# Properties

 Label 1053.2.e.b.703.1 Level $1053$ Weight $2$ Character 1053.703 Analytic conductor $8.408$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1053 = 3^{4} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1053.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.40824733284$$ 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 39) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 703.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1053.703 Dual form 1053.2.e.b.352.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -3.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(2.00000 - 3.46410i) q^{7} -3.00000 q^{8} +2.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(2.00000 + 3.46410i) q^{14} +(0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +(1.00000 - 1.73205i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +4.00000 q^{28} +(5.00000 - 8.66025i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{34} -8.00000 q^{35} -2.00000 q^{37} +(3.00000 + 5.19615i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(6.00000 - 10.3923i) q^{43} -4.00000 q^{44} +(-4.50000 - 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{52} +6.00000 q^{53} +8.00000 q^{55} +(-6.00000 + 10.3923i) q^{56} +(5.00000 + 8.66025i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +7.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(4.00000 + 6.92820i) q^{67} +(1.00000 + 1.73205i) q^{68} +(4.00000 - 6.92820i) q^{70} +2.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(8.00000 + 13.8564i) q^{77} +(-4.00000 + 6.92820i) q^{79} -2.00000 q^{80} +6.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-2.00000 - 3.46410i) q^{85} +(6.00000 + 10.3923i) q^{86} +(6.00000 - 10.3923i) q^{88} -2.00000 q^{89} -4.00000 q^{91} +(-5.00000 + 8.66025i) q^{97} +9.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10})$$ 2 * q - q^2 + q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 $$2 q - q^{2} + q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} + 4 q^{10} - 4 q^{11} - q^{13} + 4 q^{14} + q^{16} + 4 q^{17} + 2 q^{20} - 4 q^{22} + q^{25} + 2 q^{26} + 8 q^{28} + 10 q^{29} - 4 q^{31} - 5 q^{32} - 2 q^{34} - 16 q^{35} - 4 q^{37} + 6 q^{40} - 6 q^{41} + 12 q^{43} - 8 q^{44} - 9 q^{49} + q^{50} + q^{52} + 12 q^{53} + 16 q^{55} - 12 q^{56} + 10 q^{58} - 12 q^{59} + 2 q^{61} + 8 q^{62} + 14 q^{64} - 2 q^{65} + 8 q^{67} + 2 q^{68} + 8 q^{70} + 4 q^{73} + 2 q^{74} + 16 q^{77} - 8 q^{79} - 4 q^{80} + 12 q^{82} - 4 q^{83} - 4 q^{85} + 12 q^{86} + 12 q^{88} - 4 q^{89} - 8 q^{91} - 10 q^{97} + 18 q^{98}+O(q^{100})$$ 2 * q - q^2 + q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 + 4 * q^10 - 4 * q^11 - q^13 + 4 * q^14 + q^16 + 4 * q^17 + 2 * q^20 - 4 * q^22 + q^25 + 2 * q^26 + 8 * q^28 + 10 * q^29 - 4 * q^31 - 5 * q^32 - 2 * q^34 - 16 * q^35 - 4 * q^37 + 6 * q^40 - 6 * q^41 + 12 * q^43 - 8 * q^44 - 9 * q^49 + q^50 + q^52 + 12 * q^53 + 16 * q^55 - 12 * q^56 + 10 * q^58 - 12 * q^59 + 2 * q^61 + 8 * q^62 + 14 * q^64 - 2 * q^65 + 8 * q^67 + 2 * q^68 + 8 * q^70 + 4 * q^73 + 2 * q^74 + 16 * q^77 - 8 * q^79 - 4 * q^80 + 12 * q^82 - 4 * q^83 - 4 * q^85 + 12 * q^86 + 12 * q^88 - 4 * q^89 - 8 * q^91 - 10 * q^97 + 18 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$730$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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 −0.986869 0.161521i $$-0.948360\pi$$
0.633316 + 0.773893i $$0.281693\pi$$
$$3$$ 0 0
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i $$-0.314250\pi$$
−0.998203 + 0.0599153i $$0.980917\pi$$
$$6$$ 0 0
$$7$$ 2.00000 3.46410i 0.755929 1.30931i −0.188982 0.981981i $$-0.560519\pi$$
0.944911 0.327327i $$-0.106148\pi$$
$$8$$ −3.00000 −1.06066
$$9$$ 0 0
$$10$$ 2.00000 0.632456
$$11$$ −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i $$0.372704\pi$$
−0.992361 + 0.123371i $$0.960630\pi$$
$$12$$ 0 0
$$13$$ −0.500000 0.866025i −0.138675 0.240192i
$$14$$ 2.00000 + 3.46410i 0.534522 + 0.925820i
$$15$$ 0 0
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 1.00000 1.73205i 0.223607 0.387298i
$$21$$ 0 0
$$22$$ −2.00000 3.46410i −0.426401 0.738549i
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 1.00000 0.196116
$$27$$ 0 0
$$28$$ 4.00000 0.755929
$$29$$ 5.00000 8.66025i 0.928477 1.60817i 0.142605 0.989780i $$-0.454452\pi$$
0.785872 0.618389i $$-0.212214\pi$$
$$30$$ 0 0
$$31$$ −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i $$-0.283621\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ −2.50000 4.33013i −0.441942 0.765466i
$$33$$ 0 0
$$34$$ −1.00000 + 1.73205i −0.171499 + 0.297044i
$$35$$ −8.00000 −1.35225
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 3.00000 + 5.19615i 0.474342 + 0.821584i
$$41$$ −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i $$-0.321880\pi$$
−0.999353 + 0.0359748i $$0.988546\pi$$
$$42$$ 0 0
$$43$$ 6.00000 10.3923i 0.914991 1.58481i 0.108078 0.994142i $$-0.465531\pi$$
0.806914 0.590669i $$-0.201136\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0 0
$$49$$ −4.50000 7.79423i −0.642857 1.11346i
$$50$$ 0.500000 + 0.866025i 0.0707107 + 0.122474i
$$51$$ 0 0
$$52$$ 0.500000 0.866025i 0.0693375 0.120096i
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 8.00000 1.07872
$$56$$ −6.00000 + 10.3923i −0.801784 + 1.38873i
$$57$$ 0 0
$$58$$ 5.00000 + 8.66025i 0.656532 + 1.13715i
$$59$$ −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
$$61$$ 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i $$-0.792466\pi$$
0.922916 + 0.385002i $$0.125799\pi$$
$$62$$ 4.00000 0.508001
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ −1.00000 + 1.73205i −0.124035 + 0.214834i
$$66$$ 0 0
$$67$$ 4.00000 + 6.92820i 0.488678 + 0.846415i 0.999915 0.0130248i $$-0.00414604\pi$$
−0.511237 + 0.859440i $$0.670813\pi$$
$$68$$ 1.00000 + 1.73205i 0.121268 + 0.210042i
$$69$$ 0 0
$$70$$ 4.00000 6.92820i 0.478091 0.828079i
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ 1.00000 1.73205i 0.116248 0.201347i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 8.00000 + 13.8564i 0.911685 + 1.57908i
$$78$$ 0 0
$$79$$ −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i $$-0.981922\pi$$
0.548352 + 0.836247i $$0.315255\pi$$
$$80$$ −2.00000 −0.223607
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ −2.00000 + 3.46410i −0.219529 + 0.380235i −0.954664 0.297686i $$-0.903785\pi$$
0.735135 + 0.677920i $$0.237119\pi$$
$$84$$ 0 0
$$85$$ −2.00000 3.46410i −0.216930 0.375735i
$$86$$ 6.00000 + 10.3923i 0.646997 + 1.12063i
$$87$$ 0 0
$$88$$ 6.00000 10.3923i 0.639602 1.10782i
$$89$$ −2.00000 −0.212000 −0.106000 0.994366i $$-0.533804\pi$$
−0.106000 + 0.994366i $$0.533804\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −5.00000 + 8.66025i −0.507673 + 0.879316i 0.492287 + 0.870433i $$0.336161\pi$$
−0.999961 + 0.00888289i $$0.997172\pi$$
$$98$$ 9.00000 0.909137
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i $$-0.480128\pi$$
0.833143 0.553058i $$-0.186539\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$104$$ 1.50000 + 2.59808i 0.147087 + 0.254762i
$$105$$ 0 0
$$106$$ −3.00000 + 5.19615i −0.291386 + 0.504695i
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ −4.00000 + 6.92820i −0.381385 + 0.660578i
$$111$$ 0 0
$$112$$ −2.00000 3.46410i −0.188982 0.327327i
$$113$$ 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i $$-0.0755971\pi$$
−0.689714 + 0.724082i $$0.742264\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 10.0000 0.928477
$$117$$ 0 0
$$118$$ 12.0000 1.10469
$$119$$ 4.00000 6.92820i 0.366679 0.635107i
$$120$$ 0 0
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ 1.00000 + 1.73205i 0.0905357 + 0.156813i
$$123$$ 0 0
$$124$$ 2.00000 3.46410i 0.179605 0.311086i
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ 1.50000 2.59808i 0.132583 0.229640i
$$129$$ 0 0
$$130$$ −1.00000 1.73205i −0.0877058 0.151911i
$$131$$ −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i $$-0.222575\pi$$
−0.940072 + 0.340977i $$0.889242\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i $$-0.915839\pi$$
0.708942 + 0.705266i $$0.249173\pi$$
$$138$$ 0 0
$$139$$ −6.00000 10.3923i −0.508913 0.881464i −0.999947 0.0103230i $$-0.996714\pi$$
0.491033 0.871141i $$-0.336619\pi$$
$$140$$ −4.00000 6.92820i −0.338062 0.585540i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 4.00000 0.334497
$$144$$ 0 0
$$145$$ −20.0000 −1.66091
$$146$$ −1.00000 + 1.73205i −0.0827606 + 0.143346i
$$147$$ 0 0
$$148$$ −1.00000 1.73205i −0.0821995 0.142374i
$$149$$ 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i $$-0.0876260\pi$$
−0.716578 + 0.697507i $$0.754293\pi$$
$$150$$ 0 0
$$151$$ −2.00000 + 3.46410i −0.162758 + 0.281905i −0.935857 0.352381i $$-0.885372\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ −16.0000 −1.28932
$$155$$ −4.00000 + 6.92820i −0.321288 + 0.556487i
$$156$$ 0 0
$$157$$ 9.00000 + 15.5885i 0.718278 + 1.24409i 0.961681 + 0.274169i $$0.0884028\pi$$
−0.243403 + 0.969925i $$0.578264\pi$$
$$158$$ −4.00000 6.92820i −0.318223 0.551178i
$$159$$ 0 0
$$160$$ −5.00000 + 8.66025i −0.395285 + 0.684653i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 8.00000 0.626608 0.313304 0.949653i $$-0.398564\pi$$
0.313304 + 0.949653i $$0.398564\pi$$
$$164$$ 3.00000 5.19615i 0.234261 0.405751i
$$165$$ 0 0
$$166$$ −2.00000 3.46410i −0.155230 0.268866i
$$167$$ 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i $$-0.0664952\pi$$
−0.668730 + 0.743505i $$0.733162\pi$$
$$168$$ 0 0
$$169$$ −0.500000 + 0.866025i −0.0384615 + 0.0666173i
$$170$$ 4.00000 0.306786
$$171$$ 0 0
$$172$$ 12.0000 0.914991
$$173$$ −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i $$-0.906580\pi$$
0.729155 + 0.684349i $$0.239913\pi$$
$$174$$ 0 0
$$175$$ −2.00000 3.46410i −0.151186 0.261861i
$$176$$ 2.00000 + 3.46410i 0.150756 + 0.261116i
$$177$$ 0 0
$$178$$ 1.00000 1.73205i 0.0749532 0.129823i
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 2.00000 3.46410i 0.148250 0.256776i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.00000 + 3.46410i 0.147043 + 0.254686i
$$186$$ 0 0
$$187$$ −4.00000 + 6.92820i −0.292509 + 0.506640i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i $$-0.926799\pi$$
0.684244 + 0.729253i $$0.260132\pi$$
$$192$$ 0 0
$$193$$ −9.00000 15.5885i −0.647834 1.12208i −0.983639 0.180150i $$-0.942342\pi$$
0.335805 0.941932i $$-0.390992\pi$$
$$194$$ −5.00000 8.66025i −0.358979 0.621770i
$$195$$ 0 0
$$196$$ 4.50000 7.79423i 0.321429 0.556731i
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ −1.50000 + 2.59808i −0.106066 + 0.183712i
$$201$$ 0 0
$$202$$ 9.00000 + 15.5885i 0.633238 + 1.09680i
$$203$$ −20.0000 34.6410i −1.40372 2.43132i
$$204$$ 0 0
$$205$$ −6.00000 + 10.3923i −0.419058 + 0.725830i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.00000 −0.0693375
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 10.0000 + 17.3205i 0.688428 + 1.19239i 0.972346 + 0.233544i $$0.0750324\pi$$
−0.283918 + 0.958849i $$0.591634\pi$$
$$212$$ 3.00000 + 5.19615i 0.206041 + 0.356873i
$$213$$ 0 0
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ −24.0000 −1.63679
$$216$$ 0 0
$$217$$ −16.0000 −1.08615
$$218$$ 1.00000 1.73205i 0.0677285 0.117309i
$$219$$ 0 0
$$220$$ 4.00000 + 6.92820i 0.269680 + 0.467099i
$$221$$ −1.00000 1.73205i −0.0672673 0.116510i
$$222$$ 0 0
$$223$$ −2.00000 + 3.46410i −0.133930 + 0.231973i −0.925188 0.379509i $$-0.876093\pi$$
0.791258 + 0.611482i $$0.209426\pi$$
$$224$$ −20.0000 −1.33631
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ 10.0000 17.3205i 0.663723 1.14960i −0.315906 0.948790i $$-0.602309\pi$$
0.979630 0.200812i $$-0.0643581\pi$$
$$228$$ 0 0
$$229$$ 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i $$-0.0594799\pi$$
−0.652183 + 0.758062i $$0.726147\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −15.0000 + 25.9808i −0.984798 + 1.70572i
$$233$$ −14.0000 −0.917170 −0.458585 0.888650i $$-0.651644\pi$$
−0.458585 + 0.888650i $$0.651644\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 6.00000 10.3923i 0.390567 0.676481i
$$237$$ 0 0
$$238$$ 4.00000 + 6.92820i 0.259281 + 0.449089i
$$239$$ 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i $$0.116196\pi$$
−0.157893 + 0.987456i $$0.550470\pi$$
$$240$$ 0 0
$$241$$ −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i $$-0.937715\pi$$
0.658838 + 0.752285i $$0.271048\pi$$
$$242$$ 5.00000 0.321412
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ −9.00000 + 15.5885i −0.574989 + 0.995910i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 6.00000 + 10.3923i 0.381000 + 0.659912i
$$249$$ 0 0
$$250$$ 6.00000 10.3923i 0.379473 0.657267i
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 8.00000 13.8564i 0.501965 0.869428i
$$255$$ 0 0
$$256$$ 8.50000 + 14.7224i 0.531250 + 0.920152i
$$257$$ −13.0000 22.5167i −0.810918 1.40455i −0.912222 0.409695i $$-0.865635\pi$$
0.101305 0.994855i $$-0.467698\pi$$
$$258$$ 0 0
$$259$$ −4.00000 + 6.92820i −0.248548 + 0.430498i
$$260$$ −2.00000 −0.124035
$$261$$ 0 0
$$262$$ 4.00000 0.247121
$$263$$ −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i $$0.431818\pi$$
−0.952517 + 0.304487i $$0.901515\pi$$
$$264$$ 0 0
$$265$$ −6.00000 10.3923i −0.368577 0.638394i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −4.00000 + 6.92820i −0.244339 + 0.423207i
$$269$$ 22.0000 1.34136 0.670682 0.741745i $$-0.266002\pi$$
0.670682 + 0.741745i $$0.266002\pi$$
$$270$$ 0 0
$$271$$ −12.0000 −0.728948 −0.364474 0.931214i $$-0.618751\pi$$
−0.364474 + 0.931214i $$0.618751\pi$$
$$272$$ 1.00000 1.73205i 0.0606339 0.105021i
$$273$$ 0 0
$$274$$ −3.00000 5.19615i −0.181237 0.313911i
$$275$$ 2.00000 + 3.46410i 0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i $$-0.736206\pi$$
0.976231 + 0.216731i $$0.0695395\pi$$
$$278$$ 12.0000 0.719712
$$279$$ 0 0
$$280$$ 24.0000 1.43427
$$281$$ 5.00000 8.66025i 0.298275 0.516627i −0.677466 0.735554i $$-0.736922\pi$$
0.975741 + 0.218926i $$0.0702554\pi$$
$$282$$ 0 0
$$283$$ −6.00000 10.3923i −0.356663 0.617758i 0.630738 0.775996i $$-0.282752\pi$$
−0.987401 + 0.158237i $$0.949419\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −2.00000 + 3.46410i −0.118262 + 0.204837i
$$287$$ −24.0000 −1.41668
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 10.0000 17.3205i 0.587220 1.01710i
$$291$$ 0 0
$$292$$ 1.00000 + 1.73205i 0.0585206 + 0.101361i
$$293$$ 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i $$-0.110589\pi$$
−0.764990 + 0.644042i $$0.777256\pi$$
$$294$$ 0 0
$$295$$ −12.0000 + 20.7846i −0.698667 + 1.21013i
$$296$$ 6.00000 0.348743
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −24.0000 41.5692i −1.38334 2.39601i
$$302$$ −2.00000 3.46410i −0.115087 0.199337i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −4.00000 −0.229039
$$306$$ 0 0
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ −8.00000 + 13.8564i −0.455842 + 0.789542i
$$309$$ 0 0
$$310$$ −4.00000 6.92820i −0.227185 0.393496i
$$311$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$312$$ 0 0
$$313$$ 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i $$-0.779095\pi$$
0.938269 + 0.345907i $$0.112429\pi$$
$$314$$ −18.0000 −1.01580
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ −13.0000 + 22.5167i −0.730153 + 1.26466i 0.226665 + 0.973973i $$0.427218\pi$$
−0.956818 + 0.290689i $$0.906116\pi$$
$$318$$ 0 0
$$319$$ 20.0000 + 34.6410i 1.11979 + 1.93952i
$$320$$ −7.00000 12.1244i −0.391312 0.677772i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −1.00000 −0.0554700
$$326$$ −4.00000 + 6.92820i −0.221540 + 0.383718i
$$327$$ 0 0
$$328$$ 9.00000 + 15.5885i 0.496942 + 0.860729i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 8.00000 13.8564i 0.439720 0.761617i −0.557948 0.829876i $$-0.688411\pi$$
0.997668 + 0.0682590i $$0.0217444\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ 0 0
$$334$$ −8.00000 −0.437741
$$335$$ 8.00000 13.8564i 0.437087 0.757056i
$$336$$ 0 0
$$337$$ −9.00000 15.5885i −0.490261 0.849157i 0.509676 0.860366i $$-0.329765\pi$$
−0.999937 + 0.0112091i $$0.996432\pi$$
$$338$$ −0.500000 0.866025i −0.0271964 0.0471056i
$$339$$ 0 0
$$340$$ 2.00000 3.46410i 0.108465 0.187867i
$$341$$ 16.0000 0.866449
$$342$$ 0 0
$$343$$ −8.00000 −0.431959
$$344$$ −18.0000 + 31.1769i −0.970495 + 1.68095i
$$345$$ 0 0
$$346$$ −3.00000 5.19615i −0.161281 0.279347i
$$347$$ 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i $$-0.0622790\pi$$
−0.658824 + 0.752297i $$0.728946\pi$$
$$348$$ 0 0
$$349$$ 13.0000 22.5167i 0.695874 1.20529i −0.274011 0.961727i $$-0.588351\pi$$
0.969885 0.243563i $$-0.0783162\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ 20.0000 1.06600
$$353$$ 1.00000 1.73205i 0.0532246 0.0921878i −0.838186 0.545385i $$-0.816383\pi$$
0.891410 + 0.453197i $$0.149717\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −1.00000 1.73205i −0.0529999 0.0917985i
$$357$$ 0 0
$$358$$ −2.00000 + 3.46410i −0.105703 + 0.183083i
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 5.00000 8.66025i 0.262794 0.455173i
$$363$$ 0 0
$$364$$ −2.00000 3.46410i −0.104828 0.181568i
$$365$$ −2.00000 3.46410i −0.104685 0.181319i
$$366$$ 0 0
$$367$$ −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i $$-0.970461\pi$$
0.578101 + 0.815966i $$0.303794\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −4.00000 −0.207950
$$371$$ 12.0000 20.7846i 0.623009 1.07908i
$$372$$ 0 0
$$373$$ 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i $$0.0683772\pi$$
−0.303902 + 0.952703i $$0.598289\pi$$
$$374$$ −4.00000 6.92820i −0.206835 0.358249i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −10.0000 −0.515026
$$378$$ 0 0
$$379$$ −24.0000 −1.23280 −0.616399 0.787434i $$-0.711409\pi$$
−0.616399 + 0.787434i $$0.711409\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −4.00000 6.92820i −0.204658 0.354478i
$$383$$ 8.00000 + 13.8564i 0.408781 + 0.708029i 0.994753 0.102302i $$-0.0326207\pi$$
−0.585973 + 0.810331i $$0.699287\pi$$
$$384$$ 0 0
$$385$$ 16.0000 27.7128i 0.815436 1.41238i
$$386$$ 18.0000 0.916176
$$387$$ 0 0
$$388$$ −10.0000 −0.507673
$$389$$ −11.0000 + 19.0526i −0.557722 + 0.966003i 0.439964 + 0.898015i $$0.354991\pi$$
−0.997686 + 0.0679877i $$0.978342\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 13.5000 + 23.3827i 0.681853 + 1.18100i
$$393$$ 0 0
$$394$$ −9.00000 + 15.5885i −0.453413 + 0.785335i
$$395$$ 16.0000 0.805047
$$396$$ 0 0
$$397$$ 38.0000 1.90717 0.953583 0.301131i $$-0.0973643\pi$$
0.953583 + 0.301131i $$0.0973643\pi$$
$$398$$ −4.00000 + 6.92820i −0.200502 + 0.347279i
$$399$$ 0 0
$$400$$ −0.500000 0.866025i −0.0250000 0.0433013i
$$401$$ −11.0000 19.0526i −0.549314 0.951439i −0.998322 0.0579116i $$-0.981556\pi$$
0.449008 0.893528i $$-0.351777\pi$$
$$402$$ 0 0
$$403$$ −2.00000 + 3.46410i −0.0996271 + 0.172559i
$$404$$ 18.0000 0.895533
$$405$$ 0 0
$$406$$ 40.0000 1.98517
$$407$$ 4.00000 6.92820i 0.198273 0.343418i
$$408$$ 0 0
$$409$$ −17.0000 29.4449i −0.840596 1.45595i −0.889392 0.457146i $$-0.848872\pi$$
0.0487958 0.998809i $$-0.484462\pi$$
$$410$$ −6.00000 10.3923i −0.296319 0.513239i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −48.0000 −2.36193
$$414$$ 0 0
$$415$$ 8.00000 0.392705
$$416$$ −2.50000 + 4.33013i −0.122573 + 0.212302i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −2.00000 3.46410i −0.0977064 0.169232i 0.813029 0.582224i $$-0.197817\pi$$
−0.910735 + 0.412991i $$0.864484\pi$$
$$420$$ 0 0
$$421$$ 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i $$-0.754977\pi$$
0.961761 + 0.273890i $$0.0883103\pi$$
$$422$$ −20.0000 −0.973585
$$423$$ 0 0
$$424$$ −18.0000 −0.874157
$$425$$ 1.00000 1.73205i 0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ −4.00000 6.92820i −0.193574 0.335279i
$$428$$ 6.00000 + 10.3923i 0.290021 + 0.502331i
$$429$$ 0 0
$$430$$ 12.0000 20.7846i 0.578691 1.00232i
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 34.0000 1.63394 0.816968 0.576683i $$-0.195653\pi$$
0.816968 + 0.576683i $$0.195653\pi$$
$$434$$ 8.00000 13.8564i 0.384012 0.665129i
$$435$$ 0 0
$$436$$ −1.00000 1.73205i −0.0478913 0.0829502i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −16.0000 + 27.7128i −0.763638 + 1.32266i 0.177325 + 0.984152i $$0.443256\pi$$
−0.940963 + 0.338508i $$0.890078\pi$$
$$440$$ −24.0000 −1.14416
$$441$$ 0 0
$$442$$ 2.00000 0.0951303
$$443$$ 2.00000 3.46410i 0.0950229 0.164584i −0.814595 0.580030i $$-0.803041\pi$$
0.909618 + 0.415445i $$0.136374\pi$$
$$444$$ 0 0
$$445$$ 2.00000 + 3.46410i 0.0948091 + 0.164214i
$$446$$ −2.00000 3.46410i −0.0947027 0.164030i
$$447$$ 0 0
$$448$$ 14.0000 24.2487i 0.661438 1.14564i
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ 24.0000 1.13012
$$452$$ −3.00000 + 5.19615i −0.141108 + 0.244406i
$$453$$ 0 0
$$454$$ 10.0000 + 17.3205i 0.469323 + 0.812892i
$$455$$ 4.00000 + 6.92820i 0.187523 + 0.324799i
$$456$$ 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 −0.467269
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 19.0000 32.9090i 0.884918 1.53272i 0.0391109 0.999235i $$-0.487547\pi$$
0.845807 0.533488i $$-0.179119\pi$$
$$462$$ 0 0
$$463$$ −2.00000 3.46410i −0.0929479 0.160990i 0.815802 0.578331i $$-0.196296\pi$$
−0.908750 + 0.417340i $$0.862962\pi$$
$$464$$ −5.00000 8.66025i −0.232119 0.402042i
$$465$$ 0 0
$$466$$ 7.00000 12.1244i 0.324269 0.561650i
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 0 0
$$469$$ 32.0000 1.47762
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 18.0000 + 31.1769i 0.828517 + 1.43503i
$$473$$ 24.0000 + 41.5692i 1.10352 + 1.91135i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 8.00000 0.366679
$$477$$ 0 0
$$478$$ −24.0000 −1.09773
$$479$$ 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i $$-0.648611\pi$$
0.998392 0.0566937i $$-0.0180558\pi$$
$$480$$ 0 0
$$481$$ 1.00000 + 1.73205i 0.0455961 + 0.0789747i
$$482$$ −5.00000 8.66025i −0.227744 0.394464i
$$483$$ 0 0
$$484$$ 2.50000 4.33013i 0.113636 0.196824i
$$485$$ 20.0000 0.908153
$$486$$ 0 0
$$487$$ 12.0000 0.543772 0.271886 0.962329i $$-0.412353\pi$$
0.271886 + 0.962329i $$0.412353\pi$$
$$488$$ −3.00000 + 5.19615i −0.135804 + 0.235219i
$$489$$ 0 0
$$490$$ −9.00000 15.5885i −0.406579 0.704215i
$$491$$ 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i $$-0.0793863\pi$$
−0.698285 + 0.715820i $$0.746053\pi$$
$$492$$ 0 0
$$493$$ 10.0000 17.3205i 0.450377 0.780076i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 12.0000 + 20.7846i 0.537194 + 0.930447i 0.999054 + 0.0434940i $$0.0138489\pi$$
−0.461860 + 0.886953i $$0.652818\pi$$
$$500$$ −6.00000 10.3923i −0.268328 0.464758i
$$501$$ 0 0
$$502$$ 6.00000 10.3923i 0.267793 0.463831i
$$503$$ −8.00000 −0.356702 −0.178351 0.983967i $$-0.557076\pi$$
−0.178351 + 0.983967i $$0.557076\pi$$
$$504$$ 0 0
$$505$$ −36.0000 −1.60198
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −8.00000 13.8564i −0.354943 0.614779i
$$509$$ −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i $$-0.237801\pi$$
−0.955300 + 0.295637i $$0.904468\pi$$
$$510$$ 0 0
$$511$$ 4.00000 6.92820i 0.176950 0.306486i
$$512$$ −11.0000 −0.486136
$$513$$ 0 0
$$514$$ 26.0000 1.14681
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −4.00000 6.92820i −0.175750 0.304408i
$$519$$ 0 0
$$520$$ 3.00000 5.19615i 0.131559 0.227866i
$$521$$ 18.0000 0.788594 0.394297 0.918983i $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ 0 0
$$523$$ 44.0000 1.92399 0.961993 0.273075i $$-0.0880406\pi$$
0.961993 + 0.273075i $$0.0880406\pi$$
$$524$$ 2.00000 3.46410i 0.0873704 0.151330i
$$525$$ 0 0
$$526$$ −12.0000 20.7846i −0.523225 0.906252i
$$527$$ −4.00000 6.92820i −0.174243 0.301797i
$$528$$ 0 0
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 12.0000 0.521247
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3.00000 + 5.19615i −0.129944 + 0.225070i
$$534$$ 0 0
$$535$$ −12.0000 20.7846i −0.518805 0.898597i
$$536$$ −12.0000 20.7846i −0.518321 0.897758i
$$537$$ 0 0
$$538$$ −11.0000 + 19.0526i −0.474244 + 0.821414i
$$539$$ 36.0000 1.55063
$$540$$ 0 0
$$541$$ 30.0000 1.28980 0.644900 0.764267i $$-0.276899\pi$$
0.644900 + 0.764267i $$0.276899\pi$$
$$542$$ 6.00000 10.3923i 0.257722 0.446388i
$$543$$ 0 0
$$544$$ −5.00000 8.66025i −0.214373 0.371305i
$$545$$ 2.00000 + 3.46410i 0.0856706 + 0.148386i
$$546$$ 0 0
$$547$$ −2.00000 + 3.46410i −0.0855138 + 0.148114i −0.905610 0.424111i $$-0.860587\pi$$
0.820096 + 0.572226i $$0.193920\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 0 0
$$550$$ −4.00000 −0.170561
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 16.0000 + 27.7128i 0.680389 + 1.17847i
$$554$$ 5.00000 + 8.66025i 0.212430 + 0.367939i
$$555$$ 0 0
$$556$$ 6.00000 10.3923i 0.254457 0.440732i
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 0 0
$$559$$ −12.0000 −0.507546
$$560$$ −4.00000 + 6.92820i −0.169031 + 0.292770i
$$561$$ 0 0
$$562$$ 5.00000 + 8.66025i 0.210912 + 0.365311i
$$563$$ 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i $$-0.0852922\pi$$
−0.711445 + 0.702742i $$0.751959\pi$$
$$564$$ 0 0
$$565$$ 6.00000 10.3923i 0.252422 0.437208i
$$566$$ 12.0000 0.504398
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −17.0000 + 29.4449i −0.712677 + 1.23439i 0.251172 + 0.967943i $$0.419184\pi$$
−0.963849 + 0.266450i $$0.914149\pi$$
$$570$$ 0 0
$$571$$ 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i $$-0.139994\pi$$
−0.821138 + 0.570730i $$0.806660\pi$$
$$572$$ 2.00000 + 3.46410i 0.0836242 + 0.144841i
$$573$$ 0 0
$$574$$ 12.0000 20.7846i 0.500870 0.867533i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −46.0000 −1.91501 −0.957503 0.288425i $$-0.906868\pi$$
−0.957503 + 0.288425i $$0.906868\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ 0 0
$$580$$ −10.0000 17.3205i −0.415227 0.719195i
$$581$$ 8.00000 + 13.8564i 0.331896 + 0.574861i
$$582$$ 0 0
$$583$$ −12.0000 + 20.7846i −0.496989 + 0.860811i
$$584$$ −6.00000 −0.248282
$$585$$ 0 0
$$586$$ −6.00000 −0.247858
$$587$$ −14.0000 + 24.2487i −0.577842 + 1.00085i 0.417885 + 0.908500i $$0.362772\pi$$
−0.995726 + 0.0923513i $$0.970562\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −12.0000 20.7846i −0.494032 0.855689i
$$591$$ 0 0
$$592$$ −1.00000 + 1.73205i −0.0410997 + 0.0711868i
$$593$$ −26.0000 −1.06769 −0.533846 0.845582i $$-0.679254\pi$$
−0.533846 + 0.845582i $$0.679254\pi$$
$$594$$ 0 0
$$595$$ −16.0000 −0.655936
$$596$$ −3.00000 + 5.19615i −0.122885 + 0.212843i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 20.0000 + 34.6410i 0.817178 + 1.41539i 0.907754 + 0.419504i $$0.137796\pi$$
−0.0905757 + 0.995890i $$0.528871\pi$$
$$600$$ 0 0
$$601$$ 19.0000 32.9090i 0.775026 1.34238i −0.159754 0.987157i $$-0.551070\pi$$
0.934780 0.355228i $$-0.115597\pi$$
$$602$$ 48.0000 1.95633
$$603$$ 0 0
$$604$$ −4.00000 −0.162758
$$605$$ −5.00000 + 8.66025i −0.203279 + 0.352089i
$$606$$ 0 0
$$607$$ 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i $$-0.0614000\pi$$
−0.656744 + 0.754114i $$0.728067\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 2.00000 3.46410i 0.0809776 0.140257i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −2.00000 −0.0807792 −0.0403896 0.999184i $$-0.512860\pi$$
−0.0403896 + 0.999184i $$0.512860\pi$$
$$614$$ 8.00000 13.8564i 0.322854 0.559199i
$$615$$ 0 0
$$616$$ −24.0000 41.5692i −0.966988 1.67487i
$$617$$ −11.0000 19.0526i −0.442843 0.767027i 0.555056 0.831813i $$-0.312697\pi$$
−0.997899 + 0.0647859i $$0.979364\pi$$
$$618$$ 0 0
$$619$$ −12.0000 + 20.7846i −0.482321 + 0.835404i −0.999794 0.0202954i $$-0.993539\pi$$
0.517473 + 0.855699i $$0.326873\pi$$
$$620$$ −8.00000 −0.321288
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4.00000 + 6.92820i −0.160257 + 0.277573i
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 3.00000 + 5.19615i 0.119904 + 0.207680i
$$627$$ 0 0
$$628$$ −9.00000 + 15.5885i −0.359139 + 0.622047i
$$629$$ −4.00000 −0.159490
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ 12.0000 20.7846i 0.477334 0.826767i
$$633$$ 0 0
$$634$$ −13.0000 22.5167i −0.516296 0.894251i
$$635$$ 16.0000 + 27.7128i 0.634941 + 1.09975i
$$636$$ 0 0
$$637$$ −4.50000 + 7.79423i −0.178296 + 0.308819i
$$638$$ −40.0000 −1.58362
$$639$$ 0 0
$$640$$ −6.00000 −0.237171
$$641$$ −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i $$-0.845909\pi$$
0.845601 + 0.533816i $$0.179242\pi$$
$$642$$ 0 0
$$643$$ 20.0000 + 34.6410i 0.788723 + 1.36611i 0.926750 + 0.375680i $$0.122591\pi$$
−0.138027 + 0.990429i $$0.544076\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −8.00000 −0.314512 −0.157256 0.987558i $$-0.550265\pi$$
−0.157256 + 0.987558i $$0.550265\pi$$
$$648$$ 0 0
$$649$$ 48.0000 1.88416
$$650$$ 0.500000 0.866025i 0.0196116 0.0339683i
$$651$$ 0 0
$$652$$ 4.00000 + 6.92820i 0.156652 + 0.271329i
$$653$$ −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i $$-0.204122\pi$$
−0.918736 + 0.394872i $$0.870789\pi$$
$$654$$ 0 0
$$655$$ −4.00000 + 6.92820i −0.156293 + 0.270707i
$$656$$ −6.00000 −0.234261
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i $$0.350275\pi$$
−0.998584 + 0.0531977i $$0.983059\pi$$
$$660$$ 0 0
$$661$$ −15.0000 25.9808i −0.583432 1.01053i −0.995069 0.0991864i $$-0.968376\pi$$
0.411636 0.911348i $$-0.364957\pi$$
$$662$$ 8.00000 + 13.8564i 0.310929 + 0.538545i
$$663$$ 0 0
$$664$$ 6.00000 10.3923i 0.232845 0.403300i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −4.00000 + 6.92820i −0.154765 + 0.268060i
$$669$$ 0 0
$$670$$ 8.00000 + 13.8564i 0.309067 + 0.535320i
$$671$$ 4.00000 + 6.92820i 0.154418 + 0.267460i
$$672$$ 0 0
$$673$$ 7.00000 12.1244i 0.269830 0.467360i −0.698988 0.715134i $$-0.746366\pi$$
0.968818 + 0.247774i $$0.0796991\pi$$
$$674$$ 18.0000 0.693334
$$675$$ 0 0
$$676$$ −1.00000 −0.0384615
$$677$$ −11.0000 + 19.0526i −0.422764 + 0.732249i −0.996209 0.0869952i $$-0.972274\pi$$
0.573444 + 0.819244i $$0.305607\pi$$
$$678$$ 0 0
$$679$$ 20.0000 + 34.6410i 0.767530 + 1.32940i
$$680$$ 6.00000 + 10.3923i 0.230089 + 0.398527i
$$681$$ 0 0
$$682$$ −8.00000 + 13.8564i −0.306336 + 0.530589i
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ 12.0000 0.458496
$$686$$ 4.00000 6.92820i 0.152721 0.264520i
$$687$$ 0 0
$$688$$ −6.00000 10.3923i −0.228748 0.396203i
$$689$$ −3.00000 5.19615i −0.114291 0.197958i
$$690$$ 0 0
$$691$$ 12.0000 20.7846i 0.456502 0.790684i −0.542272 0.840203i $$-0.682436\pi$$
0.998773 + 0.0495194i $$0.0157690\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ −12.0000 + 20.7846i −0.455186 + 0.788405i
$$696$$ 0 0
$$697$$ −6.00000 10.3923i −0.227266 0.393637i
$$698$$ 13.0000 + 22.5167i 0.492057 + 0.852268i
$$699$$ 0 0
$$700$$ 2.00000 3.46410i 0.0755929 0.130931i
$$701$$ −34.0000 −1.28416 −0.642081 0.766637i $$-0.721929\pi$$
−0.642081 + 0.766637i $$0.721929\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −14.0000 + 24.2487i −0.527645 + 0.913908i
$$705$$ 0 0
$$706$$ 1.00000 + 1.73205i 0.0376355 + 0.0651866i
$$707$$ −36.0000 62.3538i −1.35392 2.34506i
$$708$$ 0 0
$$709$$ 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i $$-0.670978\pi$$
0.999908 + 0.0135434i $$0.00431112\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 6.00000 0.224860
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −4.00000 6.92820i −0.149592 0.259100i
$$716$$ 2.00000 + 3.46410i 0.0747435 + 0.129460i
$$717$$ 0 0
$$718$$ −12.0000 + 20.7846i −0.447836 + 0.775675i
$$719$$ −24.0000 −0.895049 −0.447524 0.894272i $$-0.647694\pi$$
−0.447524 + 0.894272i $$0.647694\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 9.50000 16.4545i 0.353553 0.612372i
$$723$$ 0 0
$$724$$ −5.00000 8.66025i −0.185824 0.321856i
$$725$$ −5.00000 8.66025i −0.185695 0.321634i
$$726$$ 0 0
$$727$$ −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i $$-0.880730\pi$$
0.782267 + 0.622944i $$0.214063\pi$$
$$728$$ 12.0000 0.444750
$$729$$ 0 0
$$730$$ 4.00000 0.148047
$$731$$ 12.0000 20.7846i 0.443836 0.768747i
$$732$$ 0 0
$$733$$ −15.0000 25.9808i −0.554038 0.959621i −0.997978 0.0635649i $$-0.979753\pi$$
0.443940 0.896056i $$-0.353580\pi$$
$$734$$ −8.00000 13.8564i −0.295285 0.511449i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −32.0000 −1.17874
$$738$$ 0 0
$$739$$ 32.0000 1.17714 0.588570 0.808447i $$-0.299691\pi$$
0.588570 + 0.808447i $$0.299691\pi$$
$$740$$ −2.00000 + 3.46410i −0.0735215 + 0.127343i
$$741$$ 0 0
$$742$$ 12.0000 + 20.7846i 0.440534 + 0.763027i
$$743$$ −24.0000 41.5692i −0.880475 1.52503i −0.850814 0.525467i $$-0.823891\pi$$
−0.0296605 0.999560i $$-0.509443\pi$$
$$744$$ 0 0
$$745$$ 6.00000 10.3923i 0.219823 0.380745i
$$746$$ −26.0000 −0.951928
$$747$$ 0 0
$$748$$ −8.00000 −0.292509
$$749$$ 24.0000 41.5692i 0.876941 1.51891i
$$750$$ 0 0
$$751$$ −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i $$-0.213294\pi$$
−0.929731 + 0.368238i $$0.879961\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 5.00000 8.66025i 0.182089 0.315388i
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ 22.0000 0.799604 0.399802 0.916602i $$-0.369079\pi$$
0.399802 + 0.916602i $$0.369079\pi$$
$$758$$ 12.0000 20.7846i 0.435860 0.754931i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 5.00000 + 8.66025i 0.181250 + 0.313934i 0.942306 0.334752i $$-0.108652\pi$$
−0.761057 + 0.648686i $$0.775319\pi$$
$$762$$ 0 0
$$763$$ −4.00000 + 6.92820i −0.144810 + 0.250818i
$$764$$ −8.00000 −0.289430
$$765$$ 0 0
$$766$$ −16.0000 −0.578103
$$767$$ −6.00000 + 10.3923i −0.216647 + 0.375244i
$$768$$ 0 0
$$769$$ 15.0000 + 25.9808i 0.540914 + 0.936890i 0.998852 + 0.0479061i $$0.0152548\pi$$
−0.457938 + 0.888984i $$0.651412\pi$$
$$770$$ 16.0000 + 27.7128i 0.576600 + 0.998700i
$$771$$ 0 0
$$772$$ 9.00000 15.5885i 0.323917 0.561041i
$$773$$ 10.0000 0.359675 0.179838 0.983696i $$-0.442443\pi$$
0.179838 + 0.983696i $$0.442443\pi$$
$$774$$ 0 0
$$775$$ −4.00000 −0.143684
$$776$$ 15.0000 25.9808i 0.538469 0.932655i
$$777$$ 0 0
$$778$$ −11.0000 19.0526i −0.394369 0.683067i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −9.00000 −0.321429
$$785$$ 18.0000 31.1769i 0.642448 1.11275i
$$786$$ 0 0
$$787$$ 16.0000 + 27.7128i 0.570338 + 0.987855i 0.996531 + 0.0832226i $$0.0265213\pi$$
−0.426193 + 0.904632i $$0.640145\pi$$
$$788$$ 9.00000 + 15.5885i 0.320612 + 0.555316i
$$789$$ 0 0
$$790$$ −8.00000 + 13.8564i −0.284627 + 0.492989i
$$791$$ 24.0000 0.853342
$$792$$ 0