# Properties

 Label 950.2.e.a.201.1 Level $950$ Weight $2$ Character 950.201 Analytic conductor $7.586$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 201.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 950.201 Dual form 950.2.e.a.501.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} -3.00000 q^{11} +1.00000 q^{12} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} -6.00000 q^{26} -5.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} -8.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{36} -8.00000 q^{37} +(-4.00000 + 1.73205i) q^{38} -6.00000 q^{39} +(-2.50000 + 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(1.50000 + 2.59808i) q^{44} +8.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} -3.00000 q^{49} +(1.00000 + 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -2.00000 q^{56} +(-4.00000 + 1.73205i) q^{57} -2.00000 q^{58} +(-2.50000 + 4.33013i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(4.00000 - 6.92820i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} -2.00000 q^{68} +8.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(1.00000 + 1.73205i) q^{72} +(-4.50000 + 7.79423i) q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 - 4.33013i) q^{76} +6.00000 q^{77} +(3.00000 - 5.19615i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} +11.0000 q^{83} -2.00000 q^{84} -2.00000 q^{87} -3.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(-6.00000 - 10.3923i) q^{91} +(-4.00000 + 6.92820i) q^{92} +(4.00000 - 6.92820i) q^{93} +6.00000 q^{94} +1.00000 q^{96} +(-7.50000 + 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{3} - q^{4} - q^{6} - 4q^{7} + 2q^{8} + 2q^{9} + O(q^{10})$$ $$2q - q^{2} - q^{3} - q^{4} - q^{6} - 4q^{7} + 2q^{8} + 2q^{9} - 6q^{11} + 2q^{12} + 6q^{13} + 2q^{14} - q^{16} + 2q^{17} - 4q^{18} + 7q^{19} + 2q^{21} + 3q^{22} - 8q^{23} - q^{24} - 12q^{26} - 10q^{27} + 2q^{28} + 2q^{29} - 16q^{31} - q^{32} + 3q^{33} + 2q^{34} + 2q^{36} - 16q^{37} - 8q^{38} - 12q^{39} - 5q^{41} + 2q^{42} + 3q^{44} + 16q^{46} - 6q^{47} - q^{48} - 6q^{49} + 2q^{51} + 6q^{52} + 6q^{53} + 5q^{54} - 4q^{56} - 8q^{57} - 4q^{58} - 5q^{59} - 14q^{61} + 8q^{62} - 4q^{63} + 2q^{64} + 3q^{66} - 5q^{67} - 4q^{68} + 16q^{69} + 6q^{71} + 2q^{72} - 9q^{73} + 8q^{74} + q^{76} + 12q^{77} + 6q^{78} - 8q^{79} - q^{81} - 5q^{82} + 22q^{83} - 4q^{84} - 4q^{87} - 6q^{88} - 14q^{89} - 12q^{91} - 8q^{92} + 8q^{93} + 12q^{94} + 2q^{96} - 15q^{97} + 3q^{98} - 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i $$-0.926548\pi$$
0.684819 + 0.728714i $$0.259881\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0
$$6$$ −0.500000 0.866025i −0.204124 0.353553i
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i $$0.146166\pi$$
−0.0643593 + 0.997927i $$0.520500\pi$$
$$14$$ 1.00000 1.73205i 0.267261 0.462910i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i $$-0.755354\pi$$
0.961436 + 0.275029i $$0.0886875\pi$$
$$18$$ −2.00000 −0.471405
$$19$$ 3.50000 + 2.59808i 0.802955 + 0.596040i
$$20$$ 0 0
$$21$$ 1.00000 1.73205i 0.218218 0.377964i
$$22$$ 1.50000 2.59808i 0.319801 0.553912i
$$23$$ −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i $$-0.852679\pi$$
0.0607377 0.998154i $$-0.480655\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ 0 0
$$26$$ −6.00000 −1.17670
$$27$$ −5.00000 −0.962250
$$28$$ 1.00000 + 1.73205i 0.188982 + 0.327327i
$$29$$ 1.00000 + 1.73205i 0.185695 + 0.321634i 0.943811 0.330487i $$-0.107213\pi$$
−0.758115 + 0.652121i $$0.773880\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 1.50000 2.59808i 0.261116 0.452267i
$$34$$ 1.00000 + 1.73205i 0.171499 + 0.297044i
$$35$$ 0 0
$$36$$ 1.00000 1.73205i 0.166667 0.288675i
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ −4.00000 + 1.73205i −0.648886 + 0.280976i
$$39$$ −6.00000 −0.960769
$$40$$ 0 0
$$41$$ −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i $$-0.961009\pi$$
0.602072 + 0.798441i $$0.294342\pi$$
$$42$$ 1.00000 + 1.73205i 0.154303 + 0.267261i
$$43$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$44$$ 1.50000 + 2.59808i 0.226134 + 0.391675i
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i $$-0.310836\pi$$
−0.997503 + 0.0706177i $$0.977503\pi$$
$$48$$ −0.500000 0.866025i −0.0721688 0.125000i
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 1.00000 + 1.73205i 0.140028 + 0.242536i
$$52$$ 3.00000 5.19615i 0.416025 0.720577i
$$53$$ 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i $$-0.0314685\pi$$
−0.583036 + 0.812447i $$0.698135\pi$$
$$54$$ 2.50000 4.33013i 0.340207 0.589256i
$$55$$ 0 0
$$56$$ −2.00000 −0.267261
$$57$$ −4.00000 + 1.73205i −0.529813 + 0.229416i
$$58$$ −2.00000 −0.262613
$$59$$ −2.50000 + 4.33013i −0.325472 + 0.563735i −0.981608 0.190909i $$-0.938857\pi$$
0.656136 + 0.754643i $$0.272190\pi$$
$$60$$ 0 0
$$61$$ −7.00000 12.1244i −0.896258 1.55236i −0.832240 0.554416i $$-0.812942\pi$$
−0.0640184 0.997949i $$-0.520392\pi$$
$$62$$ 4.00000 6.92820i 0.508001 0.879883i
$$63$$ −2.00000 3.46410i −0.251976 0.436436i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 1.50000 + 2.59808i 0.184637 + 0.319801i
$$67$$ −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i $$-0.265465\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i $$-0.717462\pi$$
0.987294 + 0.158901i $$0.0507952\pi$$
$$72$$ 1.00000 + 1.73205i 0.117851 + 0.204124i
$$73$$ −4.50000 + 7.79423i −0.526685 + 0.912245i 0.472831 + 0.881153i $$0.343232\pi$$
−0.999517 + 0.0310925i $$0.990101\pi$$
$$74$$ 4.00000 6.92820i 0.464991 0.805387i
$$75$$ 0 0
$$76$$ 0.500000 4.33013i 0.0573539 0.496700i
$$77$$ 6.00000 0.683763
$$78$$ 3.00000 5.19615i 0.339683 0.588348i
$$79$$ −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i $$-0.981922\pi$$
0.548352 + 0.836247i $$0.315255\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ −2.50000 4.33013i −0.276079 0.478183i
$$83$$ 11.0000 1.20741 0.603703 0.797209i $$-0.293691\pi$$
0.603703 + 0.797209i $$0.293691\pi$$
$$84$$ −2.00000 −0.218218
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −2.00000 −0.214423
$$88$$ −3.00000 −0.319801
$$89$$ −7.00000 12.1244i −0.741999 1.28518i −0.951584 0.307389i $$-0.900545\pi$$
0.209585 0.977790i $$-0.432789\pi$$
$$90$$ 0 0
$$91$$ −6.00000 10.3923i −0.628971 1.08941i
$$92$$ −4.00000 + 6.92820i −0.417029 + 0.722315i
$$93$$ 4.00000 6.92820i 0.414781 0.718421i
$$94$$ 6.00000 0.618853
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ −7.50000 + 12.9904i −0.761510 + 1.31897i 0.180563 + 0.983563i $$0.442208\pi$$
−0.942072 + 0.335410i $$0.891125\pi$$
$$98$$ 1.50000 2.59808i 0.151523 0.262445i
$$99$$ −3.00000 5.19615i −0.301511 0.522233i
$$100$$ 0 0
$$101$$ 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i $$-0.000911295\pi$$
−0.502477 + 0.864590i $$0.667578\pi$$
$$102$$ −2.00000 −0.198030
$$103$$ −6.00000 −0.591198 −0.295599 0.955312i $$-0.595519\pi$$
−0.295599 + 0.955312i $$0.595519\pi$$
$$104$$ 3.00000 + 5.19615i 0.294174 + 0.509525i
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 2.50000 + 4.33013i 0.240563 + 0.416667i
$$109$$ 4.00000 6.92820i 0.383131 0.663602i −0.608377 0.793648i $$-0.708179\pi$$
0.991508 + 0.130046i $$0.0415126\pi$$
$$110$$ 0 0
$$111$$ 4.00000 6.92820i 0.379663 0.657596i
$$112$$ 1.00000 1.73205i 0.0944911 0.163663i
$$113$$ 13.0000 1.22294 0.611469 0.791269i $$-0.290579\pi$$
0.611469 + 0.791269i $$0.290579\pi$$
$$114$$ 0.500000 4.33013i 0.0468293 0.405554i
$$115$$ 0 0
$$116$$ 1.00000 1.73205i 0.0928477 0.160817i
$$117$$ −6.00000 + 10.3923i −0.554700 + 0.960769i
$$118$$ −2.50000 4.33013i −0.230144 0.398621i
$$119$$ −2.00000 + 3.46410i −0.183340 + 0.317554i
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 14.0000 1.26750
$$123$$ −2.50000 4.33013i −0.225417 0.390434i
$$124$$ 4.00000 + 6.92820i 0.359211 + 0.622171i
$$125$$ 0 0
$$126$$ 4.00000 0.356348
$$127$$ 3.00000 + 5.19615i 0.266207 + 0.461084i 0.967879 0.251416i $$-0.0808962\pi$$
−0.701672 + 0.712500i $$0.747563\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −3.50000 + 6.06218i −0.305796 + 0.529655i −0.977438 0.211221i $$-0.932256\pi$$
0.671642 + 0.740876i $$0.265589\pi$$
$$132$$ −3.00000 −0.261116
$$133$$ −7.00000 5.19615i −0.606977 0.450564i
$$134$$ 5.00000 0.431934
$$135$$ 0 0
$$136$$ 1.00000 1.73205i 0.0857493 0.148522i
$$137$$ −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i $$-0.207572\pi$$
−0.922961 + 0.384893i $$0.874238\pi$$
$$138$$ −4.00000 + 6.92820i −0.340503 + 0.589768i
$$139$$ −4.50000 7.79423i −0.381685 0.661098i 0.609618 0.792695i $$-0.291323\pi$$
−0.991303 + 0.131597i $$0.957989\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 3.00000 + 5.19615i 0.251754 + 0.436051i
$$143$$ −9.00000 15.5885i −0.752618 1.30357i
$$144$$ −2.00000 −0.166667
$$145$$ 0 0
$$146$$ −4.50000 7.79423i −0.372423 0.645055i
$$147$$ 1.50000 2.59808i 0.123718 0.214286i
$$148$$ 4.00000 + 6.92820i 0.328798 + 0.569495i
$$149$$ −2.00000 + 3.46410i −0.163846 + 0.283790i −0.936245 0.351348i $$-0.885723\pi$$
0.772399 + 0.635138i $$0.219057\pi$$
$$150$$ 0 0
$$151$$ 12.0000 0.976546 0.488273 0.872691i $$-0.337627\pi$$
0.488273 + 0.872691i $$0.337627\pi$$
$$152$$ 3.50000 + 2.59808i 0.283887 + 0.210732i
$$153$$ 4.00000 0.323381
$$154$$ −3.00000 + 5.19615i −0.241747 + 0.418718i
$$155$$ 0 0
$$156$$ 3.00000 + 5.19615i 0.240192 + 0.416025i
$$157$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$158$$ −4.00000 6.92820i −0.318223 0.551178i
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ 8.00000 + 13.8564i 0.630488 + 1.09204i
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ −3.00000 −0.234978 −0.117489 0.993074i $$-0.537485\pi$$
−0.117489 + 0.993074i $$0.537485\pi$$
$$164$$ 5.00000 0.390434
$$165$$ 0 0
$$166$$ −5.50000 + 9.52628i −0.426883 + 0.739383i
$$167$$ 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i $$-0.0664952\pi$$
−0.668730 + 0.743505i $$0.733162\pi$$
$$168$$ 1.00000 1.73205i 0.0771517 0.133631i
$$169$$ −11.5000 + 19.9186i −0.884615 + 1.53220i
$$170$$ 0 0
$$171$$ −1.00000 + 8.66025i −0.0764719 + 0.662266i
$$172$$ 0 0
$$173$$ −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i $$0.406540\pi$$
−0.973670 + 0.227964i $$0.926793\pi$$
$$174$$ 1.00000 1.73205i 0.0758098 0.131306i
$$175$$ 0 0
$$176$$ 1.50000 2.59808i 0.113067 0.195837i
$$177$$ −2.50000 4.33013i −0.187912 0.325472i
$$178$$ 14.0000 1.04934
$$179$$ 3.00000 0.224231 0.112115 0.993695i $$-0.464237\pi$$
0.112115 + 0.993695i $$0.464237\pi$$
$$180$$ 0 0
$$181$$ 8.00000 + 13.8564i 0.594635 + 1.02994i 0.993598 + 0.112972i $$0.0360369\pi$$
−0.398963 + 0.916967i $$0.630630\pi$$
$$182$$ 12.0000 0.889499
$$183$$ 14.0000 1.03491
$$184$$ −4.00000 6.92820i −0.294884 0.510754i
$$185$$ 0 0
$$186$$ 4.00000 + 6.92820i 0.293294 + 0.508001i
$$187$$ −3.00000 + 5.19615i −0.219382 + 0.379980i
$$188$$ −3.00000 + 5.19615i −0.218797 + 0.378968i
$$189$$ 10.0000 0.727393
$$190$$ 0 0
$$191$$ −4.00000 −0.289430 −0.144715 0.989473i $$-0.546227\pi$$
−0.144715 + 0.989473i $$0.546227\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i $$-0.716141\pi$$
0.987945 + 0.154805i $$0.0494748\pi$$
$$194$$ −7.50000 12.9904i −0.538469 0.932655i
$$195$$ 0 0
$$196$$ 1.50000 + 2.59808i 0.107143 + 0.185577i
$$197$$ −8.00000 −0.569976 −0.284988 0.958531i $$-0.591990\pi$$
−0.284988 + 0.958531i $$0.591990\pi$$
$$198$$ 6.00000 0.426401
$$199$$ 11.0000 + 19.0526i 0.779769 + 1.35060i 0.932075 + 0.362267i $$0.117997\pi$$
−0.152305 + 0.988334i $$0.548670\pi$$
$$200$$ 0 0
$$201$$ 5.00000 0.352673
$$202$$ −10.0000 −0.703598
$$203$$ −2.00000 3.46410i −0.140372 0.243132i
$$204$$ 1.00000 1.73205i 0.0700140 0.121268i
$$205$$ 0 0
$$206$$ 3.00000 5.19615i 0.209020 0.362033i
$$207$$ 8.00000 13.8564i 0.556038 0.963087i
$$208$$ −6.00000 −0.416025
$$209$$ −10.5000 7.79423i −0.726300 0.539138i
$$210$$ 0 0
$$211$$ 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i $$-0.789367\pi$$
0.926620 + 0.375999i $$0.122700\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ 3.00000 + 5.19615i 0.205557 + 0.356034i
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ 0 0
$$216$$ −5.00000 −0.340207
$$217$$ 16.0000 1.08615
$$218$$ 4.00000 + 6.92820i 0.270914 + 0.469237i
$$219$$ −4.50000 7.79423i −0.304082 0.526685i
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 4.00000 + 6.92820i 0.268462 + 0.464991i
$$223$$ −8.00000 + 13.8564i −0.535720 + 0.927894i 0.463409 + 0.886145i $$0.346626\pi$$
−0.999128 + 0.0417488i $$0.986707\pi$$
$$224$$ 1.00000 + 1.73205i 0.0668153 + 0.115728i
$$225$$ 0 0
$$226$$ −6.50000 + 11.2583i −0.432374 + 0.748893i
$$227$$ 7.00000 0.464606 0.232303 0.972643i $$-0.425374\pi$$
0.232303 + 0.972643i $$0.425374\pi$$
$$228$$ 3.50000 + 2.59808i 0.231793 + 0.172062i
$$229$$ −24.0000 −1.58596 −0.792982 0.609245i $$-0.791473\pi$$
−0.792982 + 0.609245i $$0.791473\pi$$
$$230$$ 0 0
$$231$$ −3.00000 + 5.19615i −0.197386 + 0.341882i
$$232$$ 1.00000 + 1.73205i 0.0656532 + 0.113715i
$$233$$ 5.50000 9.52628i 0.360317 0.624087i −0.627696 0.778459i $$-0.716002\pi$$
0.988013 + 0.154371i $$0.0493352\pi$$
$$234$$ −6.00000 10.3923i −0.392232 0.679366i
$$235$$ 0 0
$$236$$ 5.00000 0.325472
$$237$$ −4.00000 6.92820i −0.259828 0.450035i
$$238$$ −2.00000 3.46410i −0.129641 0.224544i
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ 9.50000 + 16.4545i 0.611949 + 1.05993i 0.990912 + 0.134515i $$0.0429475\pi$$
−0.378963 + 0.925412i $$0.623719\pi$$
$$242$$ 1.00000 1.73205i 0.0642824 0.111340i
$$243$$ −8.00000 13.8564i −0.513200 0.888889i
$$244$$ −7.00000 + 12.1244i −0.448129 + 0.776182i
$$245$$ 0 0
$$246$$ 5.00000 0.318788
$$247$$ −3.00000 + 25.9808i −0.190885 + 1.65312i
$$248$$ −8.00000 −0.508001
$$249$$ −5.50000 + 9.52628i −0.348548 + 0.603703i
$$250$$ 0 0
$$251$$ 8.50000 + 14.7224i 0.536515 + 0.929272i 0.999088 + 0.0426905i $$0.0135929\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$252$$ −2.00000 + 3.46410i −0.125988 + 0.218218i
$$253$$ 12.0000 + 20.7846i 0.754434 + 1.30672i
$$254$$ −6.00000 −0.376473
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i $$-0.136840\pi$$
−0.815442 + 0.578838i $$0.803506\pi$$
$$258$$ 0 0
$$259$$ 16.0000 0.994192
$$260$$ 0 0
$$261$$ −2.00000 + 3.46410i −0.123797 + 0.214423i
$$262$$ −3.50000 6.06218i −0.216231 0.374523i
$$263$$ −13.0000 + 22.5167i −0.801614 + 1.38844i 0.116939 + 0.993139i $$0.462692\pi$$
−0.918553 + 0.395298i $$0.870641\pi$$
$$264$$ 1.50000 2.59808i 0.0923186 0.159901i
$$265$$ 0 0
$$266$$ 8.00000 3.46410i 0.490511 0.212398i
$$267$$ 14.0000 0.856786
$$268$$ −2.50000 + 4.33013i −0.152712 + 0.264505i
$$269$$ 14.0000 24.2487i 0.853595 1.47847i −0.0243472 0.999704i $$-0.507751\pi$$
0.877942 0.478766i $$-0.158916\pi$$
$$270$$ 0 0
$$271$$ 11.0000 19.0526i 0.668202 1.15736i −0.310204 0.950670i $$-0.600397\pi$$
0.978406 0.206691i $$-0.0662693\pi$$
$$272$$ 1.00000 + 1.73205i 0.0606339 + 0.105021i
$$273$$ 12.0000 0.726273
$$274$$ 3.00000 0.181237
$$275$$ 0 0
$$276$$ −4.00000 6.92820i −0.240772 0.417029i
$$277$$ 14.0000 0.841178 0.420589 0.907251i $$-0.361823\pi$$
0.420589 + 0.907251i $$0.361823\pi$$
$$278$$ 9.00000 0.539784
$$279$$ −8.00000 13.8564i −0.478947 0.829561i
$$280$$ 0 0
$$281$$ −3.50000 6.06218i −0.208792 0.361639i 0.742542 0.669800i $$-0.233620\pi$$
−0.951334 + 0.308160i $$0.900287\pi$$
$$282$$ −3.00000 + 5.19615i −0.178647 + 0.309426i
$$283$$ −14.5000 + 25.1147i −0.861936 + 1.49292i 0.00812260 + 0.999967i $$0.497414\pi$$
−0.870058 + 0.492949i $$0.835919\pi$$
$$284$$ −6.00000 −0.356034
$$285$$ 0 0
$$286$$ 18.0000 1.06436
$$287$$ 5.00000 8.66025i 0.295141 0.511199i
$$288$$ 1.00000 1.73205i 0.0589256 0.102062i
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ −7.50000 12.9904i −0.439658 0.761510i
$$292$$ 9.00000 0.526685
$$293$$ −22.0000 −1.28525 −0.642627 0.766179i $$-0.722155\pi$$
−0.642627 + 0.766179i $$0.722155\pi$$
$$294$$ 1.50000 + 2.59808i 0.0874818 + 0.151523i
$$295$$ 0 0
$$296$$ −8.00000 −0.464991
$$297$$ 15.0000 0.870388
$$298$$ −2.00000 3.46410i −0.115857 0.200670i
$$299$$ 24.0000 41.5692i 1.38796 2.40401i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −6.00000 + 10.3923i −0.345261 + 0.598010i
$$303$$ −10.0000 −0.574485
$$304$$ −4.00000 + 1.73205i −0.229416 + 0.0993399i
$$305$$ 0 0
$$306$$ −2.00000 + 3.46410i −0.114332 + 0.198030i
$$307$$ −2.50000 + 4.33013i −0.142683 + 0.247133i −0.928506 0.371318i $$-0.878906\pi$$
0.785823 + 0.618451i $$0.212239\pi$$
$$308$$ −3.00000 5.19615i −0.170941 0.296078i
$$309$$ 3.00000 5.19615i 0.170664 0.295599i
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ −6.00000 −0.339683
$$313$$ 6.50000 + 11.2583i 0.367402 + 0.636358i 0.989158 0.146852i $$-0.0469141\pi$$
−0.621757 + 0.783210i $$0.713581\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i $$-0.847759\pi$$
0.0453045 0.998973i $$-0.485574\pi$$
$$318$$ 3.00000 5.19615i 0.168232 0.291386i
$$319$$ −3.00000 5.19615i −0.167968 0.290929i
$$320$$ 0 0
$$321$$ −6.00000 + 10.3923i −0.334887 + 0.580042i
$$322$$ −16.0000 −0.891645
$$323$$ 8.00000 3.46410i 0.445132 0.192748i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 1.50000 2.59808i 0.0830773 0.143894i
$$327$$ 4.00000 + 6.92820i 0.221201 + 0.383131i
$$328$$ −2.50000 + 4.33013i −0.138039 + 0.239091i
$$329$$ 6.00000 + 10.3923i 0.330791 + 0.572946i
$$330$$ 0 0
$$331$$ −17.0000 −0.934405 −0.467202 0.884150i $$-0.654738\pi$$
−0.467202 + 0.884150i $$0.654738\pi$$
$$332$$ −5.50000 9.52628i −0.301852 0.522823i
$$333$$ −8.00000 13.8564i −0.438397 0.759326i
$$334$$ −8.00000 −0.437741
$$335$$ 0 0
$$336$$ 1.00000 + 1.73205i 0.0545545 + 0.0944911i
$$337$$ 9.50000 16.4545i 0.517498 0.896333i −0.482295 0.876009i $$-0.660197\pi$$
0.999793 0.0203242i $$-0.00646983\pi$$
$$338$$ −11.5000 19.9186i −0.625518 1.08343i
$$339$$ −6.50000 + 11.2583i −0.353032 + 0.611469i
$$340$$ 0 0
$$341$$ 24.0000 1.29967
$$342$$ −7.00000 5.19615i −0.378517 0.280976i
$$343$$ 20.0000 1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −9.00000 15.5885i −0.483843 0.838041i
$$347$$ −13.5000 + 23.3827i −0.724718 + 1.25525i 0.234372 + 0.972147i $$0.424697\pi$$
−0.959090 + 0.283101i $$0.908637\pi$$
$$348$$ 1.00000 + 1.73205i 0.0536056 + 0.0928477i
$$349$$ 16.0000 0.856460 0.428230 0.903670i $$-0.359137\pi$$
0.428230 + 0.903670i $$0.359137\pi$$
$$350$$ 0 0
$$351$$ −15.0000 25.9808i −0.800641 1.38675i
$$352$$ 1.50000 + 2.59808i 0.0799503 + 0.138478i
$$353$$ 21.0000 1.11772 0.558859 0.829263i $$-0.311239\pi$$
0.558859 + 0.829263i $$0.311239\pi$$
$$354$$ 5.00000 0.265747
$$355$$ 0 0
$$356$$ −7.00000 + 12.1244i −0.370999 + 0.642590i
$$357$$ −2.00000 3.46410i −0.105851 0.183340i
$$358$$ −1.50000 + 2.59808i −0.0792775 + 0.137313i
$$359$$ −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i $$0.384981\pi$$
−0.986865 + 0.161546i $$0.948352\pi$$
$$360$$ 0 0
$$361$$ 5.50000 + 18.1865i 0.289474 + 0.957186i
$$362$$ −16.0000 −0.840941
$$363$$ 1.00000 1.73205i 0.0524864 0.0909091i
$$364$$ −6.00000 + 10.3923i −0.314485 + 0.544705i
$$365$$ 0 0
$$366$$ −7.00000 + 12.1244i −0.365896 + 0.633750i
$$367$$ −14.0000 24.2487i −0.730794 1.26577i −0.956544 0.291587i $$-0.905817\pi$$
0.225750 0.974185i $$-0.427517\pi$$
$$368$$ 8.00000 0.417029
$$369$$ −10.0000 −0.520579
$$370$$ 0 0
$$371$$ −6.00000 10.3923i −0.311504 0.539542i
$$372$$ −8.00000 −0.414781
$$373$$ 24.0000 1.24267 0.621336 0.783544i $$-0.286590\pi$$
0.621336 + 0.783544i $$0.286590\pi$$
$$374$$ −3.00000 5.19615i −0.155126 0.268687i
$$375$$ 0 0
$$376$$ −3.00000 5.19615i −0.154713 0.267971i
$$377$$ −6.00000 + 10.3923i −0.309016 + 0.535231i
$$378$$ −5.00000 + 8.66025i −0.257172 + 0.445435i
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 0 0
$$381$$ −6.00000 −0.307389
$$382$$ 2.00000 3.46410i 0.102329 0.177239i
$$383$$ 3.00000 5.19615i 0.153293 0.265511i −0.779143 0.626846i $$-0.784346\pi$$
0.932436 + 0.361335i $$0.117679\pi$$
$$384$$ −0.500000 0.866025i −0.0255155 0.0441942i
$$385$$ 0 0
$$386$$ 5.00000 + 8.66025i 0.254493 + 0.440795i
$$387$$ 0 0
$$388$$ 15.0000 0.761510
$$389$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ −3.00000 −0.151523
$$393$$ −3.50000 6.06218i −0.176552 0.305796i
$$394$$ 4.00000 6.92820i 0.201517 0.349038i
$$395$$ 0 0
$$396$$ −3.00000 + 5.19615i −0.150756 + 0.261116i
$$397$$ 8.00000 13.8564i 0.401508 0.695433i −0.592400 0.805644i $$-0.701819\pi$$
0.993908 + 0.110211i $$0.0351527\pi$$
$$398$$ −22.0000 −1.10276
$$399$$ 8.00000 3.46410i 0.400501 0.173422i
$$400$$ 0 0
$$401$$ 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i $$-0.809468\pi$$
0.901046 + 0.433724i $$0.142801\pi$$
$$402$$ −2.50000 + 4.33013i −0.124689 + 0.215967i
$$403$$ −24.0000 41.5692i −1.19553 2.07071i
$$404$$ 5.00000 8.66025i 0.248759 0.430864i
$$405$$ 0 0
$$406$$ 4.00000 0.198517
$$407$$ 24.0000 1.18964
$$408$$ 1.00000 + 1.73205i 0.0495074 + 0.0857493i
$$409$$ 9.50000 + 16.4545i 0.469745 + 0.813622i 0.999402 0.0345902i $$-0.0110126\pi$$
−0.529657 + 0.848212i $$0.677679\pi$$
$$410$$ 0 0
$$411$$ 3.00000 0.147979
$$412$$ 3.00000 + 5.19615i 0.147799 + 0.255996i
$$413$$ 5.00000 8.66025i 0.246034 0.426143i
$$414$$ 8.00000 + 13.8564i 0.393179 + 0.681005i
$$415$$ 0 0
$$416$$ 3.00000 5.19615i 0.147087 0.254762i
$$417$$ 9.00000 0.440732
$$418$$ 12.0000 5.19615i 0.586939 0.254152i
$$419$$ 28.0000 1.36789 0.683945 0.729534i $$-0.260263\pi$$
0.683945 + 0.729534i $$0.260263\pi$$
$$420$$ 0 0
$$421$$ 4.00000 6.92820i 0.194948 0.337660i −0.751935 0.659237i $$-0.770879\pi$$
0.946883 + 0.321577i $$0.104213\pi$$
$$422$$ 2.00000 + 3.46410i 0.0973585 + 0.168630i
$$423$$ 6.00000 10.3923i 0.291730 0.505291i
$$424$$ 3.00000 + 5.19615i 0.145693 + 0.252347i
$$425$$ 0 0
$$426$$ −6.00000 −0.290701
$$427$$ 14.0000 + 24.2487i 0.677507 + 1.17348i
$$428$$ −6.00000 10.3923i −0.290021 0.502331i
$$429$$ 18.0000 0.869048
$$430$$ 0 0
$$431$$ 3.00000 + 5.19615i 0.144505 + 0.250290i 0.929188 0.369607i $$-0.120508\pi$$
−0.784683 + 0.619897i $$0.787174\pi$$
$$432$$ 2.50000 4.33013i 0.120281 0.208333i
$$433$$ 15.0000 + 25.9808i 0.720854 + 1.24856i 0.960658 + 0.277734i $$0.0895835\pi$$
−0.239804 + 0.970821i $$0.577083\pi$$
$$434$$ −8.00000 + 13.8564i −0.384012 + 0.665129i
$$435$$ 0 0
$$436$$ −8.00000 −0.383131
$$437$$ 4.00000 34.6410i 0.191346 1.65710i
$$438$$ 9.00000 0.430037
$$439$$ 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i $$-0.772190\pi$$
0.945552 + 0.325471i $$0.105523\pi$$
$$440$$ 0 0
$$441$$ −3.00000 5.19615i −0.142857 0.247436i
$$442$$ −6.00000 + 10.3923i −0.285391 + 0.494312i
$$443$$ −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i $$-0.235251\pi$$
−0.952901 + 0.303281i $$0.901918\pi$$
$$444$$ −8.00000 −0.379663
$$445$$ 0 0
$$446$$ −8.00000 13.8564i −0.378811 0.656120i
$$447$$ −2.00000 3.46410i −0.0945968 0.163846i
$$448$$ −2.00000 −0.0944911
$$449$$ 29.0000 1.36859 0.684297 0.729203i $$-0.260109\pi$$
0.684297 + 0.729203i $$0.260109\pi$$
$$450$$ 0 0
$$451$$ 7.50000 12.9904i 0.353161 0.611693i
$$452$$ −6.50000 11.2583i −0.305734 0.529547i
$$453$$ −6.00000 + 10.3923i −0.281905 + 0.488273i
$$454$$ −3.50000 + 6.06218i −0.164263 + 0.284512i
$$455$$ 0 0
$$456$$ −4.00000 + 1.73205i −0.187317 + 0.0811107i
$$457$$ −13.0000 −0.608114 −0.304057 0.952654i $$-0.598341\pi$$
−0.304057 + 0.952654i $$0.598341\pi$$
$$458$$ 12.0000 20.7846i 0.560723 0.971201i
$$459$$ −5.00000 + 8.66025i −0.233380 + 0.404226i
$$460$$ 0 0
$$461$$ 11.0000 19.0526i 0.512321 0.887366i −0.487577 0.873080i $$-0.662119\pi$$
0.999898 0.0142861i $$-0.00454755\pi$$
$$462$$ −3.00000 5.19615i −0.139573 0.241747i
$$463$$ −34.0000 −1.58011 −0.790057 0.613033i $$-0.789949\pi$$
−0.790057 + 0.613033i $$0.789949\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 0 0
$$466$$ 5.50000 + 9.52628i 0.254783 + 0.441296i
$$467$$ −7.00000 −0.323921 −0.161961 0.986797i $$-0.551782\pi$$
−0.161961 + 0.986797i $$0.551782\pi$$
$$468$$ 12.0000 0.554700
$$469$$ 5.00000 + 8.66025i 0.230879 + 0.399893i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −2.50000 + 4.33013i −0.115072 + 0.199310i
$$473$$ 0 0
$$474$$ 8.00000 0.367452
$$475$$ 0 0
$$476$$ 4.00000 0.183340
$$477$$ −6.00000 + 10.3923i −0.274721 + 0.475831i
$$478$$ −6.00000 + 10.3923i −0.274434 + 0.475333i
$$479$$ −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i $$-0.255062\pi$$
−0.969920 + 0.243426i $$0.921729\pi$$
$$480$$ 0 0
$$481$$ −24.0000 41.5692i −1.09431 1.89539i
$$482$$ −19.0000 −0.865426
$$483$$ −16.0000 −0.728025
$$484$$ 1.00000 + 1.73205i 0.0454545 + 0.0787296i
$$485$$ 0 0
$$486$$ 16.0000 0.725775
$$487$$ −4.00000 −0.181257 −0.0906287 0.995885i $$-0.528888\pi$$
−0.0906287 + 0.995885i $$0.528888\pi$$
$$488$$ −7.00000 12.1244i −0.316875 0.548844i
$$489$$ 1.50000 2.59808i 0.0678323 0.117489i
$$490$$ 0 0
$$491$$ −10.0000 + 17.3205i −0.451294 + 0.781664i −0.998467 0.0553560i $$-0.982371\pi$$
0.547173 + 0.837020i $$0.315704\pi$$
$$492$$ −2.50000 + 4.33013i −0.112709 + 0.195217i
$$493$$ 4.00000 0.180151
$$494$$ −21.0000 15.5885i −0.944835 0.701358i
$$495$$ 0 0
$$496$$ 4.00000 6.92820i 0.179605 0.311086i
$$497$$ −6.00000 + 10.3923i −0.269137 + 0.466159i
$$498$$ −5.50000 9.52628i −0.246461 0.426883i
$$499$$ −16.5000 + 28.5788i −0.738641 + 1.27936i 0.214466 + 0.976732i $$0.431199\pi$$
−0.953107 + 0.302633i $$0.902134\pi$$
$$500$$ 0 0
$$501$$ −8.00000 −0.357414
$$502$$ −17.0000 −0.758747
$$503$$ 2.00000 + 3.46410i 0.0891756 + 0.154457i 0.907163 0.420780i $$-0.138243\pi$$
−0.817987 + 0.575236i $$0.804910\pi$$
$$504$$ −2.00000 3.46410i −0.0890871 0.154303i
$$505$$ 0 0
$$506$$ −24.0000 −1.06693
$$507$$ −11.5000 19.9186i −0.510733 0.884615i
$$508$$ 3.00000 5.19615i 0.133103 0.230542i
$$509$$ −6.00000 10.3923i −0.265945 0.460631i 0.701866 0.712309i $$-0.252351\pi$$
−0.967811 + 0.251679i $$0.919017\pi$$
$$510$$ 0 0
$$511$$ 9.00000 15.5885i 0.398137 0.689593i
$$512$$ 1.00000 0.0441942
$$513$$ −17.5000 12.9904i −0.772644 0.573539i
$$514$$ −3.00000 −0.132324
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 9.00000 + 15.5885i 0.395820 + 0.685580i
$$518$$ −8.00000 + 13.8564i −0.351500 + 0.608816i
$$519$$ −9.00000 15.5885i −0.395056 0.684257i
$$520$$ 0 0
$$521$$ 21.0000 0.920027 0.460013 0.887912i $$-0.347845\pi$$
0.460013 + 0.887912i $$0.347845\pi$$
$$522$$ −2.00000 3.46410i −0.0875376 0.151620i
$$523$$ 4.00000 + 6.92820i 0.174908 + 0.302949i 0.940129 0.340818i $$-0.110704\pi$$
−0.765222 + 0.643767i $$0.777371\pi$$
$$524$$ 7.00000 0.305796
$$525$$ 0 0
$$526$$ −13.0000 22.5167i −0.566827 0.981773i
$$527$$ −8.00000 + 13.8564i −0.348485 + 0.603595i
$$528$$ 1.50000 + 2.59808i 0.0652791 + 0.113067i
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ 0 0
$$531$$ −10.0000 −0.433963
$$532$$ −1.00000 + 8.66025i −0.0433555 + 0.375470i
$$533$$ −30.0000 −1.29944
$$534$$ −7.00000 + 12.1244i −0.302920 + 0.524672i
$$535$$ 0 0
$$536$$ −2.50000 4.33013i −0.107984 0.187033i
$$537$$ −1.50000 + 2.59808i −0.0647298 + 0.112115i
$$538$$ 14.0000 + 24.2487i 0.603583 + 1.04544i
$$539$$ 9.00000 0.387657
$$540$$ 0 0
$$541$$ −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i $$-0.221681\pi$$
−0.939110 + 0.343617i $$0.888348\pi$$
$$542$$ 11.0000 + 19.0526i 0.472490 + 0.818377i
$$543$$ −16.0000 −0.686626
$$544$$ −2.00000 −0.0857493
$$545$$ 0 0
$$546$$ −6.00000 + 10.3923i −0.256776 + 0.444750i
$$547$$ −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i $$-0.221375\pi$$
−0.938779 + 0.344519i $$0.888042\pi$$
$$548$$ −1.50000 + 2.59808i −0.0640768 + 0.110984i
$$549$$ 14.0000 24.2487i 0.597505 1.03491i
$$550$$ 0 0
$$551$$ −1.00000 + 8.66025i −0.0426014 + 0.368939i
$$552$$ 8.00000 0.340503
$$553$$ 8.00000 13.8564i 0.340195 0.589234i
$$554$$ −7.00000 + 12.1244i −0.297402 + 0.515115i
$$555$$ 0 0
$$556$$ −4.50000 + 7.79423i −0.190843 + 0.330549i
$$557$$ −20.0000 34.6410i −0.847427 1.46779i −0.883497 0.468438i $$-0.844817\pi$$
0.0360693 0.999349i $$-0.488516\pi$$
$$558$$ 16.0000 0.677334
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −3.00000 5.19615i −0.126660 0.219382i
$$562$$ 7.00000 0.295277
$$563$$ 23.0000 0.969334 0.484667 0.874699i $$-0.338941\pi$$
0.484667 + 0.874699i $$0.338941\pi$$
$$564$$ −3.00000 5.19615i −0.126323 0.218797i
$$565$$ 0 0
$$566$$ −14.5000 25.1147i −0.609480 1.05565i
$$567$$ 1.00000 1.73205i 0.0419961 0.0727393i
$$568$$ 3.00000 5.19615i 0.125877 0.218026i
$$569$$ 34.0000 1.42535 0.712677 0.701492i $$-0.247483\pi$$
0.712677 + 0.701492i $$0.247483\pi$$
$$570$$ 0 0
$$571$$ −29.0000 −1.21361 −0.606806 0.794850i $$-0.707550\pi$$
−0.606806 + 0.794850i $$0.707550\pi$$
$$572$$ −9.00000 + 15.5885i −0.376309 + 0.651786i
$$573$$ 2.00000 3.46410i 0.0835512 0.144715i
$$574$$ 5.00000 + 8.66025i 0.208696 + 0.361472i
$$575$$ 0 0
$$576$$ 1.00000 + 1.73205i 0.0416667 + 0.0721688i
$$577$$ −7.00000 −0.291414 −0.145707 0.989328i $$-0.546546\pi$$
−0.145707 + 0.989328i $$0.546546\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ 5.00000 + 8.66025i 0.207793 + 0.359908i
$$580$$ 0 0
$$581$$ −22.0000 −0.912714
$$582$$ 15.0000 0.621770
$$583$$ −9.00000 15.5885i −0.372742 0.645608i
$$584$$ −4.50000 + 7.79423i −0.186211 + 0.322527i
$$585$$ 0 0
$$586$$ 11.0000 19.0526i 0.454406 0.787054i
$$587$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$588$$ −3.00000 −0.123718
$$589$$ −28.0000 20.7846i −1.15372 0.856415i
$$590$$ 0 0
$$591$$ 4.00000 6.92820i 0.164538 0.284988i
$$592$$ 4.00000 6.92820i 0.164399 0.284747i
$$593$$ −6.50000 11.2583i −0.266923 0.462324i 0.701143 0.713021i $$-0.252674\pi$$
−0.968066 + 0.250697i $$0.919340\pi$$
$$594$$ −7.50000 + 12.9904i −0.307729 + 0.533002i
$$595$$ 0 0
$$596$$ 4.00000 0.163846
$$597$$ −22.0000 −0.900400
$$598$$ 24.0000 + 41.5692i 0.981433 + 1.69989i
$$599$$ −24.0000 41.5692i −0.980613 1.69847i −0.660006 0.751260i $$-0.729446\pi$$
−0.320607 0.947212i $$-0.603887\pi$$
$$600$$ 0 0
$$601$$ −37.0000 −1.50926 −0.754631 0.656150i $$-0.772184\pi$$
−0.754631 + 0.656150i $$0.772184\pi$$
$$602$$ 0 0
$$603$$ 5.00000 8.66025i 0.203616 0.352673i
$$604$$ −6.00000 10.3923i −0.244137 0.422857i
$$605$$ 0 0
$$606$$ 5.00000 8.66025i 0.203111 0.351799i
$$607$$ 14.0000 0.568242 0.284121 0.958788i $$-0.408298\pi$$
0.284121 + 0.958788i $$0.408298\pi$$
$$608$$ 0.500000 4.33013i 0.0202777 0.175610i
$$609$$ 4.00000 0.162088
$$610$$ 0 0
$$611$$ 18.0000 31.1769i 0.728202 1.26128i
$$612$$ −2.00000 3.46410i −0.0808452 0.140028i
$$613$$ −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i $$0.407575\pi$$
−0.972924 + 0.231127i $$0.925759\pi$$
$$614$$ −2.50000 4.33013i −0.100892 0.174750i
$$615$$ 0 0
$$616$$ 6.00000 0.241747
$$617$$ 9.50000 + 16.4545i 0.382456 + 0.662433i 0.991413 0.130771i $$-0.0417452\pi$$
−0.608957 + 0.793203i $$0.708412\pi$$
$$618$$ 3.00000 + 5.19615i 0.120678 + 0.209020i
$$619$$ 40.0000 1.60774 0.803868 0.594808i $$-0.202772\pi$$
0.803868 + 0.594808i $$0.202772\pi$$
$$620$$ 0 0
$$621$$ 20.0000 + 34.6410i 0.802572 + 1.39010i
$$622$$ 12.0000 20.7846i 0.481156 0.833387i
$$623$$ 14.0000 + 24.2487i 0.560898 + 0.971504i
$$624$$ 3.00000 5.19615i 0.120096 0.208013i
$$625$$ 0 0
$$626$$ −13.0000 −0.519584
$$627$$ 12.0000 5.19615i 0.479234 0.207514i
$$628$$ 0 0
$$629$$ −8.00000 + 13.8564i −0.318981 + 0.552491i
$$630$$ 0 0
$$631$$ 15.0000 + 25.9808i 0.597141 + 1.03428i 0.993241 + 0.116071i $$0.0370299\pi$$
−0.396100 + 0.918207i $$0.629637\pi$$
$$632$$ −4.00000 + 6.92820i −0.159111 + 0.275589i
$$633$$ 2.00000 + 3.46410i 0.0794929 + 0.137686i
$$634$$ 30.0000 1.19145
$$635$$ 0 0
$$636$$ 3.00000 + 5.19615i 0.118958 + 0.206041i
$$637$$ −9.00000 15.5885i −0.356593 0.617637i
$$638$$ 6.00000 0.237542
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ −10.5000 + 18.1865i −0.414725 + 0.718325i −0.995400 0.0958109i $$-0.969456\pi$$
0.580674 + 0.814136i $$0.302789\pi$$
$$642$$ −6.00000 10.3923i −0.236801 0.410152i
$$643$$ −2.50000 + 4.33013i −0.0985904 + 0.170764i −0.911101 0.412182i $$-0.864767\pi$$
0.812511 + 0.582946i $$0.198100\pi$$
$$644$$ 8.00000 13.8564i 0.315244 0.546019i
$$645$$ 0 0
$$646$$ −1.00000 + 8.66025i −0.0393445 + 0.340733i
$$647$$ −6.00000 −0.235884 −0.117942 0.993020i $$-0.537630\pi$$
−0.117942 + 0.993020i $$0.537630\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ 7.50000 12.9904i 0.294401 0.509917i
$$650$$ 0 0
$$651$$ −8.00000 + 13.8564i −0.313545 + 0.543075i
$$652$$ 1.50000 + 2.59808i 0.0587445 + 0.101749i
$$653$$ 36.0000 1.40879 0.704394 0.709809i $$-0.251219\pi$$
0.704394 + 0.709809i $$0.251219\pi$$
$$654$$ −8.00000 −0.312825
$$655$$ 0 0
$$656$$ −2.50000 4.33013i −0.0976086 0.169063i
$$657$$ −18.0000 −0.702247
$$658$$ −12.0000 −0.467809
$$659$$ 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i $$-0.0915745\pi$$
−0.725175 + 0.688565i $$0.758241\pi$$
$$660$$ 0 0
$$661$$ 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i $$-0.0259377\pi$$
−0.568831 + 0.822454i $$0.692604\pi$$
$$662$$ 8.50000 14.7224i 0.330362 0.572204i
$$663$$ −6.00000 + 10.3923i −0.233021 + 0.403604i
$$664$$ 11.0000 0.426883
$$665$$ 0 0
$$666$$ 16.0000 0.619987
$$667$$ 8.00000 13.8564i 0.309761 0.536522i
$$668$$ 4.00000 6.92820i 0.154765 0.268060i
$$669$$ −8.00000 13.8564i −0.309298 0.535720i
$$670$$ 0 0
$$671$$ 21.0000 + 36.3731i 0.810696 + 1.40417i
$$672$$ −2.00000 −0.0771517
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ 9.50000 + 16.4545i 0.365926 + 0.633803i
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ −6.50000 11.2583i −0.249631 0.432374i
$$679$$ 15.0000 25.9808i 0.575647 0.997050i
$$680$$ 0 0
$$681$$ −3.50000 + 6.06218i −0.134120 + 0.232303i
$$682$$ −12.0000 + 20.7846i −0.459504 + 0.795884i
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 8.00000 3.46410i 0.305888 0.132453i
$$685$$ 0 0
$$686$$ −10.0000 + 17.3205i −0.381802 + 0.661300i
$$687$$ 12.0000 20.7846i 0.457829 0.792982i
$$688$$ 0 0
$$689$$ −18.0000 + 31.1769i −0.685745 + 1.18775i
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ 18.0000 0.684257
$$693$$ 6.00000 + 10.3923i 0.227921 + 0.394771i
$$694$$ −13.5000 23.3827i −0.512453 0.887595i
$$695$$ 0 0
$$696$$ −2.00000 −0.0758098
$$697$$ 5.00000 + 8.66025i 0.189389 + 0.328031i
$$698$$ −8.00000 + 13.8564i −0.302804 + 0.524473i
$$699$$ 5.50000 + 9.52628i 0.208029 + 0.360317i
$$700$$ 0 0
$$701$$ 21.0000 36.3731i 0.793159 1.37379i −0.130843 0.991403i $$-0.541768\pi$$
0.924002 0.382389i $$-0.124898\pi$$
$$702$$ 30.0000 1.13228
$$703$$ −28.0000 20.7846i −1.05604 0.783906i
$$704$$ −3.00000 −0.113067
$$705$$ 0 0
$$706$$ −10.5000 + 18.1865i −0.395173 + 0.684459i
$$707$$ −10.0000 17.3205i −0.376089 0.651405i
$$708$$ −2.50000 + 4.33013i −0.0939558 + 0.162736i
$$709$$ −10.0000 17.3205i −0.375558 0.650485i 0.614852 0.788642i $$-0.289216\pi$$
−0.990410 + 0.138157i $$0.955882\pi$$
$$710$$ 0 0
$$711$$ −16.0000 −0.600047
$$712$$ −7.00000 12.1244i −0.262336 0.454379i
$$713$$ 32.0000 + 55.4256i 1.19841 + 2.07571i
$$714$$ 4.00000 0.149696
$$715$$ 0 0
$$716$$ −1.50000 2.59808i −0.0560576 0.0970947i
$$717$$ −6.00000 + 10.3923i −0.224074 + 0.388108i
$$718$$ −12.0000 20.7846i −0.447836 0.775675i
$$719$$ −25.0000 + 43.3013i −0.932343 + 1.61486i −0.153037 + 0.988220i $$0.548906\pi$$
−0.779305 + 0.626644i $$0.784428\pi$$
$$720$$ 0 0
$$721$$ 12.0000 0.446903
$$722$$ −18.5000 4.33013i −0.688499 0.161151i
$$723$$ −19.0000 −0.706618
$$724$$ 8.00000 13.8564i 0.297318 0.514969i
$$725$$ 0 0
$$726$$ 1.00000 + 1.73205i 0.0371135 + 0.0642824i
$$727$$ 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i $$-0.785937\pi$$
0.930618 + 0.365991i $$0.119270\pi$$
$$728$$ −6.00000 10.3923i −0.222375 0.385164i
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −7.00000 12.1244i −0.258727 0.448129i
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 28.0000 1.03350
$$735$$ 0 0
$$736$$ −4.00000 + 6.92820i −0.147442 + 0.255377i
$$737$$ 7.50000 + 12.9904i 0.276266 + 0.478507i
$$738$$ 5.00000 8.66025i 0.184053 0.318788i
$$739$$ −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i $$-0.862648\pi$$
0.816373 + 0.577524i $$0.195981\pi$$
$$740$$ 0 0
$$741$$ −21.0000 15.5885i −0.771454 0.572656i
$$742$$ 12.0000 0.440534
$$743$$ 2.00000 3.46410i 0.0733729 0.127086i −0.827005 0.562195i $$-0.809957\pi$$
0.900378 + 0.435110i $$0.143290\pi$$
$$744$$ 4.00000 6.92820i 0.146647 0.254000i
$$745$$ 0 0
$$746$$ −12.0000 + 20.7846i −0.439351 + 0.760979i
$$747$$ 11.0000 + 19.0526i 0.402469 + 0.697097i
$$748$$ 6.00000 0.219382
$$749$$ −24.0000 −0.876941
$$750$$ 0 0
$$751$$ 19.0000 + 32.9090i 0.693320 + 1.20087i 0.970744 + 0.240118i $$0.0771860\pi$$
−0.277424 + 0.960748i $$0.589481\pi$$
$$752$$ 6.00000 0.218797
$$753$$ −17.0000 −0.619514
$$754$$ −6.00000 10.3923i −0.218507 0.378465i
$$755$$ 0 0
$$756$$ −5.00000 8.66025i −0.181848 0.314970i
$$757$$ 17.0000 29.4449i 0.617876 1.07019i −0.371997 0.928234i $$-0.621327\pi$$
0.989873 0.141958i $$-0.0453398\pi$$
$$758$$ 14.0000 24.2487i 0.508503 0.880753i
$$759$$ −24.0000 −0.871145
$$760$$ 0 0
$$761$$ −3.00000 −0.108750 −0.0543750 0.998521i $$-0.517317\pi$$
−0.0543750 + 0.998521i $$0.517317\pi$$
$$762$$ 3.00000 5.19615i 0.108679 0.188237i
$$763$$ −8.00000 + 13.8564i −0.289619 + 0.501636i
$$764$$ 2.00000 + 3.46410i 0.0723575 + 0.125327i
$$765$$ 0 0
$$766$$ 3.00000 + 5.19615i 0.108394 + 0.187745i
$$767$$ −30.0000 −1.08324
$$768$$ 1.00000 0.0360844
$$769$$ 25.0000 + 43.3013i 0.901523 + 1.56148i 0.825518 + 0.564376i $$0.190883\pi$$
0.0760054 + 0.997107i $$0.475783\pi$$
$$770$$ 0 0
$$771$$ −3.00000 −0.108042
$$772$$ −10.0000 −0.359908
$$773$$ 15.0000 + 25.9808i 0.539513 + 0.934463i 0.998930 + 0.0462427i $$0.0147248\pi$$
−0.459418 + 0.888220i $$0.651942\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −7.50000 + 12.9904i −0.269234 + 0.466328i
$$777$$ −8.00000 + 13.8564i −0.286998 + 0.497096i
$$778$$ 0 0
$$779$$ −20.0000 + 8.66025i −0.716574 + 0.310286i
$$780$$ 0 0
$$781$$ −9.00000 + 15.5885i −0.322045 + 0.557799i
$$782$$ 8.00000 13.8564i 0.286079 0.495504i
$$783$$ −5.00000 8.66025i −0.178685 0.309492i
$$784$$ 1.50000 2.59808i 0.0535714 0.0927884i
$$785$$ 0 0
$$786$$ 7.00000