# Properties

 Label 637.2.q.c.491.1 Level $637$ Weight $2$ Character 637.491 Analytic conductor $5.086$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.q (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 491.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.491 Dual form 637.2.q.c.589.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(4.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +(1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.00000 + 5.19615i) q^{17} -3.46410i q^{18} +(1.50000 + 0.866025i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.50000 + 0.866025i) q^{24} +2.00000 q^{25} +(-4.50000 - 4.33013i) q^{26} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 - 2.59808i) q^{30} -1.73205i q^{31} +(4.50000 + 2.59808i) q^{32} +(4.50000 + 2.59808i) q^{33} +10.3923i q^{34} +(-1.00000 - 1.73205i) q^{36} +3.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +3.00000 q^{40} +(-4.50000 + 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} -5.19615i q^{44} +(-3.00000 - 1.73205i) q^{45} -8.66025i q^{47} +(-2.50000 + 4.33013i) q^{48} +(3.00000 - 1.73205i) q^{50} -6.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(7.50000 - 4.33013i) q^{54} +(-4.50000 - 7.79423i) q^{55} +1.73205i q^{57} +(-4.50000 - 2.59808i) q^{58} +(3.00000 + 1.73205i) q^{59} -1.73205i q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} +9.00000 q^{66} +(-7.50000 + 4.33013i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.50000 + 0.866025i) q^{71} +(3.00000 + 1.73205i) q^{72} +8.66025i q^{73} +(1.00000 + 1.73205i) q^{75} +(1.50000 - 0.866025i) q^{76} +(1.50000 - 6.06218i) q^{78} -5.00000 q^{79} +(7.50000 - 4.33013i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} +3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +19.0526i q^{86} +(1.50000 - 2.59808i) q^{87} +(4.50000 + 7.79423i) q^{88} +(6.00000 - 3.46410i) q^{89} -6.00000 q^{90} +(1.50000 - 0.866025i) q^{93} +(-7.50000 - 12.9904i) q^{94} +(1.50000 - 2.59808i) q^{95} +5.19615i q^{96} +(-4.50000 - 2.59808i) q^{97} -10.3923i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 2 q^{9} + O(q^{10})$$ $$2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 2 q^{9} - 3 q^{10} + 9 q^{11} + 2 q^{12} - 2 q^{13} + 3 q^{15} + 5 q^{16} - 6 q^{17} + 3 q^{19} - 3 q^{20} + 9 q^{22} - 3 q^{24} + 4 q^{25} - 9 q^{26} + 10 q^{27} - 3 q^{29} + 3 q^{30} + 9 q^{32} + 9 q^{33} - 2 q^{36} + 6 q^{38} + 5 q^{39} + 6 q^{40} - 9 q^{41} - 11 q^{43} - 6 q^{45} - 5 q^{48} + 6 q^{50} - 12 q^{51} - 7 q^{52} - 18 q^{53} + 15 q^{54} - 9 q^{55} - 9 q^{58} + 6 q^{59} - 7 q^{61} - 3 q^{62} - 2 q^{64} - 12 q^{65} + 18 q^{66} - 15 q^{67} + 6 q^{68} + 3 q^{71} + 6 q^{72} + 2 q^{75} + 3 q^{76} + 3 q^{78} - 10 q^{79} + 15 q^{80} - q^{81} - 9 q^{82} + 18 q^{85} + 3 q^{87} + 9 q^{88} + 12 q^{89} - 12 q^{90} + 3 q^{93} - 15 q^{94} + 3 q^{95} - 9 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i $$-0.456882\pi$$
0.925615 + 0.378467i $$0.123549\pi$$
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i $$-0.0734519\pi$$
−0.684819 + 0.728714i $$0.740119\pi$$
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 1.73205i 0.774597i −0.921954 0.387298i $$-0.873408\pi$$
0.921954 0.387298i $$-0.126592\pi$$
$$6$$ 1.50000 + 0.866025i 0.612372 + 0.353553i
$$7$$ 0 0
$$8$$ 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 0.367610 0.929980i $$-0.380176\pi$$
0.989191 + 0.146631i $$0.0468429\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −1.00000 3.46410i −0.277350 0.960769i
$$14$$ 0 0
$$15$$ 1.50000 0.866025i 0.387298 0.223607i
$$16$$ 2.50000 + 4.33013i 0.625000 + 1.08253i
$$17$$ −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i $$0.426034\pi$$
−0.957892 + 0.287129i $$0.907299\pi$$
$$18$$ 3.46410i 0.816497i
$$19$$ 1.50000 + 0.866025i 0.344124 + 0.198680i 0.662094 0.749421i $$-0.269668\pi$$
−0.317970 + 0.948101i $$0.603001\pi$$
$$20$$ −1.50000 0.866025i −0.335410 0.193649i
$$21$$ 0 0
$$22$$ 4.50000 7.79423i 0.959403 1.66174i
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ −1.50000 + 0.866025i −0.306186 + 0.176777i
$$25$$ 2.00000 0.400000
$$26$$ −4.50000 4.33013i −0.882523 0.849208i
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i $$-0.256518\pi$$
−0.971023 + 0.238987i $$0.923185\pi$$
$$30$$ 1.50000 2.59808i 0.273861 0.474342i
$$31$$ 1.73205i 0.311086i −0.987829 0.155543i $$-0.950287\pi$$
0.987829 0.155543i $$-0.0497126\pi$$
$$32$$ 4.50000 + 2.59808i 0.795495 + 0.459279i
$$33$$ 4.50000 + 2.59808i 0.783349 + 0.452267i
$$34$$ 10.3923i 1.78227i
$$35$$ 0 0
$$36$$ −1.00000 1.73205i −0.166667 0.288675i
$$37$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$38$$ 3.00000 0.486664
$$39$$ 2.50000 2.59808i 0.400320 0.416025i
$$40$$ 3.00000 0.474342
$$41$$ −4.50000 + 2.59808i −0.702782 + 0.405751i −0.808383 0.588657i $$-0.799657\pi$$
0.105601 + 0.994409i $$0.466323\pi$$
$$42$$ 0 0
$$43$$ −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i $$0.483375\pi$$
−0.890947 + 0.454108i $$0.849958\pi$$
$$44$$ 5.19615i 0.783349i
$$45$$ −3.00000 1.73205i −0.447214 0.258199i
$$46$$ 0 0
$$47$$ 8.66025i 1.26323i −0.775283 0.631614i $$-0.782393\pi$$
0.775283 0.631614i $$-0.217607\pi$$
$$48$$ −2.50000 + 4.33013i −0.360844 + 0.625000i
$$49$$ 0 0
$$50$$ 3.00000 1.73205i 0.424264 0.244949i
$$51$$ −6.00000 −0.840168
$$52$$ −3.50000 0.866025i −0.485363 0.120096i
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 7.50000 4.33013i 1.02062 0.589256i
$$55$$ −4.50000 7.79423i −0.606780 1.05097i
$$56$$ 0 0
$$57$$ 1.73205i 0.229416i
$$58$$ −4.50000 2.59808i −0.590879 0.341144i
$$59$$ 3.00000 + 1.73205i 0.390567 + 0.225494i 0.682406 0.730974i $$-0.260934\pi$$
−0.291839 + 0.956467i $$0.594267\pi$$
$$60$$ 1.73205i 0.223607i
$$61$$ −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
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −6.00000 + 1.73205i −0.744208 + 0.214834i
$$66$$ 9.00000 1.10782
$$67$$ −7.50000 + 4.33013i −0.916271 + 0.529009i −0.882443 0.470418i $$-0.844103\pi$$
−0.0338274 + 0.999428i $$0.510770\pi$$
$$68$$ 3.00000 + 5.19615i 0.363803 + 0.630126i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.50000 + 0.866025i 0.178017 + 0.102778i 0.586361 0.810050i $$-0.300560\pi$$
−0.408344 + 0.912828i $$0.633893\pi$$
$$72$$ 3.00000 + 1.73205i 0.353553 + 0.204124i
$$73$$ 8.66025i 1.01361i 0.862062 + 0.506803i $$0.169173\pi$$
−0.862062 + 0.506803i $$0.830827\pi$$
$$74$$ 0 0
$$75$$ 1.00000 + 1.73205i 0.115470 + 0.200000i
$$76$$ 1.50000 0.866025i 0.172062 0.0993399i
$$77$$ 0 0
$$78$$ 1.50000 6.06218i 0.169842 0.686406i
$$79$$ −5.00000 −0.562544 −0.281272 0.959628i $$-0.590756\pi$$
−0.281272 + 0.959628i $$0.590756\pi$$
$$80$$ 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 $$0.0608868\pi$$
−0.981761 + 0.190117i $$0.939113\pi$$
$$84$$ 0 0
$$85$$ 9.00000 + 5.19615i 0.976187 + 0.563602i
$$86$$ 19.0526i 2.05449i
$$87$$ 1.50000 2.59808i 0.160817 0.278543i
$$88$$ 4.50000 + 7.79423i 0.479702 + 0.830868i
$$89$$ 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i $$-0.546985\pi$$
0.783072 + 0.621932i $$0.213652\pi$$
$$90$$ −6.00000 −0.632456
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 1.50000 0.866025i 0.155543 0.0898027i
$$94$$ −7.50000 12.9904i −0.773566 1.33986i
$$95$$ 1.50000 2.59808i 0.153897 0.266557i
$$96$$ 5.19615i 0.530330i
$$97$$ −4.50000 2.59808i −0.456906 0.263795i 0.253837 0.967247i $$-0.418307\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 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
$$103$$ −13.0000 −1.28093 −0.640464 0.767988i $$-0.721258\pi$$
−0.640464 + 0.767988i $$0.721258\pi$$
$$104$$ 6.00000 1.73205i 0.588348 0.169842i
$$105$$ 0 0
$$106$$ −13.5000 + 7.79423i −1.31124 + 0.757042i
$$107$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$108$$ 2.50000 4.33013i 0.240563 0.416667i
$$109$$ 5.19615i 0.497701i −0.968542 0.248851i $$-0.919947\pi$$
0.968542 0.248851i $$-0.0800528\pi$$
$$110$$ −13.5000 7.79423i −1.28717 0.743151i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i $$0.415962\pi$$
−0.966496 + 0.256681i $$0.917371\pi$$
$$114$$ 1.50000 + 2.59808i 0.140488 + 0.243332i
$$115$$ 0 0
$$116$$ −3.00000 −0.278543
$$117$$ −7.00000 1.73205i −0.647150 0.160128i
$$118$$ 6.00000 0.552345
$$119$$ 0 0
$$120$$ 1.50000 + 2.59808i 0.136931 + 0.237171i
$$121$$ 8.00000 13.8564i 0.727273 1.25967i
$$122$$ 12.1244i 1.09769i
$$123$$ −4.50000 2.59808i −0.405751 0.234261i
$$124$$ −1.50000 0.866025i −0.134704 0.0777714i
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ −6.50000 11.2583i −0.576782 0.999015i −0.995846 0.0910585i $$-0.970975\pi$$
0.419064 0.907957i $$-0.362358\pi$$
$$128$$ −10.5000 + 6.06218i −0.928078 + 0.535826i
$$129$$ −11.0000 −0.968496
$$130$$ −7.50000 + 7.79423i −0.657794 + 0.683599i
$$131$$ 15.0000 1.31056 0.655278 0.755388i $$-0.272551\pi$$
0.655278 + 0.755388i $$0.272551\pi$$
$$132$$ 4.50000 2.59808i 0.391675 0.226134i
$$133$$ 0 0
$$134$$ −7.50000 + 12.9904i −0.647901 + 1.12220i
$$135$$ 8.66025i 0.745356i
$$136$$ −9.00000 5.19615i −0.771744 0.445566i
$$137$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ 6.50000 11.2583i 0.551323 0.954919i −0.446857 0.894606i $$-0.647457\pi$$
0.998179 0.0603135i $$-0.0192101\pi$$
$$140$$ 0 0
$$141$$ 7.50000 4.33013i 0.631614 0.364662i
$$142$$ 3.00000 0.251754
$$143$$ −13.5000 12.9904i −1.12893 1.08631i
$$144$$ 10.0000 0.833333
$$145$$ −4.50000 + 2.59808i −0.373705 + 0.215758i
$$146$$ 7.50000 + 12.9904i 0.620704 + 1.07509i
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 16.5000 + 9.52628i 1.35173 + 0.780423i 0.988492 0.151272i $$-0.0483370\pi$$
0.363241 + 0.931695i $$0.381670\pi$$
$$150$$ 3.00000 + 1.73205i 0.244949 + 0.141421i
$$151$$ 12.1244i 0.986666i 0.869841 + 0.493333i $$0.164222\pi$$
−0.869841 + 0.493333i $$0.835778\pi$$
$$152$$ −1.50000 + 2.59808i −0.121666 + 0.210732i
$$153$$ 6.00000 + 10.3923i 0.485071 + 0.840168i
$$154$$ 0 0
$$155$$ −3.00000 −0.240966
$$156$$ −1.00000 3.46410i −0.0800641 0.277350i
$$157$$ 23.0000 1.83560 0.917800 0.397043i $$-0.129964\pi$$
0.917800 + 0.397043i $$0.129964\pi$$
$$158$$ −7.50000 + 4.33013i −0.596668 + 0.344486i
$$159$$ −4.50000 7.79423i −0.356873 0.618123i
$$160$$ 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 0.0288280 0.999584i $$-0.490822\pi$$
−0.851251 + 0.524758i $$0.824156\pi$$
$$164$$ 5.19615i 0.405751i
$$165$$ 4.50000 7.79423i 0.350325 0.606780i
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ −1.50000 + 0.866025i −0.116073 + 0.0670151i −0.556913 0.830571i $$-0.688014\pi$$
0.440839 + 0.897586i $$0.354681\pi$$
$$168$$ 0 0
$$169$$ −11.0000 + 6.92820i −0.846154 + 0.532939i
$$170$$ 18.0000 1.38054
$$171$$ 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
$$175$$ 0 0
$$176$$ 22.5000 + 12.9904i 1.69600 + 0.979187i
$$177$$ 3.46410i 0.260378i
$$178$$ 6.00000 10.3923i 0.449719 0.778936i
$$179$$ −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i $$-0.202429\pi$$
−0.916623 + 0.399753i $$0.869096\pi$$
$$180$$ −3.00000 + 1.73205i −0.223607 + 0.129099i
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ −7.00000 −0.517455
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 1.50000 2.59808i 0.109985 0.190500i
$$187$$ 31.1769i 2.27988i
$$188$$ −7.50000 4.33013i −0.546994 0.315807i
$$189$$ 0 0
$$190$$ 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 −0.553014 0.833172i $$-0.686522\pi$$
0.445041 + 0.895510i $$0.353189\pi$$
$$194$$ −9.00000 −0.646162
$$195$$ −4.50000 4.33013i −0.322252 0.310087i
$$196$$ 0 0
$$197$$ 19.5000 11.2583i 1.38932 0.802123i 0.396079 0.918216i $$-0.370371\pi$$
0.993238 + 0.116094i $$0.0370372\pi$$
$$198$$ −9.00000 15.5885i −0.639602 1.10782i
$$199$$ −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i $$-0.878615\pi$$
0.786389 + 0.617731i $$0.211948\pi$$
$$200$$ 3.46410i 0.244949i
$$201$$ −7.50000 4.33013i −0.529009 0.305424i
$$202$$ 13.5000 + 7.79423i 0.949857 + 0.548400i
$$203$$ 0 0
$$204$$ −3.00000 + 5.19615i −0.210042 + 0.363803i
$$205$$ 4.50000 + 7.79423i 0.314294 + 0.544373i
$$206$$ −19.5000 + 11.2583i −1.35863 + 0.784405i
$$207$$ 0 0
$$208$$ 12.5000 12.9904i 0.866719 0.900721i
$$209$$ 9.00000 0.622543
$$210$$ 0 0
$$211$$ −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i $$-0.314345\pi$$
−0.998221 + 0.0596196i $$0.981011\pi$$
$$212$$ −4.50000 + 7.79423i −0.309061 + 0.535310i
$$213$$ 1.73205i 0.118678i
$$214$$ 0 0
$$215$$ 16.5000 + 9.52628i 1.12529 + 0.649687i
$$216$$ 8.66025i 0.589256i
$$217$$ 0 0
$$218$$ −4.50000 7.79423i −0.304778 0.527892i
$$219$$ −7.50000 + 4.33013i −0.506803 + 0.292603i
$$220$$ −9.00000 −0.606780
$$221$$ 21.0000 + 5.19615i 1.41261 + 0.349531i
$$222$$ 0 0
$$223$$ 4.50000 2.59808i 0.301342 0.173980i −0.341703 0.939808i $$-0.611004\pi$$
0.643046 + 0.765828i $$0.277671\pi$$
$$224$$ 0 0
$$225$$ 2.00000 3.46410i 0.133333 0.230940i
$$226$$ 25.9808i 1.72821i
$$227$$ 15.0000 + 8.66025i 0.995585 + 0.574801i 0.906939 0.421262i $$-0.138413\pi$$
0.0886460 + 0.996063i $$0.471746\pi$$
$$228$$ 1.50000 + 0.866025i 0.0993399 + 0.0573539i
$$229$$ 12.1244i 0.801200i 0.916253 + 0.400600i $$0.131198\pi$$
−0.916253 + 0.400600i $$0.868802\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 4.50000 2.59808i 0.295439 0.170572i
$$233$$ 3.00000 0.196537 0.0982683 0.995160i $$-0.468670\pi$$
0.0982683 + 0.995160i $$0.468670\pi$$
$$234$$ −12.0000 + 3.46410i −0.784465 + 0.226455i
$$235$$ −15.0000 −0.978492
$$236$$ 3.00000 1.73205i 0.195283 0.112747i
$$237$$ −2.50000 4.33013i −0.162392 0.281272i
$$238$$ 0 0
$$239$$ 10.3923i 0.672222i 0.941822 + 0.336111i $$0.109112\pi$$
−0.941822 + 0.336111i $$0.890888\pi$$
$$240$$ 7.50000 + 4.33013i 0.484123 + 0.279508i
$$241$$ 6.00000 + 3.46410i 0.386494 + 0.223142i 0.680640 0.732618i $$-0.261702\pi$$
−0.294146 + 0.955761i $$0.595035\pi$$
$$242$$ 27.7128i 1.78145i
$$243$$ 8.00000 13.8564i 0.513200 0.888889i
$$244$$ 3.50000 + 6.06218i 0.224065 + 0.388091i
$$245$$ 0 0
$$246$$ −9.00000 −0.573819
$$247$$ 1.50000 6.06218i 0.0954427 0.385727i
$$248$$ 3.00000 0.190500
$$249$$ −3.00000 + 1.73205i −0.190117 + 0.109764i
$$250$$ −10.5000 18.1865i −0.664078 1.15022i
$$251$$ −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i $$-0.863516\pi$$
0.814795 + 0.579748i $$0.196849\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −19.5000 11.2583i −1.22354 0.706410i
$$255$$ 10.3923i 0.650791i
$$256$$ −9.50000 + 16.4545i −0.593750 + 1.02841i
$$257$$ −15.0000 25.9808i −0.935674 1.62064i −0.773427 0.633885i $$-0.781459\pi$$
−0.162247 0.986750i $$-0.551874\pi$$
$$258$$ −16.5000 + 9.52628i −1.02725 + 0.593080i
$$259$$ 0 0
$$260$$ −1.50000 + 6.06218i −0.0930261 + 0.375960i
$$261$$ −6.00000 −0.371391
$$262$$ 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
$$266$$ 0 0
$$267$$ 6.00000 + 3.46410i 0.367194 + 0.212000i
$$268$$ 8.66025i 0.529009i
$$269$$ 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i $$-0.774781\pi$$
0.942871 + 0.333157i $$0.108114\pi$$
$$270$$ −7.50000 12.9904i −0.456435 0.790569i
$$271$$ 15.0000 8.66025i 0.911185 0.526073i 0.0303728 0.999539i $$-0.490331\pi$$
0.880812 + 0.473466i $$0.156997\pi$$
$$272$$ −30.0000 −1.81902
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 9.00000 5.19615i 0.542720 0.313340i
$$276$$ 0 0
$$277$$ 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i $$-0.736206\pi$$
0.976231 + 0.216731i $$0.0695395\pi$$
$$278$$ 22.5167i 1.35046i
$$279$$ −3.00000 1.73205i −0.179605 0.103695i
$$280$$ 0 0
$$281$$ 6.92820i 0.413302i −0.978415 0.206651i $$-0.933744\pi$$
0.978415 0.206651i $$-0.0662565\pi$$
$$282$$ 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
$$285$$ 3.00000 0.177705
$$286$$ −31.5000 7.79423i −1.86263 0.460882i
$$287$$ 0 0
$$288$$ 9.00000 5.19615i 0.530330 0.306186i
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ −4.50000 + 7.79423i −0.264249 + 0.457693i
$$291$$ 5.19615i 0.304604i
$$292$$ 7.50000 + 4.33013i 0.438904 + 0.253402i
$$293$$ −22.5000 12.9904i −1.31446 0.758906i −0.331632 0.943409i $$-0.607599\pi$$
−0.982832 + 0.184503i $$0.940933\pi$$
$$294$$ 0 0
$$295$$ 3.00000 5.19615i 0.174667 0.302532i
$$296$$ 0 0
$$297$$ 22.5000 12.9904i 1.30558 0.753778i
$$298$$ 33.0000 1.91164
$$299$$ 0 0
$$300$$ 2.00000 0.115470
$$301$$ 0 0
$$302$$ 10.5000 + 18.1865i 0.604207 + 1.04652i
$$303$$ −4.50000 + 7.79423i −0.258518 + 0.447767i
$$304$$ 8.66025i 0.496700i
$$305$$ 10.5000 + 6.06218i 0.601228 + 0.347119i
$$306$$ 18.0000 + 10.3923i 1.02899 + 0.594089i
$$307$$ 24.2487i 1.38395i 0.721923 + 0.691974i $$0.243259\pi$$
−0.721923 + 0.691974i $$0.756741\pi$$
$$308$$ 0 0
$$309$$ −6.50000 11.2583i −0.369772 0.640464i
$$310$$ −4.50000 + 2.59808i −0.255583 + 0.147561i
$$311$$ −15.0000 −0.850572 −0.425286 0.905059i $$-0.639826\pi$$
−0.425286 + 0.905059i $$0.639826\pi$$
$$312$$ 4.50000 + 4.33013i 0.254762 + 0.245145i
$$313$$ 19.0000 1.07394 0.536972 0.843600i $$-0.319568\pi$$
0.536972 + 0.843600i $$0.319568\pi$$
$$314$$ 34.5000 19.9186i 1.94695 1.12407i
$$315$$ 0 0
$$316$$ −2.50000 + 4.33013i −0.140636 + 0.243589i
$$317$$ 5.19615i 0.291845i 0.989296 + 0.145922i $$0.0466150\pi$$
−0.989296 + 0.145922i $$0.953385\pi$$
$$318$$ −13.5000 7.79423i −0.757042 0.437079i
$$319$$ −13.5000 7.79423i −0.755855 0.436393i
$$320$$ 1.73205i 0.0968246i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −9.00000 + 5.19615i −0.500773 + 0.289122i
$$324$$ −1.00000 −0.0555556
$$325$$ −2.00000 6.92820i −0.110940 0.384308i
$$326$$ −21.0000 −1.16308
$$327$$ 4.50000 2.59808i 0.248851 0.143674i
$$328$$ −4.50000 7.79423i −0.248471 0.430364i
$$329$$ 0 0
$$330$$ 15.5885i 0.858116i
$$331$$ −28.5000 16.4545i −1.56650 0.904420i −0.996572 0.0827265i $$-0.973637\pi$$
−0.569929 0.821694i $$-0.693029\pi$$
$$332$$ 3.00000 + 1.73205i 0.164646 + 0.0950586i
$$333$$ 0 0
$$334$$ −1.50000 + 2.59808i −0.0820763 + 0.142160i
$$335$$ 7.50000 + 12.9904i 0.409769 + 0.709740i
$$336$$ 0 0
$$337$$ 22.0000 1.19842 0.599208 0.800593i $$-0.295482\pi$$
0.599208 + 0.800593i $$0.295482\pi$$
$$338$$ −10.5000 + 19.9186i −0.571125 + 1.08343i
$$339$$ −15.0000 −0.814688
$$340$$ 9.00000 5.19615i 0.488094 0.281801i
$$341$$ −4.50000 7.79423i −0.243689 0.422081i
$$342$$ 3.00000 5.19615i 0.162221 0.280976i
$$343$$ 0 0
$$344$$ −16.5000 9.52628i −0.889620 0.513623i
$$345$$ 0 0
$$346$$ 25.9808i 1.39673i
$$347$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$348$$ −1.50000 2.59808i −0.0804084 0.139272i
$$349$$ −4.50000 + 2.59808i −0.240879 + 0.139072i −0.615581 0.788074i $$-0.711079\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ −5.00000 17.3205i −0.266880 0.924500i
$$352$$ 27.0000 1.43910
$$353$$ −1.50000 + 0.866025i −0.0798369 + 0.0460939i −0.539387 0.842058i $$-0.681344\pi$$
0.459550 + 0.888152i $$0.348011\pi$$
$$354$$ 3.00000 + 5.19615i 0.159448 + 0.276172i
$$355$$ 1.50000 2.59808i 0.0796117 0.137892i
$$356$$ 6.92820i 0.367194i
$$357$$ 0 0
$$358$$ −4.50000 2.59808i −0.237832 0.137313i
$$359$$ 19.0526i 1.00556i 0.864416 + 0.502778i $$0.167689\pi$$
−0.864416 + 0.502778i $$0.832311\pi$$
$$360$$ 3.00000 5.19615i 0.158114 0.273861i
$$361$$ −8.00000 13.8564i −0.421053 0.729285i
$$362$$ 3.00000 1.73205i 0.157676 0.0910346i
$$363$$ 16.0000 0.839782
$$364$$ 0 0
$$365$$ 15.0000 0.785136
$$366$$ −10.5000 + 6.06218i −0.548844 + 0.316875i
$$367$$ −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
$$369$$ 10.3923i 0.541002i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 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
$$376$$ 15.0000 0.773566
$$377$$ −7.50000 + 7.79423i −0.386270 + 0.401423i
$$378$$ 0 0
$$379$$ −1.50000 + 0.866025i −0.0770498 + 0.0444847i −0.538030 0.842926i $$-0.680831\pi$$
0.460980 + 0.887410i $$0.347498\pi$$
$$380$$ −1.50000 2.59808i −0.0769484 0.133278i
$$381$$ 6.50000 11.2583i 0.333005 0.576782i
$$382$$ 25.9808i 1.32929i
$$383$$ 13.5000 + 7.79423i 0.689818 + 0.398266i 0.803544 0.595246i $$-0.202945\pi$$
−0.113726 + 0.993512i $$0.536279\pi$$
$$384$$ −10.5000 6.06218i −0.535826 0.309359i
$$385$$ 0 0
$$386$$ −1.50000 + 2.59808i −0.0763480 + 0.132239i
$$387$$ 11.0000 + 19.0526i 0.559161 + 0.968496i
$$388$$ −4.50000 + 2.59808i −0.228453 + 0.131897i
$$389$$ 3.00000 0.152106 0.0760530 0.997104i $$-0.475768\pi$$
0.0760530 + 0.997104i $$0.475768\pi$$
$$390$$ −10.5000 2.59808i −0.531688 0.131559i
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 7.50000 + 12.9904i 0.378325 + 0.655278i
$$394$$ 19.5000 33.7750i 0.982396 1.70156i
$$395$$ 8.66025i 0.435745i
$$396$$ −9.00000 5.19615i −0.452267 0.261116i
$$397$$ −31.5000 18.1865i −1.58094 0.912756i −0.994722 0.102602i $$-0.967283\pi$$
−0.586217 0.810154i $$-0.699383\pi$$
$$398$$ 6.92820i 0.347279i
$$399$$ 0 0
$$400$$ 5.00000 + 8.66025i 0.250000 + 0.433013i
$$401$$ 6.00000 3.46410i 0.299626 0.172989i −0.342649 0.939463i $$-0.611324\pi$$
0.642275 + 0.766475i $$0.277991\pi$$
$$402$$ −15.0000 −0.748132
$$403$$ −6.00000 + 1.73205i −0.298881 + 0.0862796i
$$404$$ 9.00000 0.447767
$$405$$ −1.50000 + 0.866025i −0.0745356 + 0.0430331i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 10.3923i 0.514496i
$$409$$ −6.00000 3.46410i −0.296681 0.171289i 0.344270 0.938871i $$-0.388126\pi$$
−0.640951 + 0.767582i $$0.721460\pi$$
$$410$$ 13.5000 + 7.79423i 0.666717 + 0.384930i
$$411$$ 0 0
$$412$$ −6.50000 + 11.2583i −0.320232 + 0.554658i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 6.00000 0.294528
$$416$$ 4.50000 18.1865i 0.220631 0.891668i
$$417$$ 13.0000 0.636613
$$418$$ 13.5000 7.79423i 0.660307 0.381228i
$$419$$ −10.5000 18.1865i −0.512959 0.888470i −0.999887 0.0150285i $$-0.995216\pi$$
0.486928 0.873442i $$-0.338117\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ −19.5000 11.2583i −0.949245 0.548047i
$$423$$ −15.0000 8.66025i −0.729325 0.421076i
$$424$$ 15.5885i 0.757042i
$$425$$ −6.00000 + 10.3923i −0.291043 + 0.504101i
$$426$$ 1.50000 + 2.59808i 0.0726752 + 0.125877i
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 4.50000 18.1865i 0.217262 0.878054i
$$430$$ 33.0000 1.59140
$$431$$ 28.5000 16.4545i 1.37280 0.792585i 0.381517 0.924362i $$-0.375402\pi$$
0.991279 + 0.131777i $$0.0420683\pi$$
$$432$$ 12.5000 + 21.6506i 0.601407 + 1.04167i
$$433$$ −9.50000 + 16.4545i −0.456541 + 0.790752i −0.998775 0.0494752i $$-0.984245\pi$$
0.542234 + 0.840227i $$0.317578\pi$$
$$434$$ 0 0
$$435$$ −4.50000 2.59808i −0.215758 0.124568i
$$436$$ −4.50000 2.59808i −0.215511 0.124425i
$$437$$ 0 0
$$438$$ −7.50000 + 12.9904i −0.358364 + 0.620704i
$$439$$ −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i $$-0.227810\pi$$
−0.945552 + 0.325471i $$0.894477\pi$$
$$440$$ 13.5000 7.79423i 0.643587 0.371575i
$$441$$ 0 0
$$442$$ 36.0000 10.3923i 1.71235 0.494312i
$$443$$ 15.0000 0.712672 0.356336 0.934358i $$-0.384026\pi$$
0.356336 + 0.934358i $$0.384026\pi$$
$$444$$ 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
$$448$$ 0 0
$$449$$ 1.50000 + 0.866025i 0.0707894 + 0.0408703i 0.534977 0.844867i $$-0.320320\pi$$
−0.464188 + 0.885737i $$0.653654\pi$$
$$450$$ 6.92820i 0.326599i
$$451$$ −13.5000 + 23.3827i −0.635690 + 1.10105i
$$452$$ 7.50000 + 12.9904i 0.352770 + 0.611016i
$$453$$ −10.5000 + 6.06218i −0.493333 + 0.284826i
$$454$$ 30.0000 1.40797
$$455$$ 0 0
$$456$$ −3.00000 −0.140488
$$457$$ 30.0000 17.3205i 1.40334 0.810219i 0.408607 0.912710i $$-0.366015\pi$$
0.994734 + 0.102491i $$0.0326814\pi$$
$$458$$ 10.5000 + 18.1865i 0.490633 + 0.849801i
$$459$$ −15.0000 + 25.9808i −0.700140 + 1.21268i
$$460$$ 0 0
$$461$$ 25.5000 + 14.7224i 1.18765 + 0.685692i 0.957773 0.287527i $$-0.0928330\pi$$
0.229881 + 0.973219i $$0.426166\pi$$
$$462$$ 0 0
$$463$$ 24.2487i 1.12693i −0.826139 0.563467i $$-0.809467\pi$$
0.826139 0.563467i $$-0.190533\pi$$
$$464$$ 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
$$467$$ −21.0000 −0.971764 −0.485882 0.874024i $$-0.661502\pi$$
−0.485882 + 0.874024i $$0.661502\pi$$
$$468$$ −5.00000 + 5.19615i −0.231125 + 0.240192i
$$469$$ 0 0
$$470$$ −22.5000 + 12.9904i −1.03785 + 0.599202i
$$471$$ 11.5000 + 19.9186i 0.529892 + 0.917800i
$$472$$ −3.00000 + 5.19615i −0.138086 + 0.239172i
$$473$$ 57.1577i 2.62811i
$$474$$ −7.50000 4.33013i −0.344486 0.198889i
$$475$$ 3.00000 + 1.73205i 0.137649 + 0.0794719i
$$476$$ 0 0
$$477$$ −9.00000 + 15.5885i −0.412082 + 0.713746i
$$478$$ 9.00000 + 15.5885i 0.411650 + 0.712999i
$$479$$ −25.5000 + 14.7224i −1.16512 + 0.672685i −0.952527 0.304455i $$-0.901526\pi$$
−0.212598 + 0.977140i $$0.568192\pi$$
$$480$$ 9.00000 0.410792
$$481$$ 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
$$486$$ 27.7128i 1.25708i
$$487$$ 21.0000 + 12.1244i 0.951601 + 0.549407i 0.893578 0.448908i $$-0.148187\pi$$
0.0580230 + 0.998315i $$0.481520\pi$$
$$488$$ −10.5000 6.06218i −0.475313 0.274422i
$$489$$ 12.1244i 0.548282i
$$490$$ 0 0
$$491$$ 13.5000 + 23.3827i 0.609246 + 1.05525i 0.991365 + 0.131132i $$0.0418613\pi$$
−0.382118 + 0.924113i $$0.624805\pi$$
$$492$$ −4.50000 + 2.59808i −0.202876 + 0.117130i
$$493$$ 18.0000 0.810679
$$494$$ −3.00000 10.3923i −0.134976 0.467572i
$$495$$ −18.0000 −0.809040
$$496$$ 7.50000 4.33013i 0.336760 0.194428i
$$497$$ 0 0
$$498$$ −3.00000 + 5.19615i −0.134433 + 0.232845i
$$499$$ 1.73205i 0.0775372i −0.999248 0.0387686i $$-0.987656\pi$$
0.999248 0.0387686i $$-0.0123435\pi$$
$$500$$ −10.5000 6.06218i −0.469574 0.271109i
$$501$$ −1.50000 0.866025i −0.0670151 0.0386912i
$$502$$ 5.19615i 0.231916i
$$503$$ 4.50000 7.79423i 0.200645 0.347527i −0.748091 0.663596i $$-0.769030\pi$$
0.948736 + 0.316068i $$0.102363\pi$$
$$504$$ 0 0
$$505$$ 13.5000 7.79423i 0.600742 0.346839i
$$506$$ 0 0
$$507$$ −11.5000 6.06218i −0.510733 0.269231i
$$508$$ −13.0000 −0.576782
$$509$$ 6.00000 3.46410i 0.265945 0.153544i −0.361098 0.932528i $$-0.617598\pi$$
0.627044 + 0.778984i $$0.284265\pi$$
$$510$$ 9.00000 + 15.5885i 0.398527 + 0.690268i
$$511$$ 0 0
$$512$$ 8.66025i 0.382733i
$$513$$ 7.50000 + 4.33013i 0.331133 + 0.191180i
$$514$$ −45.0000 25.9808i −1.98486 1.14596i
$$515$$ 22.5167i 0.992203i
$$516$$ −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
$$520$$ −3.00000 10.3923i −0.131559 0.455733i
$$521$$ 39.0000 1.70862 0.854311 0.519763i $$-0.173980\pi$$
0.854311 + 0.519763i $$0.173980\pi$$
$$522$$ −9.00000 + 5.19615i −0.393919 + 0.227429i
$$523$$ 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i $$-0.138794\pi$$
−0.818980 + 0.573822i $$0.805460\pi$$
$$524$$ 7.50000 12.9904i 0.327639 0.567487i
$$525$$ 0 0
$$526$$ −4.50000 2.59808i −0.196209 0.113282i
$$527$$ 9.00000 + 5.19615i 0.392046 + 0.226348i
$$528$$ 25.9808i 1.13067i
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 13.5000 + 23.3827i 0.586403 + 1.01568i
$$531$$ 6.00000 3.46410i 0.260378 0.150329i
$$532$$ 0 0
$$533$$ 13.5000 + 12.9904i 0.584750 + 0.562676i
$$534$$ 12.0000 0.519291
$$535$$ 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
$$539$$ 0 0
$$540$$ −7.50000 4.33013i −0.322749 0.186339i
$$541$$ 12.1244i 0.521267i 0.965438 + 0.260633i $$0.0839314\pi$$
−0.965438 + 0.260633i $$0.916069\pi$$
$$542$$ 15.0000 25.9808i 0.644305 1.11597i
$$543$$ 1.00000 + 1.73205i 0.0429141 + 0.0743294i
$$544$$ −27.0000 + 15.5885i −1.15762 + 0.668350i
$$545$$ −9.00000 −0.385518
$$546$$ 0 0
$$547$$ −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
$$550$$ 9.00000 15.5885i 0.383761 0.664694i
$$551$$ 5.19615i 0.221364i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 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 −0.757953 0.652309i $$-0.773800\pi$$
0.185940 + 0.982561i $$0.440467\pi$$
$$558$$ −6.00000 −0.254000
$$559$$ 38.5000 + 9.52628i 1.62838 + 0.402919i
$$560$$ 0 0
$$561$$ −27.0000 + 15.5885i −1.13994 + 0.658145i
$$562$$ −6.00000 10.3923i −0.253095 0.438373i
$$563$$ 18.0000 31.1769i 0.758610 1.31395i −0.184950 0.982748i $$-0.559212\pi$$
0.943560 0.331202i $$-0.107454\pi$$
$$564$$ 8.66025i 0.364662i
$$565$$ 22.5000 + 12.9904i 0.946582 + 0.546509i
$$566$$ −28.5000 16.4545i −1.19794 0.691633i
$$567$$ 0 0
$$568$$ −1.50000 + 2.59808i −0.0629386 + 0.109013i
$$569$$ 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i $$-0.126528\pi$$
−0.796266 + 0.604947i $$0.793194\pi$$
$$570$$ 4.50000 2.59808i 0.188484 0.108821i
$$571$$ −23.0000 −0.962520 −0.481260 0.876578i $$-0.659821\pi$$
−0.481260 + 0.876578i $$0.659821\pi$$
$$572$$ −18.0000 + 5.19615i −0.752618 + 0.217262i
$$573$$ 15.0000 0.626634
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1.00000 + 1.73205i −0.0416667 + 0.0721688i
$$577$$ 15.5885i 0.648956i 0.945893 + 0.324478i $$0.105189\pi$$
−0.945893 + 0.324478i $$0.894811\pi$$
$$578$$ −28.5000 16.4545i −1.18544 0.684416i
$$579$$ −1.50000 0.866025i −0.0623379 0.0359908i
$$580$$ 5.19615i 0.215758i
$$581$$ 0 0
$$582$$ −4.50000 7.79423i −0.186531 0.323081i
$$583$$ −40.5000 + 23.3827i −1.67734 + 0.968412i
$$584$$ −15.0000 −0.620704
$$585$$ −3.00000 + 12.1244i −0.124035 + 0.501280i
$$586$$ −45.0000 −1.85893
$$587$$ −13.5000 + 7.79423i −0.557205 + 0.321702i −0.752023 0.659137i $$-0.770922\pi$$
0.194818 + 0.980839i $$0.437588\pi$$
$$588$$ 0 0
$$589$$ 1.50000 2.59808i 0.0618064 0.107052i
$$590$$ 10.3923i 0.427844i
$$591$$ 19.5000 + 11.2583i 0.802123 + 0.463106i
$$592$$ 0 0
$$593$$ 5.19615i 0.213380i 0.994292 + 0.106690i $$0.0340253\pi$$
−0.994292 + 0.106690i $$0.965975\pi$$
$$594$$ 22.5000 38.9711i 0.923186 1.59901i
$$595$$ 0 0
$$596$$ 16.5000 9.52628i 0.675866 0.390212i
$$597$$ −4.00000 −0.163709
$$598$$ 0 0
$$599$$ 9.00000 0.367730 0.183865 0.982952i $$-0.441139\pi$$
0.183865 + 0.982952i $$0.441139\pi$$
$$600$$ −3.00000 + 1.73205i −0.122474 + 0.0707107i
$$601$$ −9.50000 16.4545i −0.387513 0.671192i 0.604601 0.796528i $$-0.293332\pi$$
−0.992114 + 0.125336i $$0.959999\pi$$
$$602$$ 0 0
$$603$$ 17.3205i 0.705346i
$$604$$ 10.5000 + 6.06218i 0.427239 + 0.246667i
$$605$$ −24.0000 13.8564i −0.975739 0.563343i
$$606$$ 15.5885i 0.633238i
$$607$$ 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
$$609$$ 0 0
$$610$$ 21.0000 0.850265
$$611$$ −30.0000 + 8.66025i −1.21367 + 0.350356i
$$612$$ 12.0000 0.485071
$$613$$ −31.5000 + 18.1865i −1.27227 + 0.734547i −0.975415 0.220375i $$-0.929272\pi$$
−0.296858 + 0.954922i $$0.595939\pi$$
$$614$$ 21.0000 + 36.3731i 0.847491 + 1.46790i
$$615$$ −4.50000 + 7.79423i −0.181458 + 0.314294i
$$616$$ 0 0
$$617$$ 37.5000 + 21.6506i 1.50969 + 0.871622i 0.999936 + 0.0113033i $$0.00359804\pi$$
0.509757 + 0.860318i $$0.329735\pi$$
$$618$$ −19.5000 11.2583i −0.784405 0.452876i
$$619$$ 19.0526i 0.765787i 0.923792 + 0.382893i $$0.125072\pi$$
−0.923792 + 0.382893i $$0.874928\pi$$
$$620$$ −1.50000 + 2.59808i −0.0602414 + 0.104341i
$$621$$ 0 0
$$622$$ −22.5000 + 12.9904i −0.902168 + 0.520867i
$$623$$ 0 0
$$624$$ 17.5000 + 4.33013i 0.700561 + 0.173344i
$$625$$ −11.0000 −0.440000
$$626$$ 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
$$630$$ 0 0
$$631$$ −40.5000 23.3827i −1.61228 0.930850i −0.988841 0.148978i $$-0.952402\pi$$
−0.623439 0.781872i $$-0.714265\pi$$
$$632$$ 8.66025i 0.344486i
$$633$$ 6.50000 11.2583i 0.258352 0.447478i
$$634$$ 4.50000 + 7.79423i 0.178718 + 0.309548i
$$635$$ −19.5000 + 11.2583i −0.773834 + 0.446773i
$$636$$ −9.00000 −0.356873
$$637$$ 0 0
$$638$$ −27.0000 −1.06894
$$639$$ 3.00000 1.73205i 0.118678 0.0685189i
$$640$$ 10.5000 + 18.1865i 0.415049 + 0.718886i
$$641$$ −15.0000 + 25.9808i −0.592464 + 1.02618i 0.401435 + 0.915888i $$0.368512\pi$$
−0.993899 + 0.110291i $$0.964822\pi$$
$$642$$ 0 0
$$643$$ −4.50000 2.59808i −0.177463 0.102458i 0.408637 0.912697i $$-0.366004\pi$$
−0.586100 + 0.810239i $$0.699337\pi$$
$$644$$ 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
$$649$$ 18.0000 0.706562
$$650$$ −9.00000 8.66025i −0.353009 0.339683i
$$651$$ 0 0
$$652$$ −10.5000 + 6.06218i −0.411212 + 0.237413i
$$653$$ 15.0000 + 25.9808i 0.586995 + 1.01671i 0.994623 + 0.103558i $$0.0330227\pi$$
−0.407628 + 0.913148i $$0.633644\pi$$
$$654$$ 4.50000 7.79423i 0.175964 0.304778i
$$655$$ 25.9808i 1.01515i
$$656$$ −22.5000 12.9904i −0.878477 0.507189i
$$657$$ 15.0000 + 8.66025i 0.585206 + 0.337869i
$$658$$ 0 0
$$659$$ −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i $$-0.927707\pi$$
0.682161 + 0.731202i $$0.261040\pi$$
$$660$$ −4.50000 7.79423i −0.175162 0.303390i
$$661$$ −31.5000 + 18.1865i −1.22521 + 0.707374i −0.966024 0.258454i $$-0.916787\pi$$
−0.259184 + 0.965828i $$0.583454\pi$$
$$662$$ −57.0000 −2.21537
$$663$$ 6.00000 + 20.7846i 0.233021 + 0.807207i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.73205i 0.0670151i
$$669$$ 4.50000 + 2.59808i 0.173980 + 0.100447i
$$670$$ 22.5000 + 12.9904i 0.869251 + 0.501862i
$$671$$ 36.3731i 1.40417i
$$672$$ 0 0
$$673$$ 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i $$-0.160531\pi$$
−0.856228 + 0.516599i $$0.827198\pi$$
$$674$$ 33.0000 19.0526i 1.27111 0.733877i
$$675$$ 10.0000 0.384900
$$676$$ 0.500000 + 12.9904i 0.0192308 + 0.499630i
$$677$$ 27.0000 1.03769 0.518847 0.854867i $$-0.326361\pi$$
0.518847 + 0.854867i $$0.326361\pi$$
$$678$$ −22.5000 + 12.9904i −0.864107 + 0.498893i
$$679$$ 0 0
$$680$$ −9.00000 + 15.5885i −0.345134 + 0.597790i
$$681$$ 17.3205i 0.663723i
$$682$$ −13.5000 7.79423i −0.516942 0.298456i
$$683$$ −21.0000 12.1244i −0.803543 0.463926i 0.0411658 0.999152i $$-0.486893\pi$$
−0.844708 + 0.535227i $$0.820226\pi$$
$$684$$ 3.46410i 0.132453i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −10.5000 + 6.06218i −0.400600 + 0.231287i
$$688$$ −55.0000 −2.09686
$$689$$ 9.00000 + 31.1769i 0.342873 + 1.18775i
$$690$$ 0 0
$$691$$ −27.0000 + 15.5885i −1.02713 + 0.593013i −0.916161 0.400811i $$-0.868728\pi$$
−0.110968 + 0.993824i $$0.535395\pi$$
$$692$$ 7.50000 + 12.9904i 0.285107 + 0.493820i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −19.5000 11.2583i −0.739677 0.427053i
$$696$$ 4.50000 + 2.59808i 0.170572 + 0.0984798i
$$697$$ 31.1769i 1.18091i
$$698$$ −4.50000 + 7.79423i −0.170328 + 0.295016i
$$699$$ 1.50000 + 2.59808i 0.0567352 + 0.0982683i
$$700$$ 0 0
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ −22.5000 21.6506i −0.849208 0.817151i
$$703$$ 0 0
$$704$$ −4.50000 + 2.59808i −0.169600 + 0.0979187i
$$705$$ −7.50000 12.9904i −0.282466 0.489246i
$$706$$ −1.50000 + 2.59808i −0.0564532 + 0.0977799i
$$707$$ 0 0
$$708$$ 3.00000 + 1.73205i 0.112747 + 0.0650945i
$$709$$ 10.5000 + 6.06218i 0.394336 + 0.227670i 0.684037 0.729447i $$-0.260223\pi$$
−0.289701 + 0.957117i $$0.593556\pi$$
$$710$$ 5.19615i 0.195008i
$$711$$ −5.00000 + 8.66025i −0.187515 + 0.324785i
$$712$$ 6.00000 + 10.3923i 0.224860 + 0.389468i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −22.5000 + 23.3827i −0.841452 + 0.874463i
$$716$$ −3.00000 −0.112115
$$717$$ −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
$$721$$ 0 0
$$722$$ −24.0000 13.8564i −0.893188 0.515682i
$$723$$ 6.92820i 0.257663i
$$724$$ 1.00000 1.73205i 0.0371647 0.0643712i
$$725$$ −3.00000 5.19615i −0.111417 0.192980i
$$726$$ 24.0000 13.8564i 0.890724 0.514259i
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 22.5000 12.9904i 0.832762 0.480796i
$$731$$ −33.0000 57.1577i −1.22055 2.11405i
$$732$$ −3.50000 + 6.06218i −0.129364 + 0.224065i
$$733$$ 50.2295i 1.85527i −0.373491 0.927634i $$-0.621839\pi$$
0.373491 0.927634i $$-0.378161\pi$$
$$734$$ −34.5000 19.9186i −1.27342 0.735208i
$$735$$ 0 0
$$736$$ 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 0.294285 0.955718i $$-0.404919\pi$$
0.974818 + 0.223001i $$0.0715853\pi$$
$$740$$ 0 0
$$741$$ 6.00000 1.73205i 0.220416 0.0636285i
$$742$$ 0 0
$$743$$ −1.50000 + 0.866025i −0.0550297 + 0.0317714i −0.527262 0.849703i $$-0.676782\pi$$
0.472233 + 0.881474i $$0.343448\pi$$
$$744$$ 1.50000 + 2.59808i 0.0549927 + 0.0952501i
$$745$$ 16.5000 28.5788i 0.604513 1.04705i
$$746$$ 32.9090i 1.20488i
$$747$$ 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
$$751$$ −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i $$-0.285565\pi$$
−0.988761 + 0.149505i $$0.952232\pi$$
$$752$$ 37.5000 21.6506i 1.36748 0.789517i
$$753$$ −3.00000 −0.109326
$$754$$ −4.50000 + 18.1865i −0.163880 + 0.662314i
$$755$$ 21.0000 0.764268
$$756$$ 0 0
$$757$$ 8.50000 + 14.7224i 0.308938 + 0.535096i 0.978130 0.207993i $$-0.0666932\pi$$
−0.669193 + 0.743089i $$0.733360\pi$$
$$758$$ −1.50000 + 2.59808i −0.0544825 + 0.0943664i
$$759$$ 0 0
$$760$$ 4.50000 + 2.59808i 0.163232 + 0.0942421i
$$761$$ −25.5000 14.7224i −0.924374 0.533688i −0.0393463 0.999226i $$-0.512528\pi$$
−0.885028 + 0.465538i $$0.845861\pi$$
$$762$$ 22.5167i 0.815693i
$$763$$ 0 0
$$764$$ −7.50000 12.9904i −0.271340 0.469975i
$$765$$ 18.0000 10.3923i 0.650791 0.375735i
$$766$$ 27.0000 0.975550
$$767$$ 3.00000 12.1244i 0.108324 0.437785i
$$768$$ −19.0000 −0.685603
$$769$$ −16.5000 + 9.52628i −0.595005 + 0.343526i −0.767074 0.641558i $$-0.778288\pi$$
0.172069 + 0.985085i $$0.444955\pi$$
$$770$$ 0 0
$$771$$ 15.0000 25.9808i 0.540212 0.935674i
$$772$$ 1.73205i 0.0623379i
$$773$$ 12.0000 + 6.92820i 0.431610 + 0.249190i 0.700032 0.714111i $$-0.253169\pi$$
−0.268422 + 0.963301i $$0.586502\pi$$
$$774$$ 33.0000 + 19.0526i 1.18616 + 0.684830i
$$775$$ 3.46410i 0.124434i
$$776$$ 4.50000 7.79423i 0.161541 0.279797i
$$777$$ 0 0
$$778$$ 4.50000 2.59808i 0.161333 0.0931455i
$$779$$ −9.00000 −0.322458
$$780$$ −6.00000 + 1.73205i −0.214834 + 0.0620174i
$$781$$ 9.00000 0.322045
$$782$$ 0 0
$$783$$ −7.50000 12.9904i −0.268028 0.464238i