Properties

 Label 1755.2.i.b.586.1 Level $1755$ Weight $2$ Character 1755.586 Analytic conductor $14.014$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1755 = 3^{3} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1755.i (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$14.0137455547$$ 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 585) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 586.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1755.586 Dual form 1755.2.i.b.1171.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -3.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -3.00000 q^{8} +1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(0.500000 - 0.866025i) q^{16} -2.00000 q^{17} -3.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{26} -2.00000 q^{28} +(2.50000 - 4.33013i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-2.50000 - 4.33013i) q^{32} +(1.00000 - 1.73205i) q^{34} +2.00000 q^{35} -5.00000 q^{37} +(1.50000 - 2.59808i) q^{38} +(1.50000 + 2.59808i) q^{40} +(4.00000 - 6.92820i) q^{43} -1.00000 q^{44} +(-1.00000 + 1.73205i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.500000 + 0.866025i) q^{52} -14.0000 q^{53} +1.00000 q^{55} +(3.00000 - 5.19615i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} -1.00000 q^{62} +7.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(-7.00000 - 12.1244i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-1.00000 + 1.73205i) q^{70} +6.00000 q^{73} +(2.50000 - 4.33013i) q^{74} +(-1.50000 - 2.59808i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(6.00000 - 10.3923i) q^{79} -1.00000 q^{80} +(-5.00000 + 8.66025i) q^{83} +(1.00000 + 1.73205i) q^{85} +(4.00000 + 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{88} -2.00000 q^{89} -2.00000 q^{91} +(-1.00000 - 1.73205i) q^{94} +(1.50000 + 2.59808i) q^{95} +(-0.500000 + 0.866025i) q^{97} -3.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10})$$ 2 * q - q^2 + q^4 - q^5 - 2 * q^7 - 6 * q^8 $$2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 2 q^{10} - q^{11} + q^{13} - 2 q^{14} + q^{16} - 4 q^{17} - 6 q^{19} + q^{20} - q^{22} - q^{25} - 2 q^{26} - 4 q^{28} + 5 q^{29} + q^{31} - 5 q^{32} + 2 q^{34} + 4 q^{35} - 10 q^{37} + 3 q^{38} + 3 q^{40} + 8 q^{43} - 2 q^{44} - 2 q^{47} + 3 q^{49} - q^{50} - q^{52} - 28 q^{53} + 2 q^{55} + 6 q^{56} + 5 q^{58} - 9 q^{59} + q^{61} - 2 q^{62} + 14 q^{64} + q^{65} - 14 q^{67} - 2 q^{68} - 2 q^{70} + 12 q^{73} + 5 q^{74} - 3 q^{76} - 2 q^{77} + 12 q^{79} - 2 q^{80} - 10 q^{83} + 2 q^{85} + 8 q^{86} + 3 q^{88} - 4 q^{89} - 4 q^{91} - 2 q^{94} + 3 q^{95} - q^{97} - 6 q^{98}+O(q^{100})$$ 2 * q - q^2 + q^4 - q^5 - 2 * q^7 - 6 * q^8 + 2 * q^10 - q^11 + q^13 - 2 * q^14 + q^16 - 4 * q^17 - 6 * q^19 + q^20 - q^22 - q^25 - 2 * q^26 - 4 * q^28 + 5 * q^29 + q^31 - 5 * q^32 + 2 * q^34 + 4 * q^35 - 10 * q^37 + 3 * q^38 + 3 * q^40 + 8 * q^43 - 2 * q^44 - 2 * q^47 + 3 * q^49 - q^50 - q^52 - 28 * q^53 + 2 * q^55 + 6 * q^56 + 5 * q^58 - 9 * q^59 + q^61 - 2 * q^62 + 14 * q^64 + q^65 - 14 * q^67 - 2 * q^68 - 2 * q^70 + 12 * q^73 + 5 * q^74 - 3 * q^76 - 2 * q^77 + 12 * q^79 - 2 * q^80 - 10 * q^83 + 2 * q^85 + 8 * q^86 + 3 * q^88 - 4 * q^89 - 4 * q^91 - 2 * q^94 + 3 * q^95 - q^97 - 6 * q^98

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$1081$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

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
$$5$$ −0.500000 0.866025i −0.223607 0.387298i
$$6$$ 0 0
$$7$$ −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i $$-0.956709\pi$$
0.612801 + 0.790237i $$0.290043\pi$$
$$8$$ −3.00000 −1.06066
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i $$-0.881504\pi$$
0.780750 + 0.624844i $$0.214837\pi$$
$$12$$ 0 0
$$13$$ 0.500000 + 0.866025i 0.138675 + 0.240192i
$$14$$ −1.00000 1.73205i −0.267261 0.462910i
$$15$$ 0 0
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ −3.00000 −0.688247 −0.344124 0.938924i $$-0.611824\pi$$
−0.344124 + 0.938924i $$0.611824\pi$$
$$20$$ 0.500000 0.866025i 0.111803 0.193649i
$$21$$ 0 0
$$22$$ −0.500000 0.866025i −0.106600 0.184637i
$$23$$ 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
$$28$$ −2.00000 −0.377964
$$29$$ 2.50000 4.33013i 0.464238 0.804084i −0.534928 0.844897i $$-0.679661\pi$$
0.999167 + 0.0408130i $$0.0129948\pi$$
$$30$$ 0 0
$$31$$ 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i $$-0.138043\pi$$
−0.817625 + 0.575751i $$0.804710\pi$$
$$32$$ −2.50000 4.33013i −0.441942 0.765466i
$$33$$ 0 0
$$34$$ 1.00000 1.73205i 0.171499 0.297044i
$$35$$ 2.00000 0.338062
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ 1.50000 2.59808i 0.243332 0.421464i
$$39$$ 0 0
$$40$$ 1.50000 + 2.59808i 0.237171 + 0.410792i
$$41$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$42$$ 0 0
$$43$$ 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i $$-0.624505\pi$$
0.991241 0.132068i $$-0.0421616\pi$$
$$44$$ −1.00000 −0.150756
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i $$-0.879930\pi$$
0.783830 + 0.620975i $$0.213263\pi$$
$$48$$ 0 0
$$49$$ 1.50000 + 2.59808i 0.214286 + 0.371154i
$$50$$ −0.500000 0.866025i −0.0707107 0.122474i
$$51$$ 0 0
$$52$$ −0.500000 + 0.866025i −0.0693375 + 0.120096i
$$53$$ −14.0000 −1.92305 −0.961524 0.274721i $$-0.911414\pi$$
−0.961524 + 0.274721i $$0.911414\pi$$
$$54$$ 0 0
$$55$$ 1.00000 0.134840
$$56$$ 3.00000 5.19615i 0.400892 0.694365i
$$57$$ 0 0
$$58$$ 2.50000 + 4.33013i 0.328266 + 0.568574i
$$59$$ −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i $$-0.967427\pi$$
0.408919 0.912571i $$-0.365906\pi$$
$$60$$ 0 0
$$61$$ 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i $$-0.812942\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ −1.00000 −0.127000
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 0.500000 0.866025i 0.0620174 0.107417i
$$66$$ 0 0
$$67$$ −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i $$-0.840109\pi$$
0.0212861 0.999773i $$-0.493224\pi$$
$$68$$ −1.00000 1.73205i −0.121268 0.210042i
$$69$$ 0 0
$$70$$ −1.00000 + 1.73205i −0.119523 + 0.207020i
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 2.50000 4.33013i 0.290619 0.503367i
$$75$$ 0 0
$$76$$ −1.50000 2.59808i −0.172062 0.298020i
$$77$$ −1.00000 1.73205i −0.113961 0.197386i
$$78$$ 0 0
$$79$$ 6.00000 10.3923i 0.675053 1.16923i −0.301401 0.953498i $$-0.597454\pi$$
0.976453 0.215728i $$-0.0692125\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −5.00000 + 8.66025i −0.548821 + 0.950586i 0.449534 + 0.893263i $$0.351590\pi$$
−0.998356 + 0.0573233i $$0.981743\pi$$
$$84$$ 0 0
$$85$$ 1.00000 + 1.73205i 0.108465 + 0.187867i
$$86$$ 4.00000 + 6.92820i 0.431331 + 0.747087i
$$87$$ 0 0
$$88$$ 1.50000 2.59808i 0.159901 0.276956i
$$89$$ −2.00000 −0.212000 −0.106000 0.994366i $$-0.533804\pi$$
−0.106000 + 0.994366i $$0.533804\pi$$
$$90$$ 0 0
$$91$$ −2.00000 −0.209657
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −1.00000 1.73205i −0.103142 0.178647i
$$95$$ 1.50000 + 2.59808i 0.153897 + 0.266557i
$$96$$ 0 0
$$97$$ −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i $$-0.849500\pi$$
0.839525 + 0.543321i $$0.182833\pi$$
$$98$$ −3.00000 −0.303046
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i $$-0.785646\pi$$
0.930953 + 0.365140i $$0.118979\pi$$
$$102$$ 0 0
$$103$$ 0.500000 + 0.866025i 0.0492665 + 0.0853320i 0.889607 0.456727i $$-0.150978\pi$$
−0.840341 + 0.542059i $$0.817645\pi$$
$$104$$ −1.50000 2.59808i −0.147087 0.254762i
$$105$$ 0 0
$$106$$ 7.00000 12.1244i 0.679900 1.17762i
$$107$$ −19.0000 −1.83680 −0.918400 0.395654i $$-0.870518\pi$$
−0.918400 + 0.395654i $$0.870518\pi$$
$$108$$ 0 0
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ −0.500000 + 0.866025i −0.0476731 + 0.0825723i
$$111$$ 0 0
$$112$$ 1.00000 + 1.73205i 0.0944911 + 0.163663i
$$113$$ 5.00000 + 8.66025i 0.470360 + 0.814688i 0.999425 0.0338931i $$-0.0107906\pi$$
−0.529065 + 0.848581i $$0.677457\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 5.00000 0.464238
$$117$$ 0 0
$$118$$ 9.00000 0.828517
$$119$$ 2.00000 3.46410i 0.183340 0.317554i
$$120$$ 0 0
$$121$$ 5.00000 + 8.66025i 0.454545 + 0.787296i
$$122$$ 0.500000 + 0.866025i 0.0452679 + 0.0784063i
$$123$$ 0 0
$$124$$ −0.500000 + 0.866025i −0.0449013 + 0.0777714i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 1.50000 2.59808i 0.132583 0.229640i
$$129$$ 0 0
$$130$$ 0.500000 + 0.866025i 0.0438529 + 0.0759555i
$$131$$ −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
$$133$$ 3.00000 5.19615i 0.260133 0.450564i
$$134$$ 14.0000 1.20942
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ −2.50000 + 4.33013i −0.213589 + 0.369948i −0.952835 0.303488i $$-0.901849\pi$$
0.739246 + 0.673436i $$0.235182\pi$$
$$138$$ 0 0
$$139$$ −6.00000 10.3923i −0.508913 0.881464i −0.999947 0.0103230i $$-0.996714\pi$$
0.491033 0.871141i $$-0.336619\pi$$
$$140$$ 1.00000 + 1.73205i 0.0845154 + 0.146385i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1.00000 −0.0836242
$$144$$ 0 0
$$145$$ −5.00000 −0.415227
$$146$$ −3.00000 + 5.19615i −0.248282 + 0.430037i
$$147$$ 0 0
$$148$$ −2.50000 4.33013i −0.205499 0.355934i
$$149$$ 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
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 9.00000 0.729996
$$153$$ 0 0
$$154$$ 2.00000 0.161165
$$155$$ 0.500000 0.866025i 0.0401610 0.0695608i
$$156$$ 0 0
$$157$$ 3.00000 + 5.19615i 0.239426 + 0.414698i 0.960550 0.278108i $$-0.0897074\pi$$
−0.721124 + 0.692806i $$0.756374\pi$$
$$158$$ 6.00000 + 10.3923i 0.477334 + 0.826767i
$$159$$ 0 0
$$160$$ −2.50000 + 4.33013i −0.197642 + 0.342327i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −12.0000 −0.939913 −0.469956 0.882690i $$-0.655730\pi$$
−0.469956 + 0.882690i $$0.655730\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −5.00000 8.66025i −0.388075 0.672166i
$$167$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$168$$ 0 0
$$169$$ −0.500000 + 0.866025i −0.0384615 + 0.0666173i
$$170$$ −2.00000 −0.153393
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ 6.00000 10.3923i 0.456172 0.790112i −0.542583 0.840002i $$-0.682554\pi$$
0.998755 + 0.0498898i $$0.0158870\pi$$
$$174$$ 0 0
$$175$$ −1.00000 1.73205i −0.0755929 0.130931i
$$176$$ 0.500000 + 0.866025i 0.0376889 + 0.0652791i
$$177$$ 0 0
$$178$$ 1.00000 1.73205i 0.0749532 0.129823i
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ 0 0
$$181$$ 17.0000 1.26360 0.631800 0.775131i $$-0.282316\pi$$
0.631800 + 0.775131i $$0.282316\pi$$
$$182$$ 1.00000 1.73205i 0.0741249 0.128388i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.50000 + 4.33013i 0.183804 + 0.318357i
$$186$$ 0 0
$$187$$ 1.00000 1.73205i 0.0731272 0.126660i
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ −3.00000 −0.217643
$$191$$ 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i $$-0.607592\pi$$
0.982828 0.184525i $$-0.0590746\pi$$
$$192$$ 0 0
$$193$$ −6.50000 11.2583i −0.467880 0.810392i 0.531446 0.847092i $$-0.321649\pi$$
−0.999326 + 0.0366998i $$0.988315\pi$$
$$194$$ −0.500000 0.866025i −0.0358979 0.0621770i
$$195$$ 0 0
$$196$$ −1.50000 + 2.59808i −0.107143 + 0.185577i
$$197$$ −15.0000 −1.06871 −0.534353 0.845262i $$-0.679445\pi$$
−0.534353 + 0.845262i $$0.679445\pi$$
$$198$$ 0 0
$$199$$ −22.0000 −1.55954 −0.779769 0.626067i $$-0.784664\pi$$
−0.779769 + 0.626067i $$0.784664\pi$$
$$200$$ 1.50000 2.59808i 0.106066 0.183712i
$$201$$ 0 0
$$202$$ 1.50000 + 2.59808i 0.105540 + 0.182800i
$$203$$ 5.00000 + 8.66025i 0.350931 + 0.607831i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −1.00000 −0.0696733
$$207$$ 0 0
$$208$$ 1.00000 0.0693375
$$209$$ 1.50000 2.59808i 0.103757 0.179713i
$$210$$ 0 0
$$211$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$212$$ −7.00000 12.1244i −0.480762 0.832704i
$$213$$ 0 0
$$214$$ 9.50000 16.4545i 0.649407 1.12481i
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ −2.00000 −0.135769
$$218$$ 7.00000 12.1244i 0.474100 0.821165i
$$219$$ 0 0
$$220$$ 0.500000 + 0.866025i 0.0337100 + 0.0583874i
$$221$$ −1.00000 1.73205i −0.0672673 0.116510i
$$222$$ 0 0
$$223$$ 13.0000 22.5167i 0.870544 1.50783i 0.00910984 0.999959i $$-0.497100\pi$$
0.861435 0.507869i $$-0.169566\pi$$
$$224$$ 10.0000 0.668153
$$225$$ 0 0
$$226$$ −10.0000 −0.665190
$$227$$ −13.0000 + 22.5167i −0.862840 + 1.49448i 0.00633544 + 0.999980i $$0.497983\pi$$
−0.869176 + 0.494503i $$0.835350\pi$$
$$228$$ 0 0
$$229$$ 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i $$0.0106368\pi$$
−0.470787 + 0.882247i $$0.656030\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −7.50000 + 12.9904i −0.492399 + 0.852860i
$$233$$ 14.0000 0.917170 0.458585 0.888650i $$-0.348356\pi$$
0.458585 + 0.888650i $$0.348356\pi$$
$$234$$ 0 0
$$235$$ 2.00000 0.130466
$$236$$ 4.50000 7.79423i 0.292925 0.507361i
$$237$$ 0 0
$$238$$ 2.00000 + 3.46410i 0.129641 + 0.224544i
$$239$$ 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i $$-0.00543724\pi$$
−0.514719 + 0.857359i $$0.672104\pi$$
$$240$$ 0 0
$$241$$ −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i $$-0.937715\pi$$
0.658838 + 0.752285i $$0.271048\pi$$
$$242$$ −10.0000 −0.642824
$$243$$ 0 0
$$244$$ 1.00000 0.0640184
$$245$$ 1.50000 2.59808i 0.0958315 0.165985i
$$246$$ 0 0
$$247$$ −1.50000 2.59808i −0.0954427 0.165312i
$$248$$ −1.50000 2.59808i −0.0952501 0.164978i
$$249$$ 0 0
$$250$$ −0.500000 + 0.866025i −0.0316228 + 0.0547723i
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 4.00000 6.92820i 0.250982 0.434714i
$$255$$ 0 0
$$256$$ 8.50000 + 14.7224i 0.531250 + 0.920152i
$$257$$ −14.0000 24.2487i −0.873296 1.51259i −0.858567 0.512702i $$-0.828645\pi$$
−0.0147291 0.999892i $$-0.504689\pi$$
$$258$$ 0 0
$$259$$ 5.00000 8.66025i 0.310685 0.538122i
$$260$$ 1.00000 0.0620174
$$261$$ 0 0
$$262$$ 4.00000 0.247121
$$263$$ −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i $$-0.997543\pi$$
0.506669 + 0.862141i $$0.330877\pi$$
$$264$$ 0 0
$$265$$ 7.00000 + 12.1244i 0.430007 + 0.744793i
$$266$$ 3.00000 + 5.19615i 0.183942 + 0.318597i
$$267$$ 0 0
$$268$$ 7.00000 12.1244i 0.427593 0.740613i
$$269$$ −3.00000 −0.182913 −0.0914566 0.995809i $$-0.529152\pi$$
−0.0914566 + 0.995809i $$0.529152\pi$$
$$270$$ 0 0
$$271$$ −7.00000 −0.425220 −0.212610 0.977137i $$-0.568196\pi$$
−0.212610 + 0.977137i $$0.568196\pi$$
$$272$$ −1.00000 + 1.73205i −0.0606339 + 0.105021i
$$273$$ 0 0
$$274$$ −2.50000 4.33013i −0.151031 0.261593i
$$275$$ −0.500000 0.866025i −0.0301511 0.0522233i
$$276$$ 0 0
$$277$$ −5.00000 + 8.66025i −0.300421 + 0.520344i −0.976231 0.216731i $$-0.930460\pi$$
0.675810 + 0.737075i $$0.263794\pi$$
$$278$$ 12.0000 0.719712
$$279$$ 0 0
$$280$$ −6.00000 −0.358569
$$281$$ −6.00000 + 10.3923i −0.357930 + 0.619953i −0.987615 0.156898i $$-0.949851\pi$$
0.629685 + 0.776851i $$0.283184\pi$$
$$282$$ 0 0
$$283$$ 12.5000 + 21.6506i 0.743048 + 1.28700i 0.951101 + 0.308879i $$0.0999539\pi$$
−0.208053 + 0.978117i $$0.566713\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0.500000 0.866025i 0.0295656 0.0512092i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 2.50000 4.33013i 0.146805 0.254274i
$$291$$ 0 0
$$292$$ 3.00000 + 5.19615i 0.175562 + 0.304082i
$$293$$ 0.500000 + 0.866025i 0.0292103 + 0.0505937i 0.880261 0.474490i $$-0.157367\pi$$
−0.851051 + 0.525084i $$0.824034\pi$$
$$294$$ 0 0
$$295$$ −4.50000 + 7.79423i −0.262000 + 0.453798i
$$296$$ 15.0000 0.871857
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 8.00000 + 13.8564i 0.461112 + 0.798670i
$$302$$ 4.00000 + 6.92820i 0.230174 + 0.398673i
$$303$$ 0 0
$$304$$ −1.50000 + 2.59808i −0.0860309 + 0.149010i
$$305$$ −1.00000 −0.0572598
$$306$$ 0 0
$$307$$ 2.00000 0.114146 0.0570730 0.998370i $$-0.481823\pi$$
0.0570730 + 0.998370i $$0.481823\pi$$
$$308$$ 1.00000 1.73205i 0.0569803 0.0986928i
$$309$$ 0 0
$$310$$ 0.500000 + 0.866025i 0.0283981 + 0.0491869i
$$311$$ −2.00000 3.46410i −0.113410 0.196431i 0.803733 0.594990i $$-0.202844\pi$$
−0.917143 + 0.398559i $$0.869511\pi$$
$$312$$ 0 0
$$313$$ 14.0000 24.2487i 0.791327 1.37062i −0.133819 0.991006i $$-0.542724\pi$$
0.925146 0.379612i $$-0.123943\pi$$
$$314$$ −6.00000 −0.338600
$$315$$ 0 0
$$316$$ 12.0000 0.675053
$$317$$ −13.5000 + 23.3827i −0.758236 + 1.31330i 0.185514 + 0.982642i $$0.440605\pi$$
−0.943750 + 0.330661i $$0.892728\pi$$
$$318$$ 0 0
$$319$$ 2.50000 + 4.33013i 0.139973 + 0.242441i
$$320$$ −3.50000 6.06218i −0.195656 0.338886i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 6.00000 0.333849
$$324$$ 0 0
$$325$$ −1.00000 −0.0554700
$$326$$ 6.00000 10.3923i 0.332309 0.575577i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −2.00000 3.46410i −0.110264 0.190982i
$$330$$ 0 0
$$331$$ −13.5000 + 23.3827i −0.742027 + 1.28523i 0.209544 + 0.977799i $$0.432802\pi$$
−0.951571 + 0.307429i $$0.900531\pi$$
$$332$$ −10.0000 −0.548821
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −7.00000 + 12.1244i −0.382451 + 0.662424i
$$336$$ 0 0
$$337$$ 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i $$0.0378512\pi$$
−0.393730 + 0.919226i $$0.628816\pi$$
$$338$$ −0.500000 0.866025i −0.0271964 0.0471056i
$$339$$ 0 0
$$340$$ −1.00000 + 1.73205i −0.0542326 + 0.0939336i
$$341$$ −1.00000 −0.0541530
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ −12.0000 + 20.7846i −0.646997 + 1.12063i
$$345$$ 0 0
$$346$$ 6.00000 + 10.3923i 0.322562 + 0.558694i
$$347$$ 8.50000 + 14.7224i 0.456304 + 0.790342i 0.998762 0.0497412i $$-0.0158397\pi$$
−0.542458 + 0.840083i $$0.682506\pi$$
$$348$$ 0 0
$$349$$ −6.00000 + 10.3923i −0.321173 + 0.556287i −0.980730 0.195367i $$-0.937410\pi$$
0.659558 + 0.751654i $$0.270744\pi$$
$$350$$ 2.00000 0.106904
$$351$$ 0 0
$$352$$ 5.00000 0.266501
$$353$$ −1.50000 + 2.59808i −0.0798369 + 0.138282i −0.903179 0.429263i $$-0.858773\pi$$
0.823343 + 0.567545i $$0.192107\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −1.00000 1.73205i −0.0529999 0.0917985i
$$357$$ 0 0
$$358$$ −9.00000 + 15.5885i −0.475665 + 0.823876i
$$359$$ 31.0000 1.63612 0.818059 0.575135i $$-0.195050\pi$$
0.818059 + 0.575135i $$0.195050\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ −8.50000 + 14.7224i −0.446750 + 0.773794i
$$363$$ 0 0
$$364$$ −1.00000 1.73205i −0.0524142 0.0907841i
$$365$$ −3.00000 5.19615i −0.157027 0.271979i
$$366$$ 0 0
$$367$$ −12.5000 + 21.6506i −0.652495 + 1.13015i 0.330021 + 0.943974i $$0.392944\pi$$
−0.982516 + 0.186180i $$0.940389\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −5.00000 −0.259938
$$371$$ 14.0000 24.2487i 0.726844 1.25893i
$$372$$ 0 0
$$373$$ 10.0000 + 17.3205i 0.517780 + 0.896822i 0.999787 + 0.0206542i $$0.00657489\pi$$
−0.482006 + 0.876168i $$0.660092\pi$$
$$374$$ 1.00000 + 1.73205i 0.0517088 + 0.0895622i
$$375$$ 0 0
$$376$$ 3.00000 5.19615i 0.154713 0.267971i
$$377$$ 5.00000 0.257513
$$378$$ 0 0
$$379$$ −23.0000 −1.18143 −0.590715 0.806880i $$-0.701154\pi$$
−0.590715 + 0.806880i $$0.701154\pi$$
$$380$$ −1.50000 + 2.59808i −0.0769484 + 0.133278i
$$381$$ 0 0
$$382$$ 9.00000 + 15.5885i 0.460480 + 0.797575i
$$383$$ −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i $$-0.265853\pi$$
−0.977613 + 0.210411i $$0.932520\pi$$
$$384$$ 0 0
$$385$$ −1.00000 + 1.73205i −0.0509647 + 0.0882735i
$$386$$ 13.0000 0.661683
$$387$$ 0 0
$$388$$ −1.00000 −0.0507673
$$389$$ −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
$$392$$ −4.50000 7.79423i −0.227284 0.393668i
$$393$$ 0 0
$$394$$ 7.50000 12.9904i 0.377845 0.654446i
$$395$$ −12.0000 −0.603786
$$396$$ 0 0
$$397$$ −30.0000 −1.50566 −0.752828 0.658217i $$-0.771311\pi$$
−0.752828 + 0.658217i $$0.771311\pi$$
$$398$$ 11.0000 19.0526i 0.551380 0.955018i
$$399$$ 0 0
$$400$$ 0.500000 + 0.866025i 0.0250000 + 0.0433013i
$$401$$ 14.0000 + 24.2487i 0.699127 + 1.21092i 0.968770 + 0.247962i $$0.0797610\pi$$
−0.269643 + 0.962960i $$0.586906\pi$$
$$402$$ 0 0
$$403$$ −0.500000 + 0.866025i −0.0249068 + 0.0431398i
$$404$$ 3.00000 0.149256
$$405$$ 0 0
$$406$$ −10.0000 −0.496292
$$407$$ 2.50000 4.33013i 0.123920 0.214636i
$$408$$ 0 0
$$409$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −0.500000 + 0.866025i −0.0246332 + 0.0426660i
$$413$$ 18.0000 0.885722
$$414$$ 0 0
$$415$$ 10.0000 0.490881
$$416$$ 2.50000 4.33013i 0.122573 0.212302i
$$417$$ 0 0
$$418$$ 1.50000 + 2.59808i 0.0733674 + 0.127076i
$$419$$ 10.0000 + 17.3205i 0.488532 + 0.846162i 0.999913 0.0131919i $$-0.00419923\pi$$
−0.511381 + 0.859354i $$0.670866\pi$$
$$420$$ 0 0
$$421$$ −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i $$-0.911690\pi$$
0.718076 + 0.695965i $$0.245023\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 42.0000 2.03970
$$425$$ 1.00000 1.73205i 0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ 1.00000 + 1.73205i 0.0483934 + 0.0838198i
$$428$$ −9.50000 16.4545i −0.459200 0.795357i
$$429$$ 0 0
$$430$$ 4.00000 6.92820i 0.192897 0.334108i
$$431$$ −17.0000 −0.818861 −0.409431 0.912341i $$-0.634273\pi$$
−0.409431 + 0.912341i $$0.634273\pi$$
$$432$$ 0 0
$$433$$ −38.0000 −1.82616 −0.913082 0.407777i $$-0.866304\pi$$
−0.913082 + 0.407777i $$0.866304\pi$$
$$434$$ 1.00000 1.73205i 0.0480015 0.0831411i
$$435$$ 0 0
$$436$$ −7.00000 12.1244i −0.335239 0.580651i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$440$$ −3.00000 −0.143019
$$441$$ 0 0
$$442$$ 2.00000 0.0951303
$$443$$ −3.50000 + 6.06218i −0.166290 + 0.288023i −0.937113 0.349027i $$-0.886512\pi$$
0.770823 + 0.637050i $$0.219845\pi$$
$$444$$ 0 0
$$445$$ 1.00000 + 1.73205i 0.0474045 + 0.0821071i
$$446$$ 13.0000 + 22.5167i 0.615568 + 1.06619i
$$447$$ 0 0
$$448$$ −7.00000 + 12.1244i −0.330719 + 0.572822i
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −5.00000 + 8.66025i −0.235180 + 0.407344i
$$453$$ 0 0
$$454$$ −13.0000 22.5167i −0.610120 1.05676i
$$455$$ 1.00000 + 1.73205i 0.0468807 + 0.0811998i
$$456$$ 0 0
$$457$$ −13.0000 + 22.5167i −0.608114 + 1.05328i 0.383437 + 0.923567i $$0.374740\pi$$
−0.991551 + 0.129718i $$0.958593\pi$$
$$458$$ −16.0000 −0.747631
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −13.0000 + 22.5167i −0.605470 + 1.04871i 0.386507 + 0.922287i $$0.373682\pi$$
−0.991977 + 0.126419i $$0.959652\pi$$
$$462$$ 0 0
$$463$$ 3.00000 + 5.19615i 0.139422 + 0.241486i 0.927278 0.374374i $$-0.122142\pi$$
−0.787856 + 0.615859i $$0.788809\pi$$
$$464$$ −2.50000 4.33013i −0.116060 0.201021i
$$465$$ 0 0
$$466$$ −7.00000 + 12.1244i −0.324269 + 0.561650i
$$467$$ 28.0000 1.29569 0.647843 0.761774i $$-0.275671\pi$$
0.647843 + 0.761774i $$0.275671\pi$$
$$468$$ 0 0
$$469$$ 28.0000 1.29292
$$470$$ −1.00000 + 1.73205i −0.0461266 + 0.0798935i
$$471$$ 0 0
$$472$$ 13.5000 + 23.3827i 0.621388 + 1.07628i
$$473$$ 4.00000 + 6.92820i 0.183920 + 0.318559i
$$474$$ 0 0
$$475$$ 1.50000 2.59808i 0.0688247 0.119208i
$$476$$ 4.00000 0.183340
$$477$$ 0 0
$$478$$ −15.0000 −0.686084
$$479$$ 7.50000 12.9904i 0.342684 0.593546i −0.642246 0.766498i $$-0.721997\pi$$
0.984930 + 0.172953i $$0.0553307\pi$$
$$480$$ 0 0
$$481$$ −2.50000 4.33013i −0.113990 0.197437i
$$482$$ −5.00000 8.66025i −0.227744 0.394464i
$$483$$ 0 0
$$484$$ −5.00000 + 8.66025i −0.227273 + 0.393648i
$$485$$ 1.00000 0.0454077
$$486$$ 0 0
$$487$$ −34.0000 −1.54069 −0.770344 0.637629i $$-0.779915\pi$$
−0.770344 + 0.637629i $$0.779915\pi$$
$$488$$ −1.50000 + 2.59808i −0.0679018 + 0.117609i
$$489$$ 0 0
$$490$$ 1.50000 + 2.59808i 0.0677631 + 0.117369i
$$491$$ −3.00000 5.19615i −0.135388 0.234499i 0.790358 0.612646i $$-0.209895\pi$$
−0.925746 + 0.378147i $$0.876561\pi$$
$$492$$ 0 0
$$493$$ −5.00000 + 8.66025i −0.225189 + 0.390038i
$$494$$ 3.00000 0.134976
$$495$$ 0 0
$$496$$ 1.00000 0.0449013
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i $$-0.951061\pi$$
0.361478 0.932381i $$-0.382272\pi$$
$$500$$ 0.500000 + 0.866025i 0.0223607 + 0.0387298i
$$501$$ 0 0
$$502$$ 6.00000 10.3923i 0.267793 0.463831i
$$503$$ 9.00000 0.401290 0.200645 0.979664i $$-0.435696\pi$$
0.200645 + 0.979664i $$0.435696\pi$$
$$504$$ 0 0
$$505$$ −3.00000 −0.133498
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −4.00000 6.92820i −0.177471 0.307389i
$$509$$ −12.0000 20.7846i −0.531891 0.921262i −0.999307 0.0372243i $$-0.988148\pi$$
0.467416 0.884037i $$-0.345185\pi$$
$$510$$ 0 0
$$511$$ −6.00000 + 10.3923i −0.265424 + 0.459728i
$$512$$ −11.0000 −0.486136
$$513$$ 0 0
$$514$$ 28.0000 1.23503
$$515$$ 0.500000 0.866025i 0.0220326 0.0381616i
$$516$$ 0 0
$$517$$ −1.00000 1.73205i −0.0439799 0.0761755i
$$518$$ 5.00000 + 8.66025i 0.219687 + 0.380510i
$$519$$ 0 0
$$520$$ −1.50000 + 2.59808i −0.0657794 + 0.113933i
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 0 0
$$523$$ −15.0000 −0.655904 −0.327952 0.944694i $$-0.606358\pi$$
−0.327952 + 0.944694i $$0.606358\pi$$
$$524$$ 2.00000 3.46410i 0.0873704 0.151330i
$$525$$ 0 0
$$526$$ −8.00000 13.8564i −0.348817 0.604168i
$$527$$ −1.00000 1.73205i −0.0435607 0.0754493i
$$528$$ 0 0
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ −14.0000 −0.608121
$$531$$ 0 0
$$532$$ 6.00000 0.260133
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 9.50000 + 16.4545i 0.410721 + 0.711389i
$$536$$ 21.0000 + 36.3731i 0.907062 + 1.57108i
$$537$$ 0 0
$$538$$ 1.50000 2.59808i 0.0646696 0.112011i
$$539$$ −3.00000 −0.129219
$$540$$ 0 0
$$541$$ 32.0000 1.37579 0.687894 0.725811i $$-0.258536\pi$$
0.687894 + 0.725811i $$0.258536\pi$$
$$542$$ 3.50000 6.06218i 0.150338 0.260393i
$$543$$ 0 0
$$544$$ 5.00000 + 8.66025i 0.214373 + 0.371305i
$$545$$ 7.00000 + 12.1244i 0.299847 + 0.519350i
$$546$$ 0 0
$$547$$ 7.50000 12.9904i 0.320677 0.555429i −0.659951 0.751309i $$-0.729423\pi$$
0.980628 + 0.195880i $$0.0627563\pi$$
$$548$$ −5.00000 −0.213589
$$549$$ 0 0
$$550$$ 1.00000 0.0426401
$$551$$ −7.50000 + 12.9904i −0.319511 + 0.553409i
$$552$$ 0 0
$$553$$ 12.0000 + 20.7846i 0.510292 + 0.883852i
$$554$$ −5.00000 8.66025i −0.212430 0.367939i
$$555$$ 0 0
$$556$$ 6.00000 10.3923i 0.254457 0.440732i
$$557$$ 5.00000 0.211857 0.105928 0.994374i $$-0.466219\pi$$
0.105928 + 0.994374i $$0.466219\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 1.00000 1.73205i 0.0422577 0.0731925i
$$561$$ 0 0
$$562$$ −6.00000 10.3923i −0.253095 0.438373i
$$563$$ −9.50000 16.4545i −0.400377 0.693474i 0.593394 0.804912i $$-0.297788\pi$$
−0.993771 + 0.111438i $$0.964454\pi$$
$$564$$ 0 0
$$565$$ 5.00000 8.66025i 0.210352 0.364340i
$$566$$ −25.0000 −1.05083
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −5.50000 + 9.52628i −0.230572 + 0.399362i −0.957977 0.286846i $$-0.907393\pi$$
0.727405 + 0.686209i $$0.240726\pi$$
$$570$$ 0 0
$$571$$ −6.00000 10.3923i −0.251092 0.434904i 0.712735 0.701434i $$-0.247456\pi$$
−0.963827 + 0.266529i $$0.914123\pi$$
$$572$$ −0.500000 0.866025i −0.0209061 0.0362103i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 11.0000 0.457936 0.228968 0.973434i $$-0.426465\pi$$
0.228968 + 0.973434i $$0.426465\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ 0 0
$$580$$ −2.50000 4.33013i −0.103807 0.179799i
$$581$$ −10.0000 17.3205i −0.414870 0.718576i
$$582$$ 0 0
$$583$$ 7.00000 12.1244i 0.289910 0.502140i
$$584$$ −18.0000 −0.744845
$$585$$ 0 0
$$586$$ −1.00000 −0.0413096
$$587$$ −7.00000 + 12.1244i −0.288921 + 0.500426i −0.973552 0.228464i $$-0.926630\pi$$
0.684632 + 0.728889i $$0.259963\pi$$
$$588$$ 0 0
$$589$$ −1.50000 2.59808i −0.0618064 0.107052i
$$590$$ −4.50000 7.79423i −0.185262 0.320883i
$$591$$ 0 0
$$592$$ −2.50000 + 4.33013i −0.102749 + 0.177967i
$$593$$ 31.0000 1.27302 0.636509 0.771270i $$-0.280378\pi$$
0.636509 + 0.771270i $$0.280378\pi$$
$$594$$ 0 0
$$595$$ −4.00000 −0.163984
$$596$$ −3.00000 + 5.19615i −0.122885 + 0.212843i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 7.00000 + 12.1244i 0.286012 + 0.495388i 0.972854 0.231419i $$-0.0743369\pi$$
−0.686842 + 0.726807i $$0.741004\pi$$
$$600$$ 0 0
$$601$$ 8.50000 14.7224i 0.346722 0.600541i −0.638943 0.769254i $$-0.720628\pi$$
0.985665 + 0.168714i $$0.0539613\pi$$
$$602$$ −16.0000 −0.652111
$$603$$ 0 0
$$604$$ 8.00000 0.325515
$$605$$ 5.00000 8.66025i 0.203279 0.352089i
$$606$$ 0 0
$$607$$ 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i $$-0.114758\pi$$
−0.773358 + 0.633970i $$0.781424\pi$$
$$608$$ 7.50000 + 12.9904i 0.304165 + 0.526830i
$$609$$ 0 0
$$610$$ 0.500000 0.866025i 0.0202444 0.0350643i
$$611$$ −2.00000 −0.0809113
$$612$$ 0 0
$$613$$ 30.0000 1.21169 0.605844 0.795583i $$-0.292835\pi$$
0.605844 + 0.795583i $$0.292835\pi$$
$$614$$ −1.00000 + 1.73205i −0.0403567 + 0.0698999i
$$615$$ 0 0
$$616$$ 3.00000 + 5.19615i 0.120873 + 0.209359i
$$617$$ 4.50000 + 7.79423i 0.181163 + 0.313784i 0.942277 0.334835i $$-0.108680\pi$$
−0.761114 + 0.648618i $$0.775347\pi$$
$$618$$ 0 0
$$619$$ 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i $$-0.762380\pi$$
0.955131 + 0.296183i $$0.0957138\pi$$
$$620$$ 1.00000 0.0401610
$$621$$ 0 0
$$622$$ 4.00000 0.160385
$$623$$ 2.00000 3.46410i 0.0801283 0.138786i
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 14.0000 + 24.2487i 0.559553 + 0.969173i
$$627$$ 0 0
$$628$$ −3.00000 + 5.19615i −0.119713 + 0.207349i
$$629$$ 10.0000 0.398726
$$630$$ 0 0
$$631$$ −5.00000 −0.199047 −0.0995234 0.995035i $$-0.531732\pi$$
−0.0995234 + 0.995035i $$0.531732\pi$$
$$632$$ −18.0000 + 31.1769i −0.716002 + 1.24015i
$$633$$ 0 0
$$634$$ −13.5000 23.3827i −0.536153 0.928645i
$$635$$ 4.00000 + 6.92820i 0.158735 + 0.274937i
$$636$$ 0 0
$$637$$ −1.50000 + 2.59808i −0.0594322 + 0.102940i
$$638$$ −5.00000 −0.197952
$$639$$ 0 0
$$640$$ −3.00000 −0.118585
$$641$$ 8.50000 14.7224i 0.335730 0.581501i −0.647895 0.761730i $$-0.724350\pi$$
0.983625 + 0.180229i $$0.0576838\pi$$
$$642$$ 0 0
$$643$$ −16.0000 27.7128i −0.630978 1.09289i −0.987352 0.158543i $$-0.949320\pi$$
0.356374 0.934344i $$-0.384013\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −3.00000 + 5.19615i −0.118033 + 0.204440i
$$647$$ −41.0000 −1.61188 −0.805938 0.592000i $$-0.798339\pi$$
−0.805938 + 0.592000i $$0.798339\pi$$
$$648$$ 0 0
$$649$$ 9.00000 0.353281
$$650$$ 0.500000 0.866025i 0.0196116 0.0339683i
$$651$$ 0 0
$$652$$ −6.00000 10.3923i −0.234978 0.406994i
$$653$$ 24.0000 + 41.5692i 0.939193 + 1.62673i 0.766982 + 0.641669i $$0.221758\pi$$
0.172211 + 0.985060i $$0.444909\pi$$
$$654$$ 0 0
$$655$$ −2.00000 + 3.46410i −0.0781465 + 0.135354i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 4.00000 0.155936
$$659$$ −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i $$0.414010\pi$$
−0.968052 + 0.250748i $$0.919323\pi$$
$$660$$ 0 0
$$661$$ −19.0000 32.9090i −0.739014 1.28001i −0.952940 0.303160i $$-0.901958\pi$$
0.213925 0.976850i $$-0.431375\pi$$
$$662$$ −13.5000 23.3827i −0.524692 0.908794i
$$663$$ 0 0
$$664$$ 15.0000 25.9808i 0.582113 1.00825i
$$665$$ −6.00000 −0.232670
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ −7.00000 12.1244i −0.270434 0.468405i
$$671$$ 0.500000 + 0.866025i 0.0193023 + 0.0334325i
$$672$$ 0 0
$$673$$ −12.0000 + 20.7846i −0.462566 + 0.801188i −0.999088 0.0426985i $$-0.986405\pi$$
0.536522 + 0.843886i $$0.319738\pi$$
$$674$$ −22.0000 −0.847408
$$675$$ 0 0
$$676$$ −1.00000 −0.0384615
$$677$$ 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i $$-0.796551\pi$$
0.917899 + 0.396813i $$0.129884\pi$$
$$678$$ 0 0
$$679$$ −1.00000 1.73205i −0.0383765 0.0664700i
$$680$$ −3.00000 5.19615i −0.115045 0.199263i
$$681$$ 0 0
$$682$$ 0.500000 0.866025i 0.0191460 0.0331618i
$$683$$ 20.0000 0.765279 0.382639 0.923898i $$-0.375015\pi$$
0.382639 + 0.923898i $$0.375015\pi$$
$$684$$ 0 0
$$685$$ 5.00000 0.191040
$$686$$ 10.0000 17.3205i 0.381802 0.661300i
$$687$$ 0 0
$$688$$ −4.00000 6.92820i −0.152499 0.264135i
$$689$$ −7.00000 12.1244i −0.266679 0.461901i
$$690$$ 0 0
$$691$$ −0.500000 + 0.866025i −0.0190209 + 0.0329452i −0.875379 0.483437i $$-0.839388\pi$$
0.856358 + 0.516382i $$0.172722\pi$$
$$692$$ 12.0000 0.456172
$$693$$ 0 0
$$694$$ −17.0000 −0.645311
$$695$$ −6.00000 + 10.3923i −0.227593 + 0.394203i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −6.00000 10.3923i −0.227103 0.393355i
$$699$$ 0 0
$$700$$ 1.00000 1.73205i 0.0377964 0.0654654i
$$701$$ 5.00000 0.188847 0.0944237 0.995532i $$-0.469899\pi$$
0.0944237 + 0.995532i $$0.469899\pi$$
$$702$$ 0 0
$$703$$ 15.0000 0.565736
$$704$$ −3.50000 + 6.06218i −0.131911 + 0.228477i
$$705$$ 0 0
$$706$$ −1.50000 2.59808i −0.0564532 0.0977799i
$$707$$ 3.00000 + 5.19615i 0.112827 + 0.195421i
$$708$$ 0 0
$$709$$ −2.00000 + 3.46410i −0.0751116 + 0.130097i −0.901135 0.433539i $$-0.857265\pi$$
0.826023 + 0.563636i $$0.190598\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 6.00000 0.224860
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0.500000 + 0.866025i 0.0186989 + 0.0323875i
$$716$$ 9.00000 + 15.5885i 0.336346 + 0.582568i
$$717$$ 0 0
$$718$$ −15.5000 + 26.8468i −0.578455 + 1.00191i
$$719$$ 2.00000 0.0745874 0.0372937 0.999304i $$-0.488126\pi$$
0.0372937 + 0.999304i $$0.488126\pi$$
$$720$$ 0 0
$$721$$ −2.00000 −0.0744839
$$722$$ 5.00000 8.66025i 0.186081 0.322301i
$$723$$ 0 0
$$724$$ 8.50000 + 14.7224i 0.315900 + 0.547155i
$$725$$ 2.50000 + 4.33013i 0.0928477 + 0.160817i
$$726$$ 0 0
$$727$$ −24.0000 + 41.5692i −0.890111 + 1.54172i −0.0503692 + 0.998731i $$0.516040\pi$$
−0.839742 + 0.542986i $$0.817294\pi$$
$$728$$ 6.00000 0.222375
$$729$$ 0 0
$$730$$ 6.00000 0.222070
$$731$$ −8.00000 + 13.8564i −0.295891 + 0.512498i
$$732$$ 0 0
$$733$$ −6.50000 11.2583i −0.240083 0.415836i 0.720655 0.693294i $$-0.243841\pi$$
−0.960738 + 0.277458i $$0.910508\pi$$
$$734$$ −12.5000 21.6506i −0.461383 0.799140i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 14.0000 0.515697
$$738$$ 0 0
$$739$$ 9.00000 0.331070 0.165535 0.986204i $$-0.447065\pi$$
0.165535 + 0.986204i $$0.447065\pi$$
$$740$$ −2.50000 + 4.33013i −0.0919018 + 0.159179i
$$741$$ 0 0
$$742$$ 14.0000 + 24.2487i 0.513956 + 0.890198i
$$743$$ −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
$$745$$ 3.00000 5.19615i 0.109911 0.190372i
$$746$$ −20.0000 −0.732252
$$747$$ 0 0
$$748$$ 2.00000 0.0731272
$$749$$ 19.0000 32.9090i 0.694245 1.20247i
$$750$$ 0 0
$$751$$ −1.00000 1.73205i −0.0364905 0.0632034i 0.847203 0.531269i $$-0.178285\pi$$
−0.883694 + 0.468065i $$0.844951\pi$$
$$752$$ 1.00000 + 1.73205i 0.0364662 + 0.0631614i
$$753$$ 0 0
$$754$$ −2.50000 + 4.33013i −0.0910446 + 0.157694i
$$755$$ −8.00000 −0.291150
$$756$$ 0 0
$$757$$ −16.0000 −0.581530 −0.290765 0.956795i $$-0.593910\pi$$
−0.290765 + 0.956795i $$0.593910\pi$$
$$758$$ 11.5000 19.9186i 0.417699 0.723476i
$$759$$ 0 0
$$760$$ −4.50000 7.79423i −0.163232 0.282726i
$$761$$ −18.0000 31.1769i −0.652499 1.13016i −0.982514 0.186187i $$-0.940387\pi$$
0.330015 0.943976i $$-0.392946\pi$$
$$762$$ 0 0
$$763$$ 14.0000 24.2487i 0.506834 0.877862i
$$764$$ 18.0000 0.651217
$$765$$ 0 0
$$766$$ 12.0000 0.433578
$$767$$ 4.50000 7.79423i 0.162486 0.281433i
$$768$$ 0 0
$$769$$ 20.0000 + 34.6410i 0.721218 + 1.24919i 0.960512 + 0.278240i $$0.0897509\pi$$
−0.239293 + 0.970947i $$0.576916\pi$$
$$770$$ −1.00000 1.73205i −0.0360375 0.0624188i
$$771$$ 0 0
$$772$$ 6.50000 11.2583i 0.233940 0.405196i
$$773$$ −31.0000 −1.11499 −0.557496 0.830179i $$-0.688238\pi$$
−0.557496 + 0.830179i $$0.688238\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −0.0359211
$$776$$ 1.50000 2.59808i 0.0538469 0.0932655i
$$777$$ 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
$$784$$ 3.00000 0.107143
$$785$$ 3.00000 5.19615i 0.107075 0.185459i
$$786$$ 0 0
$$787$$ −19.0000 32.9090i −0.677277 1.17308i −0.975798 0.218675i $$-0.929827\pi$$
0.298521 0.954403i $$-0.403507\pi$$
$$788$$ −7.50000 12.9904i −0.267176 0.462763i
$$789$$ 0 0
$$790$$ 6.00000 10.3923i 0.213470 0.369742i