000 6.06218i −0.251285 0.435239i
$$195$$ 0 0
$$196$$ 6.98261 + 0.493069i 0.498758 + 0.0352192i
$$197$$ −12.4826 −0.889349 −0.444675 0.895692i $$-0.646681\pi$$
−0.444675 + 0.895692i $$0.646681\pi$$
$$198$$ 0.500000 + 0.866025i 0.0355335 + 0.0615457i
$$199$$ 7.09382 12.2869i 0.502867 0.870992i −0.497127 0.867678i $$-0.665612\pi$$
0.999995 0.00331424i $$-0.00105496\pi$$
$$200$$ −1.43570 + 2.48671i −0.101520 + 0.175837i
$$201$$ −3.54691 6.14343i −0.250180 0.433324i
$$202$$ 10.7398 0.755650
$$203$$ −7.19440 + 11.5047i −0.504948 + 0.807471i
$$204$$ −7.96523 −0.557677
$$205$$ −7.14562 12.3766i −0.499071 0.864417i
$$206$$ −1.48261 + 2.56796i −0.103299 + 0.178918i
$$207$$ 2.64411 4.57973i 0.183778 0.318313i
$$208$$ 0 0
$$209$$ 6.48261 0.448412
$$210$$ 7.41832 + 0.261592i 0.511912 + 0.0180516i
$$211$$ −20.8336 −1.43425 −0.717123 0.696947i $$-0.754541\pi$$
−0.717123 + 0.696947i $$0.754541\pi$$
$$212$$ −4.00000 6.92820i −0.274721 0.475831i
$$213$$ −3.72392 + 6.45002i −0.255159 + 0.441948i
$$214$$ −2.41832 + 4.18865i −0.165313 + 0.286330i
$$215$$ 16.0590 + 27.8151i 1.09522 + 1.89697i
$$216$$ −1.00000 −0.0680414
$$217$$ 11.1286 + 20.9471i 0.755458 + 1.42198i
$$218$$ −10.1596 −0.688096
$$219$$ 6.28822 + 10.8915i 0.424918 + 0.735980i
$$220$$ −1.40280 + 2.42972i −0.0945769 + 0.163812i
$$221$$ 0 0
$$222$$ 5.24131 + 9.07821i 0.351773 + 0.609289i
$$223$$ 12.5764 0.842180 0.421090 0.907019i $$-0.361648\pi$$
0.421090 + 0.907019i $$0.361648\pi$$
$$224$$ −1.24131 2.33648i −0.0829383 0.156113i
$$225$$ 2.87141 0.191427
$$226$$ −5.48261 9.49616i −0.364698 0.631675i
$$227$$ −10.0295 + 17.3716i −0.665683 + 1.15300i 0.313417 + 0.949616i $$0.398526\pi$$
−0.979100 + 0.203381i $$0.934807\pi$$
$$228$$ −3.24131 + 5.61411i −0.214661 + 0.371803i
$$229$$ 11.2882 + 19.5518i 0.745946 + 1.29202i 0.949751 + 0.313005i $$0.101336\pi$$
−0.203805 + 0.979011i $$0.565331\pi$$
$$230$$ 14.8366 0.978299
$$231$$ 2.64411 + 0.0932392i 0.173970 + 0.00613469i
$$232$$ 5.12859 0.336709
$$233$$ 0.371407 + 0.643296i 0.0243317 + 0.0421437i 0.877935 0.478780i $$-0.158921\pi$$
−0.853603 + 0.520924i $$0.825588\pi$$
$$234$$ 0 0
$$235$$ 0.453091 0.784776i 0.0295564 0.0511931i
$$236$$ 0.435704 + 0.754661i 0.0283619 + 0.0491242i
$$237$$ −6.80560 −0.442071
$$238$$ −11.1736 + 17.8680i −0.724279 + 1.15821i
$$239$$ 4.31925 0.279389 0.139694 0.990195i $$-0.455388\pi$$
0.139694 + 0.990195i $$0.455388\pi$$
$$240$$ −1.40280 2.42972i −0.0905504 0.156838i
$$241$$ 9.09382 15.7510i 0.585784 1.01461i −0.408993 0.912538i $$-0.634120\pi$$
0.994777 0.102071i $$-0.0325468\pi$$
$$242$$ −0.500000 + 0.866025i −0.0321412 + 0.0556702i
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 2.15962 0.138256
$$245$$ 10.9932 16.2741i 0.702332 1.03972i
$$246$$ 5.09382 0.324770
$$247$$ 0 0
$$248$$ 4.48261 7.76411i 0.284646 0.493022i
$$249$$ 7.54691 13.0716i 0.478266 0.828381i
$$250$$ −2.98599 5.17189i −0.188851 0.327099i
$$251$$ 28.6703 1.80965 0.904825 0.425784i $$-0.140001\pi$$
0.904825 + 0.425784i $$0.140001\pi$$
$$252$$ −1.40280 + 2.24325i −0.0883682 + 0.141311i
$$253$$ 5.28822 0.332467
$$254$$ 4.64411 + 8.04383i 0.291397 + 0.504715i
$$255$$ −11.1736 + 19.3533i −0.699720 + 1.21195i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 6.80560 + 11.7876i 0.424522 + 0.735293i 0.996376 0.0850621i $$-0.0271089\pi$$
−0.571854 + 0.820356i $$0.693776\pi$$
$$258$$ −11.4478 −0.712711
$$259$$ 27.7172 + 0.977390i 1.72226 + 0.0607321i
$$260$$ 0 0
$$261$$ −2.56430 4.44149i −0.158726 0.274921i
$$262$$ −6.48261 + 11.2282i −0.400497 + 0.693681i
$$263$$ 1.80560 3.12740i 0.111338 0.192843i −0.804972 0.593313i $$-0.797820\pi$$
0.916310 + 0.400470i $$0.131153\pi$$
$$264$$ −0.500000 0.866025i −0.0307729 0.0533002i
$$265$$ −22.4448 −1.37877
$$266$$ 8.04691 + 15.1465i 0.493388 + 0.928693i
$$267$$ −1.61121 −0.0986042
$$268$$ 3.54691 + 6.14343i 0.216662 + 0.375270i
$$269$$ 4.69102 8.12508i 0.286016 0.495395i −0.686839 0.726810i $$-0.741002\pi$$
0.972855 + 0.231415i $$0.0743355\pi$$
$$270$$ −1.40280 + 2.42972i −0.0853718 + 0.147868i
$$271$$ −2.80560 4.85945i −0.170428 0.295190i 0.768141 0.640280i $$-0.221182\pi$$
−0.938570 + 0.345090i $$0.887848\pi$$
$$272$$ 7.96523 0.482963
$$273$$ 0 0
$$274$$ 5.61121 0.338985
$$275$$ 1.43570 + 2.48671i 0.0865762 + 0.149954i
$$276$$ −2.64411 + 4.57973i −0.159157 + 0.275667i
$$277$$ 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i $$-0.673726\pi$$
0.999754 + 0.0221745i $$0.00705893\pi$$
$$278$$ −6.56430 11.3697i −0.393700 0.681909i
$$279$$ −8.96523 −0.536734
$$280$$ −7.41832 0.261592i −0.443329 0.0156331i
$$281$$ 24.1529 1.44084 0.720420 0.693539i $$-0.243949\pi$$
0.720420 + 0.693539i $$0.243949\pi$$
$$282$$ 0.161495 + 0.279717i 0.00961688 + 0.0166569i
$$283$$ −3.77083 + 6.53127i −0.224152 + 0.388244i −0.956065 0.293155i $$-0.905295\pi$$
0.731912 + 0.681399i $$0.238628\pi$$
$$284$$ 3.72392 6.45002i 0.220974 0.382738i
$$285$$ 9.09382 + 15.7510i 0.538671 + 0.933006i
$$286$$ 0 0
$$287$$ 7.14562 11.4267i 0.421792 0.674496i
$$288$$ 1.00000 0.0589256
$$289$$ −23.2224 40.2224i −1.36602 2.36602i
$$290$$ 7.19440 12.4611i 0.422470 0.731739i
$$291$$ 3.50000 6.06218i 0.205174 0.355371i
$$292$$ −6.28822 10.8915i −0.367990 0.637377i
$$293$$ 7.90618 0.461884 0.230942 0.972968i $$-0.425819\pi$$
0.230942 + 0.972968i $$0.425819\pi$$
$$294$$ 3.06430 + 6.29365i 0.178713 + 0.367053i
$$295$$ 2.44482 0.142343
$$296$$ −5.24131 9.07821i −0.304645 0.527660i
$$297$$ −0.500000 + 0.866025i −0.0290129 + 0.0502519i
$$298$$ −8.36990 + 14.4971i −0.484855 + 0.839794i
$$299$$ 0 0
$$300$$ −2.87141 −0.165781
$$301$$ −16.0590 + 25.6803i −0.925628 + 1.48019i
$$302$$ 10.8994 0.627191
$$303$$ 5.36990 + 9.30094i 0.308493 + 0.534325i
$$304$$ 3.24131 5.61411i 0.185902 0.321991i
$$305$$ 3.02952 5.24729i 0.173470 0.300459i
$$306$$ −3.98261 6.89809i −0.227671 0.394337i
$$307$$ 12.8957 0.735995 0.367998 0.929827i $$-0.380043\pi$$
0.367998 + 0.929827i $$0.380043\pi$$
$$308$$ −2.64411 0.0932392i −0.150662 0.00531279i
$$309$$ −2.96523 −0.168686
$$310$$ −12.5764 21.7830i −0.714293 1.23719i
$$311$$ −5.44971 + 9.43918i −0.309025 + 0.535247i −0.978149 0.207904i $$-0.933336\pi$$
0.669125 + 0.743150i $$0.266669\pi$$
$$312$$ 0 0
$$313$$ 4.56430 + 7.90559i 0.257989 + 0.446851i 0.965703 0.259649i $$-0.0836067\pi$$
−0.707714 + 0.706499i $$0.750273\pi$$
$$314$$ 1.77457 0.100145
$$315$$ 3.48261 + 6.55525i 0.196223 + 0.369346i
$$316$$ 6.80560 0.382845
$$317$$ 4.75682 + 8.23906i 0.267170 + 0.462752i 0.968130 0.250449i $$-0.0805782\pi$$
−0.700960 + 0.713201i $$0.747245\pi$$
$$318$$ 4.00000 6.92820i 0.224309 0.388514i
$$319$$ 2.56430 4.44149i 0.143573 0.248676i
$$320$$ 1.40280 + 2.42972i 0.0784190 + 0.135826i
$$321$$ −4.83663 −0.269955
$$322$$ 6.56430 + 12.3558i 0.365814 + 0.688564i
$$323$$ −51.6355 −2.87307
$$324$$ −0.500000 0.866025i −0.0277778 0.0481125i
$$325$$ 0 0
$$326$$ 2.02952 3.51524i 0.112405 0.194691i
$$327$$ −5.07981 8.79849i −0.280914 0.486558i
$$328$$ −5.09382 −0.281259
$$329$$ 0.854020 + 0.0301153i 0.0470837 + 0.00166031i
$$330$$ −2.80560 −0.154443
$$331$$ −0.546909 0.947275i −0.0300609 0.0520669i 0.850604 0.525807i $$-0.176237\pi$$
−0.880664 + 0.473741i $$0.842903\pi$$
$$332$$ −7.54691 + 13.0716i −0.414190 + 0.717399i
$$333$$ −5.24131 + 9.07821i −0.287222 + 0.497483i
$$334$$ −6.93420 12.0104i −0.379422 0.657179i
$$335$$ 19.9024 1.08739
$$336$$ 1.40280 2.24325i 0.0765291 0.122379i
$$337$$ −25.7988 −1.40535 −0.702676 0.711510i $$-0.748012\pi$$
−0.702676 + 0.711510i $$0.748012\pi$$
$$338$$ 6.50000 + 11.2583i 0.353553 + 0.612372i
$$339$$ 5.48261 9.49616i 0.297775 0.515761i
$$340$$ 11.1736 19.3533i 0.605975 1.04958i
$$341$$ −4.48261 7.76411i −0.242747 0.420450i
$$342$$ −6.48261 −0.350540
$$343$$ 18.4168 + 1.95478i 0.994414 + 0.105548i
$$344$$ 11.4478 0.617226
$$345$$ 7.41832 + 12.8489i 0.399389 + 0.691762i
$$346$$ −8.48261 + 14.6923i −0.456028 + 0.789864i
$$347$$ −10.3835 + 17.9848i −0.557418 + 0.965476i 0.440293 + 0.897854i $$0.354874\pi$$
−0.997711 + 0.0676219i $$0.978459\pi$$
$$348$$ 2.56430 + 4.44149i 0.137461 + 0.238089i
$$349$$ −9.51364 −0.509254 −0.254627 0.967039i $$-0.581953\pi$$
−0.254627 + 0.967039i $$0.581953\pi$$
$$350$$ −4.02801 + 6.44127i −0.215306 + 0.344300i
$$351$$ 0 0
$$352$$ 0.500000 + 0.866025i 0.0266501 + 0.0461593i
$$353$$ 6.28822 10.8915i 0.334688 0.579697i −0.648737 0.761013i $$-0.724702\pi$$
0.983425 + 0.181316i $$0.0580358\pi$$
$$354$$ −0.435704 + 0.754661i −0.0231574 + 0.0401098i
$$355$$ −10.4478 18.0962i −0.554514 0.960446i
$$356$$ 1.61121 0.0853937
$$357$$ −21.0609 0.742671i −1.11466 0.0393063i
$$358$$ −12.6703 −0.669644
$$359$$ 0.0347742 + 0.0602306i 0.00183531 + 0.00317885i 0.866942 0.498410i $$-0.166082\pi$$
−0.865106 + 0.501589i $$0.832749\pi$$
$$360$$ 1.40280 2.42972i 0.0739341 0.128058i
$$361$$ −11.5121 + 19.9396i −0.605902 + 1.04945i
$$362$$ 1.28822 + 2.23126i 0.0677071 + 0.117272i
$$363$$ −1.00000 −0.0524864
$$364$$ 0 0
$$365$$ −35.2845 −1.84687
$$366$$ 1.07981 + 1.87029i 0.0564427 + 0.0977615i
$$367$$ 15.7708 27.3159i 0.823231 1.42588i −0.0800336 0.996792i $$-0.525503\pi$$
0.903264 0.429085i $$-0.141164\pi$$
$$368$$ 2.64411 4.57973i 0.137834 0.238735i
$$369$$ 2.54691 + 4.41138i 0.132587 + 0.229647i
$$370$$ −29.4100 −1.52896
$$371$$ −9.93045 18.6919i −0.515563 0.970434i
$$372$$ 8.96523 0.464825
$$373$$ −7.65624 13.2610i −0.396425 0.686629i 0.596857 0.802348i $$-0.296416\pi$$
−0.993282 + 0.115719i $$0.963083\pi$$
$$374$$ 3.98261 6.89809i 0.205936 0.356692i
$$375$$ 2.98599 5.17189i 0.154196 0.267075i
$$376$$ −0.161495 0.279717i −0.00832847 0.0144253i
$$377$$ 0 0
$$378$$ −2.64411 0.0932392i −0.135998 0.00479570i
$$379$$ 16.0590 0.824898 0.412449 0.910981i $$-0.364674\pi$$
0.412449 + 0.910981i $$0.364674\pi$$
$$380$$ −9.09382 15.7510i −0.466503 0.808007i
$$381$$ −4.64411 + 8.04383i −0.237925 + 0.412098i
$$382$$ 1.19440 2.06876i 0.0611107 0.105847i
$$383$$ 0.369899 + 0.640684i 0.0189010 + 0.0327374i 0.875321 0.483542i $$-0.160650\pi$$
−0.856420 + 0.516279i $$0.827317\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ −3.93570 + 6.29365i −0.200582 + 0.320754i
$$386$$ −14.5764 −0.741921
$$387$$ −5.72392 9.91412i −0.290963 0.503963i
$$388$$ −3.50000 + 6.06218i −0.177686 + 0.307760i
$$389$$ −1.79160 + 3.10313i −0.0908375 + 0.157335i −0.907864 0.419265i $$-0.862288\pi$$
0.817026 + 0.576600i $$0.195621\pi$$
$$390$$ 0 0
$$391$$ −42.1218 −2.13019
$$392$$ −3.06430 6.29365i −0.154770 0.317878i
$$393$$ −12.9652 −0.654009
$$394$$ 6.24131 + 10.8103i 0.314432 + 0.544613i
$$395$$ 9.54691 16.5357i 0.480357 0.832003i
$$396$$ 0.500000 0.866025i 0.0251259 0.0435194i
$$397$$ 12.5643 + 21.7620i 0.630584 + 1.09220i 0.987433 + 0.158041i $$0.0505179\pi$$
−0.356849 + 0.934162i $$0.616149\pi$$
$$398$$ −14.1876 −0.711162
$$399$$ −9.09382 + 14.5421i −0.455260 + 0.728015i
$$400$$ 2.87141 0.143570
$$401$$ 1.93420 + 3.35013i 0.0965891 + 0.167297i 0.910271 0.414014i $$-0.135873\pi$$
−0.813682 + 0.581311i $$0.802540\pi$$
$$402$$ −3.54691 + 6.14343i −0.176904 + 0.306406i
$$403$$ 0 0
$$404$$ −5.36990 9.30094i −0.267162 0.462739i
$$405$$ −2.80560 −0.139412
$$406$$ 13.5606 + 0.478186i 0.672999 + 0.0237320i
$$407$$ −10.4826 −0.519604
$$408$$ 3.98261 + 6.89809i 0.197169 + 0.341506i
$$409$$ −2.32299 + 4.02354i −0.114864 + 0.198951i −0.917726 0.397215i $$-0.869977\pi$$
0.802861 + 0.596166i $$0.203310\pi$$
$$410$$ −7.14562 + 12.3766i −0.352897 + 0.611235i
$$411$$ 2.80560 + 4.85945i 0.138390 + 0.239699i
$$412$$ 2.96523 0.146086
$$413$$ 1.08168 + 2.03603i 0.0532262 + 0.100186i
$$414$$ −5.28822 −0.259902
$$415$$ 21.1736 + 36.6738i 1.03937 + 1.80025i
$$416$$ 0 0
$$417$$ 6.56430 11.3697i 0.321455 0.556776i
$$418$$ −3.24131 5.61411i −0.158537 0.274595i
$$419$$ −19.5174 −0.953487 −0.476743 0.879043i $$-0.658183\pi$$
−0.476743 + 0.879043i $$0.658183\pi$$
$$420$$ −3.48261 6.55525i −0.169934 0.319863i
$$421$$ 15.5174 0.756271 0.378136 0.925750i $$-0.376565\pi$$
0.378136 + 0.925750i $$0.376565\pi$$
$$422$$ 10.4168 + 18.0424i 0.507082 + 0.878292i
$$423$$ −0.161495 + 0.279717i −0.00785215 + 0.0136003i
$$424$$ −4.00000 + 6.92820i −0.194257 + 0.336463i
$$425$$ −11.4357 19.8072i −0.554713 0.960791i
$$426$$ 7.44784 0.360849
$$427$$ 5.71028 + 0.201361i 0.276340 + 0.00974456i
$$428$$ 4.83663 0.233787
$$429$$ 0 0
$$430$$ 16.0590 27.8151i 0.774436 1.34136i
$$431$$ 7.19440 12.4611i 0.346542 0.600228i −0.639091 0.769131i $$-0.720689\pi$$
0.985633 + 0.168903i $$0.0540225\pi$$
$$432$$ 0.500000 + 0.866025i 0.0240563 + 0.0416667i
$$433$$ 2.03477 0.0977850 0.0488925 0.998804i $$-0.484431\pi$$
0.0488925 + 0.998804i $$0.484431\pi$$
$$434$$ 12.5764 20.1112i 0.603688 0.965368i
$$435$$ 14.3888 0.689890
$$436$$ 5.07981 + 8.79849i 0.243279 + 0.421371i
$$437$$ −17.1407 + 29.6886i −0.819952 + 1.42020i
$$438$$ 6.28822 10.8915i 0.300463 0.520416i
$$439$$ −1.61308 2.79393i −0.0769880 0.133347i 0.824961 0.565190i $$-0.191197\pi$$
−0.901949 + 0.431842i $$0.857864\pi$$
$$440$$ 2.80560 0.133752
$$441$$ −3.91832 + 5.80059i −0.186587 + 0.276218i
$$442$$ 0 0
$$443$$ 11.0469 + 19.1338i 0.524854 + 0.909075i 0.999581 + 0.0289413i $$0.00921360\pi$$
−0.474727 + 0.880133i $$0.657453\pi$$
$$444$$ 5.24131 9.07821i 0.248741 0.430833i
$$445$$ 2.26020 3.91478i 0.107144 0.185579i
$$446$$ −6.28822 10.8915i −0.297756 0.515728i
$$447$$ −16.7398 −0.791765
$$448$$ −1.40280 + 2.24325i −0.0662761 + 0.105983i
$$449$$ 22.2497 1.05003 0.525014 0.851094i $$-0.324060\pi$$
0.525014 + 0.851094i $$0.324060\pi$$
$$450$$ −1.43570 2.48671i −0.0676797 0.117225i
$$451$$ −2.54691 + 4.41138i −0.119929 + 0.207724i
$$452$$ −5.48261 + 9.49616i −0.257880 + 0.446662i
$$453$$ 5.44971 + 9.43918i 0.256050 + 0.443491i
$$454$$ 20.0590 0.941418
$$455$$ 0 0
$$456$$ 6.48261 0.303576
$$457$$ 9.31925 + 16.1414i 0.435936 + 0.755063i 0.997372 0.0724572i $$-0.0230841\pi$$
−0.561436 + 0.827520i $$0.689751\pi$$
$$458$$ 11.2882 19.5518i 0.527464 0.913594i
$$459$$ 3.98261 6.89809i 0.185892 0.321975i
$$460$$ −7.41832 12.8489i −0.345881 0.599083i
$$461$$ −20.9895 −0.977578 −0.488789 0.872402i $$-0.662561\pi$$
−0.488789 + 0.872402i $$0.662561\pi$$
$$462$$ −1.24131 2.33648i −0.0577508 0.108703i
$$463$$ −5.35402 −0.248822 −0.124411 0.992231i $$-0.539704\pi$$
−0.124411 + 0.992231i $$0.539704\pi$$
$$464$$ −2.56430 4.44149i −0.119044 0.206191i
$$465$$ 12.5764 21.7830i 0.583218 1.01016i
$$466$$ 0.371407 0.643296i 0.0172051 0.0298001i
$$467$$ −13.0121 22.5377i −0.602130 1.04292i −0.992498 0.122261i $$-0.960986\pi$$
0.390368 0.920659i $$-0.372348\pi$$
$$468$$ 0 0
$$469$$ 8.80560 + 16.5746i 0.406605 + 0.765344i
$$470$$ −0.906181 −0.0417990
$$471$$ 0.887286 + 1.53682i 0.0408840 + 0.0708132i
$$472$$ 0.435704 0.754661i 0.0200549 0.0347361i
$$473$$ 5.72392 9.91412i 0.263186 0.455852i
$$474$$ 3.40280 + 5.89382i 0.156296 + 0.270712i
$$475$$ −18.6142 −0.854079
$$476$$ 21.0609 + 0.742671i 0.965326 + 0.0340403i
$$477$$ 8.00000 0.366295
$$478$$ −2.15962 3.74058i −0.0987789 0.171090i
$$479$$ 1.80560 3.12740i 0.0825001 0.142894i −0.821823 0.569743i $$-0.807043\pi$$
0.904323 + 0.426848i $$0.140376\pi$$
$$480$$ −1.40280 + 2.42972i −0.0640288 + 0.110901i
$$481$$ 0 0
$$482$$ −18.1876 −0.828424
$$483$$ −7.41832 + 11.8628i −0.337545 + 0.539774i
$$484$$ 1.00000 0.0454545
$$485$$ 9.81961 + 17.0081i 0.445886 + 0.772296i
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ 4.03103 6.98195i 0.182663 0.316382i −0.760123 0.649779i $$-0.774861\pi$$
0.942787 + 0.333397i $$0.108195\pi$$
$$488$$ −1.07981 1.87029i −0.0488808 0.0846640i
$$489$$ 4.05904 0.183556
$$490$$ −19.5904 1.38336i −0.885006 0.0624936i
$$491$$ 20.9062 0.943483 0.471741 0.881737i $$-0.343626\pi$$
0.471741 + 0.881737i $$0.343626\pi$$
$$492$$ −2.54691 4.41138i −0.114824 0.198880i
$$493$$ −20.4252 + 35.3775i −0.919905 + 1.59332i
$$494$$ 0 0
$$495$$ −1.40280 2.42972i −0.0630512 0.109208i
$$496$$ −8.96523 −0.402551
$$497$$ 10.4478 16.7073i 0.468650 0.749426i
$$498$$ −15.0938 −0.676370
$$499$$ −2.48261 4.30001i −0.111137 0.192495i 0.805092 0.593150i $$-0.202116\pi$$
−0.916229 + 0.400655i $$0.868783\pi$$
$$500$$ −2.98599 + 5.17189i −0.133538 + 0.231294i
$$501$$ 6.93420 12.0104i 0.309797 0.536584i
$$502$$ −14.3351 24.8292i −0.639808 1.10818i
$$503$$ −17.7988 −0.793611 −0.396806 0.917903i $$-0.629881\pi$$
−0.396806 + 0.917903i $$0.629881\pi$$
$$504$$ 2.64411 + 0.0932392i 0.117778 + 0.00415320i
$$505$$ −30.1316 −1.34084
$$506$$ −2.64411 4.57973i −0.117545 0.203594i
$$507$$ −6.50000 + 11.2583i −0.288675 + 0.500000i
$$508$$ 4.64411 8.04383i 0.206049 0.356887i
$$509$$ −2.25719 3.90956i −0.100048 0.173288i 0.811656 0.584135i $$-0.198566\pi$$
−0.911704 + 0.410847i $$0.865233\pi$$
$$510$$ 22.3473 0.989553
$$511$$ −15.6112 29.3846i −0.690599 1.29990i
$$512$$ 1.00000 0.0441942
$$513$$ −3.24131 5.61411i −0.143107 0.247869i
$$514$$ 6.80560 11.7876i 0.300182 0.519931i
$$515$$ 4.15962 7.20468i 0.183295 0.317476i
$$516$$ 5.72392 + 9.91412i 0.251982 + 0.436445i
$$517$$ −0.322990 −0.0142051
$$518$$ −13.0121 24.4925i −0.571720 1.07614i
$$519$$ −16.9652 −0.744691
$$520$$ 0 0
$$521$$ 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i $$-0.704321\pi$$
0.993011 + 0.118020i $$0.0376547\pi$$
$$522$$ −2.56430 + 4.44149i −0.112236 + 0.194399i
$$523$$ −3.45158 5.97832i −0.150927 0.261414i 0.780641 0.624979i $$-0.214893\pi$$
−0.931569 + 0.363566i $$0.881559\pi$$
$$524$$ 12.9652 0.566389
$$525$$ −7.59231 0.267728i −0.331356 0.0116846i
$$526$$ −3.61121 −0.157456
$$527$$ 35.7050 + 61.8429i 1.55534 + 2.69392i
$$528$$ −0.500000 + 0.866025i −0.0217597 + 0.0376889i
$$529$$ −2.48261 + 4.30001i −0.107940 + 0.186957i
$$530$$ 11.2224 + 19.4378i 0.487470 + 0.844323i
$$531$$ −0.871407 −0.0378159
$$532$$ 9.09382 14.5421i 0.394267 0.630480i
$$533$$ 0 0
$$534$$ 0.805603 + 1.39535i 0.0348618 + 0.0603825i
$$535$$ 6.78484 11.7517i 0.293334 0.508069i
$$536$$ 3.54691 6.14343i 0.153203 0.265356i
$$537$$ −6.33513 10.9728i −0.273381 0.473509i
$$538$$ −9.38203 −0.404488
$$539$$ −6.98261 0.493069i −0.300762 0.0212380i
$$540$$ 2.80560 0.120734
$$541$$ −1.40280 2.42972i −0.0603111 0.104462i 0.834293 0.551321i $$-0.185876\pi$$
−0.894604 + 0.446859i $$0.852543\pi$$
$$542$$ −2.80560 + 4.85945i −0.120511 + 0.208731i
$$543$$ −1.28822 + 2.23126i −0.0552826 + 0.0957523i
$$544$$ −3.98261 6.89809i −0.170753 0.295753i
$$545$$ 28.5039 1.22097
$$546$$ 0 0
$$547$$ 32.9274 1.40788 0.703938 0.710262i $$-0.251423\pi$$
0.703938 + 0.710262i $$0.251423\pi$$
$$548$$ −2.80560 4.85945i −0.119849 0.207585i
$$549$$ −1.07981 + 1.87029i −0.0460852 + 0.0798220i
$$550$$ 1.43570 2.48671i 0.0612186 0.106034i
$$551$$ 16.6233 + 28.7925i 0.708178 + 1.22660i
$$552$$ 5.28822 0.225081
$$553$$ 17.9947 + 0.634549i 0.765215 + 0.0269838i
$$554$$ −16.0000 −0.679775
$$555$$ −14.7050 25.4698i −0.624194 1.08113i
$$556$$ −6.56430 + 11.3697i −0.278388 + 0.482182i
$$557$$ −11.8525 + 20.5292i −0.502207 + 0.869848i 0.497790 + 0.867298i $$0.334145\pi$$
−0.999997 + 0.00255037i $$0.999188\pi$$
$$558$$ 4.48261 + 7.76411i 0.189764 + 0.328681i
$$559$$ 0 0
$$560$$ 3.48261 + 6.55525i 0.147167 + 0.277010i
$$561$$ 7.96523 0.336292
$$562$$ −12.0764 20.9170i −0.509414 0.882330i
$$563$$ −15.2224 + 26.3660i −0.641548 + 1.11119i 0.343539 + 0.939138i $$0.388374\pi$$
−0.985087 + 0.172056i $$0.944959\pi$$
$$564$$ 0.161495 0.279717i 0.00680016 0.0117782i
$$565$$ 15.3820 + 26.6425i 0.647127 + 1.12086i
$$566$$ 7.54166 0.317000
$$567$$ −1.24131 2.33648i −0.0521300 0.0981231i
$$568$$ −7.44784 −0.312504
$$569$$ −11.1407 19.2963i −0.467044 0.808943i 0.532248 0.846589i $$-0.321348\pi$$
−0.999291 + 0.0376455i $$0.988014\pi$$
$$570$$ 9.09382 15.7510i 0.380898 0.659735i
$$571$$ 1.43570 2.48671i 0.0600823 0.104066i −0.834420 0.551130i $$-0.814197\pi$$
0.894502 + 0.447064i $$0.147530\pi$$
$$572$$ 0 0
$$573$$ 2.38879 0.0997933
$$574$$ −13.4686 0.474943i −0.562169 0.0198238i
$$575$$ −15.1846 −0.633242
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ 7.51214 13.0114i 0.312734 0.541672i −0.666219 0.745756i $$-0.732088\pi$$
0.978953 + 0.204084i $$0.0654217\pi$$
$$578$$ −23.2224 + 40.2224i −0.965925 + 1.67303i
$$579$$ −7.28822 12.6236i −0.302888 0.524617i
$$580$$ −14.3888 −0.597462
$$581$$ −21.1736 + 33.8591i −0.878430 + 1.40471i
$$582$$ −7.00000 −0.290159
$$583$$ 4.00000 + 6.92820i 0.165663 + 0.286937i
$$584$$ −6.28822 + 10.8915i −0.260208 + 0.450694i
$$585$$ 0 0
$$586$$ −3.95309 6.84695i −0.163301 0.282845i
$$587$$ −42.5069 −1.75445 −0.877223 0.480082i $$-0.840607\pi$$
−0.877223 + 0.480082i $$0.840607\pi$$
$$588$$ 3.91832 5.80059i 0.161589 0.239212i
$$589$$ 58.1181 2.39471
$$590$$ −1.22241 2.11728i −0.0503259 0.0871670i
$$591$$ −6.24131 + 10.8103i −0.256733 + 0.444675i
$$592$$ −5.24131 + 9.07821i −0.215416 + 0.373112i
$$593$$ −7.69289 13.3245i −0.315909 0.547171i 0.663721 0.747980i $$-0.268976\pi$$
−0.979630 + 0.200809i $$0.935643\pi$$
$$594$$ 1.00000 0.0410305
$$595$$ 31.3488 50.1304i 1.28517 2.05515i
$$596$$ 16.7398 0.685689
$$597$$ −7.09382 12.2869i −0.290331 0.502867i
$$598$$ 0 0
$$599$$ 19.8196 34.3286i 0.809807 1.40263i −0.103190 0.994662i $$-0.532905\pi$$
0.912997 0.407966i $$-0.133762\pi$$
$$600$$ 1.43570 + 2.48671i 0.0586124 + 0.101520i
$$601$$ 33.3405 1.35999 0.679994 0.733218i $$-0.261983\pi$$
0.679994 + 0.733218i $$0.261983\pi$$
$$602$$ 30.2693 + 1.06739i 1.23369 + 0.0435034i
$$603$$ −7.09382 −0.288883
$$604$$ −5.44971 9.43918i −0.221746 0.384075i
$$605$$ 1.40280 2.42972i 0.0570320 0.0987823i
$$606$$ 5.36990 9.30094i 0.218137 0.377825i
$$607$$ −7.97923 13.8204i −0.323867 0.560954i 0.657415 0.753528i $$-0.271650\pi$$
−0.981282 + 0.192574i $$0.938316\pi$$
$$608$$ −6.48261 −0.262905
$$609$$ 6.36616 + 11.9829i 0.257970 + 0.485571i
$$610$$ −6.05904 −0.245324
$$611$$ 0 0
$$612$$ −3.98261 + 6.89809i −0.160988 + 0.278839i
$$613$$ −23.3333 + 40.4144i −0.942421 + 1.63232i −0.181587 + 0.983375i $$0.558123\pi$$
−0.760834 + 0.648947i $$0.775210\pi$$
$$614$$ −6.44784 11.1680i −0.260214 0.450703i
$$615$$ −14.2912 −0.576278
$$616$$ 1.24131 + 2.33648i 0.0500137 + 0.0941396i
$$617$$ −9.28447 −0.373779 −0.186889 0.982381i $$-0.559841\pi$$
−0.186889 + 0.982381i $$0.559841\pi$$
$$618$$ 1.48261 + 2.56796i 0.0596394 + 0.103299i
$$619$$ −16.9947 + 29.4358i −0.683077 + 1.18312i 0.290961 + 0.956735i $$0.406025\pi$$
−0.974037 + 0.226388i $$0.927308\pi$$
$$620$$ −12.5764 + 21.7830i −0.505082 + 0.874827i
$$621$$ −2.64411 4.57973i −0.106104 0.183778i
$$622$$ 10.8994 0.437027
$$623$$ 4.26020 + 0.150227i 0.170681 + 0.00601874i
$$624$$ 0 0
$$625$$ 15.5560 + 26.9438i 0.622241 + 1.07775i
$$626$$ 4.56430 7.90559i 0.182426 0.315971i
$$627$$ 3.24131 5.61411i 0.129445 0.224206i
$$628$$ −0.887286 1.53682i −0.0354066 0.0613260i
$$629$$ 83.4964 3.32922
$$630$$ 3.93570 6.29365i 0.156802 0.250745i
$$631$$ −14.6460 −0.583047 −0.291524 0.956564i $$-0.594162\pi$$
−0.291524 + 0.956564i $$0.594162\pi$$
$$632$$ −3.40280 5.89382i −0.135356 0.234444i
$$633$$ −10.4168 + 18.0424i −0.414031 + 0.717123i
$$634$$ 4.75682 8.23906i 0.188918 0.327215i
$$635$$ −13.0295 22.5678i −0.517061 0.895576i
$$636$$ −8.00000 −0.317221
$$637$$ 0 0
$$638$$ −5.12859 −0.203043
$$639$$ 3.72392 + 6.45002i 0.147316 + 0.255159i
$$640$$ 1.40280 2.42972i 0.0554506 0.0960432i
$$641$$ −10.4826 + 18.1564i −0.414038 + 0.717135i −0.995327 0.0965620i $$-0.969215\pi$$
0.581289 + 0.813697i $$0.302549\pi$$
$$642$$ 2.41832 + 4.18865i 0.0954433 + 0.165313i
$$643$$ −23.6733 −0.933582 −0.466791 0.884368i $$-0.654590\pi$$
−0.466791 + 0.884368i $$0.654590\pi$$
$$644$$ 7.41832 11.8628i 0.292323 0.467458i
$$645$$ 32.1181 1.26465
$$646$$ 25.8177 + 44.7176i 1.01579 + 1.75939i
$$647$$ 6.20840 10.7533i 0.244078 0.422755i −0.717794 0.696255i $$-0.754848\pi$$
0.961872 + 0.273500i $$0.0881815\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ −0.435704 0.754661i −0.0171029 0.0296230i
$$650$$ 0 0
$$651$$ 23.7050 + 0.835910i 0.929073 + 0.0327619i
$$652$$ −4.05904 −0.158964
$$653$$ 0.0487812 + 0.0844916i 0.00190896 + 0.00330641i 0.866978 0.498346i $$-0.166059\pi$$
−0.865069 + 0.501652i $$0.832726\pi$$
$$654$$ −5.07981 + 8.79849i −0.198636 + 0.344048i
$$655$$ 18.1876 31.5019i 0.710650 1.23088i
$$656$$ 2.54691 + 4.41138i 0.0994401 + 0.172235i
$$657$$ 12.5764 0.490653
$$658$$ −0.400929 0.754661i −0.0156299 0.0294197i
$$659$$ −35.0243 −1.36435 −0.682176 0.731188i $$-0.738966\pi$$
−0.682176 + 0.731188i $$0.738966\pi$$
$$660$$ 1.40280 + 2.42972i 0.0546040 + 0.0945769i
$$661$$ −14.8177 + 25.6651i −0.576343 + 0.998256i 0.419551 + 0.907732i $$0.362188\pi$$
−0.995894 + 0.0905240i $$0.971146\pi$$
$$662$$ −0.546909 + 0.947275i −0.0212562 + 0.0368169i
$$663$$ 0 0
$$664$$ 15.0938 0.585754
$$665$$ −22.5764 42.4951i −0.875476 1.64789i
$$666$$ 10.4826 0.406193
$$667$$ 13.5606 + 23.4876i 0.525067 + 0.909442i
$$668$$ −6.93420 + 12.0104i −0.268292 + 0.464696i
$$669$$ 6.28822 10.8915i 0.243116 0.421090i
$$670$$ −9.95122 17.2360i −0.384449 0.665885i
$$671$$ −2.15962 −0.0833713
$$672$$ −2.64411 0.0932392i −0.101999 0.00359678i
$$673$$ 16.8957 0.651281 0.325640 0.945494i $$-0.394420\pi$$
0.325640 + 0.945494i $$0.394420\pi$$
$$674$$ 12.8994 + 22.3425i 0.496867 + 0.860599i
$$675$$ 1.43570 2.48671i 0.0552603 0.0957136i
$$676$$ 6.50000 11.2583i 0.250000 0.433013i
$$677$$ −6.59533 11.4234i −0.253479 0.439038i 0.711002 0.703190i $$-0.248242\pi$$
−0.964481 + 0.264151i $$0.914908\pi$$
$$678$$ −10.9652 −0.421117
$$679$$ −9.81961 + 15.7027i −0.376842 + 0.602615i
$$680$$ −22.3473 −0.856978
$$681$$ 10.0295 + 17.3716i 0.384332 + 0.665683i
$$682$$ −4.48261 + 7.76411i −0.171648 + 0.297303i
$$683$$ −4.91832 + 8.51877i −0.188194 + 0.325962i −0.944648 0.328085i $$-0.893597\pi$$
0.756454 + 0.654047i $$0.226930\pi$$
$$684$$ 3.24131 + 5.61411i 0.123934 + 0.214661i
$$685$$ −15.7428 −0.601502
$$686$$ −7.51552 16.9268i −0.286944 0.646269i
$$687$$ 22.5764 0.861345
$$688$$ −5.72392 9.91412i −0.218222 0.377972i
$$689$$ 0 0
$$690$$ 7.41832 12.8489i 0.282410 0.489149i
$$691$$ 24.9947 + 43.2922i 0.950845 + 1.64691i 0.743602 + 0.668622i $$0.233116\pi$$
0.207243 + 0.978290i $$0.433551\pi$$
$$692$$ 16.9652 0.644921
$$693$$ 1.40280 2.24325i 0.0532880 0.0852138i
$$694$$ 20.7671 0.788308
$$695$$ 18.4168 + 31.8988i 0.698589 + 1.20999i
$$696$$ 2.56430 4.44149i 0.0971994 0.168354i
$$697$$ 20.2867 35.1376i 0.768414 1.33093i
$$698$$ 4.75682 + 8.23906i 0.180048 + 0.311853i
$$699$$ 0.742815 0.0280958
$$700$$ 7.59231 + 0.267728i 0.286962 + 0.0101192i
$$701$$ −17.7050 −0.668710 −0.334355 0.942447i $$-0.608518\pi$$
−0.334355 + 0.942447i $$0.608518\pi$$
$$702$$ 0 0
$$703$$ 33.9774 58.8505i 1.28148 2.21959i
$$704$$ 0.500000 0.866025i 0.0188445 0.0326396i
$$705$$ −0.453091 0.784776i −0.0170644 0.0295564i
$$706$$ −12.5764 −0.473320
$$707$$ −13.3314 25.0934i −0.501378 0.943733i
$$708$$ 0.871407 0.0327495
$$709$$ 15.9774 + 27.6736i 0.600042 + 1.03930i 0.992814 + 0.119668i $$0.0381830\pi$$
−0.392772 + 0.919636i $$0.628484\pi$$
$$710$$ −10.4478 + 18.0962i −0.392100 + 0.679138i
$$711$$ −3.40280 + 5.89382i −0.127615 + 0.221036i
$$712$$ −0.805603 1.39535i −0.0301912 0.0522928i
$$713$$ 47.4100 1.77552
$$714$$ 9.88729 + 18.6106i 0.370022 + 0.696485i
$$715$$ 0 0
$$716$$ 6.33513 + 10.9728i 0.236755 + 0.410071i
$$717$$ 2.15962 3.74058i 0.0806526 0.139694i
$$718$$ 0.0347742 0.0602306i 0.00129776 0.00224779i
$$719$$ −10.8975 18.8751i −0.406410 0.703923i 0.588074 0.808807i $$-0.299886\pi$$
−0.994484 + 0.104884i $$0.966553\pi$$
$$720$$ −2.80560 −0.104559
$$721$$ 7.84038 + 0.276475i 0.291991 + 0.0102965i
$$722$$ 23.0243 0.856875
$$723$$ −9.09382 15.7510i −0.338203 0.585784i
$$724$$ 1.28822 2.23126i 0.0478762 0.0829239i
$$725$$ −7.36314 + 12.7533i −0.273460 + 0.473647i
$$726$$ 0.500000 + 0.866025i 0.0185567 + 0.0321412i
$$727$$ −4.84714 −0.179770 −0.0898852 0.995952i $$-0.528650\pi$$
−0.0898852 + 0.995952i $$0.528650\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 17.6422 + 30.5572i 0.652968 + 1.13097i
$$731$$ −45.5923 + 78.9682i −1.68629 + 2.92074i
$$732$$ 1.07981 1.87029i 0.0399110 0.0691278i
$$733$$ −6.11459 10.5908i −0.225847 0.391179i 0.730726 0.682671i $$-0.239182\pi$$
−0.956573 + 0.291492i $$0.905848\pi$$
$$734$$ −31.5417 −1.16422
$$735$$ −8.59720 17.6575i −0.317112 0.651307i
$$736$$ −5.28822 −0.194926
$$737$$ −3.54691 6.14343i −0.130652 0.226296i
$$738$$ 2.54691 4.41138i 0.0937530 0.162385i
$$739$$ 0.517387 0.896141i 0.0190324 0.0329651i −0.856352 0.516392i $$-0.827275\pi$$
0.875385 + 0.483427i $$0.160608\pi$$
$$740$$ 14.7050 + 25.4698i 0.540567 + 0.936290i
$$741$$ 0 0
$$742$$ −11.2224 + 17.9460i −0.411988 + 0.658817i
$$743$$ −23.9925 −0.880200 −0.440100 0.897949i $$-0.645057\pi$$
−0.440100 + 0.897949i $$0.645057\pi$$
$$744$$ −4.48261 7.76411i −0.164341 0.284646i
$$745$$ 23.4826 40.6731i 0.860336 1.49015i
$$746$$ −7.65624 + 13.2610i −0.280315 + 0.485520i
$$747$$ −7.54691 13.0716i −0.276127 0.478266i
$$748$$ −7.96523 −0.291238
$$749$$ 12.7886 + 0.450964i 0.467285 + 0.0164779i
$$750$$ −5.97199 −0.218066
$$751$$ −10.2534 17.7595i −0.374153 0.648053i 0.616047 0.787710i $$-0.288733\pi$$
−0.990200 + 0.139657i $$0.955400\pi$$
$$752$$ −0.161495 + 0.279717i −0.00588912 + 0.0102002i
$$753$$ 14.3351 24.8292i 0.522401 0.904825i
$$754$$ 0 0
$$755$$ −30.5794 −1.11290
$$756$$ 1.24131 + 2.33648i 0.0451459 + 0.0849771i
$$757$$ −16.8019 −0.610674 −0.305337 0.952244i $$-0.598769\pi$$
−0.305337 + 0.952244i $$0.598769\pi$$
$$758$$ −8.02952 13.9075i −0.291645 0.505145i
$$759$$ 2.64411 4.57973i 0.0959750 0.166234i
$$760$$ −9.09382 + 15.7510i −0.329867 + 0.571347i
$$761$$ 7.25495 + 12.5659i 0.262992 + 0.455515i 0.967036 0.254642i $$-0.0819575\pi$$
−0.704044 + 0.710157i $$0.748624\pi$$
$$762$$ 9.28822 0.336477
$$763$$ 12.6112 + 23.7378i 0.456556 + 0.859366i
$$764$$ −2.38879 −0.0864235
$$765$$ 11.1736 + 19.3533i 0.403983 + 0.699720i
$$766$$ 0.369899 0.640684i 0.0133650 0.0231489i
$$767$$ 0 0
$$768$$ 0.500000 + 0.866025i 0.0180422 + 0.0312500i
$$769$$ 3.35402 0.120949 0.0604745 0.998170i $$-0.480739\pi$$
0.0604745 + 0.998170i $$0.480739\pi$$
$$770$$ 7.41832 + 0.261592i 0.267338 + 0.00942712i
$$771$$ 13.6112 0.490196
$$772$$ 7.28822 + 12.6236i 0.262309 + 0.454332i
$$773$$ −0.920188 + 1.59381i −0.0330969 + 0.0573255i −0.882099 0.471063i $$-0.843870\pi$$
0.849003 + 0.528389i $$0.177204\pi$$
$$774$$ −5.72392 + 9.91412i −0.205742 + 0.356356i
$$775$$ 12.8714 + 22.2939i 0.462355 + 0.800822i
$$776$$ 7.00000 0.251285
$$777$$ 14.7050 23.5151i 0.527540 0.843598i
$$778$$ 3.58319 0.128464
$$779$$ −16.5106 28.5972i −0.591555 1.02460i
$$780$$ 0 0