# Properties

 Label 1078.2.e.f.67.1 Level $1078$ Weight $2$ Character 1078.67 Analytic conductor $8.608$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.60787333789$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.67 Dual form 1078.2.e.f.177.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(1.00000 - 1.73205i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.50000 + 2.59808i) q^{12} +7.00000 q^{13} +6.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{18} -2.00000 q^{20} -1.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(1.50000 - 2.59808i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.50000 - 6.06218i) q^{26} -9.00000 q^{27} -5.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} -2.00000 q^{34} +6.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(10.5000 - 18.1865i) q^{39} +(1.00000 + 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(6.00000 - 10.3923i) q^{45} +(4.00000 - 6.92820i) q^{46} +(1.00000 + 1.73205i) q^{47} -3.00000 q^{48} -1.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-3.50000 + 6.06218i) q^{52} +(3.00000 - 5.19615i) q^{53} +(4.50000 + 7.79423i) q^{54} +2.00000 q^{55} +(2.50000 + 4.33013i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(0.500000 + 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(7.00000 + 12.1244i) q^{65} +(-1.50000 + 2.59808i) q^{66} +(-4.50000 + 7.79423i) q^{67} +(1.00000 + 1.73205i) q^{68} +24.0000 q^{69} -2.00000 q^{71} +(-3.00000 - 5.19615i) q^{72} +(2.00000 - 3.46410i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-1.50000 - 2.59808i) q^{75} -21.0000 q^{78} +(-4.50000 - 7.79423i) q^{79} +(1.00000 - 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(2.00000 + 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(4.00000 + 6.92820i) q^{86} +(-7.50000 + 12.9904i) q^{87} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} -12.0000 q^{90} -8.00000 q^{92} +(-6.00000 - 10.3923i) q^{93} +(1.00000 - 1.73205i) q^{94} +(1.50000 + 2.59808i) q^{96} -7.00000 q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10})$$ 2 * q - q^2 + 3 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 $$2 q - q^{2} + 3 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + 14 q^{13} + 12 q^{15} - q^{16} + 2 q^{17} - 6 q^{18} - 4 q^{20} - 2 q^{22} + 8 q^{23} + 3 q^{24} + q^{25} - 7 q^{26} - 18 q^{27} - 10 q^{29} - 6 q^{30} + 4 q^{31} - q^{32} - 3 q^{33} - 4 q^{34} + 12 q^{36} - 4 q^{37} + 21 q^{39} + 2 q^{40} - 8 q^{41} - 16 q^{43} + q^{44} + 12 q^{45} + 8 q^{46} + 2 q^{47} - 6 q^{48} - 2 q^{50} - 6 q^{51} - 7 q^{52} + 6 q^{53} + 9 q^{54} + 4 q^{55} + 5 q^{58} + 3 q^{59} - 6 q^{60} + q^{61} - 8 q^{62} + 2 q^{64} + 14 q^{65} - 3 q^{66} - 9 q^{67} + 2 q^{68} + 48 q^{69} - 4 q^{71} - 6 q^{72} + 4 q^{73} - 4 q^{74} - 3 q^{75} - 42 q^{78} - 9 q^{79} + 2 q^{80} - 9 q^{81} + 4 q^{82} - 12 q^{83} + 8 q^{85} + 8 q^{86} - 15 q^{87} + q^{88} + 6 q^{89} - 24 q^{90} - 16 q^{92} - 12 q^{93} + 2 q^{94} + 3 q^{96} - 14 q^{97} - 12 q^{99}+O(q^{100})$$ 2 * q - q^2 + 3 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 + 2 * q^10 + q^11 + 3 * q^12 + 14 * q^13 + 12 * q^15 - q^16 + 2 * q^17 - 6 * q^18 - 4 * q^20 - 2 * q^22 + 8 * q^23 + 3 * q^24 + q^25 - 7 * q^26 - 18 * q^27 - 10 * q^29 - 6 * q^30 + 4 * q^31 - q^32 - 3 * q^33 - 4 * q^34 + 12 * q^36 - 4 * q^37 + 21 * q^39 + 2 * q^40 - 8 * q^41 - 16 * q^43 + q^44 + 12 * q^45 + 8 * q^46 + 2 * q^47 - 6 * q^48 - 2 * q^50 - 6 * q^51 - 7 * q^52 + 6 * q^53 + 9 * q^54 + 4 * q^55 + 5 * q^58 + 3 * q^59 - 6 * q^60 + q^61 - 8 * q^62 + 2 * q^64 + 14 * q^65 - 3 * q^66 - 9 * q^67 + 2 * q^68 + 48 * q^69 - 4 * q^71 - 6 * q^72 + 4 * q^73 - 4 * q^74 - 3 * q^75 - 42 * q^78 - 9 * q^79 + 2 * q^80 - 9 * q^81 + 4 * q^82 - 12 * q^83 + 8 * q^85 + 8 * q^86 - 15 * q^87 + q^88 + 6 * q^89 - 24 * q^90 - 16 * q^92 - 12 * q^93 + 2 * q^94 + 3 * q^96 - 14 * q^97 - 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$3$$ 1.50000 2.59808i 0.866025 1.50000i 1.00000i $$-0.5\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i $$-0.0190830\pi$$
−0.550990 + 0.834512i $$0.685750\pi$$
$$6$$ −3.00000 −1.22474
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ −3.00000 5.19615i −1.00000 1.73205i
$$10$$ 1.00000 1.73205i 0.316228 0.547723i
$$11$$ 0.500000 0.866025i 0.150756 0.261116i
$$12$$ 1.50000 + 2.59808i 0.433013 + 0.750000i
$$13$$ 7.00000 1.94145 0.970725 0.240192i $$-0.0772105\pi$$
0.970725 + 0.240192i $$0.0772105\pi$$
$$14$$ 0 0
$$15$$ 6.00000 1.54919
$$16$$ −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 $$0.0886875\pi$$
$$18$$ −3.00000 + 5.19615i −0.707107 + 1.22474i
$$19$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$20$$ −2.00000 −0.447214
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i $$0.147321\pi$$
−0.0607377 + 0.998154i $$0.519345\pi$$
$$24$$ 1.50000 2.59808i 0.306186 0.530330i
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ −3.50000 6.06218i −0.686406 1.18889i
$$27$$ −9.00000 −1.73205
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ −3.00000 5.19615i −0.547723 0.948683i
$$31$$ 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i $$-0.716379\pi$$
0.987829 + 0.155543i $$0.0497126\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −1.50000 2.59808i −0.261116 0.452267i
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 6.00000 1.00000
$$37$$ −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i $$-0.273310\pi$$
−0.982274 + 0.187453i $$0.939977\pi$$
$$38$$ 0 0
$$39$$ 10.5000 18.1865i 1.68135 2.91218i
$$40$$ 1.00000 + 1.73205i 0.158114 + 0.273861i
$$41$$ −4.00000 −0.624695 −0.312348 0.949968i $$-0.601115\pi$$
−0.312348 + 0.949968i $$0.601115\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0.500000 + 0.866025i 0.0753778 + 0.130558i
$$45$$ 6.00000 10.3923i 0.894427 1.54919i
$$46$$ 4.00000 6.92820i 0.589768 1.02151i
$$47$$ 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i $$-0.120070\pi$$
−0.783830 + 0.620975i $$0.786737\pi$$
$$48$$ −3.00000 −0.433013
$$49$$ 0 0
$$50$$ −1.00000 −0.141421
$$51$$ −3.00000 5.19615i −0.420084 0.727607i
$$52$$ −3.50000 + 6.06218i −0.485363 + 0.840673i
$$53$$ 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i $$-0.698135\pi$$
0.995117 + 0.0987002i $$0.0314685\pi$$
$$54$$ 4.50000 + 7.79423i 0.612372 + 1.06066i
$$55$$ 2.00000 0.269680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 2.50000 + 4.33013i 0.328266 + 0.568574i
$$59$$ 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i $$-0.770771\pi$$
0.946993 + 0.321253i $$0.104104\pi$$
$$60$$ −3.00000 + 5.19615i −0.387298 + 0.670820i
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 7.00000 + 12.1244i 0.868243 + 1.50384i
$$66$$ −1.50000 + 2.59808i −0.184637 + 0.319801i
$$67$$ −4.50000 + 7.79423i −0.549762 + 0.952217i 0.448528 + 0.893769i $$0.351948\pi$$
−0.998290 + 0.0584478i $$0.981385\pi$$
$$68$$ 1.00000 + 1.73205i 0.121268 + 0.210042i
$$69$$ 24.0000 2.88926
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ −3.00000 5.19615i −0.353553 0.612372i
$$73$$ 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i $$-0.758125\pi$$
0.959006 + 0.283387i $$0.0914581\pi$$
$$74$$ −2.00000 + 3.46410i −0.232495 + 0.402694i
$$75$$ −1.50000 2.59808i −0.173205 0.300000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ −21.0000 −2.37778
$$79$$ −4.50000 7.79423i −0.506290 0.876919i −0.999974 0.00727784i $$-0.997683\pi$$
0.493684 0.869641i $$-0.335650\pi$$
$$80$$ 1.00000 1.73205i 0.111803 0.193649i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 2.00000 + 3.46410i 0.220863 + 0.382546i
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ 0 0
$$85$$ 4.00000 0.433861
$$86$$ 4.00000 + 6.92820i 0.431331 + 0.747087i
$$87$$ −7.50000 + 12.9904i −0.804084 + 1.39272i
$$88$$ 0.500000 0.866025i 0.0533002 0.0923186i
$$89$$ 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i $$-0.0636557\pi$$
−0.662071 + 0.749441i $$0.730322\pi$$
$$90$$ −12.0000 −1.26491
$$91$$ 0 0
$$92$$ −8.00000 −0.834058
$$93$$ −6.00000 10.3923i −0.622171 1.07763i
$$94$$ 1.00000 1.73205i 0.103142 0.178647i
$$95$$ 0 0
$$96$$ 1.50000 + 2.59808i 0.153093 + 0.265165i
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0.500000 + 0.866025i 0.0500000 + 0.0866025i
$$101$$ −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i $$-0.981114\pi$$
0.550474 + 0.834853i $$0.314447\pi$$
$$102$$ −3.00000 + 5.19615i −0.297044 + 0.514496i
$$103$$ 9.00000 + 15.5885i 0.886796 + 1.53598i 0.843641 + 0.536908i $$0.180408\pi$$
0.0431555 + 0.999068i $$0.486259\pi$$
$$104$$ 7.00000 0.686406
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ −1.00000 1.73205i −0.0966736 0.167444i 0.813632 0.581380i $$-0.197487\pi$$
−0.910306 + 0.413936i $$0.864154\pi$$
$$108$$ 4.50000 7.79423i 0.433013 0.750000i
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ −1.00000 1.73205i −0.0953463 0.165145i
$$111$$ −12.0000 −1.13899
$$112$$ 0 0
$$113$$ 5.00000 0.470360 0.235180 0.971952i $$-0.424432\pi$$
0.235180 + 0.971952i $$0.424432\pi$$
$$114$$ 0 0
$$115$$ −8.00000 + 13.8564i −0.746004 + 1.29212i
$$116$$ 2.50000 4.33013i 0.232119 0.402042i
$$117$$ −21.0000 36.3731i −1.94145 3.36269i
$$118$$ −3.00000 −0.276172
$$119$$ 0 0
$$120$$ 6.00000 0.547723
$$121$$ −0.500000 0.866025i −0.0454545 0.0787296i
$$122$$ 0.500000 0.866025i 0.0452679 0.0784063i
$$123$$ −6.00000 + 10.3923i −0.541002 + 0.937043i
$$124$$ 2.00000 + 3.46410i 0.179605 + 0.311086i
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ −19.0000 −1.68598 −0.842989 0.537931i $$-0.819206\pi$$
−0.842989 + 0.537931i $$0.819206\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ −12.0000 + 20.7846i −1.05654 + 1.82998i
$$130$$ 7.00000 12.1244i 0.613941 1.06338i
$$131$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$132$$ 3.00000 0.261116
$$133$$ 0 0
$$134$$ 9.00000 0.777482
$$135$$ −9.00000 15.5885i −0.774597 1.34164i
$$136$$ 1.00000 1.73205i 0.0857493 0.148522i
$$137$$ −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i $$-0.874238\pi$$
0.794808 + 0.606861i $$0.207572\pi$$
$$138$$ −12.0000 20.7846i −1.02151 1.76930i
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 1.00000 + 1.73205i 0.0839181 + 0.145350i
$$143$$ 3.50000 6.06218i 0.292685 0.506945i
$$144$$ −3.00000 + 5.19615i −0.250000 + 0.433013i
$$145$$ −5.00000 8.66025i −0.415227 0.719195i
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ 4.00000 0.328798
$$149$$ 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i $$-0.0323294\pi$$
−0.585231 + 0.810867i $$0.698996\pi$$
$$150$$ −1.50000 + 2.59808i −0.122474 + 0.212132i
$$151$$ 1.50000 2.59808i 0.122068 0.211428i −0.798515 0.601975i $$-0.794381\pi$$
0.920583 + 0.390547i $$0.127714\pi$$
$$152$$ 0 0
$$153$$ −12.0000 −0.970143
$$154$$ 0 0
$$155$$ 8.00000 0.642575
$$156$$ 10.5000 + 18.1865i 0.840673 + 1.45609i
$$157$$ 8.00000 13.8564i 0.638470 1.10586i −0.347299 0.937754i $$-0.612901\pi$$
0.985769 0.168107i $$-0.0537655\pi$$
$$158$$ −4.50000 + 7.79423i −0.358001 + 0.620076i
$$159$$ −9.00000 15.5885i −0.713746 1.23625i
$$160$$ −2.00000 −0.158114
$$161$$ 0 0
$$162$$ 9.00000 0.707107
$$163$$ 8.50000 + 14.7224i 0.665771 + 1.15315i 0.979076 + 0.203497i $$0.0652307\pi$$
−0.313304 + 0.949653i $$0.601436\pi$$
$$164$$ 2.00000 3.46410i 0.156174 0.270501i
$$165$$ 3.00000 5.19615i 0.233550 0.404520i
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ −19.0000 −1.47026 −0.735132 0.677924i $$-0.762880\pi$$
−0.735132 + 0.677924i $$0.762880\pi$$
$$168$$ 0 0
$$169$$ 36.0000 2.76923
$$170$$ −2.00000 3.46410i −0.153393 0.265684i
$$171$$ 0 0
$$172$$ 4.00000 6.92820i 0.304997 0.528271i
$$173$$ 12.5000 + 21.6506i 0.950357 + 1.64607i 0.744652 + 0.667453i $$0.232616\pi$$
0.205706 + 0.978614i $$0.434051\pi$$
$$174$$ 15.0000 1.13715
$$175$$ 0 0
$$176$$ −1.00000 −0.0753778
$$177$$ −4.50000 7.79423i −0.338241 0.585850i
$$178$$ 3.00000 5.19615i 0.224860 0.389468i
$$179$$ −9.50000 + 16.4545i −0.710063 + 1.22987i 0.254770 + 0.967002i $$0.418000\pi$$
−0.964833 + 0.262864i $$0.915333\pi$$
$$180$$ 6.00000 + 10.3923i 0.447214 + 0.774597i
$$181$$ 22.0000 1.63525 0.817624 0.575753i $$-0.195291\pi$$
0.817624 + 0.575753i $$0.195291\pi$$
$$182$$ 0 0
$$183$$ 3.00000 0.221766
$$184$$ 4.00000 + 6.92820i 0.294884 + 0.510754i
$$185$$ 4.00000 6.92820i 0.294086 0.509372i
$$186$$ −6.00000 + 10.3923i −0.439941 + 0.762001i
$$187$$ −1.00000 1.73205i −0.0731272 0.126660i
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.00000 1.73205i −0.0723575 0.125327i 0.827577 0.561353i $$-0.189719\pi$$
−0.899934 + 0.436026i $$0.856386\pi$$
$$192$$ 1.50000 2.59808i 0.108253 0.187500i
$$193$$ −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i $$-0.926299\pi$$
0.685388 + 0.728178i $$0.259632\pi$$
$$194$$ 3.50000 + 6.06218i 0.251285 + 0.435239i
$$195$$ 42.0000 3.00768
$$196$$ 0 0
$$197$$ 15.0000 1.06871 0.534353 0.845262i $$-0.320555\pi$$
0.534353 + 0.845262i $$0.320555\pi$$
$$198$$ 3.00000 + 5.19615i 0.213201 + 0.369274i
$$199$$ 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i $$-0.788052\pi$$
0.928166 + 0.372168i $$0.121385\pi$$
$$200$$ 0.500000 0.866025i 0.0353553 0.0612372i
$$201$$ 13.5000 + 23.3827i 0.952217 + 1.64929i
$$202$$ 9.00000 0.633238
$$203$$ 0 0
$$204$$ 6.00000 0.420084
$$205$$ −4.00000 6.92820i −0.279372 0.483887i
$$206$$ 9.00000 15.5885i 0.627060 1.08610i
$$207$$ 24.0000 41.5692i 1.66812 2.88926i
$$208$$ −3.50000 6.06218i −0.242681 0.420336i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ 3.00000 + 5.19615i 0.206041 + 0.356873i
$$213$$ −3.00000 + 5.19615i −0.205557 + 0.356034i
$$214$$ −1.00000 + 1.73205i −0.0683586 + 0.118401i
$$215$$ −8.00000 13.8564i −0.545595 0.944999i
$$216$$ −9.00000 −0.612372
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ −6.00000 10.3923i −0.405442 0.702247i
$$220$$ −1.00000 + 1.73205i −0.0674200 + 0.116775i
$$221$$ 7.00000 12.1244i 0.470871 0.815572i
$$222$$ 6.00000 + 10.3923i 0.402694 + 0.697486i
$$223$$ −4.00000 −0.267860 −0.133930 0.990991i $$-0.542760\pi$$
−0.133930 + 0.990991i $$0.542760\pi$$
$$224$$ 0 0
$$225$$ −6.00000 −0.400000
$$226$$ −2.50000 4.33013i −0.166298 0.288036i
$$227$$ −1.00000 + 1.73205i −0.0663723 + 0.114960i −0.897302 0.441417i $$-0.854476\pi$$
0.830930 + 0.556378i $$0.187809\pi$$
$$228$$ 0 0
$$229$$ −14.0000 24.2487i −0.925146 1.60240i −0.791326 0.611394i $$-0.790609\pi$$
−0.133820 0.991006i $$-0.542724\pi$$
$$230$$ 16.0000 1.05501
$$231$$ 0 0
$$232$$ −5.00000 −0.328266
$$233$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$234$$ −21.0000 + 36.3731i −1.37281 + 2.37778i
$$235$$ −2.00000 + 3.46410i −0.130466 + 0.225973i
$$236$$ 1.50000 + 2.59808i 0.0976417 + 0.169120i
$$237$$ −27.0000 −1.75384
$$238$$ 0 0
$$239$$ −5.00000 −0.323423 −0.161712 0.986838i $$-0.551701\pi$$
−0.161712 + 0.986838i $$0.551701\pi$$
$$240$$ −3.00000 5.19615i −0.193649 0.335410i
$$241$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$242$$ −0.500000 + 0.866025i −0.0321412 + 0.0556702i
$$243$$ 0 0
$$244$$ −1.00000 −0.0640184
$$245$$ 0 0
$$246$$ 12.0000 0.765092
$$247$$ 0 0
$$248$$ 2.00000 3.46410i 0.127000 0.219971i
$$249$$ −9.00000 + 15.5885i −0.570352 + 0.987878i
$$250$$ −6.00000 10.3923i −0.379473 0.657267i
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ 9.50000 + 16.4545i 0.596083 + 1.03245i
$$255$$ 6.00000 10.3923i 0.375735 0.650791i
$$256$$ −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 $$0.803506\pi$$
$$258$$ 24.0000 1.49417
$$259$$ 0 0
$$260$$ −14.0000 −0.868243
$$261$$ 15.0000 + 25.9808i 0.928477 + 1.60817i
$$262$$ 0 0
$$263$$ −13.5000 + 23.3827i −0.832446 + 1.44184i 0.0636476 + 0.997972i $$0.479727\pi$$
−0.896093 + 0.443866i $$0.853607\pi$$
$$264$$ −1.50000 2.59808i −0.0923186 0.159901i
$$265$$ 12.0000 0.737154
$$266$$ 0 0
$$267$$ 18.0000 1.10158
$$268$$ −4.50000 7.79423i −0.274881 0.476108i
$$269$$ −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i $$0.427917\pi$$
−0.956176 + 0.292791i $$0.905416\pi$$
$$270$$ −9.00000 + 15.5885i −0.547723 + 0.948683i
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 3.00000 0.181237
$$275$$ −0.500000 0.866025i −0.0301511 0.0522233i
$$276$$ −12.0000 + 20.7846i −0.722315 + 1.25109i
$$277$$ 4.50000 7.79423i 0.270379 0.468310i −0.698580 0.715532i $$-0.746184\pi$$
0.968959 + 0.247222i $$0.0795177\pi$$
$$278$$ −2.00000 3.46410i −0.119952 0.207763i
$$279$$ −24.0000 −1.43684
$$280$$ 0 0
$$281$$ −28.0000 −1.67034 −0.835170 0.549992i $$-0.814631\pi$$
−0.835170 + 0.549992i $$0.814631\pi$$
$$282$$ −3.00000 5.19615i −0.178647 0.309426i
$$283$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$284$$ 1.00000 1.73205i 0.0593391 0.102778i
$$285$$ 0 0
$$286$$ −7.00000 −0.413919
$$287$$ 0 0
$$288$$ 6.00000 0.353553
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ −5.00000 + 8.66025i −0.293610 + 0.508548i
$$291$$ −10.5000 + 18.1865i −0.615521 + 1.06611i
$$292$$ 2.00000 + 3.46410i 0.117041 + 0.202721i
$$293$$ 18.0000 1.05157 0.525786 0.850617i $$-0.323771\pi$$
0.525786 + 0.850617i $$0.323771\pi$$
$$294$$ 0 0
$$295$$ 6.00000 0.349334
$$296$$ −2.00000 3.46410i −0.116248 0.201347i
$$297$$ −4.50000 + 7.79423i −0.261116 + 0.452267i
$$298$$ 5.00000 8.66025i 0.289642 0.501675i
$$299$$ 28.0000 + 48.4974i 1.61928 + 2.80468i
$$300$$ 3.00000 0.173205
$$301$$ 0 0
$$302$$ −3.00000 −0.172631
$$303$$ 13.5000 + 23.3827i 0.775555 + 1.34330i
$$304$$ 0 0
$$305$$ −1.00000 + 1.73205i −0.0572598 + 0.0991769i
$$306$$ 6.00000 + 10.3923i 0.342997 + 0.594089i
$$307$$ −2.00000 −0.114146 −0.0570730 0.998370i $$-0.518177\pi$$
−0.0570730 + 0.998370i $$0.518177\pi$$
$$308$$ 0 0
$$309$$ 54.0000 3.07195
$$310$$ −4.00000 6.92820i −0.227185 0.393496i
$$311$$ −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i $$-0.924837\pi$$
0.688726 + 0.725022i $$0.258170\pi$$
$$312$$ 10.5000 18.1865i 0.594445 1.02961i
$$313$$ 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i $$-0.157669\pi$$
−0.851549 + 0.524276i $$0.824336\pi$$
$$314$$ −16.0000 −0.902932
$$315$$ 0 0
$$316$$ 9.00000 0.506290
$$317$$ 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i $$-0.0572566\pi$$
−0.646872 + 0.762598i $$0.723923\pi$$
$$318$$ −9.00000 + 15.5885i −0.504695 + 0.874157i
$$319$$ −2.50000 + 4.33013i −0.139973 + 0.242441i
$$320$$ 1.00000 + 1.73205i 0.0559017 + 0.0968246i
$$321$$ −6.00000 −0.334887
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −4.50000 7.79423i −0.250000 0.433013i
$$325$$ 3.50000 6.06218i 0.194145 0.336269i
$$326$$ 8.50000 14.7224i 0.470771 0.815400i
$$327$$ −3.00000 5.19615i −0.165900 0.287348i
$$328$$ −4.00000 −0.220863
$$329$$ 0 0
$$330$$ −6.00000 −0.330289
$$331$$ −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i $$-0.282960\pi$$
−0.987504 + 0.157593i $$0.949627\pi$$
$$332$$ 3.00000 5.19615i 0.164646 0.285176i
$$333$$ −12.0000 + 20.7846i −0.657596 + 1.13899i
$$334$$ 9.50000 + 16.4545i 0.519817 + 0.900349i
$$335$$ −18.0000 −0.983445
$$336$$ 0 0
$$337$$ −12.0000 −0.653682 −0.326841 0.945079i $$-0.605984\pi$$
−0.326841 + 0.945079i $$0.605984\pi$$
$$338$$ −18.0000 31.1769i −0.979071 1.69580i
$$339$$ 7.50000 12.9904i 0.407344 0.705541i
$$340$$ −2.00000 + 3.46410i −0.108465 + 0.187867i
$$341$$ −2.00000 3.46410i −0.108306 0.187592i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −8.00000 −0.431331
$$345$$ 24.0000 + 41.5692i 1.29212 + 2.23801i
$$346$$ 12.5000 21.6506i 0.672004 1.16395i
$$347$$ 11.0000 19.0526i 0.590511 1.02279i −0.403653 0.914912i $$-0.632260\pi$$
0.994164 0.107883i $$-0.0344071\pi$$
$$348$$ −7.50000 12.9904i −0.402042 0.696358i
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 0 0
$$351$$ −63.0000 −3.36269
$$352$$ 0.500000 + 0.866025i 0.0266501 + 0.0461593i
$$353$$ −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i $$-0.992342\pi$$
0.520689 + 0.853746i $$0.325675\pi$$
$$354$$ −4.50000 + 7.79423i −0.239172 + 0.414259i
$$355$$ −2.00000 3.46410i −0.106149 0.183855i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 19.0000 1.00418
$$359$$ 9.50000 + 16.4545i 0.501391 + 0.868434i 0.999999 + 0.00160673i $$0.000511438\pi$$
−0.498608 + 0.866828i $$0.666155\pi$$
$$360$$ 6.00000 10.3923i 0.316228 0.547723i
$$361$$ 9.50000 16.4545i 0.500000 0.866025i
$$362$$ −11.0000 19.0526i −0.578147 1.00138i
$$363$$ −3.00000 −0.157459
$$364$$ 0 0
$$365$$ 8.00000 0.418739
$$366$$ −1.50000 2.59808i −0.0784063 0.135804i
$$367$$ 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i $$-0.800041\pi$$
0.913493 + 0.406855i $$0.133375\pi$$
$$368$$ 4.00000 6.92820i 0.208514 0.361158i
$$369$$ 12.0000 + 20.7846i 0.624695 + 1.08200i
$$370$$ −8.00000 −0.415900
$$371$$ 0 0
$$372$$ 12.0000 0.622171
$$373$$ −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i $$-0.258587\pi$$
−0.972556 + 0.232671i $$0.925254\pi$$
$$374$$ −1.00000 + 1.73205i −0.0517088 + 0.0895622i
$$375$$ 18.0000 31.1769i 0.929516 1.60997i
$$376$$ 1.00000 + 1.73205i 0.0515711 + 0.0893237i
$$377$$ −35.0000 −1.80259
$$378$$ 0 0
$$379$$ 1.00000 0.0513665 0.0256833 0.999670i $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ 0 0
$$381$$ −28.5000 + 49.3634i −1.46010 + 2.52897i
$$382$$ −1.00000 + 1.73205i −0.0511645 + 0.0886194i
$$383$$ 13.0000 + 22.5167i 0.664269 + 1.15055i 0.979483 + 0.201527i $$0.0645904\pi$$
−0.315214 + 0.949021i $$0.602076\pi$$
$$384$$ −3.00000 −0.153093
$$385$$ 0 0
$$386$$ 8.00000 0.407189
$$387$$ 24.0000 + 41.5692i 1.21999 + 2.11308i
$$388$$ 3.50000 6.06218i 0.177686 0.307760i
$$389$$ −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i $$-0.984165\pi$$
0.542445 + 0.840091i $$0.317499\pi$$
$$390$$ −21.0000 36.3731i −1.06338 1.84182i
$$391$$ 16.0000 0.809155
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −7.50000 12.9904i −0.377845 0.654446i
$$395$$ 9.00000 15.5885i 0.452839 0.784340i
$$396$$ 3.00000 5.19615i 0.150756 0.261116i
$$397$$ 3.00000 + 5.19615i 0.150566 + 0.260787i 0.931436 0.363906i $$-0.118557\pi$$
−0.780870 + 0.624694i $$0.785224\pi$$
$$398$$ −4.00000 −0.200502
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ 4.50000 + 7.79423i 0.224719 + 0.389225i 0.956235 0.292599i $$-0.0945202\pi$$
−0.731516 + 0.681824i $$0.761187\pi$$
$$402$$ 13.5000 23.3827i 0.673319 1.16622i
$$403$$ 14.0000 24.2487i 0.697390 1.20791i
$$404$$ −4.50000 7.79423i −0.223883 0.387777i
$$405$$ −18.0000 −0.894427
$$406$$ 0 0
$$407$$ −4.00000 −0.198273
$$408$$ −3.00000 5.19615i −0.148522 0.257248i
$$409$$ 11.0000 19.0526i 0.543915 0.942088i −0.454759 0.890614i $$-0.650275\pi$$
0.998674 0.0514740i $$-0.0163919\pi$$
$$410$$ −4.00000 + 6.92820i −0.197546 + 0.342160i
$$411$$ 4.50000 + 7.79423i 0.221969 + 0.384461i
$$412$$ −18.0000 −0.886796
$$413$$ 0 0
$$414$$ −48.0000 −2.35907
$$415$$ −6.00000 10.3923i −0.294528 0.510138i
$$416$$ −3.50000 + 6.06218i −0.171602 + 0.297223i
$$417$$ 6.00000 10.3923i 0.293821 0.508913i
$$418$$ 0 0
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ 10.0000 + 17.3205i 0.486792 + 0.843149i
$$423$$ 6.00000 10.3923i 0.291730 0.505291i
$$424$$ 3.00000 5.19615i 0.145693 0.252347i
$$425$$ −1.00000 1.73205i −0.0485071 0.0840168i
$$426$$ 6.00000 0.290701
$$427$$ 0 0
$$428$$ 2.00000 0.0966736
$$429$$ −10.5000 18.1865i −0.506945 0.878054i
$$430$$ −8.00000 + 13.8564i −0.385794 + 0.668215i
$$431$$ −12.5000 + 21.6506i −0.602104 + 1.04287i 0.390398 + 0.920646i $$0.372337\pi$$
−0.992502 + 0.122228i $$0.960996\pi$$
$$432$$ 4.50000 + 7.79423i 0.216506 + 0.375000i
$$433$$ 34.0000 1.63394 0.816968 0.576683i $$-0.195653\pi$$
0.816968 + 0.576683i $$0.195653\pi$$
$$434$$ 0 0
$$435$$ −30.0000 −1.43839
$$436$$ 1.00000 + 1.73205i 0.0478913 + 0.0829502i
$$437$$ 0 0
$$438$$ −6.00000 + 10.3923i −0.286691 + 0.496564i
$$439$$ −2.50000 4.33013i −0.119318 0.206666i 0.800179 0.599761i $$-0.204738\pi$$
−0.919498 + 0.393095i $$0.871404\pi$$
$$440$$ 2.00000 0.0953463
$$441$$ 0 0
$$442$$ −14.0000 −0.665912
$$443$$ −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i $$-0.840097\pi$$
0.0212481 0.999774i $$-0.493236\pi$$
$$444$$ 6.00000 10.3923i 0.284747 0.493197i
$$445$$ −6.00000 + 10.3923i −0.284427 + 0.492642i
$$446$$ 2.00000 + 3.46410i 0.0947027 + 0.164030i
$$447$$ 30.0000 1.41895
$$448$$ 0 0
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 3.00000 + 5.19615i 0.141421 + 0.244949i
$$451$$ −2.00000 + 3.46410i −0.0941763 + 0.163118i
$$452$$ −2.50000 + 4.33013i −0.117590 + 0.203672i
$$453$$ −4.50000 7.79423i −0.211428 0.366205i
$$454$$ 2.00000 0.0938647
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i $$-0.272855\pi$$
−0.982004 + 0.188858i $$0.939521\pi$$
$$458$$ −14.0000 + 24.2487i −0.654177 + 1.13307i
$$459$$ −9.00000 + 15.5885i −0.420084 + 0.727607i
$$460$$ −8.00000 13.8564i −0.373002 0.646058i
$$461$$ −27.0000 −1.25752 −0.628758 0.777601i $$-0.716436\pi$$
−0.628758 + 0.777601i $$0.716436\pi$$
$$462$$ 0 0
$$463$$ −2.00000 −0.0929479 −0.0464739 0.998920i $$-0.514798\pi$$
−0.0464739 + 0.998920i $$0.514798\pi$$
$$464$$ 2.50000 + 4.33013i 0.116060 + 0.201021i
$$465$$ 12.0000 20.7846i 0.556487 0.963863i
$$466$$ 0 0
$$467$$ 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i $$-0.0771121\pi$$
−0.693153 + 0.720791i $$0.743779\pi$$
$$468$$ 42.0000 1.94145
$$469$$ 0 0
$$470$$ 4.00000 0.184506
$$471$$ −24.0000 41.5692i −1.10586 1.91541i
$$472$$ 1.50000 2.59808i 0.0690431 0.119586i
$$473$$ −4.00000 + 6.92820i −0.183920 + 0.318559i
$$474$$ 13.5000 + 23.3827i 0.620076 + 1.07400i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −36.0000 −1.64833
$$478$$ 2.50000 + 4.33013i 0.114347 + 0.198055i
$$479$$ −0.500000 + 0.866025i −0.0228456 + 0.0395697i −0.877222 0.480085i $$-0.840606\pi$$
0.854377 + 0.519654i $$0.173939\pi$$
$$480$$ −3.00000 + 5.19615i −0.136931 + 0.237171i
$$481$$ −14.0000 24.2487i −0.638345 1.10565i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −7.00000 12.1244i −0.317854 0.550539i
$$486$$ 0 0
$$487$$ 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i $$-0.472238\pi$$
0.819181 0.573535i $$-0.194428\pi$$
$$488$$ 0.500000 + 0.866025i 0.0226339 + 0.0392031i
$$489$$ 51.0000 2.30630
$$490$$ 0 0
$$491$$ 30.0000 1.35388 0.676941 0.736038i $$-0.263305\pi$$
0.676941 + 0.736038i $$0.263305\pi$$
$$492$$ −6.00000 10.3923i −0.270501 0.468521i
$$493$$ −5.00000 + 8.66025i −0.225189 + 0.390038i
$$494$$ 0 0
$$495$$ −6.00000 10.3923i −0.269680 0.467099i
$$496$$ −4.00000 −0.179605
$$497$$ 0 0
$$498$$ 18.0000 0.806599
$$499$$ −10.0000 17.3205i −0.447661 0.775372i 0.550572 0.834788i $$-0.314410\pi$$
−0.998233 + 0.0594153i $$0.981076\pi$$
$$500$$ −6.00000 + 10.3923i −0.268328 + 0.464758i
$$501$$ −28.5000 + 49.3634i −1.27329 + 2.20540i
$$502$$ −12.0000 20.7846i −0.535586 0.927663i
$$503$$ −3.00000 −0.133763 −0.0668817 0.997761i $$-0.521305\pi$$
−0.0668817 + 0.997761i $$0.521305\pi$$
$$504$$ 0 0
$$505$$ −18.0000 −0.800989
$$506$$ −4.00000 6.92820i −0.177822 0.307996i
$$507$$ 54.0000 93.5307i 2.39822 4.15385i
$$508$$ 9.50000 16.4545i 0.421494 0.730050i
$$509$$ −11.0000 19.0526i −0.487566 0.844490i 0.512331 0.858788i $$-0.328782\pi$$
−0.999898 + 0.0142980i $$0.995449\pi$$
$$510$$ −12.0000 −0.531369
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 1.50000 2.59808i 0.0661622 0.114596i
$$515$$ −18.0000 + 31.1769i −0.793175 + 1.37382i
$$516$$ −12.0000 20.7846i −0.528271 0.914991i
$$517$$ 2.00000 0.0879599
$$518$$ 0 0
$$519$$ 75.0000 3.29213
$$520$$ 7.00000 + 12.1244i 0.306970 + 0.531688i
$$521$$ 5.00000 8.66025i 0.219054 0.379413i −0.735465 0.677563i $$-0.763036\pi$$
0.954519 + 0.298150i $$0.0963696\pi$$
$$522$$ 15.0000 25.9808i 0.656532 1.13715i
$$523$$ −5.00000 8.66025i −0.218635 0.378686i 0.735756 0.677247i $$-0.236827\pi$$
−0.954391 + 0.298560i $$0.903494\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 27.0000 1.17726
$$527$$ −4.00000 6.92820i −0.174243 0.301797i
$$528$$ −1.50000 + 2.59808i −0.0652791 + 0.113067i
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ −6.00000 10.3923i −0.260623 0.451413i
$$531$$ −18.0000 −0.781133
$$532$$ 0 0
$$533$$ −28.0000 −1.21281
$$534$$ −9.00000 15.5885i −0.389468 0.674579i
$$535$$ 2.00000 3.46410i 0.0864675 0.149766i
$$536$$ −4.50000 + 7.79423i −0.194370 + 0.336659i
$$537$$ 28.5000 + 49.3634i 1.22987 + 2.13019i
$$538$$ 24.0000 1.03471
$$539$$ 0 0
$$540$$ 18.0000 0.774597
$$541$$ −2.50000 4.33013i −0.107483 0.186167i 0.807267 0.590187i $$-0.200946\pi$$
−0.914750 + 0.404020i $$0.867613\pi$$
$$542$$ −5.50000 + 9.52628i −0.236245 + 0.409189i
$$543$$ 33.0000 57.1577i 1.41617 2.45287i
$$544$$ 1.00000 + 1.73205i 0.0428746 + 0.0742611i
$$545$$ 4.00000 0.171341
$$546$$ 0 0
$$547$$ 30.0000 1.28271 0.641354 0.767245i $$-0.278373\pi$$
0.641354 + 0.767245i $$0.278373\pi$$
$$548$$ −1.50000 2.59808i −0.0640768 0.110984i
$$549$$ 3.00000 5.19615i 0.128037 0.221766i
$$550$$ −0.500000 + 0.866025i −0.0213201 + 0.0369274i
$$551$$ 0 0
$$552$$ 24.0000 1.02151
$$553$$ 0 0
$$554$$ −9.00000 −0.382373
$$555$$ −12.0000 20.7846i −0.509372 0.882258i
$$556$$ −2.00000 + 3.46410i −0.0848189 + 0.146911i
$$557$$ −13.0000 + 22.5167i −0.550828 + 0.954062i 0.447387 + 0.894340i $$0.352355\pi$$
−0.998215 + 0.0597213i $$0.980979\pi$$
$$558$$ 12.0000 + 20.7846i 0.508001 + 0.879883i
$$559$$ −56.0000 −2.36855
$$560$$ 0 0
$$561$$ −6.00000 −0.253320
$$562$$ 14.0000 + 24.2487i 0.590554 + 1.02287i
$$563$$ 10.0000 17.3205i 0.421450 0.729972i −0.574632 0.818412i $$-0.694855\pi$$
0.996082 + 0.0884397i $$0.0281881\pi$$
$$564$$ −3.00000 + 5.19615i −0.126323 + 0.218797i
$$565$$ 5.00000 + 8.66025i 0.210352 + 0.364340i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −2.00000 −0.0839181
$$569$$ 6.00000 + 10.3923i 0.251533 + 0.435668i 0.963948 0.266090i $$-0.0857319\pi$$
−0.712415 + 0.701758i $$0.752399\pi$$
$$570$$ 0 0
$$571$$ −11.0000 + 19.0526i −0.460336 + 0.797325i −0.998978 0.0452101i $$-0.985604\pi$$
0.538642 + 0.842535i $$0.318938\pi$$
$$572$$ 3.50000 + 6.06218i 0.146342 + 0.253472i
$$573$$ −6.00000 −0.250654
$$574$$ 0 0
$$575$$ 8.00000 0.333623
$$576$$ −3.00000 5.19615i −0.125000 0.216506i
$$577$$ −21.5000 + 37.2391i −0.895057 + 1.55028i −0.0613223 + 0.998118i $$0.519532\pi$$
−0.833734 + 0.552166i $$0.813802\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ 12.0000 + 20.7846i 0.498703 + 0.863779i
$$580$$ 10.0000 0.415227
$$581$$ 0 0
$$582$$ 21.0000 0.870478
$$583$$ −3.00000 5.19615i −0.124247 0.215203i
$$584$$ 2.00000 3.46410i 0.0827606 0.143346i
$$585$$ 42.0000 72.7461i 1.73649 3.00768i
$$586$$ −9.00000 15.5885i −0.371787 0.643953i
$$587$$ −27.0000 −1.11441 −0.557205 0.830375i $$-0.688126\pi$$
−0.557205 + 0.830375i $$0.688126\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −3.00000 5.19615i −0.123508 0.213922i
$$591$$ 22.5000 38.9711i 0.925526 1.60306i
$$592$$ −2.00000 + 3.46410i −0.0821995 + 0.142374i
$$593$$ 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i $$-0.127353\pi$$
−0.797831 + 0.602881i $$0.794019\pi$$
$$594$$ 9.00000 0.369274
$$595$$ 0 0
$$596$$ −10.0000 −0.409616
$$597$$ −6.00000 10.3923i −0.245564 0.425329i
$$598$$ 28.0000 48.4974i 1.14501 1.98321i
$$599$$ −18.0000 + 31.1769i −0.735460 + 1.27385i 0.219061 + 0.975711i $$0.429701\pi$$
−0.954521 + 0.298143i $$0.903633\pi$$
$$600$$ −1.50000 2.59808i −0.0612372 0.106066i
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 54.0000 2.19905
$$604$$ 1.50000 + 2.59808i 0.0610341 + 0.105714i
$$605$$ 1.00000 1.73205i 0.0406558 0.0704179i
$$606$$ 13.5000 23.3827i 0.548400 0.949857i
$$607$$ 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i $$-0.114758\pi$$
−0.773358 + 0.633970i $$0.781424\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ 7.00000 + 12.1244i 0.283190 + 0.490499i
$$612$$ 6.00000 10.3923i 0.242536 0.420084i
$$613$$ 19.0000 32.9090i 0.767403 1.32918i −0.171564 0.985173i $$-0.554882\pi$$
0.938967 0.344008i $$-0.111785\pi$$
$$614$$ 1.00000 + 1.73205i 0.0403567 + 0.0698999i
$$615$$ −24.0000 −0.967773
$$616$$ 0 0
$$617$$ −15.0000 −0.603877 −0.301939 0.953327i $$-0.597634\pi$$
−0.301939 + 0.953327i $$0.597634\pi$$
$$618$$ −27.0000 46.7654i −1.08610 1.88118i
$$619$$ −14.0000 + 24.2487i −0.562708 + 0.974638i 0.434551 + 0.900647i $$0.356907\pi$$
−0.997259 + 0.0739910i $$0.976426\pi$$
$$620$$ −4.00000 + 6.92820i −0.160644 + 0.278243i
$$621$$ −36.0000 62.3538i −1.44463 2.50217i
$$622$$ 10.0000 0.400963
$$623$$ 0 0
$$624$$ −21.0000 −0.840673
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0.500000 0.866025i 0.0199840 0.0346133i
$$627$$ 0 0
$$628$$ 8.00000 + 13.8564i 0.319235 + 0.552931i
$$629$$ −8.00000 −0.318981
$$630$$ 0 0
$$631$$ −18.0000 −0.716569 −0.358284 0.933613i $$-0.616638\pi$$
−0.358284 + 0.933613i $$0.616638\pi$$
$$632$$ −4.50000 7.79423i −0.179000 0.310038i
$$633$$ −30.0000 + 51.9615i −1.19239 + 2.06529i
$$634$$ 6.00000 10.3923i 0.238290 0.412731i
$$635$$ −19.0000 32.9090i −0.753992 1.30595i
$$636$$ 18.0000 0.713746
$$637$$ 0 0
$$638$$ 5.00000 0.197952
$$639$$ 6.00000 + 10.3923i 0.237356 + 0.411113i
$$640$$ 1.00000 1.73205i 0.0395285 0.0684653i
$$641$$ 13.5000 23.3827i 0.533218 0.923561i −0.466029 0.884769i $$-0.654316\pi$$
0.999247 0.0387913i $$-0.0123508\pi$$
$$642$$ 3.00000 + 5.19615i 0.118401 + 0.205076i
$$643$$ −31.0000 −1.22252 −0.611260 0.791430i $$-0.709337\pi$$
−0.611260 + 0.791430i $$0.709337\pi$$
$$644$$ 0 0
$$645$$ −48.0000 −1.89000
$$646$$ 0 0
$$647$$ 15.0000 25.9808i 0.589711 1.02141i −0.404559 0.914512i $$-0.632575\pi$$
0.994270 0.106897i $$-0.0340916\pi$$
$$648$$ −4.50000 + 7.79423i −0.176777 + 0.306186i
$$649$$ −1.50000 2.59808i −0.0588802 0.101983i
$$650$$ −7.00000 −0.274563
$$651$$ 0 0
$$652$$ −17.0000 −0.665771
$$653$$ −20.0000 34.6410i −0.782660 1.35561i −0.930387 0.366579i $$-0.880529\pi$$
0.147726 0.989028i $$-0.452805\pi$$
$$654$$ −3.00000 + 5.19615i −0.117309 + 0.203186i
$$655$$ 0 0
$$656$$ 2.00000 + 3.46410i 0.0780869 + 0.135250i
$$657$$ −24.0000 −0.936329
$$658$$ 0 0
$$659$$ 28.0000 1.09073 0.545363 0.838200i $$-0.316392\pi$$
0.545363 + 0.838200i $$0.316392\pi$$
$$660$$ 3.00000 + 5.19615i 0.116775 + 0.202260i
$$661$$ −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i $$-0.974062\pi$$
0.568831 + 0.822454i $$0.307396\pi$$
$$662$$ −6.50000 + 11.2583i −0.252630 + 0.437567i
$$663$$ −21.0000 36.3731i −0.815572 1.41261i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 24.0000 0.929981
$$667$$ −20.0000 34.6410i −0.774403 1.34131i
$$668$$ 9.50000 16.4545i 0.367566 0.636643i
$$669$$ −6.00000 + 10.3923i −0.231973 + 0.401790i
$$670$$ 9.00000 + 15.5885i 0.347700 + 0.602235i
$$671$$ 1.00000 0.0386046
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 6.00000 + 10.3923i 0.231111 + 0.400297i
$$675$$ −4.50000 + 7.79423i −0.173205 + 0.300000i
$$676$$ −18.0000 + 31.1769i −0.692308 + 1.19911i
$$677$$ 7.00000 + 12.1244i 0.269032 + 0.465977i 0.968612 0.248577i $$-0.0799630\pi$$
−0.699580 + 0.714554i $$0.746630\pi$$
$$678$$ −15.0000 −0.576072
$$679$$ 0 0
$$680$$ 4.00000 0.153393
$$681$$ 3.00000 + 5.19615i 0.114960 + 0.199117i
$$682$$ −2.00000 + 3.46410i −0.0765840 + 0.132647i
$$683$$ −10.5000 + 18.1865i −0.401771 + 0.695888i −0.993940 0.109926i $$-0.964939\pi$$
0.592168 + 0.805814i $$0.298272\pi$$
$$684$$ 0 0
$$685$$ −6.00000 −0.229248
$$686$$ 0 0
$$687$$ −84.0000 −3.20480
$$688$$ 4.00000 + 6.92820i 0.152499 + 0.264135i
$$689$$ 21.0000 36.3731i 0.800036 1.38570i
$$690$$ 24.0000 41.5692i 0.913664 1.58251i
$$691$$ 16.5000 + 28.5788i 0.627690 + 1.08719i 0.988014 + 0.154363i $$0.0493326\pi$$
−0.360325 + 0.932827i $$0.617334\pi$$
$$692$$ −25.0000 −0.950357
$$693$$ 0 0
$$694$$ −22.0000 −0.835109
$$695$$ 4.00000 + 6.92820i 0.151729 + 0.262802i
$$696$$ −7.50000 + 12.9904i −0.284287 + 0.492399i
$$697$$ −4.00000 + 6.92820i −0.151511 + 0.262424i
$$698$$ 1.00000 + 1.73205i 0.0378506 + 0.0655591i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −27.0000 −1.01978 −0.509888 0.860241i $$-0.670313\pi$$
−0.509888 + 0.860241i $$0.670313\pi$$
$$702$$ 31.5000 + 54.5596i 1.18889 + 2.05922i
$$703$$ 0 0
$$704$$ 0.500000 0.866025i 0.0188445 0.0326396i
$$705$$ 6.00000 + 10.3923i 0.225973 + 0.391397i
$$706$$ 18.0000 0.677439
$$707$$ 0 0
$$708$$ 9.00000 0.338241
$$709$$ 24.0000 + 41.5692i 0.901339 + 1.56116i 0.825758 + 0.564025i $$0.190748\pi$$
0.0755813 + 0.997140i $$0.475919\pi$$
$$710$$ −2.00000 + 3.46410i −0.0750587 + 0.130005i
$$711$$ −27.0000 + 46.7654i −1.01258 + 1.75384i
$$712$$ 3.00000 + 5.19615i 0.112430 + 0.194734i
$$713$$ 32.0000 1.19841
$$714$$ 0 0
$$715$$ 14.0000 0.523570
$$716$$ −9.50000 16.4545i −0.355032 0.614933i
$$717$$ −7.50000 + 12.9904i −0.280093 + 0.485135i
$$718$$ 9.50000 16.4545i 0.354537 0.614076i
$$719$$ −19.0000 32.9090i −0.708580 1.22730i −0.965384 0.260834i $$-0.916003\pi$$
0.256803 0.966464i $$-0.417331\pi$$
$$720$$ −12.0000 −0.447214
$$721$$ 0 0
$$722$$ −19.0000 −0.707107
$$723$$ 0 0
$$724$$ −11.0000 + 19.0526i −0.408812 + 0.708083i
$$725$$ −2.50000 + 4.33013i −0.0928477 + 0.160817i
$$726$$ 1.50000 + 2.59808i 0.0556702 + 0.0964237i
$$727$$ 22.0000 0.815935 0.407967 0.912996i $$-0.366238\pi$$
0.407967 + 0.912996i $$0.366238\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ −4.00000 6.92820i −0.148047 0.256424i
$$731$$ −8.00000 + 13.8564i −0.295891 + 0.512498i
$$732$$ −1.50000 + 2.59808i −0.0554416 + 0.0960277i
$$733$$ −9.50000 16.4545i −0.350891 0.607760i 0.635515 0.772088i $$-0.280788\pi$$
−0.986406 + 0.164328i $$0.947454\pi$$
$$734$$ −4.00000 −0.147643
$$735$$ 0 0
$$736$$ −8.00000 −0.294884
$$737$$ 4.50000 + 7.79423i 0.165760 + 0.287104i
$$738$$ 12.0000 20.7846i 0.441726 0.765092i
$$739$$ −21.0000 + 36.3731i −0.772497 + 1.33800i 0.163693 + 0.986511i $$0.447659\pi$$
−0.936190 + 0.351494i $$0.885674\pi$$
$$740$$ 4.00000 + 6.92820i 0.147043 + 0.254686i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 12.0000 0.440237 0.220119 0.975473i $$-0.429356\pi$$
0.220119 + 0.975473i $$0.429356\pi$$
$$744$$ −6.00000 10.3923i −0.219971 0.381000i
$$745$$ −10.0000 + 17.3205i −0.366372 + 0.634574i
$$746$$ −5.50000 + 9.52628i −0.201369 + 0.348782i
$$747$$ 18.0000 + 31.1769i 0.658586 + 1.14070i
$$748$$ 2.00000 0.0731272
$$749$$ 0 0
$$750$$ −36.0000 −1.31453
$$751$$ −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i $$-0.995991\pi$$
0.489053 0.872254i $$-0.337342\pi$$
$$752$$ 1.00000 1.73205i 0.0364662 0.0631614i
$$753$$ 36.0000 62.3538i 1.31191 2.27230i
$$754$$ 17.5000 + 30.3109i 0.637312 + 1.10386i
$$755$$ 6.00000 0.218362
$$756$$ 0 0
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ −0.500000 0.866025i −0.0181608 0.0314555i
$$759$$ 12.0000 20.7846i 0.435572 0.754434i
$$760$$ 0 0
$$761$$ −3.00000 5.19615i −0.108750 0.188360i 0.806514 0.591215i $$-0.201351\pi$$
−0.915264 + 0.402854i $$0.868018\pi$$
$$762$$ 57.0000 2.06489
$$763$$ 0 0
$$764$$ 2.00000 0.0723575
$$765$$ −12.0000 20.7846i −0.433861 0.751469i
$$766$$ 13.0000 22.5167i 0.469709 0.813560i
$$767$$ 10.5000 18.1865i 0.379133 0.656678i
$$768$$ 1.50000 + 2.59808i 0.0541266 + 0.0937500i
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 9.00000 0.324127
$$772$$ −4.00000 6.92820i −0.143963 0.249351i
$$773$$ 12.0000 20.7846i 0.431610 0.747570i −0.565402 0.824815i $$-0.691279\pi$$
0.997012 + 0.0772449i $$0.0246123\pi$$
$$774$$ 24.0000 41.5692i 0.862662 1.49417i
$$775$$ −2.00000 3.46410i −0.0718421 0.124434i
$$776$$ −7.00000 −0.251285
$$777$$ 0 0
$$778$$ 18.0000 0.645331
$$779$$ 0 0
$$780$$ −21.0000 + 36.3731i −0.751921 + 1.30236i
$$781$$ −1.00000 + 1.73205i −0.0357828 + 0.0619777i
$$782$$ −8.00000 13.8564i −0.286079 0.495504i
$$783$$ 45.0000