# Properties

 Label 1386.2.k.o.793.1 Level $1386$ Weight $2$ Character 1386.793 Analytic conductor $11.067$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.0672657201$$ Analytic rank: $$1$$ 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 793.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1386.793 Dual form 1386.2.k.o.991.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.00000 - 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} -7.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -2.00000 q^{20} -1.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.50000 + 6.06218i) q^{26} +(2.00000 + 1.73205i) q^{28} +5.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.00000 q^{34} +(-1.00000 + 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-1.00000 + 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(4.00000 + 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(3.50000 + 6.06218i) q^{52} +(-3.00000 - 5.19615i) q^{53} -2.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(2.50000 - 4.33013i) q^{58} +(1.50000 + 2.59808i) q^{59} +(-0.500000 + 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-7.00000 + 12.1244i) q^{65} +(-4.50000 - 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 3.46410i) q^{70} +2.00000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(2.00000 + 3.46410i) q^{74} +(2.00000 + 1.73205i) q^{77} +(-4.50000 + 7.79423i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-2.00000 + 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(17.5000 - 6.06218i) q^{91} +8.00000 q^{92} +(-1.00000 - 1.73205i) q^{94} +7.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10})$$ 2 * q + q^2 - q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8 $$2 q + q^{2} - q^{4} + 2 q^{5} - 5 q^{7} - 2 q^{8} - 2 q^{10} - q^{11} - 14 q^{13} - q^{14} - q^{16} + 2 q^{17} - 4 q^{20} - 2 q^{22} - 8 q^{23} + q^{25} - 7 q^{26} + 4 q^{28} + 10 q^{29} - 4 q^{31} + q^{32} + 4 q^{34} - 2 q^{35} - 4 q^{37} - 2 q^{40} - 8 q^{41} - 16 q^{43} - q^{44} + 8 q^{46} + 2 q^{47} + 11 q^{49} + 2 q^{50} + 7 q^{52} - 6 q^{53} - 4 q^{55} + 5 q^{56} + 5 q^{58} + 3 q^{59} - q^{61} - 8 q^{62} + 2 q^{64} - 14 q^{65} - 9 q^{67} + 2 q^{68} + 8 q^{70} + 4 q^{71} - 4 q^{73} + 4 q^{74} + 4 q^{77} - 9 q^{79} + 2 q^{80} - 4 q^{82} - 12 q^{83} + 8 q^{85} - 8 q^{86} + q^{88} + 6 q^{89} + 35 q^{91} + 16 q^{92} - 2 q^{94} + 14 q^{97} - 2 q^{98}+O(q^{100})$$ 2 * q + q^2 - q^4 + 2 * q^5 - 5 * q^7 - 2 * q^8 - 2 * q^10 - q^11 - 14 * q^13 - q^14 - q^16 + 2 * q^17 - 4 * q^20 - 2 * q^22 - 8 * q^23 + q^25 - 7 * q^26 + 4 * q^28 + 10 * q^29 - 4 * q^31 + q^32 + 4 * q^34 - 2 * q^35 - 4 * q^37 - 2 * q^40 - 8 * q^41 - 16 * q^43 - q^44 + 8 * q^46 + 2 * q^47 + 11 * q^49 + 2 * q^50 + 7 * q^52 - 6 * q^53 - 4 * q^55 + 5 * q^56 + 5 * q^58 + 3 * q^59 - q^61 - 8 * q^62 + 2 * q^64 - 14 * q^65 - 9 * q^67 + 2 * q^68 + 8 * q^70 + 4 * q^71 - 4 * q^73 + 4 * q^74 + 4 * q^77 - 9 * q^79 + 2 * q^80 - 4 * q^82 - 12 * q^83 + 8 * q^85 - 8 * q^86 + q^88 + 6 * q^89 + 35 * q^91 + 16 * q^92 - 2 * q^94 + 14 * q^97 - 2 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$$.

 $$n$$ $$155$$ $$199$$ $$1135$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i $$-0.685750\pi$$
0.998203 + 0.0599153i $$0.0190830\pi$$
$$6$$ 0 0
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ −1.00000 1.73205i −0.316228 0.547723i
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ 0 0
$$13$$ −7.00000 −1.94145 −0.970725 0.240192i $$-0.922790\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ −0.500000 + 2.59808i −0.133631 + 0.694365i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i $$-0.0886875\pi$$
−0.718900 + 0.695113i $$0.755354\pi$$
$$18$$ 0 0
$$19$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$20$$ −2.00000 −0.447214
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ −4.00000 + 6.92820i −0.834058 + 1.44463i 0.0607377 + 0.998154i $$0.480655\pi$$
−0.894795 + 0.446476i $$0.852679\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ −3.50000 + 6.06218i −0.686406 + 1.18889i
$$27$$ 0 0
$$28$$ 2.00000 + 1.73205i 0.377964 + 0.327327i
$$29$$ 5.00000 0.928477 0.464238 0.885710i $$-0.346328\pi$$
0.464238 + 0.885710i $$0.346328\pi$$
$$30$$ 0 0
$$31$$ −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i $$-0.283621\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ −1.00000 + 5.19615i −0.169031 + 0.878310i
$$36$$ 0 0
$$37$$ −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i $$-0.939977\pi$$
0.653476 + 0.756948i $$0.273310\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −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
$$45$$ 0 0
$$46$$ 4.00000 + 6.92820i 0.589768 + 1.02151i
$$47$$ 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i $$-0.786737\pi$$
0.929695 + 0.368329i $$0.120070\pi$$
$$48$$ 0 0
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ 3.50000 + 6.06218i 0.485363 + 0.840673i
$$53$$ −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i $$-0.301865\pi$$
−0.995117 + 0.0987002i $$0.968532\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ 2.50000 0.866025i 0.334077 0.115728i
$$57$$ 0 0
$$58$$ 2.50000 4.33013i 0.328266 0.568574i
$$59$$ 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i $$-0.104104\pi$$
−0.751710 + 0.659494i $$0.770771\pi$$
$$60$$ 0 0
$$61$$ −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i $$-0.853725\pi$$
0.832240 + 0.554416i $$0.187058\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −7.00000 + 12.1244i −0.868243 + 1.50384i
$$66$$ 0 0
$$67$$ −4.50000 7.79423i −0.549762 0.952217i −0.998290 0.0584478i $$-0.981385\pi$$
0.448528 0.893769i $$-0.351948\pi$$
$$68$$ 1.00000 1.73205i 0.121268 0.210042i
$$69$$ 0 0
$$70$$ 4.00000 + 3.46410i 0.478091 + 0.414039i
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 0 0
$$73$$ −2.00000 3.46410i −0.234082 0.405442i 0.724923 0.688830i $$-0.241875\pi$$
−0.959006 + 0.283387i $$0.908542\pi$$
$$74$$ 2.00000 + 3.46410i 0.232495 + 0.402694i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2.00000 + 1.73205i 0.227921 + 0.197386i
$$78$$ 0 0
$$79$$ −4.50000 + 7.79423i −0.506290 + 0.876919i 0.493684 + 0.869641i $$0.335650\pi$$
−0.999974 + 0.00727784i $$0.997683\pi$$
$$80$$ 1.00000 + 1.73205i 0.111803 + 0.193649i
$$81$$ 0 0
$$82$$ −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
$$87$$ 0 0
$$88$$ 0.500000 + 0.866025i 0.0533002 + 0.0923186i
$$89$$ 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i $$-0.730322\pi$$
0.980071 + 0.198650i $$0.0636557\pi$$
$$90$$ 0 0
$$91$$ 17.5000 6.06218i 1.83450 0.635489i
$$92$$ 8.00000 0.834058
$$93$$ 0 0
$$94$$ −1.00000 1.73205i −0.103142 0.178647i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ −1.00000 6.92820i −0.101015 0.699854i
$$99$$ 0 0
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i $$-0.314447\pi$$
−0.998240 + 0.0592978i $$0.981114\pi$$
$$102$$ 0 0
$$103$$ −9.00000 + 15.5885i −0.886796 + 1.53598i −0.0431555 + 0.999068i $$0.513741\pi$$
−0.843641 + 0.536908i $$0.819592\pi$$
$$104$$ 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 $$-0.802513\pi$$
0.910306 + 0.413936i $$0.135846\pi$$
$$108$$ 0 0
$$109$$ 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i $$-0.136131\pi$$
−0.814152 + 0.580651i $$0.802798\pi$$
$$110$$ −1.00000 + 1.73205i −0.0953463 + 0.165145i
$$111$$ 0 0
$$112$$ 0.500000 2.59808i 0.0472456 0.245495i
$$113$$ −5.00000 −0.470360 −0.235180 0.971952i $$-0.575568\pi$$
−0.235180 + 0.971952i $$0.575568\pi$$
$$114$$ 0 0
$$115$$ 8.00000 + 13.8564i 0.746004 + 1.29212i
$$116$$ −2.50000 4.33013i −0.232119 0.402042i
$$117$$ 0 0
$$118$$ 3.00000 0.276172
$$119$$ −4.00000 3.46410i −0.366679 0.317554i
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ 0.500000 + 0.866025i 0.0452679 + 0.0784063i
$$123$$ 0 0
$$124$$ −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
$$129$$ 0 0
$$130$$ 7.00000 + 12.1244i 0.613941 + 1.06338i
$$131$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −9.00000 −0.777482
$$135$$ 0 0
$$136$$ −1.00000 1.73205i −0.0857493 0.148522i
$$137$$ 1.50000 + 2.59808i 0.128154 + 0.221969i 0.922961 0.384893i $$-0.125762\pi$$
−0.794808 + 0.606861i $$0.792428\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 5.00000 1.73205i 0.422577 0.146385i
$$141$$ 0 0
$$142$$ 1.00000 1.73205i 0.0839181 0.145350i
$$143$$ 3.50000 + 6.06218i 0.292685 + 0.506945i
$$144$$ 0 0
$$145$$ 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 $$-0.967671\pi$$
0.585231 + 0.810867i $$0.301004\pi$$
$$150$$ 0 0
$$151$$ 1.50000 + 2.59808i 0.122068 + 0.211428i 0.920583 0.390547i $$-0.127714\pi$$
−0.798515 + 0.601975i $$0.794381\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 2.50000 0.866025i 0.201456 0.0697863i
$$155$$ −8.00000 −0.642575
$$156$$ 0 0
$$157$$ −8.00000 13.8564i −0.638470 1.10586i −0.985769 0.168107i $$-0.946235\pi$$
0.347299 0.937754i $$-0.387099\pi$$
$$158$$ 4.50000 + 7.79423i 0.358001 + 0.620076i
$$159$$ 0 0
$$160$$ 2.00000 0.158114
$$161$$ 4.00000 20.7846i 0.315244 1.63806i
$$162$$ 0 0
$$163$$ 8.50000 14.7224i 0.665771 1.15315i −0.313304 0.949653i $$-0.601436\pi$$
0.979076 0.203497i $$-0.0652307\pi$$
$$164$$ 2.00000 + 3.46410i 0.156174 + 0.270501i
$$165$$ 0 0
$$166$$ −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 0.205706 0.978614i $$-0.434051\pi$$
0.744652 0.667453i $$-0.232616\pi$$
$$174$$ 0 0
$$175$$ −2.00000 1.73205i −0.151186 0.130931i
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ −3.00000 5.19615i −0.224860 0.389468i
$$179$$ 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i $$0.0846670\pi$$
−0.254770 + 0.967002i $$0.582000\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 3.50000 18.1865i 0.259437 1.34808i
$$183$$ 0 0
$$184$$ 4.00000 6.92820i 0.294884 0.510754i
$$185$$ 4.00000 + 6.92820i 0.294086 + 0.509372i
$$186$$ 0 0
$$187$$ 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 $$-0.810281\pi$$
0.899934 + 0.436026i $$0.143614\pi$$
$$192$$ 0 0
$$193$$ −4.00000 6.92820i −0.287926 0.498703i 0.685388 0.728178i $$-0.259632\pi$$
−0.973315 + 0.229475i $$0.926299\pi$$
$$194$$ 3.50000 6.06218i 0.251285 0.435239i
$$195$$ 0 0
$$196$$ −6.50000 2.59808i −0.464286 0.185577i
$$197$$ −15.0000 −1.06871 −0.534353 0.845262i $$-0.679445\pi$$
−0.534353 + 0.845262i $$0.679445\pi$$
$$198$$ 0 0
$$199$$ −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i $$-0.211948\pi$$
−0.928166 + 0.372168i $$0.878615\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ 0 0
$$202$$ −9.00000 −0.633238
$$203$$ −12.5000 + 4.33013i −0.877328 + 0.303915i
$$204$$ 0 0
$$205$$ −4.00000 + 6.92820i −0.279372 + 0.483887i
$$206$$ 9.00000 + 15.5885i 0.627060 + 1.08610i
$$207$$ 0 0
$$208$$ 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
$$213$$ 0 0
$$214$$ −1.00000 1.73205i −0.0683586 0.118401i
$$215$$ −8.00000 + 13.8564i −0.545595 + 0.944999i
$$216$$ 0 0
$$217$$ 8.00000 + 6.92820i 0.543075 + 0.470317i
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ 1.00000 + 1.73205i 0.0674200 + 0.116775i
$$221$$ −7.00000 12.1244i −0.470871 0.815572i
$$222$$ 0 0
$$223$$ 4.00000 0.267860 0.133930 0.990991i $$-0.457240\pi$$
0.133930 + 0.990991i $$0.457240\pi$$
$$224$$ −2.00000 1.73205i −0.133631 0.115728i
$$225$$ 0 0
$$226$$ −2.50000 + 4.33013i −0.166298 + 0.288036i
$$227$$ −1.00000 1.73205i −0.0663723 0.114960i 0.830930 0.556378i $$-0.187809\pi$$
−0.897302 + 0.441417i $$0.854476\pi$$
$$228$$ 0 0
$$229$$ 14.0000 24.2487i 0.925146 1.60240i 0.133820 0.991006i $$-0.457276\pi$$
0.791326 0.611394i $$-0.209391\pi$$
$$230$$ 16.0000 1.05501
$$231$$ 0 0
$$232$$ −5.00000 −0.328266
$$233$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$234$$ 0 0
$$235$$ −2.00000 3.46410i −0.130466 0.225973i
$$236$$ 1.50000 2.59808i 0.0976417 0.169120i
$$237$$ 0 0
$$238$$ −5.00000 + 1.73205i −0.324102 + 0.112272i
$$239$$ 5.00000 0.323423 0.161712 0.986838i $$-0.448299\pi$$
0.161712 + 0.986838i $$0.448299\pi$$
$$240$$ 0 0
$$241$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$242$$ 0.500000 + 0.866025i 0.0321412 + 0.0556702i
$$243$$ 0 0
$$244$$ 1.00000 0.0640184
$$245$$ −2.00000 13.8564i −0.127775 0.885253i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 2.00000 + 3.46410i 0.127000 + 0.219971i
$$249$$ 0 0
$$250$$ 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
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i $$-0.803506\pi$$
0.909010 + 0.416775i $$0.136840\pi$$
$$258$$ 0 0
$$259$$ 2.00000 10.3923i 0.124274 0.645746i
$$260$$ 14.0000 0.868243
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 13.5000 + 23.3827i 0.832446 + 1.44184i 0.896093 + 0.443866i $$0.146393\pi$$
−0.0636476 + 0.997972i $$0.520273\pi$$
$$264$$ 0 0
$$265$$ −12.0000 −0.737154
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −4.50000 + 7.79423i −0.274881 + 0.476108i
$$269$$ −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i $$-0.905416\pi$$
0.224523 0.974469i $$-0.427917\pi$$
$$270$$ 0 0
$$271$$ 5.50000 9.52628i 0.334101 0.578680i −0.649211 0.760609i $$-0.724901\pi$$
0.983312 + 0.181928i $$0.0582339\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 3.00000 0.181237
$$275$$ 0.500000 0.866025i 0.0301511 0.0522233i
$$276$$ 0 0
$$277$$ 4.50000 + 7.79423i 0.270379 + 0.468310i 0.968959 0.247222i $$-0.0795177\pi$$
−0.698580 + 0.715532i $$0.746184\pi$$
$$278$$ −2.00000 + 3.46410i −0.119952 + 0.207763i
$$279$$ 0 0
$$280$$ 1.00000 5.19615i 0.0597614 0.310530i
$$281$$ 28.0000 1.67034 0.835170 0.549992i $$-0.185369\pi$$
0.835170 + 0.549992i $$0.185369\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$284$$ −1.00000 1.73205i −0.0593391 0.102778i
$$285$$ 0 0
$$286$$ 7.00000 0.413919
$$287$$ 10.0000 3.46410i 0.590281 0.204479i
$$288$$ 0 0
$$289$$ 6.50000 11.2583i 0.382353 0.662255i
$$290$$ −5.00000 8.66025i −0.293610 0.508548i
$$291$$ 0 0
$$292$$ −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
$$297$$ 0 0
$$298$$ 5.00000 + 8.66025i 0.289642 + 0.501675i
$$299$$ 28.0000 48.4974i 1.61928 2.80468i
$$300$$ 0 0
$$301$$ 20.0000 6.92820i 1.15278 0.399335i
$$302$$ 3.00000 0.172631
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 1.00000 + 1.73205i 0.0572598 + 0.0991769i
$$306$$ 0 0
$$307$$ 2.00000 0.114146 0.0570730 0.998370i $$-0.481823\pi$$
0.0570730 + 0.998370i $$0.481823\pi$$
$$308$$ 0.500000 2.59808i 0.0284901 0.148039i
$$309$$ 0 0
$$310$$ −4.00000 + 6.92820i −0.227185 + 0.393496i
$$311$$ −5.00000 8.66025i −0.283524 0.491078i 0.688726 0.725022i $$-0.258170\pi$$
−0.972250 + 0.233944i $$0.924837\pi$$
$$312$$ 0 0
$$313$$ −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i $$-0.842331\pi$$
0.851549 + 0.524276i $$0.175664\pi$$
$$314$$ −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 $$-0.942743\pi$$
0.646872 + 0.762598i $$0.276077\pi$$
$$318$$ 0 0
$$319$$ −2.50000 4.33013i −0.139973 0.242441i
$$320$$ 1.00000 1.73205i 0.0559017 0.0968246i
$$321$$ 0 0
$$322$$ −16.0000 13.8564i −0.891645 0.772187i
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −3.50000 6.06218i −0.194145 0.336269i
$$326$$ −8.50000 14.7224i −0.470771 0.815400i
$$327$$ 0 0
$$328$$ 4.00000 0.220863
$$329$$ −1.00000 + 5.19615i −0.0551318 + 0.286473i
$$330$$ 0 0
$$331$$ −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i $$-0.949627\pi$$
0.630232 + 0.776407i $$0.282960\pi$$
$$332$$ 3.00000 + 5.19615i 0.164646 + 0.285176i
$$333$$ 0 0
$$334$$ −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
$$339$$ 0 0
$$340$$ −2.00000 3.46410i −0.108465 0.187867i
$$341$$ −2.00000 + 3.46410i −0.108306 + 0.187592i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ −12.5000 21.6506i −0.672004 1.16395i
$$347$$ −11.0000 19.0526i −0.590511 1.02279i −0.994164 0.107883i $$-0.965593\pi$$
0.403653 0.914912i $$-0.367740\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ −2.50000 + 0.866025i −0.133631 + 0.0462910i
$$351$$ 0 0
$$352$$ 0.500000 0.866025i 0.0266501 0.0461593i
$$353$$ −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i $$-0.325675\pi$$
−0.999711 + 0.0240566i $$0.992342\pi$$
$$354$$ 0 0
$$355$$ 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 0.498608 + 0.866828i $$0.333845\pi$$
−0.999999 + 0.00160673i $$0.999489\pi$$
$$360$$ 0 0
$$361$$ 9.50000 + 16.4545i 0.500000 + 0.866025i
$$362$$ −11.0000 + 19.0526i −0.578147 + 1.00138i
$$363$$ 0 0
$$364$$ −14.0000 12.1244i −0.733799 0.635489i
$$365$$ −8.00000 −0.418739
$$366$$ 0 0
$$367$$ −2.00000 3.46410i −0.104399 0.180825i 0.809093 0.587680i $$-0.199959\pi$$
−0.913493 + 0.406855i $$0.866625\pi$$
$$368$$ −4.00000 6.92820i −0.208514 0.361158i
$$369$$ 0 0
$$370$$ 8.00000 0.415900
$$371$$ 12.0000 + 10.3923i 0.623009 + 0.539542i
$$372$$ 0 0
$$373$$ −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i $$-0.925254\pi$$
0.687776 + 0.725923i $$0.258587\pi$$
$$374$$ −1.00000 1.73205i −0.0517088 0.0895622i
$$375$$ 0 0
$$376$$ −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
$$381$$ 0 0
$$382$$ −1.00000 1.73205i −0.0511645 0.0886194i
$$383$$ 13.0000 22.5167i 0.664269 1.15055i −0.315214 0.949021i $$-0.602076\pi$$
0.979483 0.201527i $$-0.0645904\pi$$
$$384$$ 0 0
$$385$$ 5.00000 1.73205i 0.254824 0.0882735i
$$386$$ −8.00000 −0.407189
$$387$$ 0 0
$$388$$ −3.50000 6.06218i −0.177686 0.307760i
$$389$$ 9.00000 + 15.5885i 0.456318 + 0.790366i 0.998763 0.0497253i $$-0.0158346\pi$$
−0.542445 + 0.840091i $$0.682501\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ −5.50000 + 4.33013i −0.277792 + 0.218704i
$$393$$ 0 0
$$394$$ −7.50000 + 12.9904i −0.377845 + 0.654446i
$$395$$ 9.00000 + 15.5885i 0.452839 + 0.784340i
$$396$$ 0 0
$$397$$ −3.00000 + 5.19615i −0.150566 + 0.260787i −0.931436 0.363906i $$-0.881443\pi$$
0.780870 + 0.624694i $$0.214776\pi$$
$$398$$ −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 $$-0.905480\pi$$
0.731516 + 0.681824i $$0.238813\pi$$
$$402$$ 0 0
$$403$$ 14.0000 + 24.2487i 0.697390 + 1.20791i
$$404$$ −4.50000 + 7.79423i −0.223883 + 0.387777i
$$405$$ 0 0
$$406$$ −2.50000 + 12.9904i −0.124073 + 0.644702i
$$407$$ 4.00000 0.198273
$$408$$ 0 0
$$409$$ −11.0000 19.0526i −0.543915 0.942088i −0.998674 0.0514740i $$-0.983608\pi$$
0.454759 0.890614i $$-0.349725\pi$$
$$410$$ 4.00000 + 6.92820i 0.197546 + 0.342160i
$$411$$ 0 0
$$412$$ 18.0000 0.886796
$$413$$ −6.00000 5.19615i −0.295241 0.255686i
$$414$$ 0 0
$$415$$ −6.00000 + 10.3923i −0.294528 + 0.510138i
$$416$$ −3.50000 6.06218i −0.171602 0.297223i
$$417$$ 0 0
$$418$$ 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
$$423$$ 0 0
$$424$$ 3.00000 + 5.19615i 0.145693 + 0.252347i
$$425$$ −1.00000 + 1.73205i −0.0485071 + 0.0840168i
$$426$$ 0 0
$$427$$ 0.500000 2.59808i 0.0241967 0.125730i
$$428$$ −2.00000 −0.0966736
$$429$$ 0 0
$$430$$ 8.00000 + 13.8564i 0.385794 + 0.668215i
$$431$$ 12.5000 + 21.6506i 0.602104 + 1.04287i 0.992502 + 0.122228i $$0.0390040\pi$$
−0.390398 + 0.920646i $$0.627663\pi$$
$$432$$ 0 0
$$433$$ −34.0000 −1.63394 −0.816968 0.576683i $$-0.804347\pi$$
−0.816968 + 0.576683i $$0.804347\pi$$
$$434$$ 10.0000 3.46410i 0.480015 0.166282i
$$435$$ 0 0
$$436$$ 1.00000 1.73205i 0.0478913 0.0829502i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 2.50000 4.33013i 0.119318 0.206666i −0.800179 0.599761i $$-0.795262\pi$$
0.919498 + 0.393095i $$0.128596\pi$$
$$440$$ 2.00000 0.0953463
$$441$$ 0 0
$$442$$ −14.0000 −0.665912
$$443$$ 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i $$-0.506764\pi$$
0.876454 0.481486i $$-0.159903\pi$$
$$444$$ 0 0
$$445$$ −6.00000 10.3923i −0.284427 0.492642i
$$446$$ 2.00000 3.46410i 0.0947027 0.164030i
$$447$$ 0 0
$$448$$ −2.50000 + 0.866025i −0.118114 + 0.0409159i
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ 2.00000 + 3.46410i 0.0941763 + 0.163118i
$$452$$ 2.50000 + 4.33013i 0.117590 + 0.203672i
$$453$$ 0 0
$$454$$ −2.00000 −0.0938647
$$455$$ 7.00000 36.3731i 0.328165 1.70520i
$$456$$ 0 0
$$457$$ −7.00000 + 12.1244i −0.327446 + 0.567153i −0.982004 0.188858i $$-0.939521\pi$$
0.654558 + 0.756012i $$0.272855\pi$$
$$458$$ −14.0000 24.2487i −0.654177 1.13307i
$$459$$ 0 0
$$460$$ 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
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i $$-0.743779\pi$$
0.970799 + 0.239892i $$0.0771121\pi$$
$$468$$ 0 0
$$469$$ 18.0000 + 15.5885i 0.831163 + 0.719808i
$$470$$ −4.00000 −0.184506
$$471$$ 0 0
$$472$$ −1.50000 2.59808i −0.0690431 0.119586i
$$473$$ 4.00000 + 6.92820i 0.183920 + 0.318559i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −1.00000 + 5.19615i −0.0458349 + 0.238165i
$$477$$ 0 0
$$478$$ 2.50000 4.33013i 0.114347 0.198055i
$$479$$ −0.500000 0.866025i −0.0228456 0.0395697i 0.854377 0.519654i $$-0.173939\pi$$
−0.877222 + 0.480085i $$0.840606\pi$$
$$480$$ 0 0
$$481$$ 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 0.819181 + 0.573535i $$0.194428\pi$$
0.0871056 + 0.996199i $$0.472238\pi$$
$$488$$ 0.500000 0.866025i 0.0226339 0.0392031i
$$489$$ 0 0
$$490$$ −13.0000 5.19615i −0.587280 0.234738i
$$491$$ −30.0000 −1.35388 −0.676941 0.736038i $$-0.736695\pi$$
−0.676941 + 0.736038i $$0.736695\pi$$
$$492$$ 0 0
$$493$$ 5.00000 + 8.66025i 0.225189 + 0.390038i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ −5.00000 + 1.73205i −0.224281 + 0.0776931i
$$498$$ 0 0
$$499$$ −10.0000 + 17.3205i −0.447661 + 0.775372i −0.998233 0.0594153i $$-0.981076\pi$$
0.550572 + 0.834788i $$0.314410\pi$$
$$500$$ −6.00000 10.3923i −0.268328 0.464758i
$$501$$ 0 0
$$502$$ 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
$$507$$ 0 0
$$508$$ 9.50000 + 16.4545i 0.421494 + 0.730050i
$$509$$ −11.0000 + 19.0526i −0.487566 + 0.844490i −0.999898 0.0142980i $$-0.995449\pi$$
0.512331 + 0.858788i $$0.328782\pi$$
$$510$$ 0 0
$$511$$ 8.00000 + 6.92820i 0.353899 + 0.306486i
$$512$$ −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
$$516$$ 0 0
$$517$$ −2.00000 −0.0879599
$$518$$ −8.00000 6.92820i −0.351500 0.304408i
$$519$$ 0 0
$$520$$ 7.00000 12.1244i 0.306970 0.531688i
$$521$$ 5.00000 + 8.66025i 0.219054 + 0.379413i 0.954519 0.298150i $$-0.0963696\pi$$
−0.735465 + 0.677563i $$0.763036\pi$$
$$522$$ 0 0
$$523$$ 5.00000 8.66025i 0.218635 0.378686i −0.735756 0.677247i $$-0.763173\pi$$
0.954391 + 0.298560i $$0.0965063\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 27.0000 1.17726
$$527$$ 4.00000 6.92820i 0.174243 0.301797i
$$528$$ 0 0
$$529$$ −20.5000 35.5070i −0.891304 1.54378i
$$530$$ −6.00000 + 10.3923i −0.260623 + 0.451413i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 28.0000 1.21281
$$534$$ 0 0
$$535$$ −2.00000 3.46410i −0.0864675 0.149766i
$$536$$ 4.50000 + 7.79423i 0.194370 + 0.336659i
$$537$$ 0 0
$$538$$ −24.0000 −1.03471
$$539$$ −6.50000 2.59808i −0.279975 0.111907i
$$540$$ 0 0
$$541$$ −2.50000 + 4.33013i −0.107483 + 0.186167i −0.914750 0.404020i $$-0.867613\pi$$
0.807267 + 0.590187i $$0.200946\pi$$
$$542$$ −5.50000 9.52628i −0.236245 0.409189i
$$543$$ 0 0
$$544$$ −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
$$549$$ 0 0
$$550$$ −0.500000 0.866025i −0.0213201 0.0369274i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 4.50000 23.3827i 0.191359 0.994333i
$$554$$ 9.00000 0.382373
$$555$$ 0 0
$$556$$ 2.00000 + 3.46410i 0.0848189 + 0.146911i
$$557$$ 13.0000 + 22.5167i 0.550828 + 0.954062i 0.998215 + 0.0597213i $$0.0190212\pi$$
−0.447387 + 0.894340i $$0.647645\pi$$
$$558$$ 0 0
$$559$$ 56.0000 2.36855
$$560$$ −4.00000 3.46410i −0.169031 0.146385i
$$561$$ 0 0
$$562$$ 14.0000 24.2487i 0.590554 1.02287i
$$563$$ 10.0000 + 17.3205i 0.421450 + 0.729972i 0.996082 0.0884397i $$-0.0281881\pi$$
−0.574632 + 0.818412i $$0.694855\pi$$
$$564$$ 0 0
$$565$$ −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 $$-0.914268\pi$$
0.712415 + 0.701758i $$0.247601\pi$$
$$570$$ 0 0
$$571$$ −11.0000 19.0526i −0.460336 0.797325i 0.538642 0.842535i $$-0.318938\pi$$
−0.998978 + 0.0452101i $$0.985604\pi$$
$$572$$ 3.50000 6.06218i 0.146342 0.253472i
$$573$$ 0 0
$$574$$ 2.00000 10.3923i 0.0834784 0.433766i
$$575$$ −8.00000 −0.333623
$$576$$ 0 0
$$577$$ 21.5000 + 37.2391i 0.895057 + 1.55028i 0.833734 + 0.552166i $$0.186198\pi$$
0.0613223 + 0.998118i $$0.480468\pi$$
$$578$$ −6.50000 11.2583i −0.270364 0.468285i
$$579$$ 0 0
$$580$$ −10.0000 −0.415227
$$581$$ 15.0000 5.19615i 0.622305 0.215573i
$$582$$ 0 0
$$583$$ −3.00000 + 5.19615i −0.124247 + 0.215203i
$$584$$ 2.00000 + 3.46410i 0.0827606 + 0.143346i
$$585$$ 0 0
$$586$$ 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
$$591$$ 0 0
$$592$$ −2.00000 3.46410i −0.0821995 0.142374i
$$593$$ 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i $$-0.794019\pi$$
0.921026 + 0.389501i $$0.127353\pi$$
$$594$$ 0 0
$$595$$ −10.0000 + 3.46410i −0.409960 + 0.142014i
$$596$$ 10.0000 0.409616
$$597$$ 0 0
$$598$$ −28.0000 48.4974i −1.14501 1.98321i
$$599$$ 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i $$0.0963673\pi$$
−0.219061 + 0.975711i $$0.570299\pi$$
$$600$$ 0 0
$$601$$ 26.0000 1.06056 0.530281 0.847822i $$-0.322086\pi$$
0.530281 + 0.847822i $$0.322086\pi$$
$$602$$ 4.00000 20.7846i 0.163028 0.847117i
$$603$$ 0 0
$$604$$ 1.50000 2.59808i 0.0610341 0.105714i
$$605$$ 1.00000 + 1.73205i 0.0406558 + 0.0704179i
$$606$$ 0 0
$$607$$ −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i $$-0.885242\pi$$
0.773358 + 0.633970i $$0.218576\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ −7.00000 + 12.1244i −0.283190 + 0.490499i
$$612$$ 0 0
$$613$$ 19.0000 + 32.9090i 0.767403 + 1.32918i 0.938967 + 0.344008i $$0.111785\pi$$
−0.171564 + 0.985173i $$0.554882\pi$$
$$614$$ 1.00000 1.73205i 0.0403567 0.0698999i
$$615$$ 0 0
$$616$$ −2.00000 1.73205i −0.0805823 0.0697863i
$$617$$ 15.0000 0.603877 0.301939 0.953327i $$-0.402366\pi$$
0.301939 + 0.953327i $$0.402366\pi$$
$$618$$ 0 0
$$619$$ 14.0000 + 24.2487i 0.562708 + 0.974638i 0.997259 + 0.0739910i $$0.0235736\pi$$
−0.434551 + 0.900647i $$0.643093\pi$$
$$620$$ 4.00000 + 6.92820i 0.160644 + 0.278243i
$$621$$ 0 0
$$622$$ −10.0000 −0.400963
$$623$$ −3.00000 + 15.5885i −0.120192 + 0.624538i
$$624$$ 0 0
$$625$$ 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
$$633$$ 0 0
$$634$$ 6.00000 + 10.3923i 0.238290 + 0.412731i
$$635$$ −19.0000 + 32.9090i −0.753992 + 1.30595i
$$636$$ 0 0
$$637$$ −38.5000 + 30.3109i −1.52543 + 1.20096i
$$638$$ −5.00000 −0.197952
$$639$$ 0 0
$$640$$ −1.00000 1.73205i −0.0395285 0.0684653i
$$641$$ −13.5000 23.3827i −0.533218 0.923561i −0.999247 0.0387913i $$-0.987649\pi$$
0.466029 0.884769i $$-0.345684\pi$$
$$642$$ 0 0
$$643$$ 31.0000 1.22252 0.611260 0.791430i $$-0.290663\pi$$
0.611260 + 0.791430i $$0.290663\pi$$
$$644$$ −20.0000 + 6.92820i −0.788110 + 0.273009i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 15.0000 + 25.9808i 0.589711 + 1.02141i 0.994270 + 0.106897i $$0.0340916\pi$$
−0.404559 + 0.914512i $$0.632575\pi$$
$$648$$ 0 0
$$649$$ 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 −0.147726 0.989028i $$-0.547195\pi$$
0.930387 0.366579i $$-0.119471\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 2.00000 3.46410i 0.0780869 0.135250i
$$657$$ 0 0
$$658$$ 4.00000 + 3.46410i 0.155936 + 0.135045i
$$659$$ −28.0000 −1.09073 −0.545363 0.838200i $$-0.683608\pi$$
−0.545363 + 0.838200i $$0.683608\pi$$
$$660$$ 0 0
$$661$$ 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i $$-0.0259377\pi$$
−0.568831 + 0.822454i $$0.692604\pi$$
$$662$$ 6.50000 + 11.2583i 0.252630 + 0.437567i
$$663$$ 0 0
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −20.0000 + 34.6410i −0.774403 + 1.34131i
$$668$$ 9.50000 + 16.4545i 0.367566 + 0.636643i
$$669$$ 0 0
$$670$$ −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
$$675$$ 0 0
$$676$$ −18.0000 31.1769i −0.692308 1.19911i
$$677$$ 7.00000 12.1244i 0.269032 0.465977i −0.699580 0.714554i $$-0.746630\pi$$
0.968612 + 0.248577i $$0.0799630\pi$$
$$678$$ 0 0
$$679$$ −17.5000 + 6.06218i −0.671588 + 0.232645i
$$680$$ −4.00000 −0.153393
$$681$$ 0 0
$$682$$ 2.00000 + 3.46410i 0.0765840 + 0.132647i
$$683$$ 10.5000 + 18.1865i 0.401771 + 0.695888i 0.993940 0.109926i $$-0.0350613\pi$$
−0.592168 + 0.805814i $$0.701728\pi$$
$$684$$ 0 0
$$685$$ 6.00000 0.229248
$$686$$ 8.50000 + 16.4545i 0.324532 + 0.628235i
$$687$$ 0 0
$$688$$ 4.00000 6.92820i 0.152499 0.264135i
$$689$$ 21.0000 + 36.3731i 0.800036 + 1.38570i
$$690$$ 0 0
$$691$$ −16.5000 + 28.5788i −0.627690 + 1.08719i 0.360325 + 0.932827i $$0.382666\pi$$
−0.988014 + 0.154363i $$0.950667\pi$$
$$692$$ −25.0000 −0.950357
$$693$$ 0 0
$$694$$ −22.0000 −0.835109
$$695$$ −4.00000 + 6.92820i −0.151729 + 0.262802i
$$696$$ 0 0
$$697$$ −4.00000 6.92820i −0.151511 0.262424i
$$698$$ 1.00000 1.73205i 0.0378506 0.0655591i
$$699$$ 0 0
$$700$$ −0.500000 + 2.59808i −0.0188982 + 0.0981981i
$$701$$ 27.0000 1.01978 0.509888 0.860241i $$-0.329687\pi$$
0.509888 + 0.860241i $$0.329687\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ 18.0000 + 15.5885i 0.676960 + 0.586264i
$$708$$ 0 0
$$709$$ 24.0000 41.5692i 0.901339 1.56116i 0.0755813 0.997140i $$-0.475919\pi$$
0.825758 0.564025i $$-0.190748\pi$$
$$710$$ −2.00000 3.46410i −0.0750587 0.130005i
$$711$$ 0 0
$$712$$ −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
$$717$$ 0 0
$$718$$ 9.50000 + 16.4545i 0.354537 + 0.614076i
$$719$$ −19.0000 + 32.9090i −0.708580 + 1.22730i 0.256803 + 0.966464i $$0.417331\pi$$
−0.965384 + 0.260834i $$0.916003\pi$$
$$720$$ 0 0
$$721$$ 9.00000 46.7654i 0.335178 1.74163i
$$722$$ 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
$$726$$ 0 0
$$727$$ −22.0000 −0.815935 −0.407967 0.912996i $$-0.633762\pi$$
−0.407967 + 0.912996i $$0.633762\pi$$
$$728$$ −17.5000 + 6.06218i −0.648593 + 0.224679i
$$729$$ 0 0
$$730$$ −4.00000 + 6.92820i −0.148047 + 0.256424i
$$731$$ −8.00000 13.8564i −0.295891 0.512498i
$$732$$ 0 0
$$733$$ 9.50000 16.4545i 0.350891 0.607760i −0.635515 0.772088i $$-0.719212\pi$$
0.986406 + 0.164328i $$0.0525456\pi$$
$$734$$ −4.00000 −0.147643
$$735$$ 0 0
$$736$$ −8.00000 −0.294884
$$737$$ −4.50000 + 7.79423i −0.165760 + 0.287104i
$$738$$ 0 0
$$739$$ −21.0000 36.3731i −0.772497 1.33800i −0.936190 0.351494i $$-0.885674\pi$$
0.163693 0.986511i $$-0.447659\pi$$
$$740$$ 4.00000 6.92820i 0.147043 0.254686i
$$741$$ 0 0
$$742$$ 15.0000 5.19615i 0.550667 0.190757i
$$743$$ −12.0000 −0.440237 −0.220119 0.975473i $$-0.570644\pi$$
−0.220119 + 0.975473i $$0.570644\pi$$
$$744$$ 0 0
$$745$$ 10.0000 + 17.3205i 0.366372 + 0.634574i
$$746$$ 5.50000 + 9.52628i 0.201369 + 0.348782i
$$747$$ 0 0
$$748$$ −2.00000 −0.0731272
$$749$$ −1.00000 + 5.19615i −0.0365392 + 0.189863i
$$750$$ 0 0
$$751$$ −14.0000 + 24.2487i −0.510867 + 0.884848i 0.489053 + 0.872254i $$0.337342\pi$$
−0.999921 + 0.0125942i $$0.995991\pi$$
$$752$$ 1.00000 + 1.73205i 0.0364662 + 0.0631614i
$$753$$ 0 0
$$754$$ −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
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −3.00000 + 5.19615i −0.108750 + 0.188360i −0.915264 0.402854i $$-0.868018\pi$$
0.806514 + 0.591215i $$0.201351\pi$$
$$762$$ 0 0
$$763$$ −4.00000 3.46410i −0.144810 0.125409i
$$764$$ −2.00000 −0.0723575
$$765$$ 0 0
$$766$$ −13.0000 22.5167i −0.469709 0.813560i
$$767$$ −10.5000 18.1865i −0.379133 0.656678i
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 1.00000 5.19615i 0.0360375 0.187256i
$$771$$ 0 0
$$772$$ −4.00000 + 6.92820i −0.143963 + 0.249351i
$$773$$ 12.0000 + 20.7846i 0.431610 + 0.747570i 0.997012 0.0772449i $$-0.0246123\pi$$
−0.565402 + 0.824815i $$0.691279\pi$$
$$774$$ 0 0
$$775$$ 2.00000 3.46410i 0.0718421 0.124434i
$$776$$ −7.00000 −0.251285
$$777$$ 0 0
$$778$$ 18.0000 0.645331
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −1.00000 1.73205i −0.0357828 0.0619777i
$$782$$ −8.00000 + 13.8564i −0.286079 + 0.495504i
$$783$$ 0 0
$$784$$ 1.00000 + 6.92820i 0.0357143 + 0.247436i
$$785$$ −32.0000 −1.14213
$$786$$ 0 0
$$787$$ 20.0000 + 34.6410i 0.712923 + 1.23482i 0.963755 + 0.266788i $$0.0859624\pi$$
−0.250832 + 0.968031i $$0.580704\pi$$
$$788$$ 7.50000 + 12.9904i 0.267176 + 0.462763i