# Properties

 Label 27.3.d.a.17.1 Level $27$ Weight $3$ Character 27.17 Analytic conductor $0.736$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$27 = 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 27.d (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.735696713773$$ 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 9) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 17.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 27.17 Dual form 27.3.d.a.8.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.00000 - 1.73205i) q^{7} +8.66025i q^{8} +O(q^{10})$$ $$q+(1.50000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.00000 - 1.73205i) q^{7} +8.66025i q^{8} -6.00000 q^{10} +(1.50000 - 0.866025i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-3.00000 - 1.73205i) q^{14} +(5.50000 + 9.52628i) q^{16} -15.5885i q^{17} +11.0000 q^{19} +(3.00000 - 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +(24.0000 + 13.8564i) q^{23} +(-6.50000 - 11.2583i) q^{25} -6.92820i q^{26} +2.00000 q^{28} +(-39.0000 + 22.5167i) q^{29} +(-16.0000 + 27.7128i) q^{31} +(-13.5000 - 7.79423i) q^{32} +(-13.5000 - 23.3827i) q^{34} +6.92820i q^{35} -34.0000 q^{37} +(16.5000 - 9.52628i) q^{38} +(15.0000 - 25.9808i) q^{40} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +1.73205i q^{44} +48.0000 q^{46} +(42.0000 - 24.2487i) q^{47} +(22.5000 - 38.9711i) q^{49} +(-19.5000 - 11.2583i) q^{50} +(2.00000 + 3.46410i) q^{52} -6.00000 q^{55} +(15.0000 - 8.66025i) q^{56} +(-39.0000 + 67.5500i) q^{58} +(-43.5000 - 25.1147i) q^{59} +(-28.0000 - 48.4974i) q^{61} +55.4256i q^{62} -71.0000 q^{64} +(-12.0000 + 6.92820i) q^{65} +(15.5000 - 26.8468i) q^{67} +(13.5000 + 7.79423i) q^{68} +(6.00000 + 10.3923i) q^{70} +31.1769i q^{71} +65.0000 q^{73} +(-51.0000 + 29.4449i) q^{74} +(-5.50000 + 9.52628i) q^{76} +(-3.00000 - 1.73205i) q^{77} +(-19.0000 - 32.9090i) q^{79} -38.1051i q^{80} +21.0000 q^{82} +(42.0000 - 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +(91.5000 + 52.8275i) q^{86} +(7.50000 + 12.9904i) q^{88} -124.708i q^{89} -8.00000 q^{91} +(-24.0000 + 13.8564i) q^{92} +(42.0000 - 72.7461i) q^{94} +(-33.0000 - 19.0526i) q^{95} +(57.5000 + 99.5929i) q^{97} -77.9423i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{2} - q^{4} - 6 q^{5} - 2 q^{7} + O(q^{10})$$ $$2 q + 3 q^{2} - q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{10} + 3 q^{11} + 4 q^{13} - 6 q^{14} + 11 q^{16} + 22 q^{19} + 6 q^{20} + 3 q^{22} + 48 q^{23} - 13 q^{25} + 4 q^{28} - 78 q^{29} - 32 q^{31} - 27 q^{32} - 27 q^{34} - 68 q^{37} + 33 q^{38} + 30 q^{40} + 21 q^{41} + 61 q^{43} + 96 q^{46} + 84 q^{47} + 45 q^{49} - 39 q^{50} + 4 q^{52} - 12 q^{55} + 30 q^{56} - 78 q^{58} - 87 q^{59} - 56 q^{61} - 142 q^{64} - 24 q^{65} + 31 q^{67} + 27 q^{68} + 12 q^{70} + 130 q^{73} - 102 q^{74} - 11 q^{76} - 6 q^{77} - 38 q^{79} + 42 q^{82} + 84 q^{83} - 54 q^{85} + 183 q^{86} + 15 q^{88} - 16 q^{91} - 48 q^{92} + 84 q^{94} - 66 q^{95} + 115 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.50000 0.866025i 0.750000 0.433013i −0.0756939 0.997131i $$-0.524117\pi$$
0.825694 + 0.564118i $$0.190784\pi$$
$$3$$ 0 0
$$4$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$5$$ −3.00000 1.73205i −0.600000 0.346410i 0.169042 0.985609i $$-0.445933\pi$$
−0.769042 + 0.639199i $$0.779266\pi$$
$$6$$ 0 0
$$7$$ −1.00000 1.73205i −0.142857 0.247436i 0.785714 0.618590i $$-0.212296\pi$$
−0.928571 + 0.371154i $$0.878962\pi$$
$$8$$ 8.66025i 1.08253i
$$9$$ 0 0
$$10$$ −6.00000 −0.600000
$$11$$ 1.50000 0.866025i 0.136364 0.0787296i −0.430266 0.902702i $$-0.641580\pi$$
0.566630 + 0.823972i $$0.308247\pi$$
$$12$$ 0 0
$$13$$ 2.00000 3.46410i 0.153846 0.266469i −0.778792 0.627282i $$-0.784167\pi$$
0.932638 + 0.360813i $$0.117501\pi$$
$$14$$ −3.00000 1.73205i −0.214286 0.123718i
$$15$$ 0 0
$$16$$ 5.50000 + 9.52628i 0.343750 + 0.595392i
$$17$$ 15.5885i 0.916968i −0.888703 0.458484i $$-0.848393\pi$$
0.888703 0.458484i $$-0.151607\pi$$
$$18$$ 0 0
$$19$$ 11.0000 0.578947 0.289474 0.957186i $$-0.406520\pi$$
0.289474 + 0.957186i $$0.406520\pi$$
$$20$$ 3.00000 1.73205i 0.150000 0.0866025i
$$21$$ 0 0
$$22$$ 1.50000 2.59808i 0.0681818 0.118094i
$$23$$ 24.0000 + 13.8564i 1.04348 + 0.602452i 0.920817 0.389996i $$-0.127524\pi$$
0.122662 + 0.992449i $$0.460857\pi$$
$$24$$ 0 0
$$25$$ −6.50000 11.2583i −0.260000 0.450333i
$$26$$ 6.92820i 0.266469i
$$27$$ 0 0
$$28$$ 2.00000 0.0714286
$$29$$ −39.0000 + 22.5167i −1.34483 + 0.776437i −0.987511 0.157547i $$-0.949641\pi$$
−0.357316 + 0.933984i $$0.616308\pi$$
$$30$$ 0 0
$$31$$ −16.0000 + 27.7128i −0.516129 + 0.893962i 0.483696 + 0.875236i $$0.339294\pi$$
−0.999825 + 0.0187254i $$0.994039\pi$$
$$32$$ −13.5000 7.79423i −0.421875 0.243570i
$$33$$ 0 0
$$34$$ −13.5000 23.3827i −0.397059 0.687726i
$$35$$ 6.92820i 0.197949i
$$36$$ 0 0
$$37$$ −34.0000 −0.918919 −0.459459 0.888199i $$-0.651957\pi$$
−0.459459 + 0.888199i $$0.651957\pi$$
$$38$$ 16.5000 9.52628i 0.434211 0.250692i
$$39$$ 0 0
$$40$$ 15.0000 25.9808i 0.375000 0.649519i
$$41$$ 10.5000 + 6.06218i 0.256098 + 0.147858i 0.622553 0.782578i $$-0.286095\pi$$
−0.366456 + 0.930436i $$0.619429\pi$$
$$42$$ 0 0
$$43$$ 30.5000 + 52.8275i 0.709302 + 1.22855i 0.965116 + 0.261822i $$0.0843232\pi$$
−0.255814 + 0.966726i $$0.582343\pi$$
$$44$$ 1.73205i 0.0393648i
$$45$$ 0 0
$$46$$ 48.0000 1.04348
$$47$$ 42.0000 24.2487i 0.893617 0.515930i 0.0184931 0.999829i $$-0.494113\pi$$
0.875124 + 0.483899i $$0.160780\pi$$
$$48$$ 0 0
$$49$$ 22.5000 38.9711i 0.459184 0.795329i
$$50$$ −19.5000 11.2583i −0.390000 0.225167i
$$51$$ 0 0
$$52$$ 2.00000 + 3.46410i 0.0384615 + 0.0666173i
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ −6.00000 −0.109091
$$56$$ 15.0000 8.66025i 0.267857 0.154647i
$$57$$ 0 0
$$58$$ −39.0000 + 67.5500i −0.672414 + 1.16465i
$$59$$ −43.5000 25.1147i −0.737288 0.425674i 0.0837943 0.996483i $$-0.473296\pi$$
−0.821082 + 0.570810i $$0.806629\pi$$
$$60$$ 0 0
$$61$$ −28.0000 48.4974i −0.459016 0.795040i 0.539893 0.841734i $$-0.318465\pi$$
−0.998909 + 0.0466940i $$0.985131\pi$$
$$62$$ 55.4256i 0.893962i
$$63$$ 0 0
$$64$$ −71.0000 −1.10938
$$65$$ −12.0000 + 6.92820i −0.184615 + 0.106588i
$$66$$ 0 0
$$67$$ 15.5000 26.8468i 0.231343 0.400698i −0.726860 0.686785i $$-0.759021\pi$$
0.958204 + 0.286087i $$0.0923546\pi$$
$$68$$ 13.5000 + 7.79423i 0.198529 + 0.114621i
$$69$$ 0 0
$$70$$ 6.00000 + 10.3923i 0.0857143 + 0.148461i
$$71$$ 31.1769i 0.439111i 0.975600 + 0.219556i $$0.0704608\pi$$
−0.975600 + 0.219556i $$0.929539\pi$$
$$72$$ 0 0
$$73$$ 65.0000 0.890411 0.445205 0.895428i $$-0.353131\pi$$
0.445205 + 0.895428i $$0.353131\pi$$
$$74$$ −51.0000 + 29.4449i −0.689189 + 0.397904i
$$75$$ 0 0
$$76$$ −5.50000 + 9.52628i −0.0723684 + 0.125346i
$$77$$ −3.00000 1.73205i −0.0389610 0.0224942i
$$78$$ 0 0
$$79$$ −19.0000 32.9090i −0.240506 0.416569i 0.720352 0.693608i $$-0.243980\pi$$
−0.960859 + 0.277039i $$0.910647\pi$$
$$80$$ 38.1051i 0.476314i
$$81$$ 0 0
$$82$$ 21.0000 0.256098
$$83$$ 42.0000 24.2487i 0.506024 0.292153i −0.225174 0.974319i $$-0.572295\pi$$
0.731198 + 0.682165i $$0.238962\pi$$
$$84$$ 0 0
$$85$$ −27.0000 + 46.7654i −0.317647 + 0.550181i
$$86$$ 91.5000 + 52.8275i 1.06395 + 0.614274i
$$87$$ 0 0
$$88$$ 7.50000 + 12.9904i 0.0852273 + 0.147618i
$$89$$ 124.708i 1.40121i −0.713549 0.700605i $$-0.752914\pi$$
0.713549 0.700605i $$-0.247086\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.0879121
$$92$$ −24.0000 + 13.8564i −0.260870 + 0.150613i
$$93$$ 0 0
$$94$$ 42.0000 72.7461i 0.446809 0.773895i
$$95$$ −33.0000 19.0526i −0.347368 0.200553i
$$96$$ 0 0
$$97$$ 57.5000 + 99.5929i 0.592784 + 1.02673i 0.993856 + 0.110685i $$0.0353044\pi$$
−0.401072 + 0.916047i $$0.631362\pi$$
$$98$$ 77.9423i 0.795329i
$$99$$ 0 0
$$100$$ 13.0000 0.130000
$$101$$ −39.0000 + 22.5167i −0.386139 + 0.222937i −0.680486 0.732761i $$-0.738231\pi$$
0.294347 + 0.955699i $$0.404898\pi$$
$$102$$ 0 0
$$103$$ 20.0000 34.6410i 0.194175 0.336321i −0.752455 0.658644i $$-0.771130\pi$$
0.946630 + 0.322323i $$0.104464\pi$$
$$104$$ 30.0000 + 17.3205i 0.288462 + 0.166543i
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 140.296i 1.31118i 0.755118 + 0.655589i $$0.227580\pi$$
−0.755118 + 0.655589i $$0.772420\pi$$
$$108$$ 0 0
$$109$$ −52.0000 −0.477064 −0.238532 0.971135i $$-0.576666\pi$$
−0.238532 + 0.971135i $$0.576666\pi$$
$$110$$ −9.00000 + 5.19615i −0.0818182 + 0.0472377i
$$111$$ 0 0
$$112$$ 11.0000 19.0526i 0.0982143 0.170112i
$$113$$ 78.0000 + 45.0333i 0.690265 + 0.398525i 0.803711 0.595019i $$-0.202856\pi$$
−0.113446 + 0.993544i $$0.536189\pi$$
$$114$$ 0 0
$$115$$ −48.0000 83.1384i −0.417391 0.722943i
$$116$$ 45.0333i 0.388218i
$$117$$ 0 0
$$118$$ −87.0000 −0.737288
$$119$$ −27.0000 + 15.5885i −0.226891 + 0.130995i
$$120$$ 0 0
$$121$$ −59.0000 + 102.191i −0.487603 + 0.844554i
$$122$$ −84.0000 48.4974i −0.688525 0.397520i
$$123$$ 0 0
$$124$$ −16.0000 27.7128i −0.129032 0.223490i
$$125$$ 131.636i 1.05309i
$$126$$ 0 0
$$127$$ −16.0000 −0.125984 −0.0629921 0.998014i $$-0.520064\pi$$
−0.0629921 + 0.998014i $$0.520064\pi$$
$$128$$ −52.5000 + 30.3109i −0.410156 + 0.236804i
$$129$$ 0 0
$$130$$ −12.0000 + 20.7846i −0.0923077 + 0.159882i
$$131$$ −138.000 79.6743i −1.05344 0.608201i −0.129826 0.991537i $$-0.541442\pi$$
−0.923609 + 0.383336i $$0.874775\pi$$
$$132$$ 0 0
$$133$$ −11.0000 19.0526i −0.0827068 0.143252i
$$134$$ 53.6936i 0.400698i
$$135$$ 0 0
$$136$$ 135.000 0.992647
$$137$$ 163.500 94.3968i 1.19343 0.689028i 0.234348 0.972153i $$-0.424705\pi$$
0.959083 + 0.283125i $$0.0913712\pi$$
$$138$$ 0 0
$$139$$ −2.50000 + 4.33013i −0.0179856 + 0.0311520i −0.874878 0.484343i $$-0.839059\pi$$
0.856893 + 0.515495i $$0.172392\pi$$
$$140$$ −6.00000 3.46410i −0.0428571 0.0247436i
$$141$$ 0 0
$$142$$ 27.0000 + 46.7654i 0.190141 + 0.329334i
$$143$$ 6.92820i 0.0484490i
$$144$$ 0 0
$$145$$ 156.000 1.07586
$$146$$ 97.5000 56.2917i 0.667808 0.385559i
$$147$$ 0 0
$$148$$ 17.0000 29.4449i 0.114865 0.198952i
$$149$$ 132.000 + 76.2102i 0.885906 + 0.511478i 0.872601 0.488433i $$-0.162431\pi$$
0.0133049 + 0.999911i $$0.495765\pi$$
$$150$$ 0 0
$$151$$ −10.0000 17.3205i −0.0662252 0.114705i 0.831012 0.556255i $$-0.187762\pi$$
−0.897237 + 0.441550i $$0.854429\pi$$
$$152$$ 95.2628i 0.626729i
$$153$$ 0 0
$$154$$ −6.00000 −0.0389610
$$155$$ 96.0000 55.4256i 0.619355 0.357585i
$$156$$ 0 0
$$157$$ 20.0000 34.6410i 0.127389 0.220643i −0.795276 0.606248i $$-0.792674\pi$$
0.922664 + 0.385605i $$0.126007\pi$$
$$158$$ −57.0000 32.9090i −0.360759 0.208285i
$$159$$ 0 0
$$160$$ 27.0000 + 46.7654i 0.168750 + 0.292284i
$$161$$ 55.4256i 0.344259i
$$162$$ 0 0
$$163$$ −106.000 −0.650307 −0.325153 0.945661i $$-0.605416\pi$$
−0.325153 + 0.945661i $$0.605416\pi$$
$$164$$ −10.5000 + 6.06218i −0.0640244 + 0.0369645i
$$165$$ 0 0
$$166$$ 42.0000 72.7461i 0.253012 0.438230i
$$167$$ −165.000 95.2628i −0.988024 0.570436i −0.0833409 0.996521i $$-0.526559\pi$$
−0.904683 + 0.426085i $$0.859892\pi$$
$$168$$ 0 0
$$169$$ 76.5000 + 132.502i 0.452663 + 0.784035i
$$170$$ 93.5307i 0.550181i
$$171$$ 0 0
$$172$$ −61.0000 −0.354651
$$173$$ −201.000 + 116.047i −1.16185 + 0.670794i −0.951747 0.306885i $$-0.900713\pi$$
−0.210103 + 0.977679i $$0.567380\pi$$
$$174$$ 0 0
$$175$$ −13.0000 + 22.5167i −0.0742857 + 0.128667i
$$176$$ 16.5000 + 9.52628i 0.0937500 + 0.0541266i
$$177$$ 0 0
$$178$$ −108.000 187.061i −0.606742 1.05091i
$$179$$ 62.3538i 0.348345i −0.984715 0.174173i $$-0.944275\pi$$
0.984715 0.174173i $$-0.0557251\pi$$
$$180$$ 0 0
$$181$$ −232.000 −1.28177 −0.640884 0.767638i $$-0.721432\pi$$
−0.640884 + 0.767638i $$0.721432\pi$$
$$182$$ −12.0000 + 6.92820i −0.0659341 + 0.0380671i
$$183$$ 0 0
$$184$$ −120.000 + 207.846i −0.652174 + 1.12960i
$$185$$ 102.000 + 58.8897i 0.551351 + 0.318323i
$$186$$ 0 0
$$187$$ −13.5000 23.3827i −0.0721925 0.125041i
$$188$$ 48.4974i 0.257965i
$$189$$ 0 0
$$190$$ −66.0000 −0.347368
$$191$$ −201.000 + 116.047i −1.05236 + 0.607578i −0.923308 0.384060i $$-0.874525\pi$$
−0.129048 + 0.991638i $$0.541192\pi$$
$$192$$ 0 0
$$193$$ 132.500 229.497i 0.686528 1.18910i −0.286425 0.958103i $$-0.592467\pi$$
0.972954 0.231000i $$-0.0741996\pi$$
$$194$$ 172.500 + 99.5929i 0.889175 + 0.513366i
$$195$$ 0 0
$$196$$ 22.5000 + 38.9711i 0.114796 + 0.198832i
$$197$$ 124.708i 0.633034i −0.948587 0.316517i $$-0.897487\pi$$
0.948587 0.316517i $$-0.102513\pi$$
$$198$$ 0 0
$$199$$ 290.000 1.45729 0.728643 0.684893i $$-0.240151\pi$$
0.728643 + 0.684893i $$0.240151\pi$$
$$200$$ 97.5000 56.2917i 0.487500 0.281458i
$$201$$ 0 0
$$202$$ −39.0000 + 67.5500i −0.193069 + 0.334406i
$$203$$ 78.0000 + 45.0333i 0.384236 + 0.221839i
$$204$$ 0 0
$$205$$ −21.0000 36.3731i −0.102439 0.177430i
$$206$$ 69.2820i 0.336321i
$$207$$ 0 0
$$208$$ 44.0000 0.211538
$$209$$ 16.5000 9.52628i 0.0789474 0.0455803i
$$210$$ 0 0
$$211$$ 47.0000 81.4064i 0.222749 0.385812i −0.732893 0.680344i $$-0.761830\pi$$
0.955642 + 0.294532i $$0.0951637\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 121.500 + 210.444i 0.567757 + 0.983384i
$$215$$ 211.310i 0.982838i
$$216$$ 0 0
$$217$$ 64.0000 0.294931
$$218$$ −78.0000 + 45.0333i −0.357798 + 0.206575i
$$219$$ 0 0
$$220$$ 3.00000 5.19615i 0.0136364 0.0236189i
$$221$$ −54.0000 31.1769i −0.244344 0.141072i
$$222$$ 0 0
$$223$$ 26.0000 + 45.0333i 0.116592 + 0.201943i 0.918415 0.395618i $$-0.129470\pi$$
−0.801823 + 0.597562i $$0.796136\pi$$
$$224$$ 31.1769i 0.139183i
$$225$$ 0 0
$$226$$ 156.000 0.690265
$$227$$ 163.500 94.3968i 0.720264 0.415845i −0.0945856 0.995517i $$-0.530153\pi$$
0.814850 + 0.579672i $$0.196819\pi$$
$$228$$ 0 0
$$229$$ −133.000 + 230.363i −0.580786 + 1.00595i 0.414600 + 0.910004i $$0.363921\pi$$
−0.995386 + 0.0959473i $$0.969412\pi$$
$$230$$ −144.000 83.1384i −0.626087 0.361471i
$$231$$ 0 0
$$232$$ −195.000 337.750i −0.840517 1.45582i
$$233$$ 202.650i 0.869742i −0.900493 0.434871i $$-0.856794\pi$$
0.900493 0.434871i $$-0.143206\pi$$
$$234$$ 0 0
$$235$$ −168.000 −0.714894
$$236$$ 43.5000 25.1147i 0.184322 0.106418i
$$237$$ 0 0
$$238$$ −27.0000 + 46.7654i −0.113445 + 0.196493i
$$239$$ 348.000 + 200.918i 1.45607 + 0.840661i 0.998815 0.0486764i $$-0.0155003\pi$$
0.457252 + 0.889337i $$0.348834\pi$$
$$240$$ 0 0
$$241$$ −59.5000 103.057i −0.246888 0.427623i 0.715773 0.698333i $$-0.246075\pi$$
−0.962661 + 0.270711i $$0.912741\pi$$
$$242$$ 204.382i 0.844554i
$$243$$ 0 0
$$244$$ 56.0000 0.229508
$$245$$ −135.000 + 77.9423i −0.551020 + 0.318132i
$$246$$ 0 0
$$247$$ 22.0000 38.1051i 0.0890688 0.154272i
$$248$$ −240.000 138.564i −0.967742 0.558726i
$$249$$ 0 0
$$250$$ 114.000 + 197.454i 0.456000 + 0.789815i
$$251$$ 389.711i 1.55264i 0.630342 + 0.776318i $$0.282915\pi$$
−0.630342 + 0.776318i $$0.717085\pi$$
$$252$$ 0 0
$$253$$ 48.0000 0.189723
$$254$$ −24.0000 + 13.8564i −0.0944882 + 0.0545528i
$$255$$ 0 0
$$256$$ 89.5000 155.019i 0.349609 0.605541i
$$257$$ −151.500 87.4686i −0.589494 0.340345i 0.175403 0.984497i $$-0.443877\pi$$
−0.764897 + 0.644152i $$0.777210\pi$$
$$258$$ 0 0
$$259$$ 34.0000 + 58.8897i 0.131274 + 0.227373i
$$260$$ 13.8564i 0.0532939i
$$261$$ 0 0
$$262$$ −276.000 −1.05344
$$263$$ −39.0000 + 22.5167i −0.148289 + 0.0856147i −0.572309 0.820038i $$-0.693952\pi$$
0.424020 + 0.905653i $$0.360619\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −33.0000 19.0526i −0.124060 0.0716262i
$$267$$ 0 0
$$268$$ 15.5000 + 26.8468i 0.0578358 + 0.100175i
$$269$$ 187.061i 0.695396i 0.937607 + 0.347698i $$0.113037\pi$$
−0.937607 + 0.347698i $$0.886963\pi$$
$$270$$ 0 0
$$271$$ −268.000 −0.988930 −0.494465 0.869198i $$-0.664636\pi$$
−0.494465 + 0.869198i $$0.664636\pi$$
$$272$$ 148.500 85.7365i 0.545956 0.315208i
$$273$$ 0 0
$$274$$ 163.500 283.190i 0.596715 1.03354i
$$275$$ −19.5000 11.2583i −0.0709091 0.0409394i
$$276$$ 0 0
$$277$$ −28.0000 48.4974i −0.101083 0.175081i 0.811048 0.584979i $$-0.198897\pi$$
−0.912131 + 0.409899i $$0.865564\pi$$
$$278$$ 8.66025i 0.0311520i
$$279$$ 0 0
$$280$$ −60.0000 −0.214286
$$281$$ 42.0000 24.2487i 0.149466 0.0862943i −0.423402 0.905942i $$-0.639164\pi$$
0.572868 + 0.819648i $$0.305831\pi$$
$$282$$ 0 0
$$283$$ −187.000 + 323.894i −0.660777 + 1.14450i 0.319634 + 0.947541i $$0.396440\pi$$
−0.980412 + 0.196959i $$0.936893\pi$$
$$284$$ −27.0000 15.5885i −0.0950704 0.0548889i
$$285$$ 0 0
$$286$$ −6.00000 10.3923i −0.0209790 0.0363367i
$$287$$ 24.2487i 0.0844903i
$$288$$ 0 0
$$289$$ 46.0000 0.159170
$$290$$ 234.000 135.100i 0.806897 0.465862i
$$291$$ 0 0
$$292$$ −32.5000 + 56.2917i −0.111301 + 0.192780i
$$293$$ −219.000 126.440i −0.747440 0.431535i 0.0773280 0.997006i $$-0.475361\pi$$
−0.824768 + 0.565471i $$0.808694\pi$$
$$294$$ 0 0
$$295$$ 87.0000 + 150.688i 0.294915 + 0.510808i
$$296$$ 294.449i 0.994759i
$$297$$ 0 0
$$298$$ 264.000 0.885906
$$299$$ 96.0000 55.4256i 0.321070 0.185370i
$$300$$ 0 0
$$301$$ 61.0000 105.655i 0.202658 0.351014i
$$302$$ −30.0000 17.3205i −0.0993377 0.0573527i
$$303$$ 0 0
$$304$$ 60.5000 + 104.789i 0.199013 + 0.344701i
$$305$$ 193.990i 0.636032i
$$306$$ 0 0
$$307$$ 533.000 1.73616 0.868078 0.496428i $$-0.165355\pi$$
0.868078 + 0.496428i $$0.165355\pi$$
$$308$$ 3.00000 1.73205i 0.00974026 0.00562354i
$$309$$ 0 0
$$310$$ 96.0000 166.277i 0.309677 0.536377i
$$311$$ 213.000 + 122.976i 0.684887 + 0.395420i 0.801694 0.597735i $$-0.203932\pi$$
−0.116806 + 0.993155i $$0.537266\pi$$
$$312$$ 0 0
$$313$$ −77.5000 134.234i −0.247604 0.428862i 0.715257 0.698862i $$-0.246310\pi$$
−0.962860 + 0.269999i $$0.912976\pi$$
$$314$$ 69.2820i 0.220643i
$$315$$ 0 0
$$316$$ 38.0000 0.120253
$$317$$ 42.0000 24.2487i 0.132492 0.0764944i −0.432289 0.901735i $$-0.642294\pi$$
0.564781 + 0.825241i $$0.308961\pi$$
$$318$$ 0 0
$$319$$ −39.0000 + 67.5500i −0.122257 + 0.211755i
$$320$$ 213.000 + 122.976i 0.665625 + 0.384299i
$$321$$ 0 0
$$322$$ −48.0000 83.1384i −0.149068 0.258194i
$$323$$ 171.473i 0.530876i
$$324$$ 0 0
$$325$$ −52.0000 −0.160000
$$326$$ −159.000 + 91.7987i −0.487730 + 0.281591i
$$327$$ 0 0
$$328$$ −52.5000 + 90.9327i −0.160061 + 0.277234i
$$329$$ −84.0000 48.4974i −0.255319 0.147409i
$$330$$ 0 0
$$331$$ −1.00000 1.73205i −0.00302115 0.00523278i 0.864511 0.502614i $$-0.167628\pi$$
−0.867532 + 0.497381i $$0.834295\pi$$
$$332$$ 48.4974i 0.146077i
$$333$$ 0 0
$$334$$ −330.000 −0.988024
$$335$$ −93.0000 + 53.6936i −0.277612 + 0.160279i
$$336$$ 0 0
$$337$$ −38.5000 + 66.6840i −0.114243 + 0.197875i −0.917477 0.397789i $$-0.869778\pi$$
0.803234 + 0.595664i $$0.203111\pi$$
$$338$$ 229.500 + 132.502i 0.678994 + 0.392017i
$$339$$ 0 0
$$340$$ −27.0000 46.7654i −0.0794118 0.137545i
$$341$$ 55.4256i 0.162538i
$$342$$ 0 0
$$343$$ −188.000 −0.548105
$$344$$ −457.500 + 264.138i −1.32994 + 0.767842i
$$345$$ 0 0
$$346$$ −201.000 + 348.142i −0.580925 + 1.00619i
$$347$$ −97.5000 56.2917i −0.280980 0.162224i 0.352887 0.935666i $$-0.385200\pi$$
−0.633867 + 0.773442i $$0.718533\pi$$
$$348$$ 0 0
$$349$$ −208.000 360.267i −0.595989 1.03228i −0.993407 0.114645i $$-0.963427\pi$$
0.397418 0.917638i $$-0.369906\pi$$
$$350$$ 45.0333i 0.128667i
$$351$$ 0 0
$$352$$ −27.0000 −0.0767045
$$353$$ 1.50000 0.866025i 0.00424929 0.00245333i −0.497874 0.867249i $$-0.665886\pi$$
0.502123 + 0.864796i $$0.332552\pi$$
$$354$$ 0 0
$$355$$ 54.0000 93.5307i 0.152113 0.263467i
$$356$$ 108.000 + 62.3538i 0.303371 + 0.175151i
$$357$$ 0 0
$$358$$ −54.0000 93.5307i −0.150838 0.261259i
$$359$$ 592.361i 1.65003i −0.565110 0.825016i $$-0.691166\pi$$
0.565110 0.825016i $$-0.308834\pi$$
$$360$$ 0 0
$$361$$ −240.000 −0.664820
$$362$$ −348.000 + 200.918i −0.961326 + 0.555022i
$$363$$ 0 0
$$364$$ 4.00000 6.92820i 0.0109890 0.0190335i
$$365$$ −195.000 112.583i −0.534247 0.308447i
$$366$$ 0 0
$$367$$ 179.000 + 310.037i 0.487738 + 0.844788i 0.999901 0.0141011i $$-0.00448865\pi$$
−0.512162 + 0.858889i $$0.671155\pi$$
$$368$$ 304.841i 0.828372i
$$369$$ 0 0
$$370$$ 204.000 0.551351
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 290.000 502.295i 0.777480 1.34663i −0.155910 0.987771i $$-0.549831\pi$$
0.933390 0.358863i $$-0.116836\pi$$
$$374$$ −40.5000 23.3827i −0.108289 0.0625206i
$$375$$ 0 0
$$376$$ 210.000 + 363.731i 0.558511 + 0.967369i
$$377$$ 180.133i 0.477807i
$$378$$ 0 0
$$379$$ 83.0000 0.218997 0.109499 0.993987i $$-0.465075\pi$$
0.109499 + 0.993987i $$0.465075\pi$$
$$380$$ 33.0000 19.0526i 0.0868421 0.0501383i
$$381$$ 0 0
$$382$$ −201.000 + 348.142i −0.526178 + 0.911367i
$$383$$ 483.000 + 278.860i 1.26110 + 0.728094i 0.973287 0.229593i $$-0.0737395\pi$$
0.287810 + 0.957688i $$0.407073\pi$$
$$384$$ 0 0
$$385$$ 6.00000 + 10.3923i 0.0155844 + 0.0269930i
$$386$$ 458.993i 1.18910i
$$387$$ 0 0
$$388$$ −115.000 −0.296392
$$389$$ 447.000 258.076i 1.14910 0.663433i 0.200432 0.979708i $$-0.435765\pi$$
0.948668 + 0.316274i $$0.102432\pi$$
$$390$$ 0 0
$$391$$ 216.000 374.123i 0.552430 0.956836i
$$392$$ 337.500 + 194.856i 0.860969 + 0.497081i
$$393$$ 0 0
$$394$$ −108.000 187.061i −0.274112 0.474775i
$$395$$ 131.636i 0.333255i
$$396$$ 0 0
$$397$$ 362.000 0.911839 0.455919 0.890021i $$-0.349311\pi$$
0.455919 + 0.890021i $$0.349311\pi$$
$$398$$ 435.000 251.147i 1.09296 0.631024i
$$399$$ 0 0
$$400$$ 71.5000 123.842i 0.178750 0.309604i
$$401$$ −340.500 196.588i −0.849127 0.490244i 0.0112291 0.999937i $$-0.496426\pi$$
−0.860356 + 0.509693i $$0.829759\pi$$
$$402$$ 0 0
$$403$$ 64.0000 + 110.851i 0.158809 + 0.275065i
$$404$$ 45.0333i 0.111469i
$$405$$ 0 0
$$406$$ 156.000 0.384236
$$407$$ −51.0000 + 29.4449i −0.125307 + 0.0723461i
$$408$$ 0 0
$$409$$ −110.500 + 191.392i −0.270171 + 0.467950i −0.968905 0.247431i $$-0.920414\pi$$
0.698734 + 0.715381i $$0.253747\pi$$
$$410$$ −63.0000 36.3731i −0.153659 0.0887148i
$$411$$ 0 0
$$412$$ 20.0000 + 34.6410i 0.0485437 + 0.0840801i
$$413$$ 100.459i 0.243242i
$$414$$ 0 0
$$415$$ −168.000 −0.404819
$$416$$ −54.0000 + 31.1769i −0.129808 + 0.0749445i
$$417$$ 0 0
$$418$$ 16.5000 28.5788i 0.0394737 0.0683704i
$$419$$ −678.000 391.443i −1.61814 0.934233i −0.987401 0.158236i $$-0.949419\pi$$
−0.630737 0.775997i $$-0.717247\pi$$
$$420$$ 0 0
$$421$$ 341.000 + 590.629i 0.809976 + 1.40292i 0.912880 + 0.408229i $$0.133853\pi$$
−0.102903 + 0.994691i $$0.532813\pi$$
$$422$$ 162.813i 0.385812i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −175.500 + 101.325i −0.412941 + 0.238412i
$$426$$ 0 0
$$427$$ −56.0000 + 96.9948i −0.131148 + 0.227154i
$$428$$ −121.500 70.1481i −0.283879 0.163897i
$$429$$ 0 0
$$430$$ −183.000 316.965i −0.425581 0.737129i
$$431$$ 280.592i 0.651026i 0.945538 + 0.325513i $$0.105537\pi$$
−0.945538 + 0.325513i $$0.894463\pi$$
$$432$$ 0 0
$$433$$ −295.000 −0.681293 −0.340647 0.940191i $$-0.610646\pi$$
−0.340647 + 0.940191i $$0.610646\pi$$
$$434$$ 96.0000 55.4256i 0.221198 0.127709i
$$435$$ 0 0
$$436$$ 26.0000 45.0333i 0.0596330 0.103287i
$$437$$ 264.000 + 152.420i 0.604119 + 0.348788i
$$438$$ 0 0
$$439$$ −406.000 703.213i −0.924829 1.60185i −0.791836 0.610734i $$-0.790874\pi$$
−0.132993 0.991117i $$-0.542459\pi$$
$$440$$ 51.9615i 0.118094i
$$441$$ 0 0
$$442$$ −108.000 −0.244344
$$443$$ −79.5000 + 45.8993i −0.179458 + 0.103610i −0.587038 0.809559i $$-0.699706\pi$$
0.407580 + 0.913170i $$0.366373\pi$$
$$444$$ 0 0
$$445$$ −216.000 + 374.123i −0.485393 + 0.840726i
$$446$$ 78.0000 + 45.0333i 0.174888 + 0.100972i
$$447$$ 0 0
$$448$$ 71.0000 + 122.976i 0.158482 + 0.274499i
$$449$$ 639.127i 1.42344i 0.702461 + 0.711722i $$0.252085\pi$$
−0.702461 + 0.711722i $$0.747915\pi$$
$$450$$ 0 0
$$451$$ 21.0000 0.0465632
$$452$$ −78.0000 + 45.0333i −0.172566 + 0.0996312i
$$453$$ 0 0
$$454$$ 163.500 283.190i 0.360132 0.623767i
$$455$$ 24.0000 + 13.8564i 0.0527473 + 0.0304536i
$$456$$ 0 0
$$457$$ −32.5000 56.2917i −0.0711160 0.123176i 0.828275 0.560322i $$-0.189323\pi$$
−0.899391 + 0.437146i $$0.855989\pi$$
$$458$$ 460.726i 1.00595i
$$459$$ 0 0
$$460$$ 96.0000 0.208696
$$461$$ 690.000 398.372i 1.49675 0.864147i 0.496753 0.867892i $$-0.334525\pi$$
0.999993 + 0.00374501i $$0.00119208\pi$$
$$462$$ 0 0
$$463$$ −367.000 + 635.663i −0.792657 + 1.37292i 0.131660 + 0.991295i $$0.457969\pi$$
−0.924317 + 0.381627i $$0.875364\pi$$
$$464$$ −429.000 247.683i −0.924569 0.533800i
$$465$$ 0 0
$$466$$ −175.500 303.975i −0.376609 0.652307i
$$467$$ 202.650i 0.433940i 0.976178 + 0.216970i $$0.0696174\pi$$
−0.976178 + 0.216970i $$0.930383\pi$$
$$468$$ 0 0
$$469$$ −62.0000 −0.132196
$$470$$ −252.000 + 145.492i −0.536170 + 0.309558i
$$471$$ 0 0
$$472$$ 217.500 376.721i 0.460805 0.798138i
$$473$$ 91.5000 + 52.8275i 0.193446 + 0.111686i
$$474$$ 0 0
$$475$$ −71.5000 123.842i −0.150526 0.260719i
$$476$$ 31.1769i 0.0654977i
$$477$$ 0 0
$$478$$ 696.000 1.45607
$$479$$ −525.000 + 303.109i −1.09603 + 0.632795i −0.935176 0.354183i $$-0.884759\pi$$
−0.160857 + 0.986978i $$0.551426\pi$$
$$480$$ 0 0
$$481$$ −68.0000 + 117.779i −0.141372 + 0.244864i
$$482$$ −178.500 103.057i −0.370332 0.213811i
$$483$$ 0 0
$$484$$ −59.0000 102.191i −0.121901 0.211138i
$$485$$ 398.372i 0.821385i
$$486$$ 0 0
$$487$$ −106.000 −0.217659 −0.108830 0.994060i $$-0.534710\pi$$
−0.108830 + 0.994060i $$0.534710\pi$$
$$488$$ 420.000 242.487i 0.860656 0.496900i
$$489$$ 0 0
$$490$$ −135.000 + 233.827i −0.275510 + 0.477198i
$$491$$ 199.500 + 115.181i 0.406314 + 0.234585i 0.689205 0.724567i $$-0.257960\pi$$
−0.282891 + 0.959152i $$0.591293\pi$$
$$492$$ 0 0
$$493$$ 351.000 + 607.950i 0.711968 + 1.23316i
$$494$$ 76.2102i 0.154272i
$$495$$ 0 0
$$496$$ −352.000 −0.709677
$$497$$ 54.0000 31.1769i 0.108652 0.0627302i
$$498$$ 0 0
$$499$$ 393.500 681.562i 0.788577 1.36586i −0.138261 0.990396i $$-0.544151\pi$$
0.926839 0.375460i $$-0.122515\pi$$
$$500$$ −114.000 65.8179i −0.228000 0.131636i
$$501$$ 0 0
$$502$$ 337.500 + 584.567i 0.672311 + 1.16448i
$$503$$ 623.538i 1.23964i −0.784745 0.619819i $$-0.787206\pi$$
0.784745 0.619819i $$-0.212794\pi$$
$$504$$ 0 0
$$505$$ 156.000 0.308911
$$506$$ 72.0000 41.5692i 0.142292 0.0821526i
$$507$$ 0 0
$$508$$ 8.00000 13.8564i 0.0157480 0.0272764i
$$509$$ 186.000 + 107.387i 0.365422 + 0.210977i 0.671457 0.741044i $$-0.265669\pi$$
−0.306034 + 0.952020i $$0.599002\pi$$
$$510$$ 0 0
$$511$$ −65.0000 112.583i −0.127202 0.220320i
$$512$$ 552.524i 1.07915i
$$513$$ 0 0
$$514$$ −303.000 −0.589494
$$515$$ −120.000 + 69.2820i −0.233010 + 0.134528i
$$516$$ 0 0
$$517$$ 42.0000 72.7461i 0.0812379 0.140708i
$$518$$ 102.000 + 58.8897i 0.196911 + 0.113687i
$$519$$ 0 0
$$520$$ −60.0000 103.923i −0.115385 0.199852i
$$521$$ 202.650i 0.388963i 0.980906 + 0.194482i $$0.0623025\pi$$
−0.980906 + 0.194482i $$0.937698\pi$$
$$522$$ 0 0
$$523$$ −250.000 −0.478011 −0.239006 0.971018i $$-0.576821\pi$$
−0.239006 + 0.971018i $$0.576821\pi$$
$$524$$ 138.000 79.6743i 0.263359 0.152050i
$$525$$ 0 0
$$526$$ −39.0000 + 67.5500i −0.0741445 + 0.128422i
$$527$$ 432.000 + 249.415i 0.819734 + 0.473274i
$$528$$ 0 0
$$529$$ 119.500 + 206.980i 0.225898 + 0.391267i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 22.0000 0.0413534
$$533$$ 42.0000 24.2487i 0.0787992 0.0454948i
$$534$$ 0 0
$$535$$ 243.000 420.888i 0.454206 0.786707i
$$536$$ 232.500 + 134.234i 0.433769 + 0.250436i
$$537$$ 0 0
$$538$$ 162.000 + 280.592i 0.301115 + 0.521547i
$$539$$ 77.9423i 0.144605i
$$540$$ 0 0
$$541$$ 650.000 1.20148 0.600739 0.799445i $$-0.294873\pi$$
0.600739 + 0.799445i $$0.294873\pi$$
$$542$$ −402.000 + 232.095i −0.741697 + 0.428219i
$$543$$ 0 0
$$544$$ −121.500 + 210.444i −0.223346 + 0.386846i
$$545$$ 156.000 + 90.0666i 0.286239 + 0.165260i
$$546$$ 0 0
$$547$$ −311.500 539.534i −0.569470 0.986351i −0.996618 0.0821692i $$-0.973815\pi$$
0.427149 0.904181i $$-0.359518\pi$$
$$548$$ 188.794i 0.344514i
$$549$$ 0 0
$$550$$ −39.0000 −0.0709091
$$551$$ −429.000 + 247.683i −0.778584 + 0.449516i
$$552$$ 0 0
$$553$$ −38.0000 + 65.8179i −0.0687161 + 0.119020i
$$554$$ −84.0000 48.4974i −0.151625 0.0875405i
$$555$$ 0 0
$$556$$ −2.50000 4.33013i −0.00449640 0.00778800i
$$557$$ 530.008i 0.951540i −0.879570 0.475770i $$-0.842170\pi$$
0.879570 0.475770i $$-0.157830\pi$$
$$558$$ 0 0
$$559$$ 244.000 0.436494
$$560$$ −66.0000 + 38.1051i −0.117857 + 0.0680449i
$$561$$ 0 0
$$562$$ 42.0000 72.7461i 0.0747331 0.129442i
$$563$$ −97.5000 56.2917i −0.173179 0.0999852i 0.410905 0.911678i $$-0.365213\pi$$
−0.584084 + 0.811693i $$0.698546\pi$$
$$564$$ 0 0
$$565$$ −156.000 270.200i −0.276106 0.478230i
$$566$$ 647.787i 1.14450i
$$567$$ 0 0
$$568$$ −270.000 −0.475352
$$569$$ −565.500 + 326.492i −0.993849 + 0.573799i −0.906423 0.422372i $$-0.861198\pi$$
−0.0874263 + 0.996171i $$0.527864\pi$$
$$570$$ 0 0
$$571$$ −272.500 + 471.984i −0.477233 + 0.826592i −0.999660 0.0260926i $$-0.991694\pi$$
0.522427 + 0.852684i $$0.325027\pi$$
$$572$$ 6.00000 + 3.46410i 0.0104895 + 0.00605612i
$$573$$ 0 0
$$574$$ −21.0000 36.3731i −0.0365854 0.0633677i
$$575$$ 360.267i 0.626551i
$$576$$ 0 0
$$577$$ −871.000 −1.50953 −0.754766 0.655994i $$-0.772250\pi$$
−0.754766 + 0.655994i $$0.772250\pi$$
$$578$$ 69.0000 39.8372i 0.119377 0.0689224i
$$579$$ 0 0
$$580$$ −78.0000 + 135.100i −0.134483 + 0.232931i
$$581$$ −84.0000 48.4974i −0.144578 0.0834723i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 562.917i 0.963898i
$$585$$ 0 0
$$586$$ −438.000 −0.747440
$$587$$ 1.50000 0.866025i 0.00255537 0.00147534i −0.498722 0.866762i $$-0.666197\pi$$
0.501277 + 0.865287i $$0.332864\pi$$
$$588$$ 0 0
$$589$$ −176.000 + 304.841i −0.298812 + 0.517557i
$$590$$ 261.000 + 150.688i 0.442373 + 0.255404i
$$591$$ 0 0
$$592$$ −187.000 323.894i −0.315878 0.547117i
$$593$$ 187.061i 0.315449i −0.987483 0.157725i $$-0.949584\pi$$
0.987483 0.157725i $$-0.0504159\pi$$
$$594$$ 0 0
$$595$$ 108.000 0.181513
$$596$$ −132.000 + 76.2102i −0.221477 + 0.127870i
$$597$$ 0 0
$$598$$ 96.0000 166.277i 0.160535 0.278055i
$$599$$ −489.000 282.324i −0.816361 0.471326i 0.0327992 0.999462i $$-0.489558\pi$$
−0.849160 + 0.528136i $$0.822891\pi$$
$$600$$ 0 0
$$601$$ −230.500 399.238i −0.383527 0.664289i 0.608036 0.793909i $$-0.291958\pi$$
−0.991564 + 0.129620i $$0.958624\pi$$
$$602$$ 211.310i 0.351014i
$$603$$ 0 0
$$604$$ 20.0000 0.0331126
$$605$$ 354.000 204.382i 0.585124 0.337821i
$$606$$ 0 0
$$607$$ 56.0000 96.9948i 0.0922570 0.159794i −0.816204 0.577765i $$-0.803925\pi$$
0.908461 + 0.417971i $$0.137259\pi$$
$$608$$ −148.500 85.7365i −0.244243 0.141014i
$$609$$ 0 0
$$610$$ 168.000 + 290.985i 0.275410 + 0.477024i
$$611$$ 193.990i 0.317495i
$$612$$ 0 0
$$613$$ 902.000 1.47145 0.735726 0.677279i $$-0.236841\pi$$
0.735726 + 0.677279i $$0.236841\pi$$
$$614$$ 799.500 461.592i 1.30212 0.751778i
$$615$$ 0 0
$$616$$ 15.0000 25.9808i 0.0243506 0.0421766i
$$617$$ 307.500 + 177.535i 0.498379 + 0.287739i 0.728044 0.685530i $$-0.240430\pi$$
−0.229665 + 0.973270i $$0.573763\pi$$
$$618$$ 0 0
$$619$$ 399.500 + 691.954i 0.645396 + 1.11786i 0.984210 + 0.177005i $$0.0566409\pi$$
−0.338814 + 0.940853i $$0.610026\pi$$
$$620$$ 110.851i 0.178792i
$$621$$ 0 0
$$622$$ 426.000 0.684887
$$623$$ −216.000 + 124.708i −0.346709 + 0.200173i
$$624$$ 0 0
$$625$$ 65.5000 113.449i 0.104800 0.181519i
$$626$$ −232.500 134.234i −0.371406 0.214431i
$$627$$ 0 0
$$628$$ 20.0000 + 34.6410i 0.0318471 + 0.0551609i
$$629$$ 530.008i 0.842619i
$$630$$ 0 0
$$631$$ 830.000 1.31537 0.657686 0.753292i $$-0.271535\pi$$
0.657686 + 0.753292i $$0.271535\pi$$
$$632$$ 285.000 164.545i 0.450949 0.260356i
$$633$$ 0 0
$$634$$ 42.0000 72.7461i 0.0662461 0.114742i
$$635$$ 48.0000 + 27.7128i 0.0755906 + 0.0436422i
$$636$$ 0 0
$$637$$ −90.0000 155.885i −0.141287 0.244717i
$$638$$ 135.100i 0.211755i
$$639$$ 0 0
$$640$$ 210.000 0.328125
$$641$$ 325.500 187.928i 0.507800 0.293179i −0.224129 0.974560i $$-0.571954\pi$$
0.731929 + 0.681381i $$0.238620\pi$$
$$642$$ 0 0
$$643$$ 6.50000 11.2583i 0.0101089 0.0175091i −0.860927 0.508729i $$-0.830116\pi$$
0.871036 + 0.491220i $$0.163449\pi$$
$$644$$ 48.0000 + 27.7128i 0.0745342 + 0.0430323i
$$645$$ 0 0
$$646$$ −148.500 257.210i −0.229876 0.398157i
$$647$$ 467.654i 0.722803i −0.932410 0.361402i $$-0.882298\pi$$
0.932410 0.361402i $$-0.117702\pi$$
$$648$$ 0 0
$$649$$ −87.0000 −0.134052
$$650$$ −78.0000 + 45.0333i −0.120000 + 0.0692820i
$$651$$ 0 0
$$652$$ 53.0000 91.7987i 0.0812883 0.140796i
$$653$$ −327.000 188.794i −0.500766 0.289117i 0.228264 0.973599i $$-0.426695\pi$$
−0.729030 + 0.684482i $$0.760028\pi$$
$$654$$ 0 0
$$655$$ 276.000 + 478.046i 0.421374 + 0.729841i
$$656$$ 133.368i 0.203305i
$$657$$ 0 0
$$658$$ −168.000 −0.255319
$$659$$ 852.000 491.902i 1.29287 0.746438i 0.313706 0.949520i $$-0.398429\pi$$
0.979162 + 0.203082i $$0.0650959\pi$$
$$660$$ 0 0
$$661$$ 191.000 330.822i 0.288956 0.500487i −0.684605 0.728915i $$-0.740025\pi$$
0.973561 + 0.228428i $$0.0733585\pi$$
$$662$$ −3.00000 1.73205i −0.00453172 0.00261639i
$$663$$ 0 0
$$664$$ 210.000 + 363.731i 0.316265 + 0.547787i
$$665$$ 76.2102i 0.114602i
$$666$$ 0 0
$$667$$ −1248.00 −1.87106
$$668$$ 165.000 95.2628i 0.247006 0.142609i
$$669$$ 0 0
$$670$$ −93.0000 + 161.081i −0.138806 + 0.240419i
$$671$$ −84.0000 48.4974i −0.125186 0.0722763i
$$672$$ 0 0
$$673$$ −289.000 500.563i −0.429421 0.743778i 0.567401 0.823441i $$-0.307949\pi$$
−0.996822 + 0.0796633i $$0.974615\pi$$
$$674$$ 133.368i 0.197875i
$$675$$ 0 0
$$676$$ −153.000 −0.226331
$$677$$ −606.000 + 349.874i −0.895126 + 0.516801i −0.875616 0.483009i $$-0.839544\pi$$
−0.0195100 + 0.999810i $$0.506211\pi$$
$$678$$ 0 0
$$679$$ 115.000 199.186i 0.169367 0.293352i
$$680$$ −405.000 233.827i −0.595588 0.343863i
$$681$$ 0 0
$$682$$ 48.0000 + 83.1384i 0.0703812 + 0.121904i
$$683$$ 1044.43i 1.52918i 0.644520 + 0.764588i $$0.277057\pi$$
−0.644520 + 0.764588i $$0.722943\pi$$
$$684$$ 0 0
$$685$$ −654.000 −0.954745
$$686$$ −282.000 + 162.813i −0.411079 + 0.237336i
$$687$$ 0 0
$$688$$ −335.500 + 581.103i −0.487645 + 0.844627i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −91.0000 157.617i −0.131693 0.228099i 0.792636 0.609695i $$-0.208708\pi$$
−0.924329 + 0.381596i $$0.875375\pi$$
$$692$$ 232.095i 0.335397i
$$693$$ 0 0
$$694$$ −195.000 −0.280980
$$695$$ 15.0000 8.66025i 0.0215827 0.0124608i
$$696$$ 0 0
$$697$$ 94.5000 163.679i 0.135581 0.234833i
$$698$$ −624.000 360.267i −0.893983 0.516141i
$$699$$ 0 0
$$700$$ −13.0000 22.5167i −0.0185714 0.0321667i
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ −374.000 −0.532006
$$704$$ −106.500 + 61.4878i −0.151278 + 0.0873406i
$$705$$ 0 0
$$706$$ 1.50000 2.59808i 0.00212465 0.00367999i
$$707$$ 78.0000 + 45.0333i 0.110325 + 0.0636964i
$$708$$ 0 0
$$709$$ 350.000 + 606.218i 0.493653 + 0.855032i 0.999973 0.00731341i $$-0.00232795\pi$$
−0.506320 + 0.862346i $$0.668995\pi$$
$$710$$ 187.061i 0.263467i
$$711$$ 0 0
$$712$$ 1080.00 1.51685
$$713$$ −768.000 + 443.405i −1.07714 + 0.621886i
$$714$$ 0 0
$$715$$ −12.0000 + 20.7846i −0.0167832 + 0.0290694i
$$716$$ 54.0000 + 31.1769i 0.0754190 + 0.0435432i
$$717$$ 0 0
$$718$$ −513.000 888.542i −0.714485 1.23752i
$$719$$ 592.361i 0.823868i 0.911214 + 0.411934i $$0.135147\pi$$
−0.911214 + 0.411934i $$0.864853\pi$$
$$720$$ 0 0
$$721$$ −80.0000 −0.110957
$$722$$ −360.000 + 207.846i −0.498615 + 0.287875i
$$723$$ 0 0
$$724$$ 116.000 200.918i 0.160221 0.277511i
$$725$$ 507.000 + 292.717i 0.699310 + 0.403747i
$$726$$ 0 0
$$727$$ 332.000 + 575.041i 0.456671 + 0.790978i 0.998783 0.0493289i $$-0.0157082\pi$$
−0.542111 + 0.840307i $$0.682375\pi$$
$$728$$ 69.2820i 0.0951676i
$$729$$ 0 0
$$730$$ −390.000 −0.534247
$$731$$ 823.500 475.448i 1.12654 0.650408i
$$732$$ 0 0
$$733$$ 335.000 580.237i 0.457026 0.791592i −0.541776 0.840523i $$-0.682248\pi$$
0.998802 + 0.0489306i $$0.0155813\pi$$
$$734$$ 537.000 + 310.037i 0.731608 + 0.422394i
$$735$$ 0 0
$$736$$ −216.000 374.123i −0.293478 0.508319i
$$737$$ 53.6936i 0.0728542i
$$738$$ 0 0
$$739$$ 317.000 0.428958 0.214479 0.976729i $$-0.431195\pi$$
0.214479 + 0.976729i $$0.431195\pi$$
$$740$$ −102.000 + 58.8897i −0.137838 + 0.0795807i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 537.000 + 310.037i 0.722746 + 0.417277i 0.815762 0.578387i $$-0.196318\pi$$
−0.0930168 + 0.995665i $$0.529651\pi$$
$$744$$ 0 0
$$745$$ −264.000 457.261i −0.354362 0.613774i
$$746$$ 1004.59i 1.34663i
$$747$$ 0 0
$$748$$ 27.0000 0.0360963
$$749$$ 243.000 140.296i 0.324433 0.187311i
$$750$$ 0 0
$$751$$ −655.000 + 1134.49i −0.872170 + 1.51064i −0.0124237 + 0.999923i $$0.503955\pi$$
−0.859747 + 0.510721i $$0.829379\pi$$
$$752$$ 462.000 + 266.736i 0.614362 + 0.354702i
$$753$$ 0 0
$$754$$ 156.000 + 270.200i 0.206897 + 0.358355i
$$755$$ 69.2820i 0.0917643i
$$756$$ 0 0
$$757$$ 218.000 0.287979 0.143989 0.989579i $$-0.454007\pi$$
0.143989 + 0.989579i $$0.454007\pi$$
$$758$$ 124.500 71.8801i 0.164248 0.0948286i
$$759$$ 0 0
$$760$$ 165.000 285.788i 0.217105 0.376037i
$$761$$ −570.000 329.090i −0.749014 0.432444i 0.0763232 0.997083i $$-0.475682\pi$$
−0.825338 + 0.564639i $$0.809015\pi$$
$$762$$ 0 0
$$763$$ 52.0000 + 90.0666i 0.0681520 + 0.118043i
$$764$$ 232.095i 0.303789i
$$765$$ 0 0
$$766$$ 966.000 1.26110
$$767$$ −174.000 + 100.459i −0.226858 + 0.130976i
$$768$$ 0 0
$$769$$ −511.000 + 885.078i −0.664499 + 1.15095i 0.314921 + 0.949118i $$0.398022\pi$$
−0.979421 + 0.201829i $$0.935312\pi$$
$$770$$ 18.0000 + 10.3923i 0.0233766 + 0.0134965i
$$771$$ 0 0
$$772$$ 132.500 + 229.497i 0.171632 + 0.297276i
$$773$$ 1184.72i 1.53263i −0.642465 0.766315i $$-0.722088\pi$$
0.642465 0.766315i $$-0.277912\pi$$
$$774$$ 0 0
$$775$$ 416.000 0.536774
$$776$$ −862.500 + 497.965i −1.11147 + 0.641707i
$$777$$ 0 0
$$778$$ 447.000 774.227i 0.574550 0.995150i
$$779$$ 115.500 + 66.6840i 0.148267 + 0.0856020i
$$780$$ 0 0
$$781$$ 27.0000 + 46.7654i 0.0345711 + 0.0598788i
$$782$$ 748.246i 0.956836i
$$783$$ 0 0
$$784$$ 495.000 0.631378
$$785$$ −120.000 + 69.2820i −0.152866 + 0.0882574i
$$786$$ 0 0
$$787$$ 65.0000 112.583i 0.0825921 0.143054i −0.821771 0.569819i $$-0.807013\pi$$