# Properties

 Label 91.2.k.a.4.1 Level $91$ Weight $2$ Character 91.4 Analytic conductor $0.727$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$91 = 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 91.k (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.726638658394$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 4.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 91.4 Dual form 91.2.k.a.23.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.73205i q^{2} +(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(1.50000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-2.00000 + 1.73205i) q^{7} -1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q-1.73205i q^{2} +(0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(1.50000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-2.00000 + 1.73205i) q^{7} -1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-4.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 3.46410i) q^{13} +(3.00000 + 3.46410i) q^{14} +(1.50000 + 0.866025i) q^{15} -5.00000 q^{16} +6.00000 q^{17} +(-3.00000 - 1.73205i) q^{18} +(-1.50000 - 0.866025i) q^{19} +(-1.50000 + 0.866025i) q^{20} +(-2.50000 - 0.866025i) q^{21} +(4.50000 + 7.79423i) q^{22} +(1.50000 - 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(6.00000 + 1.73205i) q^{26} +5.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(1.50000 - 2.59808i) q^{30} +(-1.50000 - 0.866025i) q^{31} +5.19615i q^{32} +(-4.50000 - 2.59808i) q^{33} -10.3923i q^{34} +(-1.50000 + 4.33013i) q^{35} +(-1.00000 + 1.73205i) q^{36} +(-1.50000 + 2.59808i) q^{38} +(-3.50000 + 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-4.50000 - 2.59808i) q^{41} +(-1.50000 + 4.33013i) q^{42} +(-5.50000 - 9.52628i) q^{43} +(4.50000 - 2.59808i) q^{44} -3.46410i q^{45} +(7.50000 - 4.33013i) q^{47} +(-2.50000 - 4.33013i) q^{48} +(1.00000 - 6.92820i) q^{49} +(3.00000 + 1.73205i) q^{50} +(3.00000 + 5.19615i) q^{51} +(1.00000 - 3.46410i) q^{52} +(4.50000 - 7.79423i) q^{53} -8.66025i q^{54} +(-4.50000 + 7.79423i) q^{55} +(3.00000 + 3.46410i) q^{56} -1.73205i q^{57} +(4.50000 + 2.59808i) q^{58} +3.46410i q^{59} +(-1.50000 - 0.866025i) q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 + 2.59808i) q^{62} +(1.00000 + 5.19615i) q^{63} -1.00000 q^{64} +(1.50000 + 6.06218i) q^{65} +(-4.50000 + 7.79423i) q^{66} +(7.50000 - 4.33013i) q^{67} -6.00000 q^{68} +(7.50000 + 2.59808i) q^{70} +(1.50000 - 0.866025i) q^{71} +(-3.00000 - 1.73205i) q^{72} +(7.50000 + 4.33013i) q^{73} -2.00000 q^{75} +(1.50000 + 0.866025i) q^{76} +(4.50000 - 12.9904i) q^{77} +(1.50000 + 6.06218i) q^{78} +(2.50000 + 4.33013i) q^{79} +(-7.50000 + 4.33013i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} -3.46410i q^{83} +(2.50000 + 0.866025i) q^{84} +(9.00000 - 5.19615i) q^{85} +(-16.5000 + 9.52628i) q^{86} -3.00000 q^{87} +(4.50000 + 7.79423i) q^{88} -6.92820i q^{89} -6.00000 q^{90} +(-4.00000 - 8.66025i) q^{91} -1.73205i q^{93} +(-7.50000 - 12.9904i) q^{94} -3.00000 q^{95} +(-4.50000 + 2.59808i) q^{96} +(-4.50000 + 2.59808i) q^{97} +(-12.0000 - 1.73205i) q^{98} +10.3923i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{3} - 2q^{4} + 3q^{5} + 3q^{6} - 4q^{7} + 2q^{9} + O(q^{10})$$ $$2q + q^{3} - 2q^{4} + 3q^{5} + 3q^{6} - 4q^{7} + 2q^{9} - 3q^{10} - 9q^{11} - q^{12} - 2q^{13} + 6q^{14} + 3q^{15} - 10q^{16} + 12q^{17} - 6q^{18} - 3q^{19} - 3q^{20} - 5q^{21} + 9q^{22} + 3q^{24} - 2q^{25} + 12q^{26} + 10q^{27} + 4q^{28} - 3q^{29} + 3q^{30} - 3q^{31} - 9q^{33} - 3q^{35} - 2q^{36} - 3q^{38} - 7q^{39} - 3q^{40} - 9q^{41} - 3q^{42} - 11q^{43} + 9q^{44} + 15q^{47} - 5q^{48} + 2q^{49} + 6q^{50} + 6q^{51} + 2q^{52} + 9q^{53} - 9q^{55} + 6q^{56} + 9q^{58} - 3q^{60} - 7q^{61} - 3q^{62} + 2q^{63} - 2q^{64} + 3q^{65} - 9q^{66} + 15q^{67} - 12q^{68} + 15q^{70} + 3q^{71} - 6q^{72} + 15q^{73} - 4q^{75} + 3q^{76} + 9q^{77} + 3q^{78} + 5q^{79} - 15q^{80} - q^{81} - 9q^{82} + 5q^{84} + 18q^{85} - 33q^{86} - 6q^{87} + 9q^{88} - 12q^{90} - 8q^{91} - 15q^{94} - 6q^{95} - 9q^{96} - 9q^{97} - 24q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$$.

 $$n$$ $$15$$ $$66$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.73205i 1.22474i −0.790569 0.612372i $$-0.790215\pi$$
0.790569 0.612372i $$-0.209785\pi$$
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i $$-0.0734519\pi$$
−0.684819 + 0.728714i $$0.740119\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i $$-0.540075\pi$$
0.796387 + 0.604787i $$0.206742\pi$$
$$6$$ 1.50000 0.866025i 0.612372 0.353553i
$$7$$ −2.00000 + 1.73205i −0.755929 + 0.654654i
$$8$$ 1.73205i 0.612372i
$$9$$ 1.00000 1.73205i 0.333333 0.577350i
$$10$$ −1.50000 2.59808i −0.474342 0.821584i
$$11$$ −4.50000 + 2.59808i −1.35680 + 0.783349i −0.989191 0.146631i $$-0.953157\pi$$
−0.367610 + 0.929980i $$0.619824\pi$$
$$12$$ −0.500000 0.866025i −0.144338 0.250000i
$$13$$ −1.00000 + 3.46410i −0.277350 + 0.960769i
$$14$$ 3.00000 + 3.46410i 0.801784 + 0.925820i
$$15$$ 1.50000 + 0.866025i 0.387298 + 0.223607i
$$16$$ −5.00000 −1.25000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ −3.00000 1.73205i −0.707107 0.408248i
$$19$$ −1.50000 0.866025i −0.344124 0.198680i 0.317970 0.948101i $$-0.396999\pi$$
−0.662094 + 0.749421i $$0.730332\pi$$
$$20$$ −1.50000 + 0.866025i −0.335410 + 0.193649i
$$21$$ −2.50000 0.866025i −0.545545 0.188982i
$$22$$ 4.50000 + 7.79423i 0.959403 + 1.66174i
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 1.50000 0.866025i 0.306186 0.176777i
$$25$$ −1.00000 + 1.73205i −0.200000 + 0.346410i
$$26$$ 6.00000 + 1.73205i 1.17670 + 0.339683i
$$27$$ 5.00000 0.962250
$$28$$ 2.00000 1.73205i 0.377964 0.327327i
$$29$$ −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i $$-0.923185\pi$$
0.692480 + 0.721437i $$0.256518\pi$$
$$30$$ 1.50000 2.59808i 0.273861 0.474342i
$$31$$ −1.50000 0.866025i −0.269408 0.155543i 0.359211 0.933257i $$-0.383046\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ 5.19615i 0.918559i
$$33$$ −4.50000 2.59808i −0.783349 0.452267i
$$34$$ 10.3923i 1.78227i
$$35$$ −1.50000 + 4.33013i −0.253546 + 0.731925i
$$36$$ −1.00000 + 1.73205i −0.166667 + 0.288675i
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ −1.50000 + 2.59808i −0.243332 + 0.421464i
$$39$$ −3.50000 + 0.866025i −0.560449 + 0.138675i
$$40$$ −1.50000 2.59808i −0.237171 0.410792i
$$41$$ −4.50000 2.59808i −0.702782 0.405751i 0.105601 0.994409i $$-0.466323\pi$$
−0.808383 + 0.588657i $$0.799657\pi$$
$$42$$ −1.50000 + 4.33013i −0.231455 + 0.668153i
$$43$$ −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i $$-0.849958\pi$$
0.0522047 0.998636i $$-0.483375\pi$$
$$44$$ 4.50000 2.59808i 0.678401 0.391675i
$$45$$ 3.46410i 0.516398i
$$46$$ 0 0
$$47$$ 7.50000 4.33013i 1.09399 0.631614i 0.159352 0.987222i $$-0.449059\pi$$
0.934635 + 0.355608i $$0.115726\pi$$
$$48$$ −2.50000 4.33013i −0.360844 0.625000i
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 3.00000 + 1.73205i 0.424264 + 0.244949i
$$51$$ 3.00000 + 5.19615i 0.420084 + 0.727607i
$$52$$ 1.00000 3.46410i 0.138675 0.480384i
$$53$$ 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i $$-0.621227\pi$$
0.989828 0.142269i $$-0.0454398\pi$$
$$54$$ 8.66025i 1.17851i
$$55$$ −4.50000 + 7.79423i −0.606780 + 1.05097i
$$56$$ 3.00000 + 3.46410i 0.400892 + 0.462910i
$$57$$ 1.73205i 0.229416i
$$58$$ 4.50000 + 2.59808i 0.590879 + 0.341144i
$$59$$ 3.46410i 0.450988i 0.974245 + 0.225494i $$0.0723995\pi$$
−0.974245 + 0.225494i $$0.927600\pi$$
$$60$$ −1.50000 0.866025i −0.193649 0.111803i
$$61$$ −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i $$-0.981243\pi$$
0.550135 + 0.835076i $$0.314576\pi$$
$$62$$ −1.50000 + 2.59808i −0.190500 + 0.329956i
$$63$$ 1.00000 + 5.19615i 0.125988 + 0.654654i
$$64$$ −1.00000 −0.125000
$$65$$ 1.50000 + 6.06218i 0.186052 + 0.751921i
$$66$$ −4.50000 + 7.79423i −0.553912 + 0.959403i
$$67$$ 7.50000 4.33013i 0.916271 0.529009i 0.0338274 0.999428i $$-0.489230\pi$$
0.882443 + 0.470418i $$0.155897\pi$$
$$68$$ −6.00000 −0.727607
$$69$$ 0 0
$$70$$ 7.50000 + 2.59808i 0.896421 + 0.310530i
$$71$$ 1.50000 0.866025i 0.178017 0.102778i −0.408344 0.912828i $$-0.633893\pi$$
0.586361 + 0.810050i $$0.300560\pi$$
$$72$$ −3.00000 1.73205i −0.353553 0.204124i
$$73$$ 7.50000 + 4.33013i 0.877809 + 0.506803i 0.869935 0.493166i $$-0.164160\pi$$
0.00787336 + 0.999969i $$0.497494\pi$$
$$74$$ 0 0
$$75$$ −2.00000 −0.230940
$$76$$ 1.50000 + 0.866025i 0.172062 + 0.0993399i
$$77$$ 4.50000 12.9904i 0.512823 1.48039i
$$78$$ 1.50000 + 6.06218i 0.169842 + 0.686406i
$$79$$ 2.50000 + 4.33013i 0.281272 + 0.487177i 0.971698 0.236225i $$-0.0759104\pi$$
−0.690426 + 0.723403i $$0.742577\pi$$
$$80$$ −7.50000 + 4.33013i −0.838525 + 0.484123i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −4.50000 + 7.79423i −0.496942 + 0.860729i
$$83$$ 3.46410i 0.380235i −0.981761 0.190117i $$-0.939113\pi$$
0.981761 0.190117i $$-0.0608868\pi$$
$$84$$ 2.50000 + 0.866025i 0.272772 + 0.0944911i
$$85$$ 9.00000 5.19615i 0.976187 0.563602i
$$86$$ −16.5000 + 9.52628i −1.77924 + 1.02725i
$$87$$ −3.00000 −0.321634
$$88$$ 4.50000 + 7.79423i 0.479702 + 0.830868i
$$89$$ 6.92820i 0.734388i −0.930144 0.367194i $$-0.880318\pi$$
0.930144 0.367194i $$-0.119682\pi$$
$$90$$ −6.00000 −0.632456
$$91$$ −4.00000 8.66025i −0.419314 0.907841i
$$92$$ 0 0
$$93$$ 1.73205i 0.179605i
$$94$$ −7.50000 12.9904i −0.773566 1.33986i
$$95$$ −3.00000 −0.307794
$$96$$ −4.50000 + 2.59808i −0.459279 + 0.265165i
$$97$$ −4.50000 + 2.59808i −0.456906 + 0.263795i −0.710742 0.703452i $$-0.751641\pi$$
0.253837 + 0.967247i $$0.418307\pi$$
$$98$$ −12.0000 1.73205i −1.21218 0.174964i
$$99$$ 10.3923i 1.04447i
$$100$$ 1.00000 1.73205i 0.100000 0.173205i
$$101$$ 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i $$-0.0188862\pi$$
−0.550474 + 0.834853i $$0.685553\pi$$
$$102$$ 9.00000 5.19615i 0.891133 0.514496i
$$103$$ 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i $$0.0545913\pi$$
−0.344865 + 0.938652i $$0.612075\pi$$
$$104$$ 6.00000 + 1.73205i 0.588348 + 0.169842i
$$105$$ −4.50000 + 0.866025i −0.439155 + 0.0845154i
$$106$$ −13.5000 7.79423i −1.31124 0.757042i
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ −5.00000 −0.481125
$$109$$ −4.50000 2.59808i −0.431022 0.248851i 0.268760 0.963207i $$-0.413386\pi$$
−0.699782 + 0.714357i $$0.746719\pi$$
$$110$$ 13.5000 + 7.79423i 1.28717 + 0.743151i
$$111$$ 0 0
$$112$$ 10.0000 8.66025i 0.944911 0.818317i
$$113$$ −7.50000 12.9904i −0.705541 1.22203i −0.966496 0.256681i $$-0.917371\pi$$
0.260955 0.965351i $$-0.415962\pi$$
$$114$$ −3.00000 −0.280976
$$115$$ 0 0
$$116$$ 1.50000 2.59808i 0.139272 0.241225i
$$117$$ 5.00000 + 5.19615i 0.462250 + 0.480384i
$$118$$ 6.00000 0.552345
$$119$$ −12.0000 + 10.3923i −1.10004 + 0.952661i
$$120$$ 1.50000 2.59808i 0.136931 0.237171i
$$121$$ 8.00000 13.8564i 0.727273 1.25967i
$$122$$ 10.5000 + 6.06218i 0.950625 + 0.548844i
$$123$$ 5.19615i 0.468521i
$$124$$ 1.50000 + 0.866025i 0.134704 + 0.0777714i
$$125$$ 12.1244i 1.08444i
$$126$$ 9.00000 1.73205i 0.801784 0.154303i
$$127$$ −6.50000 + 11.2583i −0.576782 + 0.999015i 0.419064 + 0.907957i $$0.362358\pi$$
−0.995846 + 0.0910585i $$0.970975\pi$$
$$128$$ 12.1244i 1.07165i
$$129$$ 5.50000 9.52628i 0.484248 0.838742i
$$130$$ 10.5000 2.59808i 0.920911 0.227866i
$$131$$ −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i $$-0.939218\pi$$
0.326546 0.945181i $$-0.394115\pi$$
$$132$$ 4.50000 + 2.59808i 0.391675 + 0.226134i
$$133$$ 4.50000 0.866025i 0.390199 0.0750939i
$$134$$ −7.50000 12.9904i −0.647901 1.12220i
$$135$$ 7.50000 4.33013i 0.645497 0.372678i
$$136$$ 10.3923i 0.891133i
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 6.50000 + 11.2583i 0.551323 + 0.954919i 0.998179 + 0.0603135i $$0.0192101\pi$$
−0.446857 + 0.894606i $$0.647457\pi$$
$$140$$ 1.50000 4.33013i 0.126773 0.365963i
$$141$$ 7.50000 + 4.33013i 0.631614 + 0.364662i
$$142$$ −1.50000 2.59808i −0.125877 0.218026i
$$143$$ −4.50000 18.1865i −0.376309 1.52083i
$$144$$ −5.00000 + 8.66025i −0.416667 + 0.721688i
$$145$$ 5.19615i 0.431517i
$$146$$ 7.50000 12.9904i 0.620704 1.07509i
$$147$$ 6.50000 2.59808i 0.536111 0.214286i
$$148$$ 0 0
$$149$$ −16.5000 9.52628i −1.35173 0.780423i −0.363241 0.931695i $$-0.618330\pi$$
−0.988492 + 0.151272i $$0.951663\pi$$
$$150$$ 3.46410i 0.282843i
$$151$$ 10.5000 + 6.06218i 0.854478 + 0.493333i 0.862159 0.506637i $$-0.169112\pi$$
−0.00768132 + 0.999970i $$0.502445\pi$$
$$152$$ −1.50000 + 2.59808i −0.121666 + 0.210732i
$$153$$ 6.00000 10.3923i 0.485071 0.840168i
$$154$$ −22.5000 7.79423i −1.81310 0.628077i
$$155$$ −3.00000 −0.240966
$$156$$ 3.50000 0.866025i 0.280224 0.0693375i
$$157$$ −11.5000 + 19.9186i −0.917800 + 1.58968i −0.115050 + 0.993360i $$0.536703\pi$$
−0.802749 + 0.596316i $$0.796630\pi$$
$$158$$ 7.50000 4.33013i 0.596668 0.344486i
$$159$$ 9.00000 0.713746
$$160$$ 4.50000 + 7.79423i 0.355756 + 0.616188i
$$161$$ 0 0
$$162$$ −1.50000 + 0.866025i −0.117851 + 0.0680414i
$$163$$ 10.5000 + 6.06218i 0.822423 + 0.474826i 0.851251 0.524758i $$-0.175844\pi$$
−0.0288280 + 0.999584i $$0.509178\pi$$
$$164$$ 4.50000 + 2.59808i 0.351391 + 0.202876i
$$165$$ −9.00000 −0.700649
$$166$$ −6.00000 −0.465690
$$167$$ −1.50000 0.866025i −0.116073 0.0670151i 0.440839 0.897586i $$-0.354681\pi$$
−0.556913 + 0.830571i $$0.688014\pi$$
$$168$$ −1.50000 + 4.33013i −0.115728 + 0.334077i
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ −9.00000 15.5885i −0.690268 1.19558i
$$171$$ −3.00000 + 1.73205i −0.229416 + 0.132453i
$$172$$ 5.50000 + 9.52628i 0.419371 + 0.726372i
$$173$$ −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i $$0.359807\pi$$
−0.996544 + 0.0830722i $$0.973527\pi$$
$$174$$ 5.19615i 0.393919i
$$175$$ −1.00000 5.19615i −0.0755929 0.392792i
$$176$$ 22.5000 12.9904i 1.69600 0.979187i
$$177$$ −3.00000 + 1.73205i −0.225494 + 0.130189i
$$178$$ −12.0000 −0.899438
$$179$$ −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i $$-0.202429\pi$$
−0.916623 + 0.399753i $$0.869096\pi$$
$$180$$ 3.46410i 0.258199i
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ −15.0000 + 6.92820i −1.11187 + 0.513553i
$$183$$ −7.00000 −0.517455
$$184$$ 0 0
$$185$$ 0 0
$$186$$ −3.00000 −0.219971
$$187$$ −27.0000 + 15.5885i −1.97444 + 1.13994i
$$188$$ −7.50000 + 4.33013i −0.546994 + 0.315807i
$$189$$ −10.0000 + 8.66025i −0.727393 + 0.629941i
$$190$$ 5.19615i 0.376969i
$$191$$ 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i $$-0.650743\pi$$
0.998749 0.0500060i $$-0.0159241\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ 1.50000 0.866025i 0.107972 0.0623379i −0.445041 0.895510i $$-0.646811\pi$$
0.553014 + 0.833172i $$0.313478\pi$$
$$194$$ 4.50000 + 7.79423i 0.323081 + 0.559593i
$$195$$ −4.50000 + 4.33013i −0.322252 + 0.310087i
$$196$$ −1.00000 + 6.92820i −0.0714286 + 0.494872i
$$197$$ 19.5000 + 11.2583i 1.38932 + 0.802123i 0.993238 0.116094i $$-0.0370372\pi$$
0.396079 + 0.918216i $$0.370371\pi$$
$$198$$ 18.0000 1.27920
$$199$$ 4.00000 0.283552 0.141776 0.989899i $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 3.00000 + 1.73205i 0.212132 + 0.122474i
$$201$$ 7.50000 + 4.33013i 0.529009 + 0.305424i
$$202$$ 13.5000 7.79423i 0.949857 0.548400i
$$203$$ −1.50000 7.79423i −0.105279 0.547048i
$$204$$ −3.00000 5.19615i −0.210042 0.363803i
$$205$$ −9.00000 −0.628587
$$206$$ 19.5000 11.2583i 1.35863 0.784405i
$$207$$ 0 0
$$208$$ 5.00000 17.3205i 0.346688 1.20096i
$$209$$ 9.00000 0.622543
$$210$$ 1.50000 + 7.79423i 0.103510 + 0.537853i
$$211$$ −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i $$-0.981011\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ −4.50000 + 7.79423i −0.309061 + 0.535310i
$$213$$ 1.50000 + 0.866025i 0.102778 + 0.0593391i
$$214$$ 0 0
$$215$$ −16.5000 9.52628i −1.12529 0.649687i
$$216$$ 8.66025i 0.589256i
$$217$$ 4.50000 0.866025i 0.305480 0.0587896i
$$218$$ −4.50000 + 7.79423i −0.304778 + 0.527892i
$$219$$ 8.66025i 0.585206i
$$220$$ 4.50000 7.79423i 0.303390 0.525487i
$$221$$ −6.00000 + 20.7846i −0.403604 + 1.39812i
$$222$$ 0 0
$$223$$ 4.50000 + 2.59808i 0.301342 + 0.173980i 0.643046 0.765828i $$-0.277671\pi$$
−0.341703 + 0.939808i $$0.611004\pi$$
$$224$$ −9.00000 10.3923i −0.601338 0.694365i
$$225$$ 2.00000 + 3.46410i 0.133333 + 0.230940i
$$226$$ −22.5000 + 12.9904i −1.49668 + 0.864107i
$$227$$ 17.3205i 1.14960i 0.818293 + 0.574801i $$0.194921\pi$$
−0.818293 + 0.574801i $$0.805079\pi$$
$$228$$ 1.73205i 0.114708i
$$229$$ −10.5000 + 6.06218i −0.693860 + 0.400600i −0.805056 0.593198i $$-0.797865\pi$$
0.111197 + 0.993798i $$0.464532\pi$$
$$230$$ 0 0
$$231$$ 13.5000 2.59808i 0.888235 0.170941i
$$232$$ 4.50000 + 2.59808i 0.295439 + 0.170572i
$$233$$ −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i $$-0.197997\pi$$
−0.910968 + 0.412477i $$0.864664\pi$$
$$234$$ 9.00000 8.66025i 0.588348 0.566139i
$$235$$ 7.50000 12.9904i 0.489246 0.847399i
$$236$$ 3.46410i 0.225494i
$$237$$ −2.50000 + 4.33013i −0.162392 + 0.281272i
$$238$$ 18.0000 + 20.7846i 1.16677 + 1.34727i
$$239$$ 10.3923i 0.672222i −0.941822 0.336111i $$-0.890888\pi$$
0.941822 0.336111i $$-0.109112\pi$$
$$240$$ −7.50000 4.33013i −0.484123 0.279508i
$$241$$ 6.92820i 0.446285i 0.974786 + 0.223142i $$0.0716315\pi$$
−0.974786 + 0.223142i $$0.928369\pi$$
$$242$$ −24.0000 13.8564i −1.54278 0.890724i
$$243$$ 8.00000 13.8564i 0.513200 0.888889i
$$244$$ 3.50000 6.06218i 0.224065 0.388091i
$$245$$ −4.50000 11.2583i −0.287494 0.719268i
$$246$$ −9.00000 −0.573819
$$247$$ 4.50000 4.33013i 0.286328 0.275519i
$$248$$ −1.50000 + 2.59808i −0.0952501 + 0.164978i
$$249$$ 3.00000 1.73205i 0.190117 0.109764i
$$250$$ 21.0000 1.32816
$$251$$ −1.50000 2.59808i −0.0946792 0.163989i 0.814795 0.579748i $$-0.196849\pi$$
−0.909475 + 0.415759i $$0.863516\pi$$
$$252$$ −1.00000 5.19615i −0.0629941 0.327327i
$$253$$ 0 0
$$254$$ 19.5000 + 11.2583i 1.22354 + 0.706410i
$$255$$ 9.00000 + 5.19615i 0.563602 + 0.325396i
$$256$$ 19.0000 1.18750
$$257$$ 30.0000 1.87135 0.935674 0.352865i $$-0.114792\pi$$
0.935674 + 0.352865i $$0.114792\pi$$
$$258$$ −16.5000 9.52628i −1.02725 0.593080i
$$259$$ 0 0
$$260$$ −1.50000 6.06218i −0.0930261 0.375960i
$$261$$ 3.00000 + 5.19615i 0.185695 + 0.321634i
$$262$$ −22.5000 + 12.9904i −1.39005 + 0.802548i
$$263$$ −1.50000 2.59808i −0.0924940 0.160204i 0.816066 0.577959i $$-0.196151\pi$$
−0.908560 + 0.417755i $$0.862817\pi$$
$$264$$ −4.50000 + 7.79423i −0.276956 + 0.479702i
$$265$$ 15.5885i 0.957591i
$$266$$ −1.50000 7.79423i −0.0919709 0.477895i
$$267$$ 6.00000 3.46410i 0.367194 0.212000i
$$268$$ −7.50000 + 4.33013i −0.458135 + 0.264505i
$$269$$ −6.00000 −0.365826 −0.182913 0.983129i $$-0.558553\pi$$
−0.182913 + 0.983129i $$0.558553\pi$$
$$270$$ −7.50000 12.9904i −0.456435 0.790569i
$$271$$ 17.3205i 1.05215i −0.850439 0.526073i $$-0.823664\pi$$
0.850439 0.526073i $$-0.176336\pi$$
$$272$$ −30.0000 −1.81902
$$273$$ 5.50000 7.79423i 0.332875 0.471728i
$$274$$ 0 0
$$275$$ 10.3923i 0.626680i
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 19.5000 11.2583i 1.16953 0.675230i
$$279$$ −3.00000 + 1.73205i −0.179605 + 0.103695i
$$280$$ 7.50000 + 2.59808i 0.448211 + 0.155265i
$$281$$ 6.92820i 0.413302i 0.978415 + 0.206651i $$0.0662565\pi$$
−0.978415 + 0.206651i $$0.933744\pi$$
$$282$$ 7.50000 12.9904i 0.446619 0.773566i
$$283$$ −9.50000 16.4545i −0.564716 0.978117i −0.997076 0.0764162i $$-0.975652\pi$$
0.432360 0.901701i $$-0.357681\pi$$
$$284$$ −1.50000 + 0.866025i −0.0890086 + 0.0513892i
$$285$$ −1.50000 2.59808i −0.0888523 0.153897i
$$286$$ −31.5000 + 7.79423i −1.86263 + 0.460882i
$$287$$ 13.5000 2.59808i 0.796880 0.153360i
$$288$$ 9.00000 + 5.19615i 0.530330 + 0.306186i
$$289$$ 19.0000 1.11765
$$290$$ 9.00000 0.528498
$$291$$ −4.50000 2.59808i −0.263795 0.152302i
$$292$$ −7.50000 4.33013i −0.438904 0.253402i
$$293$$ −22.5000 + 12.9904i −1.31446 + 0.758906i −0.982832 0.184503i $$-0.940933\pi$$
−0.331632 + 0.943409i $$0.607599\pi$$
$$294$$ −4.50000 11.2583i −0.262445 0.656599i
$$295$$ 3.00000 + 5.19615i 0.174667 + 0.302532i
$$296$$ 0 0
$$297$$ −22.5000 + 12.9904i −1.30558 + 0.753778i
$$298$$ −16.5000 + 28.5788i −0.955819 + 1.65553i
$$299$$ 0 0
$$300$$ 2.00000 0.115470
$$301$$ 27.5000 + 9.52628i 1.58507 + 0.549086i
$$302$$ 10.5000 18.1865i 0.604207 1.04652i
$$303$$ −4.50000 + 7.79423i −0.258518 + 0.447767i
$$304$$ 7.50000 + 4.33013i 0.430155 + 0.248350i
$$305$$ 12.1244i 0.694239i
$$306$$ −18.0000 10.3923i −1.02899 0.594089i
$$307$$ 24.2487i 1.38395i −0.721923 0.691974i $$-0.756741\pi$$
0.721923 0.691974i $$-0.243259\pi$$
$$308$$ −4.50000 + 12.9904i −0.256411 + 0.740196i
$$309$$ −6.50000 + 11.2583i −0.369772 + 0.640464i
$$310$$ 5.19615i 0.295122i
$$311$$ 7.50000 12.9904i 0.425286 0.736617i −0.571161 0.820838i $$-0.693507\pi$$
0.996447 + 0.0842210i $$0.0268402\pi$$
$$312$$ 1.50000 + 6.06218i 0.0849208 + 0.343203i
$$313$$ −9.50000 16.4545i −0.536972 0.930062i −0.999065 0.0432311i $$-0.986235\pi$$
0.462093 0.886831i $$-0.347098\pi$$
$$314$$ 34.5000 + 19.9186i 1.94695 + 1.12407i
$$315$$ 6.00000 + 6.92820i 0.338062 + 0.390360i
$$316$$ −2.50000 4.33013i −0.140636 0.243589i
$$317$$ −4.50000 + 2.59808i −0.252745 + 0.145922i −0.621021 0.783794i $$-0.713282\pi$$
0.368275 + 0.929717i $$0.379948\pi$$
$$318$$ 15.5885i 0.874157i
$$319$$ 15.5885i 0.872786i
$$320$$ −1.50000 + 0.866025i −0.0838525 + 0.0484123i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −9.00000 5.19615i −0.500773 0.289122i
$$324$$ 0.500000 + 0.866025i 0.0277778 + 0.0481125i
$$325$$ −5.00000 5.19615i −0.277350 0.288231i
$$326$$ 10.5000 18.1865i 0.581541 1.00726i
$$327$$ 5.19615i 0.287348i
$$328$$ −4.50000 + 7.79423i −0.248471 + 0.430364i
$$329$$ −7.50000 + 21.6506i −0.413488 + 1.19364i
$$330$$ 15.5885i 0.858116i
$$331$$ 28.5000 + 16.4545i 1.56650 + 0.904420i 0.996572 + 0.0827265i $$0.0263628\pi$$
0.569929 + 0.821694i $$0.306971\pi$$
$$332$$ 3.46410i 0.190117i
$$333$$ 0 0
$$334$$ −1.50000 + 2.59808i −0.0820763 + 0.142160i
$$335$$ 7.50000 12.9904i 0.409769 0.709740i
$$336$$ 12.5000 + 4.33013i 0.681931 + 0.236228i
$$337$$ 22.0000 1.19842 0.599208 0.800593i $$-0.295482\pi$$
0.599208 + 0.800593i $$0.295482\pi$$
$$338$$ −12.0000 + 19.0526i −0.652714 + 1.03632i
$$339$$ 7.50000 12.9904i 0.407344 0.705541i
$$340$$ −9.00000 + 5.19615i −0.488094 + 0.281801i
$$341$$ 9.00000 0.487377
$$342$$ 3.00000 + 5.19615i 0.162221 + 0.280976i
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ −16.5000 + 9.52628i −0.889620 + 0.513623i
$$345$$ 0 0
$$346$$ 22.5000 + 12.9904i 1.20961 + 0.698367i
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 3.00000 0.160817
$$349$$ −4.50000 2.59808i −0.240879 0.139072i 0.374701 0.927146i $$-0.377745\pi$$
−0.615581 + 0.788074i $$0.711079\pi$$
$$350$$ −9.00000 + 1.73205i −0.481070 + 0.0925820i
$$351$$ −5.00000 + 17.3205i −0.266880 + 0.924500i
$$352$$ −13.5000 23.3827i −0.719552 1.24630i
$$353$$ 1.50000 0.866025i 0.0798369 0.0460939i −0.459550 0.888152i $$-0.651989\pi$$
0.539387 + 0.842058i $$0.318656\pi$$
$$354$$ 3.00000 + 5.19615i 0.159448 + 0.276172i
$$355$$ 1.50000 2.59808i 0.0796117 0.137892i
$$356$$ 6.92820i 0.367194i
$$357$$ −15.0000 5.19615i −0.793884 0.275010i
$$358$$ −4.50000 + 2.59808i −0.237832 + 0.137313i
$$359$$ −16.5000 + 9.52628i −0.870837 + 0.502778i −0.867626 0.497217i $$-0.834355\pi$$
−0.00321050 + 0.999995i $$0.501022\pi$$
$$360$$ −6.00000 −0.316228
$$361$$ −8.00000 13.8564i −0.421053 0.729285i
$$362$$ 3.46410i 0.182069i
$$363$$ 16.0000 0.839782
$$364$$ 4.00000 + 8.66025i 0.209657 + 0.453921i
$$365$$ 15.0000 0.785136
$$366$$ 12.1244i 0.633750i
$$367$$ −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i $$-0.961716\pi$$
0.392481 0.919760i $$-0.371617\pi$$
$$368$$ 0 0
$$369$$ −9.00000 + 5.19615i −0.468521 + 0.270501i
$$370$$ 0 0
$$371$$ 4.50000 + 23.3827i 0.233628 + 1.21397i
$$372$$ 1.73205i 0.0898027i
$$373$$ −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i $$-0.997028\pi$$
0.508065 + 0.861319i $$0.330361\pi$$
$$374$$ 27.0000 + 46.7654i 1.39614 + 2.41818i
$$375$$ −10.5000 + 6.06218i −0.542218 + 0.313050i
$$376$$ −7.50000 12.9904i −0.386783 0.669928i
$$377$$ −7.50000 7.79423i −0.386270 0.401423i
$$378$$ 15.0000 + 17.3205i 0.771517 + 0.890871i
$$379$$ −1.50000 0.866025i −0.0770498 0.0444847i 0.460980 0.887410i $$-0.347498\pi$$
−0.538030 + 0.842926i $$0.680831\pi$$
$$380$$ 3.00000 0.153897
$$381$$ −13.0000 −0.666010
$$382$$ −22.5000 12.9904i −1.15120 0.664646i
$$383$$ −13.5000 7.79423i −0.689818 0.398266i 0.113726 0.993512i $$-0.463721\pi$$
−0.803544 + 0.595246i $$0.797055\pi$$
$$384$$ −10.5000 + 6.06218i −0.535826 + 0.309359i
$$385$$ −4.50000 23.3827i −0.229341 1.19169i
$$386$$ −1.50000 2.59808i −0.0763480 0.132239i
$$387$$ −22.0000 −1.11832
$$388$$ 4.50000 2.59808i 0.228453 0.131897i
$$389$$ −1.50000 + 2.59808i −0.0760530 + 0.131728i −0.901544 0.432688i $$-0.857565\pi$$
0.825491 + 0.564416i $$0.190898\pi$$
$$390$$ 7.50000 + 7.79423i 0.379777 + 0.394676i
$$391$$ 0 0
$$392$$ −12.0000 1.73205i −0.606092 0.0874818i
$$393$$ 7.50000 12.9904i 0.378325 0.655278i
$$394$$ 19.5000 33.7750i 0.982396 1.70156i
$$395$$ 7.50000 + 4.33013i 0.377366 + 0.217872i
$$396$$ 10.3923i 0.522233i
$$397$$ 31.5000 + 18.1865i 1.58094 + 0.912756i 0.994722 + 0.102602i $$0.0327168\pi$$
0.586217 + 0.810154i $$0.300617\pi$$
$$398$$ 6.92820i 0.347279i
$$399$$ 3.00000 + 3.46410i 0.150188 + 0.173422i
$$400$$ 5.00000 8.66025i 0.250000 0.433013i
$$401$$ 6.92820i 0.345978i −0.984924 0.172989i $$-0.944657\pi$$
0.984924 0.172989i $$-0.0553425\pi$$
$$402$$ 7.50000 12.9904i 0.374066 0.647901i
$$403$$ 4.50000 4.33013i 0.224161 0.215699i
$$404$$ −4.50000 7.79423i −0.223883 0.387777i
$$405$$ −1.50000 0.866025i −0.0745356 0.0430331i
$$406$$ −13.5000 + 2.59808i −0.669994 + 0.128940i
$$407$$ 0 0
$$408$$ 9.00000 5.19615i 0.445566 0.257248i
$$409$$ 6.92820i 0.342578i −0.985221 0.171289i $$-0.945207\pi$$
0.985221 0.171289i $$-0.0547931\pi$$
$$410$$ 15.5885i 0.769859i
$$411$$ 0 0
$$412$$ −6.50000 11.2583i −0.320232 0.554658i
$$413$$ −6.00000 6.92820i −0.295241 0.340915i
$$414$$ 0 0
$$415$$ −3.00000 5.19615i −0.147264 0.255069i
$$416$$ −18.0000 5.19615i −0.882523 0.254762i
$$417$$ −6.50000 + 11.2583i −0.318306 + 0.551323i
$$418$$ 15.5885i 0.762456i
$$419$$ −10.5000 + 18.1865i −0.512959 + 0.888470i 0.486928 + 0.873442i $$0.338117\pi$$
−0.999887 + 0.0150285i $$0.995216\pi$$
$$420$$ 4.50000 0.866025i 0.219578 0.0422577i
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 19.5000 + 11.2583i 0.949245 + 0.548047i
$$423$$ 17.3205i 0.842152i
$$424$$ −13.5000 7.79423i −0.655618 0.378521i
$$425$$ −6.00000 + 10.3923i −0.291043 + 0.504101i
$$426$$ 1.50000 2.59808i 0.0726752 0.125877i
$$427$$ −3.50000 18.1865i −0.169377 0.880108i
$$428$$ 0 0
$$429$$ 13.5000 12.9904i 0.651786 0.627182i
$$430$$ −16.5000 + 28.5788i −0.795701 + 1.37819i
$$431$$ −28.5000 + 16.4545i −1.37280 + 0.792585i −0.991279 0.131777i $$-0.957932\pi$$
−0.381517 + 0.924362i $$0.624598\pi$$
$$432$$ −25.0000 −1.20281
$$433$$ −9.50000 16.4545i −0.456541 0.790752i 0.542234 0.840227i $$-0.317578\pi$$
−0.998775 + 0.0494752i $$0.984245\pi$$
$$434$$ −1.50000 7.79423i −0.0720023 0.374135i
$$435$$ −4.50000 + 2.59808i −0.215758 + 0.124568i
$$436$$ 4.50000 + 2.59808i 0.215511 + 0.124425i
$$437$$ 0 0
$$438$$ 15.0000 0.716728
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 13.5000 + 7.79423i 0.643587 + 0.371575i
$$441$$ −11.0000 8.66025i −0.523810 0.412393i
$$442$$ 36.0000 + 10.3923i 1.71235 + 0.494312i
$$443$$ −7.50000 12.9904i −0.356336 0.617192i 0.631010 0.775775i $$-0.282641\pi$$
−0.987346 + 0.158583i $$0.949307\pi$$
$$444$$ 0 0
$$445$$ −6.00000 10.3923i −0.284427 0.492642i
$$446$$ 4.50000 7.79423i 0.213081 0.369067i
$$447$$ 19.0526i 0.901155i
$$448$$ 2.00000 1.73205i 0.0944911 0.0818317i
$$449$$ 1.50000 0.866025i 0.0707894 0.0408703i −0.464188 0.885737i $$-0.653654\pi$$
0.534977 + 0.844867i $$0.320320\pi$$
$$450$$ 6.00000 3.46410i 0.282843 0.163299i
$$451$$ 27.0000 1.27138
$$452$$ 7.50000 + 12.9904i 0.352770 + 0.611016i
$$453$$ 12.1244i 0.569652i
$$454$$ 30.0000 1.40797
$$455$$ −13.5000 9.52628i −0.632890 0.446599i
$$456$$ −3.00000 −0.140488
$$457$$ 34.6410i 1.62044i −0.586127 0.810219i $$-0.699348\pi$$
0.586127 0.810219i $$-0.300652\pi$$
$$458$$ 10.5000 + 18.1865i 0.490633 + 0.849801i
$$459$$ 30.0000 1.40028
$$460$$ 0 0
$$461$$ 25.5000 14.7224i 1.18765 0.685692i 0.229881 0.973219i $$-0.426166\pi$$
0.957773 + 0.287527i $$0.0928330\pi$$
$$462$$ −4.50000 23.3827i −0.209359 1.08786i
$$463$$ 24.2487i 1.12693i 0.826139 + 0.563467i $$0.190533\pi$$
−0.826139 + 0.563467i $$0.809467\pi$$
$$464$$ 7.50000 12.9904i 0.348179 0.603063i
$$465$$ −1.50000 2.59808i −0.0695608 0.120483i
$$466$$ −4.50000 + 2.59808i −0.208458 + 0.120354i
$$467$$ 10.5000 + 18.1865i 0.485882 + 0.841572i 0.999868 0.0162260i $$-0.00516512\pi$$
−0.513986 + 0.857798i $$0.671832\pi$$
$$468$$ −5.00000 5.19615i −0.231125 0.240192i
$$469$$ −7.50000 + 21.6506i −0.346318 + 0.999733i
$$470$$ −22.5000 12.9904i −1.03785 0.599202i
$$471$$ −23.0000 −1.05978
$$472$$ 6.00000 0.276172
$$473$$ 49.5000 + 28.5788i 2.27601 + 1.31406i
$$474$$ 7.50000 + 4.33013i 0.344486 + 0.198889i
$$475$$ 3.00000 1.73205i 0.137649 0.0794719i
$$476$$ 12.0000 10.3923i 0.550019 0.476331i
$$477$$ −9.00000 15.5885i −0.412082 0.713746i
$$478$$ −18.0000 −0.823301
$$479$$ 25.5000 14.7224i 1.16512 0.672685i 0.212598 0.977140i $$-0.431808\pi$$
0.952527 + 0.304455i $$0.0984742\pi$$
$$480$$ −4.50000 + 7.79423i −0.205396 + 0.355756i
$$481$$ 0 0
$$482$$ 12.0000 0.546585
$$483$$ 0 0
$$484$$ −8.00000 + 13.8564i −0.363636 + 0.629837i
$$485$$ −4.50000 + 7.79423i −0.204334 + 0.353918i
$$486$$ −24.0000 13.8564i −1.08866 0.628539i
$$487$$ 24.2487i 1.09881i 0.835555 + 0.549407i $$0.185146\pi$$
−0.835555 + 0.549407i $$0.814854\pi$$
$$488$$ 10.5000 + 6.06218i 0.475313 + 0.274422i
$$489$$ 12.1244i 0.548282i
$$490$$ −19.5000 + 7.79423i −0.880920 + 0.352107i
$$491$$ 13.5000 23.3827i 0.609246 1.05525i −0.382118 0.924113i $$-0.624805\pi$$
0.991365 0.131132i $$-0.0418613\pi$$
$$492$$ 5.19615i 0.234261i
$$493$$ −9.00000 + 15.5885i −0.405340 + 0.702069i
$$494$$ −7.50000 7.79423i −0.337441 0.350679i
$$495$$ 9.00000 + 15.5885i 0.404520 + 0.700649i
$$496$$ 7.50000 + 4.33013i 0.336760 + 0.194428i
$$497$$ −1.50000 + 4.33013i −0.0672842 + 0.194233i
$$498$$ −3.00000 5.19615i −0.134433 0.232845i
$$499$$ 1.50000 0.866025i 0.0671492 0.0387686i −0.466049 0.884759i $$-0.654323\pi$$
0.533199 + 0.845990i $$0.320990\pi$$
$$500$$ 12.1244i 0.542218i
$$501$$ 1.73205i 0.0773823i
$$502$$ −4.50000 + 2.59808i −0.200845 + 0.115958i
$$503$$ 4.50000 + 7.79423i 0.200645 + 0.347527i 0.948736 0.316068i $$-0.102363\pi$$
−0.748091 + 0.663596i $$0.769030\pi$$
$$504$$ 9.00000 1.73205i 0.400892 0.0771517i
$$505$$ 13.5000 + 7.79423i 0.600742 + 0.346839i
$$506$$ 0 0
$$507$$ 0.500000 12.9904i 0.0222058 0.576923i
$$508$$ 6.50000 11.2583i 0.288391 0.499508i
$$509$$ 6.92820i 0.307087i −0.988142 0.153544i $$-0.950931\pi$$
0.988142 0.153544i $$-0.0490686\pi$$
$$510$$ 9.00000 15.5885i 0.398527 0.690268i
$$511$$ −22.5000 + 4.33013i −0.995341 + 0.191554i
$$512$$ 8.66025i 0.382733i
$$513$$ −7.50000 4.33013i −0.331133 0.191180i
$$514$$ 51.9615i 2.29192i
$$515$$ 19.5000 + 11.2583i 0.859273 + 0.496101i
$$516$$ −5.50000 + 9.52628i −0.242124 + 0.419371i
$$517$$ −22.5000 + 38.9711i −0.989549 + 1.71395i
$$518$$ 0 0
$$519$$ −15.0000 −0.658427
$$520$$ 10.5000 2.59808i 0.460455 0.113933i
$$521$$ −19.5000 + 33.7750i −0.854311 + 1.47971i 0.0229727 + 0.999736i $$0.492687\pi$$
−0.877283 + 0.479973i $$0.840646\pi$$
$$522$$ 9.00000 5.19615i 0.393919 0.227429i
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ 7.50000 + 12.9904i 0.327639 + 0.567487i
$$525$$ 4.00000 3.46410i 0.174574 0.151186i
$$526$$ −4.50000 + 2.59808i −0.196209 + 0.113282i
$$527$$ −9.00000 5.19615i −0.392046 0.226348i
$$528$$ 22.5000 + 12.9904i 0.979187 + 0.565334i
$$529$$ −23.0000 −1.00000
$$530$$ −27.0000 −1.17281
$$531$$ 6.00000 + 3.46410i 0.260378 + 0.150329i
$$532$$ −4.50000 + 0.866025i −0.195100 + 0.0375470i
$$533$$ 13.5000 12.9904i 0.584750 0.562676i
$$534$$ −6.00000 10.3923i −0.259645 0.449719i
$$535$$ 0 0
$$536$$ −7.50000 12.9904i −0.323951 0.561099i
$$537$$ 1.50000 2.59808i 0.0647298 0.112115i
$$538$$ 10.3923i 0.448044i
$$539$$ 13.5000 + 33.7750i 0.581486 + 1.45479i
$$540$$ −7.50000 + 4.33013i −0.322749 + 0.186339i
$$541$$ −10.5000 + 6.06218i −0.451430 + 0.260633i −0.708434 0.705777i $$-0.750598\pi$$
0.257004 + 0.966410i $$0.417265\pi$$
$$542$$ −30.0000 −1.28861
$$543$$ 1.00000 + 1.73205i 0.0429141 + 0.0743294i
$$544$$ 31.1769i 1.33670i
$$545$$ −9.00000 −0.385518
$$546$$ −13.5000 9.52628i −0.577747 0.407687i
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ 0 0
$$549$$ 7.00000 + 12.1244i 0.298753 + 0.517455i
$$550$$ −18.0000 −0.767523
$$551$$ 4.50000 2.59808i 0.191706 0.110682i
$$552$$ 0 0
$$553$$ −12.5000 4.33013i −0.531554 0.184136i
$$554$$ 17.3205i 0.735878i
$$555$$ 0 0
$$556$$ −6.50000 11.2583i −0.275661 0.477460i
$$557$$ 13.5000 7.79423i 0.572013 0.330252i −0.185940 0.982561i $$-0.559533\pi$$
0.757953 + 0.652309i $$0.226200\pi$$
$$558$$ 3.00000 + 5.19615i 0.127000 + 0.219971i
$$559$$ 38.5000 9.52628i 1.62838 0.402919i
$$560$$ 7.50000 21.6506i 0.316933 0.914906i
$$561$$ −27.0000 15.5885i −1.13994 0.658145i
$$562$$ 12.0000 0.506189
$$563$$ −36.0000 −1.51722 −0.758610 0.651546i $$-0.774121\pi$$
−0.758610 + 0.651546i $$0.774121\pi$$
$$564$$ −7.50000 4.33013i −0.315807 0.182331i
$$565$$ −22.5000 12.9904i −0.946582 0.546509i
$$566$$ −28.5000 + 16.4545i −1.19794 + 0.691633i
$$567$$ 2.50000 + 0.866025i 0.104990 + 0.0363696i
$$568$$ −1.50000 2.59808i −0.0629386 0.109013i
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ −4.50000 + 2.59808i −0.188484 + 0.108821i
$$571$$ 11.5000 19.9186i 0.481260 0.833567i −0.518509 0.855072i $$-0.673513\pi$$
0.999769 + 0.0215055i $$0.00684595\pi$$
$$572$$ 4.50000 + 18.1865i 0.188154 + 0.760417i
$$573$$ 15.0000 0.626634
$$574$$ −4.50000 23.3827i −0.187826 0.975974i
$$575$$ 0 0
$$576$$ −1.00000 + 1.73205i −0.0416667 + 0.0721688i
$$577$$ 13.5000 + 7.79423i 0.562012 + 0.324478i 0.753953 0.656929i $$-0.228145\pi$$
−0.191940 + 0.981407i $$0.561478\pi$$
$$578$$ 32.9090i 1.36883i
$$579$$ 1.50000 + 0.866025i 0.0623379 + 0.0359908i
$$580$$ 5.19615i 0.215758i
$$581$$ 6.00000 + 6.92820i 0.248922 + 0.287430i
$$582$$ −4.50000 + 7.79423i −0.186531 + 0.323081i
$$583$$ 46.7654i 1.93682i
$$584$$ 7.50000 12.9904i 0.310352 0.537546i
$$585$$ 12.0000 + 3.46410i 0.496139 + 0.143223i
$$586$$ 22.5000 + 38.9711i 0.929466 + 1.60988i
$$587$$ −13.5000 7.79423i −0.557205 0.321702i 0.194818 0.980839i $$-0.437588\pi$$
−0.752023 + 0.659137i $$0.770922\pi$$
$$588$$ −6.50000 + 2.59808i −0.268055 + 0.107143i
$$589$$ 1.50000 + 2.59808i 0.0618064 + 0.107052i
$$590$$ 9.00000 5.19615i 0.370524 0.213922i
$$591$$ 22.5167i 0.926212i
$$592$$ 0 0
$$593$$ −4.50000 + 2.59808i −0.184793 + 0.106690i −0.589543 0.807737i $$-0.700692\pi$$
0.404750 + 0.914428i $$0.367359\pi$$
$$594$$ 22.5000 + 38.9711i 0.923186 + 1.59901i
$$595$$ −9.00000 + 25.9808i −0.368964 + 1.06511i
$$596$$ 16.5000 + 9.52628i 0.675866 + 0.390212i
$$597$$ 2.00000 + 3.46410i 0.0818546 + 0.141776i
$$598$$ 0 0
$$599$$ −4.50000 + 7.79423i −0.183865 + 0.318464i −0.943193 0.332244i $$-0.892194\pi$$
0.759328 + 0.650708i $$0.225528\pi$$
$$600$$ 3.46410i 0.141421i
$$601$$ −9.50000 + 16.4545i −0.387513 + 0.671192i −0.992114 0.125336i $$-0.959999\pi$$
0.604601 + 0.796528i $$0.293332\pi$$
$$602$$ 16.5000 47.6314i 0.672490 1.94131i
$$603$$ 17.3205i 0.705346i
$$604$$ −10.5000 6.06218i −0.427239 0.246667i
$$605$$ 27.7128i 1.12669i
$$606$$ 13.5000 + 7.79423i 0.548400 + 0.316619i
$$607$$ 21.5000 37.2391i 0.872658 1.51149i 0.0134214 0.999910i $$-0.495728\pi$$
0.859237 0.511578i $$-0.170939\pi$$
$$608$$ 4.50000 7.79423i 0.182499 0.316098i
$$609$$ 6.00000 5.19615i 0.243132 0.210559i
$$610$$ 21.0000 0.850265
$$611$$ 7.50000 + 30.3109i 0.303418 + 1.22625i
$$612$$ −6.00000 + 10.3923i −0.242536 + 0.420084i
$$613$$ 31.5000 18.1865i 1.27227 0.734547i 0.296858 0.954922i $$-0.404061\pi$$
0.975415 + 0.220375i $$0.0707280\pi$$
$$614$$ −42.0000 −1.69498
$$615$$ −4.50000 7.79423i −0.181458 0.314294i
$$616$$ −22.5000 7.79423i −0.906551 0.314038i
$$617$$ 37.5000 21.6506i 1.50969 0.871622i 0.509757 0.860318i $$-0.329735\pi$$
0.999936 0.0113033i $$-0.00359804\pi$$
$$618$$ 19.5000 + 11.2583i 0.784405 + 0.452876i
$$619$$ 16.5000 + 9.52628i 0.663191 + 0.382893i 0.793492 0.608581i $$-0.208261\pi$$
−0.130301 + 0.991475i $$0.541594\pi$$
$$620$$ 3.00000 0.120483
$$621$$ 0 0
$$622$$ −22.5000 12.9904i −0.902168 0.520867i
$$623$$ 12.0000 + 13.8564i 0.480770 + 0.555145i
$$624$$ 17.5000 4.33013i 0.700561 0.173344i
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ −28.5000 + 16.4545i −1.13909 + 0.657653i
$$627$$ 4.50000 + 7.79423i 0.179713 + 0.311272i
$$628$$ 11.5000 19.9186i 0.458900 0.794838i
$$629$$ 0 0
$$630$$ 12.0000 10.3923i 0.478091 0.414039i
$$631$$ −40.5000 + 23.3827i −1.61228 + 0.930850i −0.623439 + 0.781872i $$0.714265\pi$$
−0.988841 + 0.148978i $$0.952402\pi$$
$$632$$ 7.50000 4.33013i 0.298334 0.172243i
$$633$$ −13.0000 −0.516704
$$634$$ 4.50000 + 7.79423i 0.178718 + 0.309548i
$$635$$ 22.5167i 0.893546i
$$636$$ −9.00000 −0.356873
$$637$$ 23.0000 + 10.3923i 0.911293 + 0.411758i
$$638$$ −27.0000 −1.06894
$$639$$ 3.46410i 0.137038i
$$640$$ 10.5000 + 18.1865i 0.415049 + 0.718886i
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ −4.50000 + 2.59808i −0.177463 + 0.102458i −0.586100 0.810239i $$-0.699337\pi$$
0.408637 + 0.912697i $$0.366004\pi$$
$$644$$ 0 0
$$645$$ 19.0526i 0.750194i
$$646$$ −9.00000 + 15.5885i −0.354100 + 0.613320i
$$647$$ 4.50000 + 7.79423i 0.176913 + 0.306423i 0.940822 0.338902i $$-0.110055\pi$$
−0.763908 + 0.645325i $$0.776722\pi$$
$$648$$ −1.50000 + 0.866025i −0.0589256 + 0.0340207i
$$649$$ −9.00000 15.5885i −0.353281 0.611900i
$$650$$ −9.00000 + 8.66025i −0.353009 + 0.339683i
$$651$$ 3.00000 + 3.46410i 0.117579 + 0.135769i
$$652$$ −10.5000 6.06218i −0.411212 0.237413i
$$653$$ −30.0000 −1.17399 −0.586995 0.809590i $$-0.699689\pi$$
−0.586995 + 0.809590i $$0.699689\pi$$
$$654$$ −9.00000 −0.351928
$$655$$ −22.5000 12.9904i −0.879148 0.507576i
$$656$$ 22.5000 + 12.9904i 0.878477 + 0.507189i
$$657$$ 15.0000 8.66025i 0.585206 0.337869i
$$658$$ 37.5000 + 12.9904i 1.46190 + 0.506418i
$$659$$ −7.50000 12.9904i −0.292159 0.506033i 0.682161 0.731202i $$-0.261040\pi$$
−0.974320 + 0.225168i $$0.927707\pi$$
$$660$$ 9.00000 0.350325
$$661$$ 31.5000 18.1865i 1.22521 0.707374i 0.259184 0.965828i $$-0.416546\pi$$
0.966024 + 0.258454i $$0.0832129\pi$$
$$662$$ 28.5000 49.3634i 1.10768 1.91856i
$$663$$ −21.0000 + 5.19615i −0.815572 + 0.201802i
$$664$$ −6.00000 −0.232845
$$665$$ 6.00000 5.19615i 0.232670 0.201498i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.50000 + 0.866025i 0.0580367 + 0.0335075i
$$669$$ 5.19615i 0.200895i
$$670$$ −22.5000 12.9904i −0.869251 0.501862i
$$671$$ 36.3731i 1.40417i
$$672$$ 4.50000 12.9904i 0.173591 0.501115i
$$673$$ 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i $$-0.827198\pi$$
0.875501 + 0.483216i $$0.160531\pi$$
$$674$$ 38.1051i 1.46775i
$$675$$ −5.00000 + 8.66025i −0.192450 + 0.333333i
$$676$$ 11.0000 + 6.92820i 0.423077 + 0.266469i
$$677$$ −13.5000 23.3827i −0.518847 0.898670i −0.999760 0.0219013i $$-0.993028\pi$$
0.480913 0.876768i $$-0.340305\pi$$
$$678$$ −22.5000 12.9904i −0.864107 0.498893i
$$679$$ 4.50000 12.9904i 0.172694 0.498525i
$$680$$ −9.00000 15.5885i −0.345134 0.597790i
$$681$$ −15.0000 + 8.66025i −0.574801 + 0.331862i
$$682$$ 15.5885i 0.596913i
$$683$$ 24.2487i 0.927851i −0.885874 0.463926i $$-0.846441\pi$$
0.885874 0.463926i $$-0.153559\pi$$
$$684$$ 3.00000 1.73205i 0.114708 0.0662266i
$$685$$ 0 0
$$686$$ 27.0000 17.3205i 1.03086 0.661300i
$$687$$ −10.5000 6.06218i −0.400600 0.231287i
$$688$$ 27.5000 + 47.6314i 1.04843 + 1.81593i
$$689$$ 22.5000 + 23.3827i 0.857182 + 0.890809i
$$690$$ 0 0
$$691$$ 31.1769i 1.18603i 0.805193 + 0.593013i $$0.202062\pi$$
−0.805193 + 0.593013i $$0.797938\pi$$
$$692$$ 7.50000 12.9904i 0.285107 0.493820i
$$693$$ −18.0000 20.7846i −0.683763 0.789542i
$$694$$ 0 0
$$695$$ 19.5000 + 11.2583i 0.739677 + 0.427053i
$$696$$ 5.19615i 0.196960i
$$697$$ −27.0000 15.5885i −1.02270 0.590455i
$$698$$ −4.50000 + 7.79423i −0.170328 + 0.295016i
$$699$$ 1.50000 2.59808i 0.0567352 0.0982683i
$$700$$ 1.00000 + 5.19615i 0.0377964 + 0.196396i
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 30.0000 + 8.66025i 1.13228 + 0.326860i
$$703$$ 0 0
$$704$$ 4.50000 2.59808i 0.169600 0.0979187i
$$705$$ 15.0000 0.564933
$$706$$ −1.50000 2.59808i −0.0564532 0.0977799i
$$707$$ −22.5000 7.79423i −0.846200 0.293132i
$$708$$ 3.00000 1.73205i 0.112747 0.0650945i
$$709$$ −10.5000 6.06218i −0.394336 0.227670i 0.289701 0.957117i $$-0.406444\pi$$
−0.684037 + 0.729447i $$0.739777\pi$$
$$710$$ −4.50000 2.59808i −0.168882 0.0975041i
$$711$$ 10.0000 0.375029
$$712$$ −12.0000 −0.449719
$$713$$ 0 0
$$714$$ −9.00000 + 25.9808i −0.336817 + 0.972306i
$$715$$ −22.5000 23.3827i −0.841452 0.874463i
$$716$$ 1.50000 + 2.59808i 0.0560576 + 0.0970947i
$$717$$ 9.00000 5.19615i 0.336111 0.194054i
$$718$$ 16.5000 + 28.5788i 0.615775 + 1.06655i
$$719$$ 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i $$-0.743097\pi$$
0.971311 + 0.237814i $$0.0764307\pi$$
$$720$$ 17.3205i 0.645497i
$$721$$ −32.5000 11.2583i −1.21036 0.419282i
$$722$$ −24.0000 + 13.8564i −0.893188 + 0.515682i
$$723$$ −6.00000 + 3.46410i −0.223142 + 0.128831i
$$724$$ −2.00000 −0.0743294
$$725$$ −3.00000 5.19615i −0.111417 0.192980i
$$726$$ 27.7128i 1.02852i
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ −15.0000 + 6.92820i −0.555937 + 0.256776i
$$729$$ 13.0000 0.481481
$$730$$ 25.9808i 0.961591i
$$731$$ −33.0000 57.1577i −1.22055 2.11405i
$$732$$ 7.00000 0.258727
$$733$$ 43.5000 25.1147i 1.60671 0.927634i 0.616609 0.787269i $$-0.288506\pi$$
0.990100 0.140365i $$-0.0448275\pi$$
$$734$$ −34.5000 + 19.9186i −1.27342 + 0.735208i
$$735$$ 7.50000 9.52628i 0.276642 0.351382i
$$736$$ 0 0
$$737$$ −22.5000 + 38.9711i −0.828798 + 1.43552i
$$738$$ 9.00000 + 15.5885i 0.331295 + 0.573819i
$$739$$ −34.5000 + 19.9186i −1.26910 + 0.732717i −0.974818 0.223001i $$-0.928415\pi$$
−0.294285 + 0.955718i $$0.595081\pi$$
$$740$$ 0 0
$$741$$ 6.00000 + 1.73205i 0.220416 + 0.0636285i
$$742$$ 40.5000 7.79423i 1.48680 0.286135i
$$743$$ −1.50000 0.866025i −0.0550297 0.0317714i 0.472233 0.881474i $$-0.343448\pi$$
−0.527262 + 0.849703i $$0.676782\pi$$
$$744$$ −3.00000 −0.109985
$$745$$ −33.0000 −1.20903
$$746$$ 28.5000 + 16.4545i 1.04346 + 0.602441i
$$747$$ −6.00000 3.46410i −0.219529 0.126745i
$$748$$ 27.0000 15.5885i 0.987218 0.569970i
$$749$$ 0 0
$$750$$ 10.5000 + 18.1865i 0.383406 + 0.664078i
$$751$$ 20.0000 0.729810 0.364905 0.931045i $$-0.381101\pi$$
0.364905 + 0.931045i $$0.381101\pi$$
$$752$$ −37.5000 + 21.6506i −1.36748 + 0.789517i
$$753$$ 1.50000 2.59808i 0.0546630 0.0946792i
$$754$$ −13.5000 + 12.9904i −0.491641 + 0.473082i
$$755$$ 21.0000 0.764268
$$756$$ 10.0000 8.66025i 0.363696 0.314970i
$$757$$ 8.50000 14.7224i 0.308938 0.535096i −0.669193 0.743089i $$-0.733360\pi$$
0.978130 + 0.207993i $$0.0666932\pi$$
$$758$$ −1.50000 + 2.59808i −0.0544825 + 0.0943664i
$$759$$ 0 0
$$760$$ 5.19615i 0.188484i
$$761$$ 25.5000 + 14.7224i 0.924374 + 0.533688i 0.885028 0.465538i $$-0.154139\pi$$
0.0393463 + 0.999226i $$0.487472\pi$$
$$762$$ 22.5167i 0.815693i
$$763$$ 13.5000 2.59808i 0.488733 0.0940567i
$$764$$ −7.50000 + 12.9904i −0.271340 + 0.469975i
$$765$$ 20.7846i 0.751469i
$$766$$ −13.5000 + 23.3827i −0.487775 + 0.844851i
$$767$$ −12.0000 3.46410i −0.433295 0.125081i
$$768$$ 9.50000 + 16.4545i 0.342802 + 0.593750i
$$769$$ −16.5000 9.52628i −0.595005 0.343526i 0.172069 0.985085i $$-0.444955\pi$$
−0.767074 + 0.641558i $$0.778288\pi$$
$$770$$ −40.5000 + 7.79423i −1.45952 + 0.280885i
$$771$$ 15.0000 + 25.9808i 0.540212 + 0.935674i
$$772$$ −1.50000 + 0.866025i −0.0539862 + 0.0311689i
$$773$$ 13.8564i 0.498380i 0.968455 + 0.249190i $$0.0801644\pi$$
−0.968455 + 0.249190i $$0.919836\pi$$
$$774$$ 38.1051i 1.36966i
$$775$$ 3.00000 1.73205i 0.107763 0.0622171i
$$776$$ 4.50000 + 7.79423i 0.161541 + 0.279797i
$$777$$ 0 0