# Properties

 Label 2394.2.o.a.505.1 Level $2394$ Weight $2$ Character 2394.505 Analytic conductor $19.116$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2394.o (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$19.1161862439$$ 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 798) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 505.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2394.505 Dual form 2394.2.o.a.1261.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} -4.00000 q^{11} +(-1.50000 - 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 + 4.33013i) q^{19} +3.00000 q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-2.00000 - 3.46410i) q^{25} +3.00000 q^{26} +(0.500000 + 0.866025i) q^{28} -6.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(1.50000 - 2.59808i) q^{35} +4.00000 q^{37} +(-3.50000 - 2.59808i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(2.00000 - 3.46410i) q^{41} +(3.00000 - 5.19615i) q^{43} +(2.00000 + 3.46410i) q^{44} -1.00000 q^{46} +(-1.00000 - 1.73205i) q^{47} +1.00000 q^{49} +4.00000 q^{50} +(-1.50000 + 2.59808i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(6.00000 - 10.3923i) q^{55} -1.00000 q^{56} +(6.50000 - 11.2583i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(3.00000 - 5.19615i) q^{62} +1.00000 q^{64} +9.00000 q^{65} +(6.00000 + 10.3923i) q^{67} +2.00000 q^{68} +(1.50000 + 2.59808i) q^{70} +(-3.50000 + 6.06218i) q^{71} +(1.00000 - 1.73205i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(4.00000 - 1.73205i) q^{76} +4.00000 q^{77} +(4.00000 - 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(2.00000 + 3.46410i) q^{82} -17.0000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(3.00000 + 5.19615i) q^{86} -4.00000 q^{88} +(2.00000 + 3.46410i) q^{89} +(1.50000 + 2.59808i) q^{91} +(0.500000 - 0.866025i) q^{92} +2.00000 q^{94} +(-10.5000 - 7.79423i) q^{95} +(5.00000 - 8.66025i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{4} - 3 q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10})$$ 2 * q - q^2 - q^4 - 3 * q^5 - 2 * q^7 + 2 * q^8 $$2 q - q^{2} - q^{4} - 3 q^{5} - 2 q^{7} + 2 q^{8} - 3 q^{10} - 8 q^{11} - 3 q^{13} + q^{14} - q^{16} - 2 q^{17} - q^{19} + 6 q^{20} + 4 q^{22} + q^{23} - 4 q^{25} + 6 q^{26} + q^{28} - 12 q^{31} - q^{32} - 2 q^{34} + 3 q^{35} + 8 q^{37} - 7 q^{38} - 3 q^{40} + 4 q^{41} + 6 q^{43} + 4 q^{44} - 2 q^{46} - 2 q^{47} + 2 q^{49} + 8 q^{50} - 3 q^{52} - 4 q^{53} + 12 q^{55} - 2 q^{56} + 13 q^{59} - 5 q^{61} + 6 q^{62} + 2 q^{64} + 18 q^{65} + 12 q^{67} + 4 q^{68} + 3 q^{70} - 7 q^{71} + 2 q^{73} - 4 q^{74} + 8 q^{76} + 8 q^{77} + 8 q^{79} - 3 q^{80} + 4 q^{82} - 34 q^{83} - 6 q^{85} + 6 q^{86} - 8 q^{88} + 4 q^{89} + 3 q^{91} + q^{92} + 4 q^{94} - 21 q^{95} + 10 q^{97} - q^{98}+O(q^{100})$$ 2 * q - q^2 - q^4 - 3 * q^5 - 2 * q^7 + 2 * q^8 - 3 * q^10 - 8 * q^11 - 3 * q^13 + q^14 - q^16 - 2 * q^17 - q^19 + 6 * q^20 + 4 * q^22 + q^23 - 4 * q^25 + 6 * q^26 + q^28 - 12 * q^31 - q^32 - 2 * q^34 + 3 * q^35 + 8 * q^37 - 7 * q^38 - 3 * q^40 + 4 * q^41 + 6 * q^43 + 4 * q^44 - 2 * q^46 - 2 * q^47 + 2 * q^49 + 8 * q^50 - 3 * q^52 - 4 * q^53 + 12 * q^55 - 2 * q^56 + 13 * q^59 - 5 * q^61 + 6 * q^62 + 2 * q^64 + 18 * q^65 + 12 * q^67 + 4 * q^68 + 3 * q^70 - 7 * q^71 + 2 * q^73 - 4 * q^74 + 8 * q^76 + 8 * q^77 + 8 * q^79 - 3 * q^80 + 4 * q^82 - 34 * q^83 - 6 * q^85 + 6 * q^86 - 8 * q^88 + 4 * q^89 + 3 * q^91 + q^92 + 4 * q^94 - 21 * q^95 + 10 * q^97 - q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$$.

 $$n$$ $$533$$ $$1009$$ $$1711$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i $$0.400725\pi$$
−0.977672 + 0.210138i $$0.932609\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −1.50000 2.59808i −0.474342 0.821584i
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 0 0
$$13$$ −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i $$-0.303244\pi$$
−0.995535 + 0.0943882i $$0.969911\pi$$
$$14$$ 0.500000 0.866025i 0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i $$-0.911312\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ 0 0
$$19$$ −0.500000 + 4.33013i −0.114708 + 0.993399i
$$20$$ 3.00000 0.670820
$$21$$ 0 0
$$22$$ 2.00000 3.46410i 0.426401 0.738549i
$$23$$ 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i $$-0.133420\pi$$
−0.809177 + 0.587565i $$0.800087\pi$$
$$24$$ 0 0
$$25$$ −2.00000 3.46410i −0.400000 0.692820i
$$26$$ 3.00000 0.588348
$$27$$ 0 0
$$28$$ 0.500000 + 0.866025i 0.0944911 + 0.163663i
$$29$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$30$$ 0 0
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −1.00000 1.73205i −0.171499 0.297044i
$$35$$ 1.50000 2.59808i 0.253546 0.439155i
$$36$$ 0 0
$$37$$ 4.00000 0.657596 0.328798 0.944400i $$-0.393356\pi$$
0.328798 + 0.944400i $$0.393356\pi$$
$$38$$ −3.50000 2.59808i −0.567775 0.421464i
$$39$$ 0 0
$$40$$ −1.50000 + 2.59808i −0.237171 + 0.410792i
$$41$$ 2.00000 3.46410i 0.312348 0.541002i −0.666523 0.745485i $$-0.732218\pi$$
0.978870 + 0.204483i $$0.0655513\pi$$
$$42$$ 0 0
$$43$$ 3.00000 5.19615i 0.457496 0.792406i −0.541332 0.840809i $$-0.682080\pi$$
0.998828 + 0.0484030i $$0.0154132\pi$$
$$44$$ 2.00000 + 3.46410i 0.301511 + 0.522233i
$$45$$ 0 0
$$46$$ −1.00000 −0.147442
$$47$$ −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i $$-0.213263\pi$$
−0.929695 + 0.368329i $$0.879930\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 4.00000 0.565685
$$51$$ 0 0
$$52$$ −1.50000 + 2.59808i −0.208013 + 0.360288i
$$53$$ −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i $$-0.255252\pi$$
−0.970065 + 0.242846i $$0.921919\pi$$
$$54$$ 0 0
$$55$$ 6.00000 10.3923i 0.809040 1.40130i
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 6.50000 11.2583i 0.846228 1.46571i −0.0383226 0.999265i $$-0.512201\pi$$
0.884551 0.466444i $$-0.154465\pi$$
$$60$$ 0 0
$$61$$ −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i $$-0.270381\pi$$
−0.980507 + 0.196485i $$0.937047\pi$$
$$62$$ 3.00000 5.19615i 0.381000 0.659912i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 9.00000 1.11631
$$66$$ 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 0.242536
$$69$$ 0 0
$$70$$ 1.50000 + 2.59808i 0.179284 + 0.310530i
$$71$$ −3.50000 + 6.06218i −0.415374 + 0.719448i −0.995468 0.0951014i $$-0.969682\pi$$
0.580094 + 0.814550i $$0.303016\pi$$
$$72$$ 0 0
$$73$$ 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i $$-0.795992\pi$$
0.918594 + 0.395203i $$0.129326\pi$$
$$74$$ −2.00000 + 3.46410i −0.232495 + 0.402694i
$$75$$ 0 0
$$76$$ 4.00000 1.73205i 0.458831 0.198680i
$$77$$ 4.00000 0.455842
$$78$$ 0 0
$$79$$ 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i $$-0.684745\pi$$
0.998388 + 0.0567635i $$0.0180781\pi$$
$$80$$ −1.50000 2.59808i −0.167705 0.290474i
$$81$$ 0 0
$$82$$ 2.00000 + 3.46410i 0.220863 + 0.382546i
$$83$$ −17.0000 −1.86599 −0.932996 0.359886i $$-0.882816\pi$$
−0.932996 + 0.359886i $$0.882816\pi$$
$$84$$ 0 0
$$85$$ −3.00000 5.19615i −0.325396 0.563602i
$$86$$ 3.00000 + 5.19615i 0.323498 + 0.560316i
$$87$$ 0 0
$$88$$ −4.00000 −0.426401
$$89$$ 2.00000 + 3.46410i 0.212000 + 0.367194i 0.952340 0.305038i $$-0.0986691\pi$$
−0.740341 + 0.672232i $$0.765336\pi$$
$$90$$ 0 0
$$91$$ 1.50000 + 2.59808i 0.157243 + 0.272352i
$$92$$ 0.500000 0.866025i 0.0521286 0.0902894i
$$93$$ 0 0
$$94$$ 2.00000 0.206284
$$95$$ −10.5000 7.79423i −1.07728 0.799671i
$$96$$ 0 0
$$97$$ 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i $$-0.663839\pi$$
0.999961 0.00888289i $$-0.00282755\pi$$
$$98$$ −0.500000 + 0.866025i −0.0505076 + 0.0874818i
$$99$$ 0 0
$$100$$ −2.00000 + 3.46410i −0.200000 + 0.346410i
$$101$$ 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i $$0.0786053\pi$$
−0.273138 + 0.961975i $$0.588061\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ −1.50000 2.59808i −0.147087 0.254762i
$$105$$ 0 0
$$106$$ 4.00000 0.388514
$$107$$ 10.0000 0.966736 0.483368 0.875417i $$-0.339413\pi$$
0.483368 + 0.875417i $$0.339413\pi$$
$$108$$ 0 0
$$109$$ 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i $$-0.771977\pi$$
0.945769 + 0.324840i $$0.105310\pi$$
$$110$$ 6.00000 + 10.3923i 0.572078 + 0.990867i
$$111$$ 0 0
$$112$$ 0.500000 0.866025i 0.0472456 0.0818317i
$$113$$ 5.00000 0.470360 0.235180 0.971952i $$-0.424432\pi$$
0.235180 + 0.971952i $$0.424432\pi$$
$$114$$ 0 0
$$115$$ −3.00000 −0.279751
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 6.50000 + 11.2583i 0.598374 + 1.03641i
$$119$$ 1.00000 1.73205i 0.0916698 0.158777i
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 5.00000 0.452679
$$123$$ 0 0
$$124$$ 3.00000 + 5.19615i 0.269408 + 0.466628i
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 5.50000 + 9.52628i 0.488046 + 0.845321i 0.999905 0.0137486i $$-0.00437646\pi$$
−0.511859 + 0.859069i $$0.671043\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −4.50000 + 7.79423i −0.394676 + 0.683599i
$$131$$ −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i $$-0.961954\pi$$
0.599699 + 0.800226i $$0.295287\pi$$
$$132$$ 0 0
$$133$$ 0.500000 4.33013i 0.0433555 0.375470i
$$134$$ −12.0000 −1.03664
$$135$$ 0 0
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ −10.5000 18.1865i −0.897076 1.55378i −0.831215 0.555952i $$-0.812354\pi$$
−0.0658609 0.997829i $$-0.520979\pi$$
$$138$$ 0 0
$$139$$ 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i $$0.0707252\pi$$
−0.296866 + 0.954919i $$0.595942\pi$$
$$140$$ −3.00000 −0.253546
$$141$$ 0 0
$$142$$ −3.50000 6.06218i −0.293713 0.508727i
$$143$$ 6.00000 + 10.3923i 0.501745 + 0.869048i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 1.00000 + 1.73205i 0.0827606 + 0.143346i
$$147$$ 0 0
$$148$$ −2.00000 3.46410i −0.164399 0.284747i
$$149$$ 10.0000 17.3205i 0.819232 1.41895i −0.0870170 0.996207i $$-0.527733\pi$$
0.906249 0.422744i $$-0.138933\pi$$
$$150$$ 0 0
$$151$$ 19.0000 1.54620 0.773099 0.634285i $$-0.218706\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ −0.500000 + 4.33013i −0.0405554 + 0.351220i
$$153$$ 0 0
$$154$$ −2.00000 + 3.46410i −0.161165 + 0.279145i
$$155$$ 9.00000 15.5885i 0.722897 1.25210i
$$156$$ 0 0
$$157$$ 4.50000 7.79423i 0.359139 0.622047i −0.628678 0.777666i $$-0.716404\pi$$
0.987817 + 0.155618i $$0.0497370\pi$$
$$158$$ 4.00000 + 6.92820i 0.318223 + 0.551178i
$$159$$ 0 0
$$160$$ 3.00000 0.237171
$$161$$ −0.500000 0.866025i −0.0394055 0.0682524i
$$162$$ 0 0
$$163$$ 14.0000 1.09656 0.548282 0.836293i $$-0.315282\pi$$
0.548282 + 0.836293i $$0.315282\pi$$
$$164$$ −4.00000 −0.312348
$$165$$ 0 0
$$166$$ 8.50000 14.7224i 0.659728 1.14268i
$$167$$ −9.00000 15.5885i −0.696441 1.20627i −0.969693 0.244328i $$-0.921432\pi$$
0.273252 0.961943i $$-0.411901\pi$$
$$168$$ 0 0
$$169$$ 2.00000 3.46410i 0.153846 0.266469i
$$170$$ 6.00000 0.460179
$$171$$ 0 0
$$172$$ −6.00000 −0.457496
$$173$$ 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i $$-0.640193\pi$$
0.996544 0.0830722i $$-0.0264732\pi$$
$$174$$ 0 0
$$175$$ 2.00000 + 3.46410i 0.151186 + 0.261861i
$$176$$ 2.00000 3.46410i 0.150756 0.261116i
$$177$$ 0 0
$$178$$ −4.00000 −0.299813
$$179$$ −10.0000 −0.747435 −0.373718 0.927543i $$-0.621917\pi$$
−0.373718 + 0.927543i $$0.621917\pi$$
$$180$$ 0 0
$$181$$ −1.50000 2.59808i −0.111494 0.193113i 0.804879 0.593439i $$-0.202230\pi$$
−0.916373 + 0.400326i $$0.868897\pi$$
$$182$$ −3.00000 −0.222375
$$183$$ 0 0
$$184$$ 0.500000 + 0.866025i 0.0368605 + 0.0638442i
$$185$$ −6.00000 + 10.3923i −0.441129 + 0.764057i
$$186$$ 0 0
$$187$$ 4.00000 6.92820i 0.292509 0.506640i
$$188$$ −1.00000 + 1.73205i −0.0729325 + 0.126323i
$$189$$ 0 0
$$190$$ 12.0000 5.19615i 0.870572 0.376969i
$$191$$ 11.0000 0.795932 0.397966 0.917400i $$-0.369716\pi$$
0.397966 + 0.917400i $$0.369716\pi$$
$$192$$ 0 0
$$193$$ −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i $$-0.890928\pi$$
0.761911 + 0.647682i $$0.224262\pi$$
$$194$$ 5.00000 + 8.66025i 0.358979 + 0.621770i
$$195$$ 0 0
$$196$$ −0.500000 0.866025i −0.0357143 0.0618590i
$$197$$ −4.00000 −0.284988 −0.142494 0.989796i $$-0.545512\pi$$
−0.142494 + 0.989796i $$0.545512\pi$$
$$198$$ 0 0
$$199$$ −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i $$-0.331945\pi$$
−0.999990 + 0.00436292i $$0.998611\pi$$
$$200$$ −2.00000 3.46410i −0.141421 0.244949i
$$201$$ 0 0
$$202$$ −14.0000 −0.985037
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 6.00000 + 10.3923i 0.419058 + 0.725830i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 3.00000 0.208013
$$209$$ 2.00000 17.3205i 0.138343 1.19808i
$$210$$ 0 0
$$211$$ 4.00000 6.92820i 0.275371 0.476957i −0.694857 0.719148i $$-0.744533\pi$$
0.970229 + 0.242190i $$0.0778659\pi$$
$$212$$ −2.00000 + 3.46410i −0.137361 + 0.237915i
$$213$$ 0 0
$$214$$ −5.00000 + 8.66025i −0.341793 + 0.592003i
$$215$$ 9.00000 + 15.5885i 0.613795 + 1.06312i
$$216$$ 0 0
$$217$$ 6.00000 0.407307
$$218$$ 2.00000 + 3.46410i 0.135457 + 0.234619i
$$219$$ 0 0
$$220$$ −12.0000 −0.809040
$$221$$ 6.00000 0.403604
$$222$$ 0 0
$$223$$ 9.00000 15.5885i 0.602685 1.04388i −0.389728 0.920930i $$-0.627431\pi$$
0.992413 0.122950i $$-0.0392356\pi$$
$$224$$ 0.500000 + 0.866025i 0.0334077 + 0.0578638i
$$225$$ 0 0
$$226$$ −2.50000 + 4.33013i −0.166298 + 0.288036i
$$227$$ −5.00000 −0.331862 −0.165931 0.986137i $$-0.553063\pi$$
−0.165931 + 0.986137i $$0.553063\pi$$
$$228$$ 0 0
$$229$$ −17.0000 −1.12339 −0.561696 0.827344i $$-0.689851\pi$$
−0.561696 + 0.827344i $$0.689851\pi$$
$$230$$ 1.50000 2.59808i 0.0989071 0.171312i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 4.50000 7.79423i 0.294805 0.510617i −0.680135 0.733087i $$-0.738079\pi$$
0.974939 + 0.222470i $$0.0714120\pi$$
$$234$$ 0 0
$$235$$ 6.00000 0.391397
$$236$$ −13.0000 −0.846228
$$237$$ 0 0
$$238$$ 1.00000 + 1.73205i 0.0648204 + 0.112272i
$$239$$ −27.0000 −1.74648 −0.873242 0.487286i $$-0.837987\pi$$
−0.873242 + 0.487286i $$0.837987\pi$$
$$240$$ 0 0
$$241$$ −11.0000 19.0526i −0.708572 1.22728i −0.965387 0.260822i $$-0.916006\pi$$
0.256814 0.966461i $$-0.417327\pi$$
$$242$$ −2.50000 + 4.33013i −0.160706 + 0.278351i
$$243$$ 0 0
$$244$$ −2.50000 + 4.33013i −0.160046 + 0.277208i
$$245$$ −1.50000 + 2.59808i −0.0958315 + 0.165985i
$$246$$ 0 0
$$247$$ 12.0000 5.19615i 0.763542 0.330623i
$$248$$ −6.00000 −0.381000
$$249$$ 0 0
$$250$$ 1.50000 2.59808i 0.0948683 0.164317i
$$251$$ 10.5000 + 18.1865i 0.662754 + 1.14792i 0.979889 + 0.199543i $$0.0639459\pi$$
−0.317135 + 0.948380i $$0.602721\pi$$
$$252$$ 0 0
$$253$$ −2.00000 3.46410i −0.125739 0.217786i
$$254$$ −11.0000 −0.690201
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i $$-0.0445601\pi$$
−0.615948 + 0.787787i $$0.711227\pi$$
$$258$$ 0 0
$$259$$ −4.00000 −0.248548
$$260$$ −4.50000 7.79423i −0.279078 0.483378i
$$261$$ 0 0
$$262$$ −4.50000 7.79423i −0.278011 0.481529i
$$263$$ −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i $$-0.862817\pi$$
0.816066 + 0.577959i $$0.196151\pi$$
$$264$$ 0 0
$$265$$ 12.0000 0.737154
$$266$$ 3.50000 + 2.59808i 0.214599 + 0.159298i
$$267$$ 0 0
$$268$$ 6.00000 10.3923i 0.366508 0.634811i
$$269$$ 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i $$-0.692975\pi$$
0.996586 + 0.0825561i $$0.0263084\pi$$
$$270$$ 0 0
$$271$$ −13.0000 + 22.5167i −0.789694 + 1.36779i 0.136461 + 0.990645i $$0.456427\pi$$
−0.926155 + 0.377144i $$0.876906\pi$$
$$272$$ −1.00000 1.73205i −0.0606339 0.105021i
$$273$$ 0 0
$$274$$ 21.0000 1.26866
$$275$$ 8.00000 + 13.8564i 0.482418 + 0.835573i
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ 0 0
$$280$$ 1.50000 2.59808i 0.0896421 0.155265i
$$281$$ −13.0000 22.5167i −0.775515 1.34323i −0.934505 0.355951i $$-0.884157\pi$$
0.158990 0.987280i $$-0.449176\pi$$
$$282$$ 0 0
$$283$$ −12.5000 + 21.6506i −0.743048 + 1.28700i 0.208053 + 0.978117i $$0.433287\pi$$
−0.951101 + 0.308879i $$0.900046\pi$$
$$284$$ 7.00000 0.415374
$$285$$ 0 0
$$286$$ −12.0000 −0.709575
$$287$$ −2.00000 + 3.46410i −0.118056 + 0.204479i
$$288$$ 0 0
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −2.00000 −0.117041
$$293$$ 19.0000 1.10999 0.554996 0.831853i $$-0.312720\pi$$
0.554996 + 0.831853i $$0.312720\pi$$
$$294$$ 0 0
$$295$$ 19.5000 + 33.7750i 1.13533 + 1.96646i
$$296$$ 4.00000 0.232495
$$297$$ 0 0
$$298$$ 10.0000 + 17.3205i 0.579284 + 1.00335i
$$299$$ 1.50000 2.59808i 0.0867472 0.150251i
$$300$$ 0 0
$$301$$ −3.00000 + 5.19615i −0.172917 + 0.299501i
$$302$$ −9.50000 + 16.4545i −0.546664 + 0.946849i
$$303$$ 0 0
$$304$$ −3.50000 2.59808i −0.200739 0.149010i
$$305$$ 15.0000 0.858898
$$306$$ 0 0
$$307$$ −7.50000 + 12.9904i −0.428048 + 0.741400i −0.996700 0.0811780i $$-0.974132\pi$$
0.568652 + 0.822578i $$0.307465\pi$$
$$308$$ −2.00000 3.46410i −0.113961 0.197386i
$$309$$ 0 0
$$310$$ 9.00000 + 15.5885i 0.511166 + 0.885365i
$$311$$ 2.00000 0.113410 0.0567048 0.998391i $$-0.481941\pi$$
0.0567048 + 0.998391i $$0.481941\pi$$
$$312$$ 0 0
$$313$$ −12.0000 20.7846i −0.678280 1.17482i −0.975499 0.220006i $$-0.929392\pi$$
0.297218 0.954810i $$-0.403941\pi$$
$$314$$ 4.50000 + 7.79423i 0.253950 + 0.439854i
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i $$-0.112775\pi$$
−0.769395 + 0.638774i $$0.779442\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −1.50000 + 2.59808i −0.0838525 + 0.145237i
$$321$$ 0 0
$$322$$ 1.00000 0.0557278
$$323$$ −7.00000 5.19615i −0.389490 0.289122i
$$324$$ 0 0
$$325$$ −6.00000 + 10.3923i −0.332820 + 0.576461i
$$326$$ −7.00000 + 12.1244i −0.387694 + 0.671506i
$$327$$ 0 0
$$328$$ 2.00000 3.46410i 0.110432 0.191273i
$$329$$ 1.00000 + 1.73205i 0.0551318 + 0.0954911i
$$330$$ 0 0
$$331$$ −24.0000 −1.31916 −0.659580 0.751635i $$-0.729266\pi$$
−0.659580 + 0.751635i $$0.729266\pi$$
$$332$$ 8.50000 + 14.7224i 0.466498 + 0.807998i
$$333$$ 0 0
$$334$$ 18.0000 0.984916
$$335$$ −36.0000 −1.96689
$$336$$ 0 0
$$337$$ −8.50000 + 14.7224i −0.463025 + 0.801982i −0.999110 0.0421818i $$-0.986569\pi$$
0.536085 + 0.844164i $$0.319902\pi$$
$$338$$ 2.00000 + 3.46410i 0.108786 + 0.188422i
$$339$$ 0 0
$$340$$ −3.00000 + 5.19615i −0.162698 + 0.281801i
$$341$$ 24.0000 1.29967
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 3.00000 5.19615i 0.161749 0.280158i
$$345$$ 0 0
$$346$$ 7.50000 + 12.9904i 0.403202 + 0.698367i
$$347$$ 11.0000 19.0526i 0.590511 1.02279i −0.403653 0.914912i $$-0.632260\pi$$
0.994164 0.107883i $$-0.0344071\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ −4.00000 −0.213809
$$351$$ 0 0
$$352$$ 2.00000 + 3.46410i 0.106600 + 0.184637i
$$353$$ −12.0000 −0.638696 −0.319348 0.947638i $$-0.603464\pi$$
−0.319348 + 0.947638i $$0.603464\pi$$
$$354$$ 0 0
$$355$$ −10.5000 18.1865i −0.557282 0.965241i
$$356$$ 2.00000 3.46410i 0.106000 0.183597i
$$357$$ 0 0
$$358$$ 5.00000 8.66025i 0.264258 0.457709i
$$359$$ 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i $$-0.615019\pi$$
0.986865 0.161546i $$-0.0516481\pi$$
$$360$$ 0 0
$$361$$ −18.5000 4.33013i −0.973684 0.227901i
$$362$$ 3.00000 0.157676
$$363$$ 0 0
$$364$$ 1.50000 2.59808i 0.0786214 0.136176i
$$365$$ 3.00000 + 5.19615i 0.157027 + 0.271979i
$$366$$ 0 0
$$367$$ −16.0000 27.7128i −0.835193 1.44660i −0.893873 0.448320i $$-0.852022\pi$$
0.0586798 0.998277i $$-0.481311\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 0 0
$$370$$ −6.00000 10.3923i −0.311925 0.540270i
$$371$$ 2.00000 + 3.46410i 0.103835 + 0.179847i
$$372$$ 0 0
$$373$$ −10.0000 −0.517780 −0.258890 0.965907i $$-0.583357\pi$$
−0.258890 + 0.965907i $$0.583357\pi$$
$$374$$ 4.00000 + 6.92820i 0.206835 + 0.358249i
$$375$$ 0 0
$$376$$ −1.00000 1.73205i −0.0515711 0.0893237i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −34.0000 −1.74646 −0.873231 0.487306i $$-0.837980\pi$$
−0.873231 + 0.487306i $$0.837980\pi$$
$$380$$ −1.50000 + 12.9904i −0.0769484 + 0.666392i
$$381$$ 0 0
$$382$$ −5.50000 + 9.52628i −0.281404 + 0.487407i
$$383$$ −2.00000 + 3.46410i −0.102195 + 0.177007i −0.912589 0.408879i $$-0.865920\pi$$
0.810394 + 0.585886i $$0.199253\pi$$
$$384$$ 0 0
$$385$$ −6.00000 + 10.3923i −0.305788 + 0.529641i
$$386$$ −2.50000 4.33013i −0.127247 0.220398i
$$387$$ 0 0
$$388$$ −10.0000 −0.507673
$$389$$ 4.00000 + 6.92820i 0.202808 + 0.351274i 0.949432 0.313972i $$-0.101660\pi$$
−0.746624 + 0.665246i $$0.768327\pi$$
$$390$$ 0 0
$$391$$ −2.00000 −0.101144
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ 2.00000 3.46410i 0.100759 0.174519i
$$395$$ 12.0000 + 20.7846i 0.603786 + 1.04579i
$$396$$ 0 0
$$397$$ −9.00000 + 15.5885i −0.451697 + 0.782362i −0.998492 0.0549046i $$-0.982515\pi$$
0.546795 + 0.837267i $$0.315848\pi$$
$$398$$ 14.0000 0.701757
$$399$$ 0 0
$$400$$ 4.00000 0.200000
$$401$$ 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i $$-0.809468\pi$$
0.901046 + 0.433724i $$0.142801\pi$$
$$402$$ 0 0
$$403$$ 9.00000 + 15.5885i 0.448322 + 0.776516i
$$404$$ 7.00000 12.1244i 0.348263 0.603209i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −16.0000 −0.793091
$$408$$ 0 0
$$409$$ −12.0000 20.7846i −0.593362 1.02773i −0.993776 0.111398i $$-0.964467\pi$$
0.400414 0.916334i $$-0.368866\pi$$
$$410$$ −12.0000 −0.592638
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −6.50000 + 11.2583i −0.319844 + 0.553986i
$$414$$ 0 0
$$415$$ 25.5000 44.1673i 1.25175 2.16809i
$$416$$ −1.50000 + 2.59808i −0.0735436 + 0.127381i
$$417$$ 0 0
$$418$$ 14.0000 + 10.3923i 0.684762 + 0.508304i
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 4.00000 6.92820i 0.194948 0.337660i −0.751935 0.659237i $$-0.770879\pi$$
0.946883 + 0.321577i $$0.104213\pi$$
$$422$$ 4.00000 + 6.92820i 0.194717 + 0.337260i
$$423$$ 0 0
$$424$$ −2.00000 3.46410i −0.0971286 0.168232i
$$425$$ 8.00000 0.388057
$$426$$ 0 0
$$427$$ 2.50000 + 4.33013i 0.120983 + 0.209550i
$$428$$ −5.00000 8.66025i −0.241684 0.418609i
$$429$$ 0 0
$$430$$ −18.0000 −0.868037
$$431$$ −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
$$433$$ 12.0000 + 20.7846i 0.576683 + 0.998845i 0.995857 + 0.0909384i $$0.0289866\pi$$
−0.419173 + 0.907906i $$0.637680\pi$$
$$434$$ −3.00000 + 5.19615i −0.144005 + 0.249423i
$$435$$ 0 0
$$436$$ −4.00000 −0.191565
$$437$$ −4.00000 + 1.73205i −0.191346 + 0.0828552i
$$438$$ 0 0
$$439$$ −5.00000 + 8.66025i −0.238637 + 0.413331i −0.960323 0.278889i $$-0.910034\pi$$
0.721686 + 0.692220i $$0.243367\pi$$
$$440$$ 6.00000 10.3923i 0.286039 0.495434i
$$441$$ 0 0
$$442$$ −3.00000 + 5.19615i −0.142695 + 0.247156i
$$443$$ 9.00000 + 15.5885i 0.427603 + 0.740630i 0.996660 0.0816684i $$-0.0260248\pi$$
−0.569057 + 0.822298i $$0.692691\pi$$
$$444$$ 0 0
$$445$$ −12.0000 −0.568855
$$446$$ 9.00000 + 15.5885i 0.426162 + 0.738135i
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ 39.0000 1.84052 0.920262 0.391303i $$-0.127976\pi$$
0.920262 + 0.391303i $$0.127976\pi$$
$$450$$ 0 0
$$451$$ −8.00000 + 13.8564i −0.376705 + 0.652473i
$$452$$ −2.50000 4.33013i −0.117590 0.203672i
$$453$$ 0 0
$$454$$ 2.50000 4.33013i 0.117331 0.203223i
$$455$$ −9.00000 −0.421927
$$456$$ 0 0
$$457$$ −7.00000 −0.327446 −0.163723 0.986506i $$-0.552350\pi$$
−0.163723 + 0.986506i $$0.552350\pi$$
$$458$$ 8.50000 14.7224i 0.397179 0.687934i
$$459$$ 0 0
$$460$$ 1.50000 + 2.59808i 0.0699379 + 0.121136i
$$461$$ −16.5000 + 28.5788i −0.768482 + 1.33105i 0.169904 + 0.985461i $$0.445654\pi$$
−0.938386 + 0.345589i $$0.887679\pi$$
$$462$$ 0 0
$$463$$ −9.00000 −0.418265 −0.209133 0.977887i $$-0.567064\pi$$
−0.209133 + 0.977887i $$0.567064\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 4.50000 + 7.79423i 0.208458 + 0.361061i
$$467$$ 4.00000 0.185098 0.0925490 0.995708i $$-0.470499\pi$$
0.0925490 + 0.995708i $$0.470499\pi$$
$$468$$ 0 0
$$469$$ −6.00000 10.3923i −0.277054 0.479872i
$$470$$ −3.00000 + 5.19615i −0.138380 + 0.239681i
$$471$$ 0 0
$$472$$ 6.50000 11.2583i 0.299187 0.518207i
$$473$$ −12.0000 + 20.7846i −0.551761 + 0.955677i
$$474$$ 0 0
$$475$$ 16.0000 6.92820i 0.734130 0.317888i
$$476$$ −2.00000 −0.0916698
$$477$$ 0 0
$$478$$ 13.5000 23.3827i 0.617476 1.06950i
$$479$$ −21.0000 36.3731i −0.959514 1.66193i −0.723681 0.690134i $$-0.757551\pi$$
−0.235833 0.971794i $$-0.575782\pi$$
$$480$$ 0 0
$$481$$ −6.00000 10.3923i −0.273576 0.473848i
$$482$$ 22.0000 1.00207
$$483$$ 0 0
$$484$$ −2.50000 4.33013i −0.113636 0.196824i
$$485$$ 15.0000 + 25.9808i 0.681115 + 1.17973i
$$486$$ 0 0
$$487$$ −28.0000 −1.26880 −0.634401 0.773004i $$-0.718753\pi$$
−0.634401 + 0.773004i $$0.718753\pi$$
$$488$$ −2.50000 4.33013i −0.113170 0.196016i
$$489$$ 0 0
$$490$$ −1.50000 2.59808i −0.0677631 0.117369i
$$491$$ 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i $$-0.746053\pi$$
0.969061 + 0.246822i $$0.0793863\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −1.50000 + 12.9904i −0.0674882 + 0.584465i
$$495$$ 0 0
$$496$$ 3.00000 5.19615i 0.134704 0.233314i
$$497$$ 3.50000 6.06218i 0.156996 0.271926i
$$498$$ 0 0
$$499$$ 5.00000 8.66025i 0.223831 0.387686i −0.732137 0.681157i $$-0.761477\pi$$
0.955968 + 0.293471i $$0.0948104\pi$$
$$500$$ 1.50000 + 2.59808i 0.0670820 + 0.116190i
$$501$$ 0 0
$$502$$ −21.0000 −0.937276
$$503$$ 11.0000 + 19.0526i 0.490466 + 0.849512i 0.999940 0.0109744i $$-0.00349334\pi$$
−0.509474 + 0.860486i $$0.670160\pi$$
$$504$$ 0 0
$$505$$ −42.0000 −1.86898
$$506$$ 4.00000 0.177822
$$507$$ 0 0
$$508$$ 5.50000 9.52628i 0.244023 0.422660i
$$509$$ −6.50000 11.2583i −0.288107 0.499017i 0.685251 0.728307i $$-0.259693\pi$$
−0.973358 + 0.229291i $$0.926359\pi$$
$$510$$ 0 0
$$511$$ −1.00000 + 1.73205i −0.0442374 + 0.0766214i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −12.0000 −0.529297
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 4.00000 + 6.92820i 0.175920 + 0.304702i
$$518$$ 2.00000 3.46410i 0.0878750 0.152204i
$$519$$ 0 0
$$520$$ 9.00000 0.394676
$$521$$ 14.0000 0.613351 0.306676 0.951814i $$-0.400783\pi$$
0.306676 + 0.951814i $$0.400783\pi$$
$$522$$ 0 0
$$523$$ 16.0000 + 27.7128i 0.699631 + 1.21180i 0.968594 + 0.248646i $$0.0799857\pi$$
−0.268963 + 0.963150i $$0.586681\pi$$
$$524$$ 9.00000 0.393167
$$525$$ 0 0
$$526$$ −1.50000 2.59808i −0.0654031 0.113282i
$$527$$ 6.00000 10.3923i 0.261364 0.452696i
$$528$$ 0 0
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ −6.00000 + 10.3923i −0.260623 + 0.451413i
$$531$$ 0 0
$$532$$ −4.00000 + 1.73205i −0.173422 + 0.0750939i
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ −15.0000 + 25.9808i −0.648507 + 1.12325i
$$536$$ 6.00000 + 10.3923i 0.259161 + 0.448879i
$$537$$ 0 0
$$538$$ 7.00000 + 12.1244i 0.301791 + 0.522718i
$$539$$ −4.00000 −0.172292
$$540$$ 0 0
$$541$$ −16.0000 27.7128i −0.687894 1.19147i −0.972518 0.232828i $$-0.925202\pi$$
0.284624 0.958639i $$-0.408131\pi$$
$$542$$ −13.0000 22.5167i −0.558398 0.967173i
$$543$$ 0 0
$$544$$ 2.00000 0.0857493
$$545$$ 6.00000 + 10.3923i 0.257012 + 0.445157i
$$546$$ 0 0
$$547$$ 23.0000 + 39.8372i 0.983409 + 1.70331i 0.648803 + 0.760956i $$0.275270\pi$$
0.334606 + 0.942358i $$0.391397\pi$$
$$548$$ −10.5000 + 18.1865i −0.448538 + 0.776890i
$$549$$ 0 0
$$550$$ −16.0000 −0.682242
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −4.00000 + 6.92820i −0.170097 + 0.294617i
$$554$$ 1.00000 1.73205i 0.0424859 0.0735878i
$$555$$ 0 0
$$556$$ 8.00000 13.8564i 0.339276 0.587643i
$$557$$ 11.0000 + 19.0526i 0.466085 + 0.807283i 0.999250 0.0387286i $$-0.0123308\pi$$
−0.533165 + 0.846011i $$0.678997\pi$$
$$558$$ 0 0
$$559$$ −18.0000 −0.761319
$$560$$ 1.50000 + 2.59808i 0.0633866 + 0.109789i
$$561$$ 0 0
$$562$$ 26.0000 1.09674
$$563$$ −33.0000 −1.39078 −0.695392 0.718631i $$-0.744769\pi$$
−0.695392 + 0.718631i $$0.744769\pi$$
$$564$$ 0 0
$$565$$ −7.50000 + 12.9904i −0.315527 + 0.546509i
$$566$$ −12.5000 21.6506i −0.525414 0.910044i
$$567$$ 0 0
$$568$$ −3.50000 + 6.06218i −0.146857 + 0.254363i
$$569$$ 9.00000 0.377300 0.188650 0.982044i $$-0.439589\pi$$
0.188650 + 0.982044i $$0.439589\pi$$
$$570$$ 0 0
$$571$$ 2.00000 0.0836974 0.0418487 0.999124i $$-0.486675\pi$$
0.0418487 + 0.999124i $$0.486675\pi$$
$$572$$ 6.00000 10.3923i 0.250873 0.434524i
$$573$$ 0 0
$$574$$ −2.00000 3.46410i −0.0834784 0.144589i
$$575$$ 2.00000 3.46410i 0.0834058 0.144463i
$$576$$ 0 0
$$577$$ −8.00000 −0.333044 −0.166522 0.986038i $$-0.553254\pi$$
−0.166522 + 0.986038i $$0.553254\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 17.0000 0.705279
$$582$$ 0 0
$$583$$ 8.00000 + 13.8564i 0.331326 + 0.573874i
$$584$$ 1.00000 1.73205i 0.0413803 0.0716728i
$$585$$ 0 0
$$586$$ −9.50000 + 16.4545i −0.392441 + 0.679728i
$$587$$ −10.0000 + 17.3205i −0.412744 + 0.714894i −0.995189 0.0979766i $$-0.968763\pi$$
0.582445 + 0.812870i $$0.302096\pi$$
$$588$$ 0 0
$$589$$ 3.00000 25.9808i 0.123613 1.07052i
$$590$$ −39.0000 −1.60560
$$591$$ 0 0
$$592$$ −2.00000 + 3.46410i −0.0821995 + 0.142374i
$$593$$ −16.0000 27.7128i −0.657041 1.13803i −0.981378 0.192087i $$-0.938474\pi$$
0.324337 0.945942i $$-0.394859\pi$$
$$594$$ 0 0
$$595$$ 3.00000 + 5.19615i 0.122988 + 0.213021i
$$596$$ −20.0000 −0.819232
$$597$$ 0 0
$$598$$ 1.50000 + 2.59808i 0.0613396 + 0.106243i
$$599$$ −21.5000 37.2391i −0.878466 1.52155i −0.853024 0.521872i $$-0.825234\pi$$
−0.0254422 0.999676i $$-0.508099\pi$$
$$600$$ 0 0
$$601$$ −6.00000 −0.244745 −0.122373 0.992484i $$-0.539050\pi$$
−0.122373 + 0.992484i $$0.539050\pi$$
$$602$$ −3.00000 5.19615i −0.122271 0.211779i
$$603$$ 0 0
$$604$$ −9.50000 16.4545i −0.386550 0.669523i
$$605$$ −7.50000 + 12.9904i −0.304918 + 0.528134i
$$606$$ 0 0
$$607$$ −16.0000 −0.649420 −0.324710 0.945814i $$-0.605267\pi$$
−0.324710 + 0.945814i $$0.605267\pi$$
$$608$$ 4.00000 1.73205i 0.162221 0.0702439i
$$609$$ 0 0
$$610$$ −7.50000 + 12.9904i −0.303666 + 0.525965i
$$611$$ −3.00000 + 5.19615i −0.121367 + 0.210214i
$$612$$ 0 0
$$613$$ 5.00000 8.66025i 0.201948 0.349784i −0.747208 0.664590i $$-0.768606\pi$$
0.949156 + 0.314806i $$0.101939\pi$$
$$614$$ −7.50000 12.9904i −0.302675 0.524249i
$$615$$ 0 0
$$616$$ 4.00000 0.161165
$$617$$ −13.5000 23.3827i −0.543490 0.941351i −0.998700 0.0509678i $$-0.983769\pi$$
0.455211 0.890384i $$-0.349564\pi$$
$$618$$ 0 0
$$619$$ −5.00000 −0.200967 −0.100483 0.994939i $$-0.532039\pi$$
−0.100483 + 0.994939i $$0.532039\pi$$
$$620$$ −18.0000 −0.722897
$$621$$ 0 0
$$622$$ −1.00000 + 1.73205i −0.0400963 + 0.0694489i
$$623$$ −2.00000 3.46410i −0.0801283 0.138786i
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ 24.0000 0.959233
$$627$$ 0 0
$$628$$ −9.00000 −0.359139
$$629$$ −4.00000 + 6.92820i −0.159490 + 0.276246i
$$630$$ 0 0
$$631$$ −4.00000 6.92820i −0.159237 0.275807i 0.775356 0.631524i $$-0.217570\pi$$
−0.934594 + 0.355716i $$0.884237\pi$$
$$632$$ 4.00000 6.92820i 0.159111 0.275589i
$$633$$ 0 0
$$634$$ −6.00000 −0.238290
$$635$$ −33.0000 −1.30957
$$636$$ 0 0
$$637$$ −1.50000 2.59808i −0.0594322 0.102940i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.50000 2.59808i −0.0592927 0.102698i
$$641$$ −8.50000 + 14.7224i −0.335730 + 0.581501i −0.983625 0.180229i $$-0.942316\pi$$
0.647895 + 0.761730i $$0.275650\pi$$
$$642$$ 0 0
$$643$$ 20.5000 35.5070i 0.808441 1.40026i −0.105502 0.994419i $$-0.533645\pi$$
0.913943 0.405842i $$-0.133022\pi$$
$$644$$ −0.500000 + 0.866025i −0.0197028 + 0.0341262i
$$645$$ 0 0
$$646$$ 8.00000 3.46410i 0.314756 0.136293i
$$647$$ −30.0000 −1.17942 −0.589711 0.807614i $$-0.700758\pi$$
−0.589711 + 0.807614i $$0.700758\pi$$
$$648$$ 0 0
$$649$$ −26.0000 + 45.0333i −1.02059 + 1.76771i
$$650$$ −6.00000 10.3923i −0.235339 0.407620i
$$651$$ 0 0
$$652$$ −7.00000 12.1244i −0.274141 0.474826i
$$653$$ −6.00000 −0.234798 −0.117399 0.993085i $$-0.537456\pi$$
−0.117399 + 0.993085i $$0.537456\pi$$
$$654$$ 0 0
$$655$$ −13.5000 23.3827i −0.527489 0.913637i
$$656$$ 2.00000 + 3.46410i 0.0780869 + 0.135250i
$$657$$ 0 0
$$658$$ −2.00000 −0.0779681
$$659$$ −13.0000 22.5167i −0.506408 0.877125i −0.999973 0.00741531i $$-0.997640\pi$$
0.493564 0.869709i $$-0.335694\pi$$
$$660$$ 0 0
$$661$$ 5.50000 + 9.52628i 0.213925 + 0.370529i 0.952940 0.303160i $$-0.0980418\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 12.0000 20.7846i 0.466393 0.807817i
$$663$$ 0 0
$$664$$ −17.0000 −0.659728
$$665$$ 10.5000 + 7.79423i 0.407173 + 0.302247i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −9.00000 + 15.5885i −0.348220 + 0.603136i
$$669$$ 0 0
$$670$$ 18.0000 31.1769i 0.695401 1.20447i
$$671$$ 10.0000 + 17.3205i 0.386046 + 0.668651i
$$672$$ 0 0
$$673$$ 11.0000 0.424019 0.212009 0.977268i $$-0.431999\pi$$
0.212009 + 0.977268i $$0.431999\pi$$
$$674$$ −8.50000 14.7224i −0.327408 0.567087i
$$675$$ 0 0
$$676$$ −4.00000 −0.153846
$$677$$ −42.0000 −1.61419 −0.807096 0.590421i $$-0.798962\pi$$
−0.807096 + 0.590421i $$0.798962\pi$$
$$678$$ 0 0
$$679$$ −5.00000 + 8.66025i −0.191882 + 0.332350i
$$680$$ −3.00000 5.19615i −0.115045 0.199263i
$$681$$ 0 0
$$682$$ −12.0000 + 20.7846i −0.459504 + 0.795884i
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ 63.0000 2.40711
$$686$$ 0.500000 0.866025i 0.0190901 0.0330650i
$$687$$ 0 0
$$688$$ 3.00000 + 5.19615i 0.114374 + 0.198101i
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −41.0000 −1.55971 −0.779857 0.625958i $$-0.784708\pi$$
−0.779857 + 0.625958i $$0.784708\pi$$
$$692$$ −15.0000 −0.570214
$$693$$ 0 0
$$694$$ 11.0000 + 19.0526i 0.417554 + 0.723225i
$$695$$ −48.0000 −1.82074
$$696$$ 0 0
$$697$$ 4.00000 + 6.92820i 0.151511 + 0.262424i
$$698$$ −5.00000 + 8.66025i −0.189253 + 0.327795i
$$699$$ 0 0
$$700$$ 2.00000 3.46410i 0.0755929 0.130931i
$$701$$ −1.00000 + 1.73205i −0.0377695 + 0.0654187i −0.884292 0.466934i $$-0.845359\pi$$
0.846523 + 0.532353i $$0.178692\pi$$
$$702$$ 0 0
$$703$$ −2.00000 + 17.3205i −0.0754314 + 0.653255i
$$704$$ −4.00000 −0.150756
$$705$$ 0 0
$$706$$ 6.00000 10.3923i 0.225813 0.391120i
$$707$$ −7.00000 12.1244i −0.263262 0.455983i
$$708$$ 0 0
$$709$$ 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i $$-0.142735\pi$$
−0.826023 + 0.563636i $$0.809402\pi$$
$$710$$ 21.0000 0.788116
$$711$$ 0 0
$$712$$ 2.00000 + 3.46410i 0.0749532 + 0.129823i
$$713$$ −3.00000 5.19615i −0.112351 0.194597i
$$714$$ 0 0
$$715$$ −36.0000 −1.34632
$$716$$ 5.00000 + 8.66025i 0.186859 + 0.323649i
$$717$$ 0 0
$$718$$ 12.0000 + 20.7846i 0.447836 + 0.775675i
$$719$$ 11.0000 19.0526i 0.410231 0.710541i −0.584684 0.811261i $$-0.698781\pi$$
0.994915 + 0.100721i $$0.0321148\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 13.0000 13.8564i 0.483810 0.515682i
$$723$$ 0 0
$$724$$ −1.50000 + 2.59808i −0.0557471 + 0.0965567i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −22.0000 + 38.1051i −0.815935 + 1.41324i 0.0927199 + 0.995692i $$0.470444\pi$$
−0.908655 + 0.417548i $$0.862889\pi$$
$$728$$ 1.50000 + 2.59808i 0.0555937 + 0.0962911i
$$729$$ 0 0
$$730$$ −6.00000 −0.222070
$$731$$ 6.00000 + 10.3923i 0.221918 + 0.384373i
$$732$$ 0 0
$$733$$ −11.0000 −0.406294 −0.203147 0.979148i $$-0.565117\pi$$
−0.203147 + 0.979148i $$0.565117\pi$$
$$734$$ 32.0000 1.18114
$$735$$ 0 0
$$736$$ 0.500000 0.866025i 0.0184302 0.0319221i
$$737$$ −24.0000 41.5692i −0.884051 1.53122i
$$738$$ 0 0
$$739$$ 22.0000 38.1051i 0.809283 1.40172i −0.104078 0.994569i $$-0.533189\pi$$
0.913361 0.407150i $$-0.133477\pi$$
$$740$$ 12.0000 0.441129
$$741$$ 0 0
$$742$$ −4.00000 −0.146845
$$743$$ −1.50000 + 2.59808i −0.0550297 + 0.0953142i −0.892228 0.451585i $$-0.850859\pi$$
0.837198 + 0.546899i $$0.184192\pi$$
$$744$$ 0 0
$$745$$ 30.0000 + 51.9615i 1.09911 + 1.90372i
$$746$$ 5.00000 8.66025i 0.183063 0.317074i
$$747$$ 0 0
$$748$$ −8.00000 −0.292509
$$749$$ −10.0000 −0.365392
$$750$$ 0 0
$$751$$ −20.0000 34.6410i −0.729810 1.26407i −0.956963 0.290209i $$-0.906275\pi$$
0.227153 0.973859i $$-0.427058\pi$$
$$752$$ 2.00000 0.0729325
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −28.5000 + 49.3634i −1.03722 + 1.79652i
$$756$$ 0 0
$$757$$ 23.0000 39.8372i 0.835949 1.44791i −0.0573060 0.998357i $$-0.518251\pi$$
0.893255 0.449550i $$-0.148416\pi$$
$$758$$ 17.0000 29.4449i 0.617468 1.06949i
$$759$$ 0 0
$$760$$ −10.5000 7.79423i −0.380875 0.282726i
$$761$$ −8.00000 −0.290000 −0.145000 0.989432i $$-0.546318\pi$$
−0.145000 + 0.989432i $$0.546318\pi$$
$$762$$ 0 0
$$763$$ −2.00000 + 3.46410i −0.0724049 + 0.125409i
$$764$$ −5.50000 9.52628i −0.198983 0.344649i
$$765$$ 0 0
$$766$$ −2.00000 3.46410i −0.0722629 0.125163i
$$767$$ −39.0000 −1.40821
$$768$$ 0 0
$$769$$ 15.0000 + 25.9808i 0.540914 + 0.936890i 0.998852 + 0.0479061i $$0.0152548\pi$$
−0.457938 + 0.888984i $$0.651412\pi$$
$$770$$ −6.00000 10.3923i −0.216225 0.374513i
$$771$$ 0 0
$$772$$ 5.00000 0.179954
$$773$$ 4.50000 + 7.79423i 0.161854 + 0.280339i 0.935534 0.353238i $$-0.114919\pi$$
−0.773680 + 0.633577i $$0.781586\pi$$
$$774$$ 0 0
$$775$$ 12.0000 + 20.7846i 0.431053 + 0.746605i
$$776$$ 5.00000 8.66025i 0.179490 0.310885i
$$777$$ 0 0
$$778$$ −8.00000 −0.286814
$$779$$ 14.0000 + 10.3923i 0.501602 + 0.372343i
$$780$$ 0 0
$$781$$ 14.0000 24.2487i 0.500959 0.867687i
$$782$$ 1.00000 1.73205i 0.0357599 0.0619380i
$$783$$ 0 0
$$784$$ −0.500000 + 0.866025i −0.0178571 + 0.0309295i
$$785$$ 13.5000 + 23.3827i 0.481836 + 0.834564i
$$786$$ 0 0
$$787$$ −47.0000 −1.67537 −0.837685 0.546154i $$-0.816091\pi$$
−0.837685 + 0.546154i $$0.816091\pi$$
$$788$$ 2.00000 + 3.46410i 0.0712470 + 0.123404i