Properties

 Label 1078.2.e.i.177.1 Level $1078$ Weight $2$ Character 1078.177 Analytic conductor $8.608$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

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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 177.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.177 Dual form 1078.2.e.i.67.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.00000 + 3.46410i) q^{10} +(0.500000 + 0.866025i) q^{11} -2.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-3.00000 + 5.19615i) q^{19} +4.00000 q^{20} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-5.50000 - 9.52628i) q^{25} +(-1.00000 + 1.73205i) q^{26} -2.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} -4.00000 q^{34} -3.00000 q^{36} +(-5.00000 + 8.66025i) q^{37} +(3.00000 + 5.19615i) q^{38} +(2.00000 - 3.46410i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(6.00000 + 10.3923i) q^{45} +(2.00000 + 3.46410i) q^{46} +(1.00000 - 1.73205i) q^{47} -11.0000 q^{50} +(1.00000 + 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} -4.00000 q^{55} +(-1.00000 + 1.73205i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-7.00000 + 12.1244i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +(6.00000 + 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{68} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(2.00000 + 3.46410i) q^{73} +(5.00000 + 8.66025i) q^{74} +6.00000 q^{76} +(-2.00000 - 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.00000 + 3.46410i) q^{82} +6.00000 q^{83} +16.0000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} +12.0000 q^{90} +4.00000 q^{92} +(-1.00000 - 1.73205i) q^{94} +(-12.0000 - 20.7846i) q^{95} +14.0000 q^{97} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{4} - 4 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10})$$ 2 * q + q^2 - q^4 - 4 * q^5 - 2 * q^8 + 3 * q^9 $$2 q + q^{2} - q^{4} - 4 q^{5} - 2 q^{8} + 3 q^{9} + 4 q^{10} + q^{11} - 4 q^{13} - q^{16} - 4 q^{17} - 3 q^{18} - 6 q^{19} + 8 q^{20} + 2 q^{22} - 4 q^{23} - 11 q^{25} - 2 q^{26} - 4 q^{29} - 2 q^{31} + q^{32} - 8 q^{34} - 6 q^{36} - 10 q^{37} + 6 q^{38} + 4 q^{40} - 8 q^{41} - 16 q^{43} + q^{44} + 12 q^{45} + 4 q^{46} + 2 q^{47} - 22 q^{50} + 2 q^{52} - 6 q^{53} - 8 q^{55} - 2 q^{58} - 12 q^{59} - 14 q^{61} - 4 q^{62} + 2 q^{64} + 8 q^{65} + 12 q^{67} - 4 q^{68} - 16 q^{71} - 3 q^{72} + 4 q^{73} + 10 q^{74} + 12 q^{76} - 4 q^{80} - 9 q^{81} - 4 q^{82} + 12 q^{83} + 32 q^{85} - 8 q^{86} - q^{88} - 6 q^{89} + 24 q^{90} + 8 q^{92} - 2 q^{94} - 24 q^{95} + 28 q^{97} + 6 q^{99}+O(q^{100})$$ 2 * q + q^2 - q^4 - 4 * q^5 - 2 * q^8 + 3 * q^9 + 4 * q^10 + q^11 - 4 * q^13 - q^16 - 4 * q^17 - 3 * q^18 - 6 * q^19 + 8 * q^20 + 2 * q^22 - 4 * q^23 - 11 * q^25 - 2 * q^26 - 4 * q^29 - 2 * q^31 + q^32 - 8 * q^34 - 6 * q^36 - 10 * q^37 + 6 * q^38 + 4 * q^40 - 8 * q^41 - 16 * q^43 + q^44 + 12 * q^45 + 4 * q^46 + 2 * q^47 - 22 * q^50 + 2 * q^52 - 6 * q^53 - 8 * q^55 - 2 * q^58 - 12 * q^59 - 14 * q^61 - 4 * q^62 + 2 * q^64 + 8 * q^65 + 12 * q^67 - 4 * q^68 - 16 * q^71 - 3 * q^72 + 4 * q^73 + 10 * q^74 + 12 * q^76 - 4 * q^80 - 9 * q^81 - 4 * q^82 + 12 * q^83 + 32 * q^85 - 8 * q^86 - q^88 - 6 * q^89 + 24 * q^90 + 8 * q^92 - 2 * q^94 - 24 * q^95 + 28 * q^97 + 6 * q^99

Character values

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

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

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 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −2.00000 + 3.46410i −0.894427 + 1.54919i −0.0599153 + 0.998203i $$0.519083\pi$$
−0.834512 + 0.550990i $$0.814250\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.50000 2.59808i 0.500000 0.866025i
$$10$$ 2.00000 + 3.46410i 0.632456 + 1.09545i
$$11$$ 0.500000 + 0.866025i 0.150756 + 0.261116i
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i $$-0.327873\pi$$
−0.999853 + 0.0171533i $$0.994540\pi$$
$$18$$ −1.50000 2.59808i −0.353553 0.612372i
$$19$$ −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i $$0.408286\pi$$
−0.972404 + 0.233301i $$0.925047\pi$$
$$20$$ 4.00000 0.894427
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ 0 0
$$25$$ −5.50000 9.52628i −1.10000 1.90526i
$$26$$ −1.00000 + 1.73205i −0.196116 + 0.339683i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i $$-0.224149\pi$$
−0.941745 + 0.336327i $$0.890815\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ −3.00000 −0.500000
$$37$$ −5.00000 + 8.66025i −0.821995 + 1.42374i 0.0821995 + 0.996616i $$0.473806\pi$$
−0.904194 + 0.427121i $$0.859528\pi$$
$$38$$ 3.00000 + 5.19615i 0.486664 + 0.842927i
$$39$$ 0 0
$$40$$ 2.00000 3.46410i 0.316228 0.547723i
$$41$$ −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
$$46$$ 2.00000 + 3.46410i 0.294884 + 0.510754i
$$47$$ 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
$$49$$ 0 0
$$50$$ −11.0000 −1.55563
$$51$$ 0 0
$$52$$ 1.00000 + 1.73205i 0.138675 + 0.240192i
$$53$$ −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
$$55$$ −4.00000 −0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −1.00000 + 1.73205i −0.131306 + 0.227429i
$$59$$ −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i $$-0.881308\pi$$
0.150148 0.988663i $$-0.452025\pi$$
$$60$$ 0 0
$$61$$ −7.00000 + 12.1244i −0.896258 + 1.55236i −0.0640184 + 0.997949i $$0.520392\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 4.00000 6.92820i 0.496139 0.859338i
$$66$$ 0 0
$$67$$ 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i $$0.0952216\pi$$
−0.222571 + 0.974916i $$0.571445\pi$$
$$68$$ −2.00000 + 3.46410i −0.242536 + 0.420084i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ −1.50000 + 2.59808i −0.176777 + 0.306186i
$$73$$ 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i $$-0.0914581\pi$$
−0.724923 + 0.688830i $$0.758125\pi$$
$$74$$ 5.00000 + 8.66025i 0.581238 + 1.00673i
$$75$$ 0 0
$$76$$ 6.00000 0.688247
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$80$$ −2.00000 3.46410i −0.223607 0.387298i
$$81$$ −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 $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 16.0000 1.73544
$$86$$ −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 −0.980071 0.198650i $$-0.936344\pi$$
0.662071 + 0.749441i $$0.269678\pi$$
$$90$$ 12.0000 1.26491
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ −1.00000 1.73205i −0.103142 0.178647i
$$95$$ −12.0000 20.7846i −1.23117 2.13246i
$$96$$ 0 0
$$97$$ 14.0000 1.42148 0.710742 0.703452i $$-0.248359\pi$$
0.710742 + 0.703452i $$0.248359\pi$$
$$98$$ 0 0
$$99$$ 3.00000 0.301511
$$100$$ −5.50000 + 9.52628i −0.550000 + 0.952628i
$$101$$ 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i $$-0.0701767\pi$$
−0.677284 + 0.735721i $$0.736843\pi$$
$$102$$ 0 0
$$103$$ 9.00000 15.5885i 0.886796 1.53598i 0.0431555 0.999068i $$-0.486259\pi$$
0.843641 0.536908i $$-0.180408\pi$$
$$104$$ 2.00000 0.196116
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 8.00000 13.8564i 0.773389 1.33955i −0.162306 0.986740i $$-0.551893\pi$$
0.935695 0.352809i $$-0.114773\pi$$
$$108$$ 0 0
$$109$$ 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i $$0.0672444\pi$$
−0.307290 + 0.951616i $$0.599422\pi$$
$$110$$ −2.00000 + 3.46410i −0.190693 + 0.330289i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ −8.00000 13.8564i −0.746004 1.29212i
$$116$$ 1.00000 + 1.73205i 0.0928477 + 0.160817i
$$117$$ −3.00000 + 5.19615i −0.277350 + 0.480384i
$$118$$ −12.0000 −1.10469
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ 7.00000 + 12.1244i 0.633750 + 1.09769i
$$123$$ 0 0
$$124$$ −1.00000 + 1.73205i −0.0898027 + 0.155543i
$$125$$ 24.0000 2.14663
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −4.00000 6.92820i −0.350823 0.607644i
$$131$$ 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i $$-0.748915\pi$$
0.966803 + 0.255524i $$0.0822479\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 2.00000 + 3.46410i 0.171499 + 0.297044i
$$137$$ −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i $$-0.249173\pi$$
−0.965250 + 0.261329i $$0.915839\pi$$
$$138$$ 0 0
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −4.00000 + 6.92820i −0.335673 + 0.581402i
$$143$$ −1.00000 1.73205i −0.0836242 0.144841i
$$144$$ 1.50000 + 2.59808i 0.125000 + 0.216506i
$$145$$ 4.00000 6.92820i 0.332182 0.575356i
$$146$$ 4.00000 0.331042
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ −1.00000 + 1.73205i −0.0819232 + 0.141895i −0.904076 0.427372i $$-0.859440\pi$$
0.822153 + 0.569267i $$0.192773\pi$$
$$150$$ 0 0
$$151$$ 12.0000 + 20.7846i 0.976546 + 1.69143i 0.674735 + 0.738060i $$0.264258\pi$$
0.301811 + 0.953368i $$0.402409\pi$$
$$152$$ 3.00000 5.19615i 0.243332 0.421464i
$$153$$ −12.0000 −0.970143
$$154$$ 0 0
$$155$$ 8.00000 0.642575
$$156$$ 0 0
$$157$$ −4.00000 6.92820i −0.319235 0.552931i 0.661094 0.750303i $$-0.270093\pi$$
−0.980329 + 0.197372i $$0.936759\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −4.00000 −0.316228
$$161$$ 0 0
$$162$$ −9.00000 −0.707107
$$163$$ −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i $$-0.883403\pi$$
0.777007 + 0.629492i $$0.216737\pi$$
$$164$$ 2.00000 + 3.46410i 0.156174 + 0.270501i
$$165$$ 0 0
$$166$$ 3.00000 5.19615i 0.232845 0.403300i
$$167$$ −4.00000 −0.309529 −0.154765 0.987951i $$-0.549462\pi$$
−0.154765 + 0.987951i $$0.549462\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 8.00000 13.8564i 0.613572 1.06274i
$$171$$ 9.00000 + 15.5885i 0.688247 + 1.19208i
$$172$$ 4.00000 + 6.92820i 0.304997 + 0.528271i
$$173$$ −7.00000 + 12.1244i −0.532200 + 0.921798i 0.467093 + 0.884208i $$0.345301\pi$$
−0.999293 + 0.0375896i $$0.988032\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.00000 −0.0753778
$$177$$ 0 0
$$178$$ 3.00000 + 5.19615i 0.224860 + 0.389468i
$$179$$ −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i $$-0.214429\pi$$
−0.931038 + 0.364922i $$0.881096\pi$$
$$180$$ 6.00000 10.3923i 0.447214 0.774597i
$$181$$ −20.0000 −1.48659 −0.743294 0.668965i $$-0.766738\pi$$
−0.743294 + 0.668965i $$0.766738\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 2.00000 3.46410i 0.147442 0.255377i
$$185$$ −20.0000 34.6410i −1.47043 2.54686i
$$186$$ 0 0
$$187$$ 2.00000 3.46410i 0.146254 0.253320i
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ −24.0000 −1.74114
$$191$$ 2.00000 3.46410i 0.144715 0.250654i −0.784552 0.620063i $$-0.787107\pi$$
0.929267 + 0.369410i $$0.120440\pi$$
$$192$$ 0 0
$$193$$ −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i $$-0.189599\pi$$
−0.899770 + 0.436365i $$0.856266\pi$$
$$194$$ 7.00000 12.1244i 0.502571 0.870478i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 1.50000 2.59808i 0.106600 0.184637i
$$199$$ −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i $$-0.331945\pi$$
−0.999990 + 0.00436292i $$0.998611\pi$$
$$200$$ 5.50000 + 9.52628i 0.388909 + 0.673610i
$$201$$ 0 0
$$202$$ 6.00000 0.422159
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 8.00000 13.8564i 0.558744 0.967773i
$$206$$ −9.00000 15.5885i −0.627060 1.08610i
$$207$$ 6.00000 + 10.3923i 0.417029 + 0.722315i
$$208$$ 1.00000 1.73205i 0.0693375 0.120096i
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ −3.00000 + 5.19615i −0.206041 + 0.356873i
$$213$$ 0 0
$$214$$ −8.00000 13.8564i −0.546869 0.947204i
$$215$$ 16.0000 27.7128i 1.09119 1.89000i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 14.0000 0.948200
$$219$$ 0 0
$$220$$ 2.00000 + 3.46410i 0.134840 + 0.233550i
$$221$$ 4.00000 + 6.92820i 0.269069 + 0.466041i
$$222$$ 0 0
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ 0 0
$$225$$ −33.0000 −2.20000
$$226$$ 7.00000 12.1244i 0.465633 0.806500i
$$227$$ −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
$$229$$ 10.0000 17.3205i 0.660819 1.14457i −0.319582 0.947559i $$-0.603543\pi$$
0.980401 0.197013i $$-0.0631241\pi$$
$$230$$ −16.0000 −1.05501
$$231$$ 0 0
$$232$$ 2.00000 0.131306
$$233$$ −15.0000 + 25.9808i −0.982683 + 1.70206i −0.330870 + 0.943676i $$0.607342\pi$$
−0.651813 + 0.758380i $$0.725991\pi$$
$$234$$ 3.00000 + 5.19615i 0.196116 + 0.339683i
$$235$$ 4.00000 + 6.92820i 0.260931 + 0.451946i
$$236$$ −6.00000 + 10.3923i −0.390567 + 0.676481i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 16.0000 1.03495 0.517477 0.855697i $$-0.326871\pi$$
0.517477 + 0.855697i $$0.326871\pi$$
$$240$$ 0 0
$$241$$ 6.00000 + 10.3923i 0.386494 + 0.669427i 0.991975 0.126432i $$-0.0403527\pi$$
−0.605481 + 0.795860i $$0.707019\pi$$
$$242$$ 0.500000 + 0.866025i 0.0321412 + 0.0556702i
$$243$$ 0 0
$$244$$ 14.0000 0.896258
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 6.00000 10.3923i 0.381771 0.661247i
$$248$$ 1.00000 + 1.73205i 0.0635001 + 0.109985i
$$249$$ 0 0
$$250$$ 12.0000 20.7846i 0.758947 1.31453i
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ −4.00000 −0.251478
$$254$$ 4.00000 6.92820i 0.250982 0.434714i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i $$-0.893253\pi$$
0.757159 + 0.653231i $$0.226587\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −8.00000 −0.496139
$$261$$ −3.00000 + 5.19615i −0.185695 + 0.321634i
$$262$$ −3.00000 5.19615i −0.185341 0.321019i
$$263$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ 0 0
$$265$$ 24.0000 1.47431
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 6.00000 10.3923i 0.366508 0.634811i
$$269$$ 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i $$-0.0474530\pi$$
−0.623082 + 0.782157i $$0.714120\pi$$
$$270$$ 0 0
$$271$$ −10.0000 + 17.3205i −0.607457 + 1.05215i 0.384201 + 0.923249i $$0.374477\pi$$
−0.991658 + 0.128897i $$0.958856\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 5.50000 9.52628i 0.331662 0.574456i
$$276$$ 0 0
$$277$$ 15.0000 + 25.9808i 0.901263 + 1.56103i 0.825857 + 0.563880i $$0.190692\pi$$
0.0754058 + 0.997153i $$0.475975\pi$$
$$278$$ −7.00000 + 12.1244i −0.419832 + 0.727171i
$$279$$ −6.00000 −0.359211
$$280$$ 0 0
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ 0 0
$$283$$ 3.00000 + 5.19615i 0.178331 + 0.308879i 0.941309 0.337546i $$-0.109597\pi$$
−0.762978 + 0.646425i $$0.776263\pi$$
$$284$$ 4.00000 + 6.92820i 0.237356 + 0.411113i
$$285$$ 0 0
$$286$$ −2.00000 −0.118262
$$287$$ 0 0
$$288$$ 3.00000 0.176777
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ −4.00000 6.92820i −0.234888 0.406838i
$$291$$ 0 0
$$292$$ 2.00000 3.46410i 0.117041 0.202721i
$$293$$ −18.0000 −1.05157 −0.525786 0.850617i $$-0.676229\pi$$
−0.525786 + 0.850617i $$0.676229\pi$$
$$294$$ 0 0
$$295$$ 48.0000 2.79467
$$296$$ 5.00000 8.66025i 0.290619 0.503367i
$$297$$ 0 0
$$298$$ 1.00000 + 1.73205i 0.0579284 + 0.100335i
$$299$$ 4.00000 6.92820i 0.231326 0.400668i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 24.0000 1.38104
$$303$$ 0 0
$$304$$ −3.00000 5.19615i −0.172062 0.298020i
$$305$$ −28.0000 48.4974i −1.60328 2.77695i
$$306$$ −6.00000 + 10.3923i −0.342997 + 0.594089i
$$307$$ 10.0000 0.570730 0.285365 0.958419i $$-0.407885\pi$$
0.285365 + 0.958419i $$0.407885\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 4.00000 6.92820i 0.227185 0.393496i
$$311$$ 7.00000 + 12.1244i 0.396934 + 0.687509i 0.993346 0.115169i $$-0.0367410\pi$$
−0.596412 + 0.802678i $$0.703408\pi$$
$$312$$ 0 0
$$313$$ −1.00000 + 1.73205i −0.0565233 + 0.0979013i −0.892903 0.450250i $$-0.851335\pi$$
0.836379 + 0.548151i $$0.184668\pi$$
$$314$$ −8.00000 −0.451466
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i $$-0.887225\pi$$
0.769395 + 0.638774i $$0.220558\pi$$
$$318$$ 0 0
$$319$$ −1.00000 1.73205i −0.0559893 0.0969762i
$$320$$ −2.00000 + 3.46410i −0.111803 + 0.193649i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ −4.50000 + 7.79423i −0.250000 + 0.433013i
$$325$$ 11.0000 + 19.0526i 0.610170 + 1.05685i
$$326$$ 2.00000 + 3.46410i 0.110770 + 0.191859i
$$327$$ 0 0
$$328$$ 4.00000 0.220863
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i $$-0.648095\pi$$
0.998298 0.0583130i $$-0.0185721\pi$$
$$332$$ −3.00000 5.19615i −0.164646 0.285176i
$$333$$ 15.0000 + 25.9808i 0.821995 + 1.42374i
$$334$$ −2.00000 + 3.46410i −0.109435 + 0.189547i
$$335$$ −48.0000 −2.62252
$$336$$ 0 0
$$337$$ −18.0000 −0.980522 −0.490261 0.871576i $$-0.663099\pi$$
−0.490261 + 0.871576i $$0.663099\pi$$
$$338$$ −4.50000 + 7.79423i −0.244768 + 0.423950i
$$339$$ 0 0
$$340$$ −8.00000 13.8564i −0.433861 0.751469i
$$341$$ 1.00000 1.73205i 0.0541530 0.0937958i
$$342$$ 18.0000 0.973329
$$343$$ 0 0
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ 7.00000 + 12.1244i 0.376322 + 0.651809i
$$347$$ −4.00000 6.92820i −0.214731 0.371925i 0.738458 0.674299i $$-0.235554\pi$$
−0.953189 + 0.302374i $$0.902221\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i $$-0.217711\pi$$
−0.934751 + 0.355303i $$0.884378\pi$$
$$354$$ 0 0
$$355$$ 16.0000 27.7128i 0.849192 1.47084i
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −4.00000 −0.211407
$$359$$ 8.00000 13.8564i 0.422224 0.731313i −0.573933 0.818902i $$-0.694583\pi$$
0.996157 + 0.0875892i $$0.0279163\pi$$
$$360$$ −6.00000 10.3923i −0.316228 0.547723i
$$361$$ −8.50000 14.7224i −0.447368 0.774865i
$$362$$ −10.0000 + 17.3205i −0.525588 + 0.910346i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −16.0000 −0.837478
$$366$$ 0 0
$$367$$ 11.0000 + 19.0526i 0.574195 + 0.994535i 0.996129 + 0.0879086i $$0.0280183\pi$$
−0.421933 + 0.906627i $$0.638648\pi$$
$$368$$ −2.00000 3.46410i −0.104257 0.180579i
$$369$$ −6.00000 + 10.3923i −0.312348 + 0.541002i
$$370$$ −40.0000 −2.07950
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i $$-0.749977\pi$$
0.965945 + 0.258748i $$0.0833099\pi$$
$$374$$ −2.00000 3.46410i −0.103418 0.179124i
$$375$$ 0 0
$$376$$ −1.00000 + 1.73205i −0.0515711 + 0.0893237i
$$377$$ 4.00000 0.206010
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ −12.0000 + 20.7846i −0.615587 + 1.06623i
$$381$$ 0 0
$$382$$ −2.00000 3.46410i −0.102329 0.177239i
$$383$$ −5.00000 + 8.66025i −0.255488 + 0.442518i −0.965028 0.262147i $$-0.915569\pi$$
0.709540 + 0.704665i $$0.248903\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.00000 −0.101797
$$387$$ −12.0000 + 20.7846i −0.609994 + 1.05654i
$$388$$ −7.00000 12.1244i −0.355371 0.615521i
$$389$$ 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i $$0.108394\pi$$
−0.182047 + 0.983290i $$0.558272\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 3.00000 5.19615i 0.151138 0.261778i
$$395$$ 0 0
$$396$$ −1.50000 2.59808i −0.0753778 0.130558i
$$397$$ 12.0000 20.7846i 0.602263 1.04315i −0.390215 0.920724i $$-0.627599\pi$$
0.992478 0.122426i $$-0.0390674\pi$$
$$398$$ −14.0000 −0.701757
$$399$$ 0 0
$$400$$ 11.0000 0.550000
$$401$$ 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i $$-0.684957\pi$$
0.998350 + 0.0574304i $$0.0182907\pi$$
$$402$$ 0 0
$$403$$ 2.00000 + 3.46410i 0.0996271 + 0.172559i
$$404$$ 3.00000 5.19615i 0.149256 0.258518i
$$405$$ 36.0000 1.78885
$$406$$ 0 0
$$407$$ −10.0000 −0.495682
$$408$$ 0 0
$$409$$ 8.00000 + 13.8564i 0.395575 + 0.685155i 0.993174 0.116639i $$-0.0372122\pi$$
−0.597600 + 0.801795i $$0.703879\pi$$
$$410$$ −8.00000 13.8564i −0.395092 0.684319i
$$411$$ 0 0
$$412$$ −18.0000 −0.886796
$$413$$ 0 0
$$414$$ 12.0000 0.589768
$$415$$ −12.0000 + 20.7846i −0.589057 + 1.02028i
$$416$$ −1.00000 1.73205i −0.0490290 0.0849208i
$$417$$ 0 0
$$418$$ −3.00000 + 5.19615i −0.146735 + 0.254152i
$$419$$ 32.0000 1.56330 0.781651 0.623716i $$-0.214378\pi$$
0.781651 + 0.623716i $$0.214378\pi$$
$$420$$ 0 0
$$421$$ −2.00000 −0.0974740 −0.0487370 0.998812i $$-0.515520\pi$$
−0.0487370 + 0.998812i $$0.515520\pi$$
$$422$$ −4.00000 + 6.92820i −0.194717 + 0.337260i
$$423$$ −3.00000 5.19615i −0.145865 0.252646i
$$424$$ 3.00000 + 5.19615i 0.145693 + 0.252347i
$$425$$ −22.0000 + 38.1051i −1.06716 + 1.84837i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −16.0000 −0.773389
$$429$$ 0 0
$$430$$ −16.0000 27.7128i −0.771589 1.33643i
$$431$$ −8.00000 13.8564i −0.385346 0.667440i 0.606471 0.795106i $$-0.292585\pi$$
−0.991817 + 0.127666i $$0.959251\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 7.00000 12.1244i 0.335239 0.580651i
$$437$$ −12.0000 20.7846i −0.574038 0.994263i
$$438$$ 0 0
$$439$$ 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i $$-0.600405\pi$$
0.978412 0.206666i $$-0.0662612\pi$$
$$440$$ 4.00000 0.190693
$$441$$ 0 0
$$442$$ 8.00000 0.380521
$$443$$ 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
$$445$$ −12.0000 20.7846i −0.568855 0.985285i
$$446$$ 1.00000 1.73205i 0.0473514 0.0820150i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ −16.5000 + 28.5788i −0.777817 + 1.34722i
$$451$$ −2.00000 3.46410i −0.0941763 0.163118i
$$452$$ −7.00000 12.1244i −0.329252 0.570282i
$$453$$ 0 0
$$454$$ −2.00000 −0.0938647
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i $$-0.848229\pi$$
0.841688 + 0.539964i $$0.181562\pi$$
$$458$$ −10.0000 17.3205i −0.467269 0.809334i
$$459$$ 0 0
$$460$$ −8.00000 + 13.8564i −0.373002 + 0.646058i
$$461$$ −30.0000 −1.39724 −0.698620 0.715493i $$-0.746202\pi$$
−0.698620 + 0.715493i $$0.746202\pi$$
$$462$$ 0 0
$$463$$ −32.0000 −1.48717 −0.743583 0.668644i $$-0.766875\pi$$
−0.743583 + 0.668644i $$0.766875\pi$$
$$464$$ 1.00000 1.73205i 0.0464238 0.0804084i
$$465$$ 0 0
$$466$$ 15.0000 + 25.9808i 0.694862 + 1.20354i
$$467$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$468$$ 6.00000 0.277350
$$469$$ 0 0
$$470$$ 8.00000 0.369012
$$471$$ 0 0
$$472$$ 6.00000 + 10.3923i 0.276172 + 0.478345i
$$473$$ −4.00000 6.92820i −0.183920 0.318559i
$$474$$ 0 0
$$475$$ 66.0000 3.02829
$$476$$ 0 0
$$477$$ −18.0000 −0.824163
$$478$$ 8.00000 13.8564i 0.365911 0.633777i
$$479$$ −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i $$-0.285779\pi$$
−0.988861 + 0.148842i $$0.952445\pi$$
$$480$$ 0 0
$$481$$ 10.0000 17.3205i 0.455961 0.789747i
$$482$$ 12.0000 0.546585
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −28.0000 + 48.4974i −1.27141 + 2.20215i
$$486$$ 0 0
$$487$$ 14.0000 + 24.2487i 0.634401 + 1.09881i 0.986642 + 0.162905i $$0.0520863\pi$$
−0.352241 + 0.935909i $$0.614580\pi$$
$$488$$ 7.00000 12.1244i 0.316875 0.548844i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −36.0000 −1.62466 −0.812329 0.583200i $$-0.801800\pi$$
−0.812329 + 0.583200i $$0.801800\pi$$
$$492$$ 0 0
$$493$$ 4.00000 + 6.92820i 0.180151 + 0.312031i
$$494$$ −6.00000 10.3923i −0.269953 0.467572i
$$495$$ −6.00000 + 10.3923i −0.269680 + 0.467099i
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −22.0000 + 38.1051i −0.984855 + 1.70582i −0.342277 + 0.939599i $$0.611198\pi$$
−0.642578 + 0.766220i $$0.722135\pi$$
$$500$$ −12.0000 20.7846i −0.536656 0.929516i
$$501$$ 0 0
$$502$$ −6.00000 + 10.3923i −0.267793 + 0.463831i
$$503$$ 36.0000 1.60516 0.802580 0.596544i $$-0.203460\pi$$
0.802580 + 0.596544i $$0.203460\pi$$
$$504$$ 0 0
$$505$$ −24.0000 −1.06799
$$506$$ −2.00000 + 3.46410i −0.0889108 + 0.153998i
$$507$$ 0 0
$$508$$ −4.00000 6.92820i −0.177471 0.307389i
$$509$$ −14.0000 + 24.2487i −0.620539 + 1.07481i 0.368846 + 0.929490i $$0.379753\pi$$
−0.989385 + 0.145315i $$0.953580\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 3.00000 + 5.19615i 0.132324 + 0.229192i
$$515$$ 36.0000 + 62.3538i 1.58635 + 2.74764i
$$516$$ 0 0
$$517$$ 2.00000 0.0879599
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −4.00000 + 6.92820i −0.175412 + 0.303822i
$$521$$ 5.00000 + 8.66025i 0.219054 + 0.379413i 0.954519 0.298150i $$-0.0963696\pi$$
−0.735465 + 0.677563i $$0.763036\pi$$
$$522$$ 3.00000 + 5.19615i 0.131306 + 0.227429i
$$523$$ −17.0000 + 29.4449i −0.743358 + 1.28753i 0.207600 + 0.978214i $$0.433435\pi$$
−0.950958 + 0.309320i $$0.899899\pi$$
$$524$$ −6.00000 −0.262111
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −4.00000 + 6.92820i −0.174243 + 0.301797i
$$528$$ 0 0
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ 12.0000 20.7846i 0.521247 0.902826i
$$531$$ −36.0000 −1.56227
$$532$$ 0 0
$$533$$ 8.00000 0.346518
$$534$$ 0 0
$$535$$ 32.0000 + 55.4256i 1.38348 + 2.39626i
$$536$$ −6.00000 10.3923i −0.259161 0.448879i
$$537$$ 0 0
$$538$$ 12.0000 0.517357
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −7.00000 + 12.1244i −0.300954 + 0.521267i −0.976352 0.216186i $$-0.930638\pi$$
0.675399 + 0.737453i $$0.263972\pi$$
$$542$$ 10.0000 + 17.3205i 0.429537 + 0.743980i
$$543$$ 0 0
$$544$$ 2.00000 3.46410i 0.0857493 0.148522i
$$545$$ −56.0000 −2.39878
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ −3.00000 + 5.19615i −0.128154 + 0.221969i
$$549$$ 21.0000 + 36.3731i 0.896258 + 1.55236i
$$550$$ −5.50000 9.52628i −0.234521 0.406202i
$$551$$ 6.00000 10.3923i 0.255609 0.442727i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 30.0000 1.27458
$$555$$ 0 0
$$556$$ 7.00000 + 12.1244i 0.296866 + 0.514187i
$$557$$ −7.00000 12.1244i −0.296600 0.513725i 0.678756 0.734364i $$-0.262519\pi$$
−0.975356 + 0.220638i $$0.929186\pi$$
$$558$$ −3.00000 + 5.19615i −0.127000 + 0.219971i
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −5.00000 + 8.66025i −0.210912 + 0.365311i
$$563$$ −17.0000 29.4449i −0.716465 1.24095i −0.962392 0.271665i $$-0.912426\pi$$
0.245927 0.969288i $$-0.420908\pi$$
$$564$$ 0 0
$$565$$ −28.0000 + 48.4974i −1.17797 + 2.04030i
$$566$$ 6.00000 0.252199
$$567$$ 0 0
$$568$$ 8.00000 0.335673
$$569$$ −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i $$-0.873472\pi$$
0.796266 + 0.604947i $$0.206806\pi$$
$$570$$ 0 0
$$571$$ −14.0000 24.2487i −0.585882 1.01478i −0.994765 0.102190i $$-0.967415\pi$$
0.408883 0.912587i $$-0.365918\pi$$
$$572$$ −1.00000 + 1.73205i −0.0418121 + 0.0724207i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 44.0000 1.83493
$$576$$ 1.50000 2.59808i 0.0625000 0.108253i
$$577$$ 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i $$-0.0725410\pi$$
−0.682730 + 0.730670i $$0.739208\pi$$
$$578$$ −0.500000 0.866025i −0.0207973 0.0360219i
$$579$$ 0 0
$$580$$ −8.00000 −0.332182
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 3.00000 5.19615i 0.124247 0.215203i
$$584$$ −2.00000 3.46410i −0.0827606 0.143346i
$$585$$ −12.0000 20.7846i −0.496139 0.859338i
$$586$$ −9.00000 + 15.5885i −0.371787 + 0.643953i
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 12.0000 0.494451
$$590$$ 24.0000 41.5692i 0.988064 1.71138i
$$591$$ 0 0
$$592$$ −5.00000 8.66025i −0.205499 0.355934i
$$593$$ −6.00000 + 10.3923i −0.246390 + 0.426761i −0.962522 0.271205i $$-0.912578\pi$$
0.716131 + 0.697966i $$0.245911\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 2.00000 0.0819232
$$597$$ 0 0
$$598$$ −4.00000 6.92820i −0.163572 0.283315i
$$599$$ −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i $$-0.329782\pi$$
−0.999938 + 0.0111569i $$0.996449\pi$$
$$600$$ 0 0
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ 0 0
$$603$$ 36.0000 1.46603
$$604$$ 12.0000 20.7846i 0.488273 0.845714i
$$605$$ −2.00000 3.46410i −0.0813116 0.140836i
$$606$$ 0 0
$$607$$ 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i $$-0.781424\pi$$
0.935713 + 0.352763i $$0.114758\pi$$
$$608$$ −6.00000 −0.243332
$$609$$ 0 0
$$610$$ −56.0000 −2.26737
$$611$$ −2.00000 + 3.46410i −0.0809113 + 0.140143i
$$612$$ 6.00000 + 10.3923i 0.242536 + 0.420084i
$$613$$ −23.0000 39.8372i −0.928961 1.60901i −0.785063 0.619416i $$-0.787370\pi$$
−0.143898 0.989593i $$-0.545964\pi$$
$$614$$ 5.00000 8.66025i 0.201784 0.349499i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000 0.724653 0.362326 0.932051i $$-0.381983\pi$$
0.362326 + 0.932051i $$0.381983\pi$$
$$618$$ 0 0
$$619$$ 4.00000 + 6.92820i 0.160774 + 0.278468i 0.935146 0.354262i $$-0.115268\pi$$
−0.774373 + 0.632730i $$0.781934\pi$$
$$620$$ −4.00000 6.92820i −0.160644 0.278243i
$$621$$ 0 0
$$622$$ 14.0000 0.561349
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −20.5000 + 35.5070i −0.820000 + 1.42028i
$$626$$ 1.00000 + 1.73205i 0.0399680 + 0.0692267i
$$627$$ 0 0
$$628$$ −4.00000 + 6.92820i −0.159617 + 0.276465i
$$629$$ 40.0000 1.59490
$$630$$ 0 0
$$631$$ −12.0000 −0.477712 −0.238856 0.971055i $$-0.576772\pi$$
−0.238856 + 0.971055i $$0.576772\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 3.00000 + 5.19615i 0.119145 + 0.206366i
$$635$$ −16.0000 + 27.7128i −0.634941 + 1.09975i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −2.00000 −0.0791808
$$639$$ −12.0000 + 20.7846i −0.474713 + 0.822226i
$$640$$ 2.00000 + 3.46410i 0.0790569 + 0.136931i
$$641$$ 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i $$-0.128860\pi$$
−0.800678 + 0.599095i $$0.795527\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 12.0000 20.7846i 0.472134 0.817760i
$$647$$ 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i $$-0.129037\pi$$
−0.801010 + 0.598651i $$0.795704\pi$$
$$648$$ 4.50000 + 7.79423i 0.176777 + 0.306186i
$$649$$ 6.00000 10.3923i 0.235521 0.407934i
$$650$$ 22.0000 0.862911
$$651$$ 0 0
$$652$$ 4.00000 0.156652
$$653$$ −5.00000 + 8.66025i −0.195665 + 0.338902i −0.947118 0.320884i $$-0.896020\pi$$
0.751453 + 0.659786i $$0.229353\pi$$
$$654$$ 0 0
$$655$$ 12.0000 + 20.7846i 0.468879 + 0.812122i
$$656$$ 2.00000 3.46410i 0.0780869 0.135250i
$$657$$ 12.0000 0.468165
$$658$$ 0 0
$$659$$ −8.00000 −0.311636 −0.155818 0.987786i $$-0.549801\pi$$
−0.155818 + 0.987786i $$0.549801\pi$$
$$660$$ 0 0
$$661$$ 10.0000 + 17.3205i 0.388955 + 0.673690i 0.992309 0.123784i $$-0.0395028\pi$$
−0.603354 + 0.797473i $$0.706170\pi$$
$$662$$ −10.0000 17.3205i −0.388661 0.673181i
$$663$$ 0 0
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 30.0000 1.16248
$$667$$ 4.00000 6.92820i 0.154881 0.268261i
$$668$$ 2.00000 + 3.46410i 0.0773823 + 0.134030i
$$669$$ 0 0
$$670$$ −24.0000 + 41.5692i −0.927201 + 1.60596i
$$671$$ −14.0000 −0.540464
$$672$$ 0 0
$$673$$ 22.0000 0.848038 0.424019 0.905653i $$-0.360619\pi$$
0.424019 + 0.905653i $$0.360619\pi$$
$$674$$ −9.00000 + 15.5885i −0.346667 + 0.600445i
$$675$$ 0 0
$$676$$ 4.50000 + 7.79423i 0.173077 + 0.299778i
$$677$$ 13.0000 22.5167i 0.499631 0.865386i −0.500369 0.865812i $$-0.666802\pi$$
1.00000 0.000426509i $$0.000135762\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −16.0000 −0.613572
$$681$$ 0 0
$$682$$ −1.00000 1.73205i −0.0382920 0.0663237i
$$683$$ −18.0000 31.1769i −0.688751 1.19295i −0.972242 0.233977i $$-0.924826\pi$$
0.283491 0.958975i $$-0.408507\pi$$
$$684$$ 9.00000 15.5885i 0.344124 0.596040i
$$685$$ 24.0000 0.916993
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 4.00000 6.92820i 0.152499 0.264135i
$$689$$ 6.00000 + 10.3923i 0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ 18.0000 31.1769i 0.684752 1.18603i −0.288762 0.957401i $$-0.593244\pi$$
0.973515 0.228625i $$-0.0734229\pi$$
$$692$$ 14.0000 0.532200
$$693$$ 0 0
$$694$$ −8.00000 −0.303676
$$695$$ 28.0000 48.4974i 1.06210 1.83961i
$$696$$ 0 0
$$697$$ 8.00000 + 13.8564i 0.303022 + 0.524849i
$$698$$ 5.00000 8.66025i 0.189253 0.327795i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ 0 0
$$703$$ −30.0000 51.9615i −1.13147 1.95977i
$$704$$ 0.500000 + 0.866025i 0.0188445 + 0.0326396i
$$705$$ 0 0
$$706$$ −6.00000 −0.225813
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −9.00000 + 15.5885i −0.338002 + 0.585437i −0.984057 0.177854i $$-0.943084\pi$$
0.646055 + 0.763291i $$0.276418\pi$$
$$710$$ −16.0000 27.7128i −0.600469 1.04004i
$$711$$ 0 0
$$712$$ 3.00000 5.19615i 0.112430 0.194734i
$$713$$ 8.00000 0.299602
$$714$$ 0 0
$$715$$ 8.00000 0.299183
$$716$$ −2.00000 + 3.46410i −0.0747435 + 0.129460i
$$717$$ 0 0
$$718$$ −8.00000 13.8564i −0.298557 0.517116i
$$719$$ −13.0000 + 22.5167i −0.484818 + 0.839730i −0.999848 0.0174426i $$-0.994448\pi$$
0.515030 + 0.857172i $$0.327781\pi$$
$$720$$ −12.0000 −0.447214
$$721$$ 0 0
$$722$$ −17.0000 −0.632674
$$723$$ 0 0
$$724$$ 10.0000 + 17.3205i 0.371647 + 0.643712i
$$725$$ 11.0000 + 19.0526i 0.408530 + 0.707594i
$$726$$ 0 0
$$727$$ 10.0000 0.370879 0.185440 0.982656i $$-0.440629\pi$$
0.185440 + 0.982656i $$0.440629\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ −8.00000 + 13.8564i −0.296093 + 0.512849i
$$731$$ 16.0000 + 27.7128i 0.591781 + 1.02500i
$$732$$ 0 0
$$733$$ −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i $$-0.966513\pi$$
0.588177 + 0.808732i $$0.299846\pi$$
$$734$$ 22.0000 0.812035
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ −6.00000 + 10.3923i −0.221013 + 0.382805i
$$738$$ 6.00000 + 10.3923i 0.220863 + 0.382546i
$$739$$ 6.00000 + 10.3923i 0.220714 + 0.382287i 0.955025 0.296526i $$-0.0958281\pi$$
−0.734311 + 0.678813i $$0.762495\pi$$
$$740$$ −20.0000 + 34.6410i −0.735215 + 1.27343i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ −4.00000 6.92820i −0.146549 0.253830i
$$746$$ −5.00000 8.66025i −0.183063 0.317074i
$$747$$ 9.00000 15.5885i 0.329293 0.570352i
$$748$$ −4.00000 −0.146254
$$749$$ 0 0
$$750$$ 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
$$754$$ 2.00000 3.46410i 0.0728357 0.126155i
$$755$$ −96.0000 −3.49380
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ 2.00000 3.46410i 0.0726433 0.125822i
$$759$$ 0 0
$$760$$ 12.0000 + 20.7846i 0.435286 + 0.753937i
$$761$$ −24.0000 + 41.5692i −0.869999 + 1.50688i −0.00800331 + 0.999968i $$0.502548\pi$$
−0.861996 + 0.506915i $$0.830786\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −4.00000 −0.144715
$$765$$ 24.0000 41.5692i 0.867722 1.50294i
$$766$$ 5.00000 + 8.66025i 0.180657 + 0.312908i
$$767$$ 12.0000 + 20.7846i 0.433295 + 0.750489i
$$768$$ 0 0
$$769$$ −16.0000 −0.576975 −0.288487 0.957484i $$-0.593152\pi$$
−0.288487 + 0.957484i $$0.593152\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −1.00000 + 1.73205i −0.0359908 + 0.0623379i
$$773$$ −24.0000 41.5692i −0.863220 1.49514i −0.868804 0.495156i $$-0.835111\pi$$
0.00558380 0.999984i $$-0.498223\pi$$
$$774$$ 12.0000 + 20.7846i 0.431331 + 0.747087i
$$775$$ −11.0000 + 19.0526i −0.395132 + 0.684388i
$$776$$ −14.0000 −0.502571
$$777$$ 0 0
$$778$$ 30.0000 1.07555
$$779$$ 12.0000 20.7846i 0.429945 0.744686i
$$780$$ 0 0
$$781$$ −4.00000 6.92820i −0.143131 0.247911i
$$782$$ 8.00000 13.8564i 0.286079 0.495504i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 32.0000 1.14213
$$786$$ 0 0
$$787$$ −11.0000 19.0526i −0.392108 0.679150i 0.600620 0.799535i $$-0.294921\pi$$
−0.992727 + 0.120384i $$0.961587\pi$$
$$788$$ −3.00000 5.19615i −0.106871 0.185105i
$$789$$ 0