# Properties

 Label 1386.2.k.n.793.1 Level $1386$ Weight $2$ Character 1386.793 Analytic conductor $11.067$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.0672657201$$ 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 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 793.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1386.793 Dual form 1386.2.k.n.991.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{11} +5.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} -1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} -3.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(3.00000 - 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +5.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(-6.00000 - 10.3923i) q^{53} +(-2.50000 + 0.866025i) q^{56} +(-1.50000 + 2.59808i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(3.50000 - 6.06218i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} +12.0000 q^{71} +(5.00000 + 8.66025i) q^{73} +(1.00000 + 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 - 1.73205i) q^{77} +(0.500000 - 0.866025i) q^{79} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(12.5000 - 4.33013i) q^{91} -6.00000 q^{92} +(-3.00000 - 5.19615i) q^{94} -13.0000 q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} + 5q^{7} - 2q^{8} + O(q^{10})$$ $$2q + q^{2} - q^{4} + 5q^{7} - 2q^{8} - q^{11} + 10q^{13} + q^{14} - q^{16} + 6q^{17} - 2q^{19} - 2q^{22} + 6q^{23} + 5q^{25} + 5q^{26} - 4q^{28} - 6q^{29} - 8q^{31} + q^{32} + 12q^{34} - 2q^{37} + 2q^{38} + 12q^{41} - 8q^{43} - q^{44} - 6q^{46} + 6q^{47} + 11q^{49} + 10q^{50} - 5q^{52} - 12q^{53} - 5q^{56} - 3q^{58} - 3q^{59} + 7q^{61} - 16q^{62} + 2q^{64} + 13q^{67} + 6q^{68} + 24q^{71} + 10q^{73} + 2q^{74} + 4q^{76} - 4q^{77} + q^{79} + 6q^{82} - 12q^{83} - 4q^{86} + q^{88} + 6q^{89} + 25q^{91} - 12q^{92} - 6q^{94} - 26q^{97} - 2q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$$.

 $$n$$ $$155$$ $$199$$ $$1135$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ 0 0
$$7$$ 2.50000 0.866025i 0.944911 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ 0 0
$$13$$ 5.00000 1.38675 0.693375 0.720577i $$-0.256123\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ 0.500000 2.59808i 0.133631 0.694365i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i $$0.0927008\pi$$
−0.230285 + 0.973123i $$0.573966\pi$$
$$18$$ 0 0
$$19$$ −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i $$-0.907015\pi$$
0.728219 + 0.685344i $$0.240348\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i $$-0.618211\pi$$
0.988436 0.151642i $$-0.0484560\pi$$
$$24$$ 0 0
$$25$$ 2.50000 + 4.33013i 0.500000 + 0.866025i
$$26$$ 2.50000 4.33013i 0.490290 0.849208i
$$27$$ 0 0
$$28$$ −2.00000 1.73205i −0.377964 0.327327i
$$29$$ −3.00000 −0.557086 −0.278543 0.960424i $$-0.589851\pi$$
−0.278543 + 0.960424i $$0.589851\pi$$
$$30$$ 0 0
$$31$$ −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i $$-0.911532\pi$$
0.243204 0.969975i $$-0.421802\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i $$-0.885902\pi$$
0.772043 + 0.635571i $$0.219235\pi$$
$$38$$ 1.00000 + 1.73205i 0.162221 + 0.280976i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ 0 0
$$46$$ −3.00000 5.19615i −0.442326 0.766131i
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 0 0
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 5.00000 0.707107
$$51$$ 0 0
$$52$$ −2.50000 4.33013i −0.346688 0.600481i
$$53$$ −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i $$-0.858312\pi$$
0.0783936 0.996922i $$-0.475021\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −2.50000 + 0.866025i −0.334077 + 0.115728i
$$57$$ 0 0
$$58$$ −1.50000 + 2.59808i −0.196960 + 0.341144i
$$59$$ −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i $$-0.229229\pi$$
−0.946993 + 0.321253i $$0.895896\pi$$
$$60$$ 0 0
$$61$$ 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i $$-0.685424\pi$$
0.998264 + 0.0588933i $$0.0187572\pi$$
$$62$$ −8.00000 −1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i $$0.125391\pi$$
−0.129307 + 0.991605i $$0.541275\pi$$
$$68$$ 3.00000 5.19615i 0.363803 0.630126i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i $$0.0323196\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ 1.00000 + 1.73205i 0.116248 + 0.201347i
$$75$$ 0 0
$$76$$ 2.00000 0.229416
$$77$$ −2.00000 1.73205i −0.227921 0.197386i
$$78$$ 0 0
$$79$$ 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i $$-0.815418\pi$$
0.892781 + 0.450490i $$0.148751\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 3.00000 5.19615i 0.331295 0.573819i
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 + 3.46410i −0.215666 + 0.373544i
$$87$$ 0 0
$$88$$ 0.500000 + 0.866025i 0.0533002 + 0.0923186i
$$89$$ 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i $$-0.730322\pi$$
0.980071 + 0.198650i $$0.0636557\pi$$
$$90$$ 0 0
$$91$$ 12.5000 4.33013i 1.31036 0.453921i
$$92$$ −6.00000 −0.625543
$$93$$ 0 0
$$94$$ −3.00000 5.19615i −0.309426 0.535942i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −13.0000 −1.31995 −0.659975 0.751288i $$-0.729433\pi$$
−0.659975 + 0.751288i $$0.729433\pi$$
$$98$$ −1.00000 6.92820i −0.101015 0.699854i
$$99$$ 0 0
$$100$$ 2.50000 4.33013i 0.250000 0.433013i
$$101$$ 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i $$-0.118979\pi$$
−0.781697 + 0.623658i $$0.785646\pi$$
$$102$$ 0 0
$$103$$ 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i $$-0.770192\pi$$
0.947576 + 0.319531i $$0.103525\pi$$
$$104$$ −5.00000 −0.490290
$$105$$ 0 0
$$106$$ −12.0000 −1.16554
$$107$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$108$$ 0 0
$$109$$ −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i $$-0.932756\pi$$
0.307290 0.951616i $$-0.400578\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −0.500000 + 2.59808i −0.0472456 + 0.245495i
$$113$$ −9.00000 −0.846649 −0.423324 0.905978i $$-0.639137\pi$$
−0.423324 + 0.905978i $$0.639137\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 1.50000 + 2.59808i 0.139272 + 0.241225i
$$117$$ 0 0
$$118$$ −3.00000 −0.276172
$$119$$ 12.0000 + 10.3923i 1.10004 + 0.952661i
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ −3.50000 6.06218i −0.316875 0.548844i
$$123$$ 0 0
$$124$$ −4.00000 + 6.92820i −0.359211 + 0.622171i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −13.0000 −1.15356 −0.576782 0.816898i $$-0.695692\pi$$
−0.576782 + 0.816898i $$0.695692\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i $$-0.748915\pi$$
0.966803 + 0.255524i $$0.0822479\pi$$
$$132$$ 0 0
$$133$$ −1.00000 + 5.19615i −0.0867110 + 0.450564i
$$134$$ 13.0000 1.12303
$$135$$ 0 0
$$136$$ −3.00000 5.19615i −0.257248 0.445566i
$$137$$ 7.50000 + 12.9904i 0.640768 + 1.10984i 0.985262 + 0.171054i $$0.0547174\pi$$
−0.344493 + 0.938789i $$0.611949\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 6.00000 10.3923i 0.503509 0.872103i
$$143$$ −2.50000 4.33013i −0.209061 0.362103i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ 2.00000 0.164399
$$149$$ −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i $$-0.912374\pi$$
0.716578 + 0.697507i $$0.245707\pi$$
$$150$$ 0 0
$$151$$ 0.500000 + 0.866025i 0.0406894 + 0.0704761i 0.885653 0.464348i $$-0.153711\pi$$
−0.844963 + 0.534824i $$0.820378\pi$$
$$152$$ 1.00000 1.73205i 0.0811107 0.140488i
$$153$$ 0 0
$$154$$ −2.50000 + 0.866025i −0.201456 + 0.0697863i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i $$-0.115641\pi$$
−0.775113 + 0.631822i $$0.782307\pi$$
$$158$$ −0.500000 0.866025i −0.0397779 0.0688973i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 3.00000 15.5885i 0.236433 1.22854i
$$162$$ 0 0
$$163$$ −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i $$0.398564\pi$$
−0.979076 + 0.203497i $$0.934769\pi$$
$$164$$ −3.00000 5.19615i −0.234261 0.405751i
$$165$$ 0 0
$$166$$ −3.00000 + 5.19615i −0.232845 + 0.403300i
$$167$$ −9.00000 −0.696441 −0.348220 0.937413i $$-0.613214\pi$$
−0.348220 + 0.937413i $$0.613214\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i $$0.359807\pi$$
−0.996544 + 0.0830722i $$0.973527\pi$$
$$174$$ 0 0
$$175$$ 10.0000 + 8.66025i 0.755929 + 0.654654i
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ −3.00000 5.19615i −0.224860 0.389468i
$$179$$ 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i $$-0.0574756\pi$$
−0.647397 + 0.762153i $$0.724142\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 2.50000 12.9904i 0.185312 0.962911i
$$183$$ 0 0
$$184$$ −3.00000 + 5.19615i −0.221163 + 0.383065i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 3.00000 5.19615i 0.219382 0.379980i
$$188$$ −6.00000 −0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i $$0.392408\pi$$
−0.982828 + 0.184525i $$0.940925\pi$$
$$192$$ 0 0
$$193$$ 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i $$0.124188\pi$$
−0.133056 + 0.991109i $$0.542479\pi$$
$$194$$ −6.50000 + 11.2583i −0.466673 + 0.808301i
$$195$$ 0 0
$$196$$ −6.50000 2.59808i −0.464286 0.185577i
$$197$$ 9.00000 0.641223 0.320612 0.947211i $$-0.396112\pi$$
0.320612 + 0.947211i $$0.396112\pi$$
$$198$$ 0 0
$$199$$ −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i $$-0.331945\pi$$
−0.999990 + 0.00436292i $$0.998611\pi$$
$$200$$ −2.50000 4.33013i −0.176777 0.306186i
$$201$$ 0 0
$$202$$ 3.00000 0.211079
$$203$$ −7.50000 + 2.59808i −0.526397 + 0.182349i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −2.00000 3.46410i −0.139347 0.241355i
$$207$$ 0 0
$$208$$ −2.50000 + 4.33013i −0.173344 + 0.300240i
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ 26.0000 1.78991 0.894957 0.446153i $$-0.147206\pi$$
0.894957 + 0.446153i $$0.147206\pi$$
$$212$$ −6.00000 + 10.3923i −0.412082 + 0.713746i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −16.0000 13.8564i −1.08615 0.940634i
$$218$$ −14.0000 −0.948200
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 15.0000 + 25.9808i 1.00901 + 1.74766i
$$222$$ 0 0
$$223$$ −10.0000 −0.669650 −0.334825 0.942280i $$-0.608677\pi$$
−0.334825 + 0.942280i $$0.608677\pi$$
$$224$$ 2.00000 + 1.73205i 0.133631 + 0.115728i
$$225$$ 0 0
$$226$$ −4.50000 + 7.79423i −0.299336 + 0.518464i
$$227$$ −3.00000 5.19615i −0.199117 0.344881i 0.749125 0.662428i $$-0.230474\pi$$
−0.948242 + 0.317547i $$0.897141\pi$$
$$228$$ 0 0
$$229$$ −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i $$0.396457\pi$$
−0.980401 + 0.197013i $$0.936876\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 3.00000 0.196960
$$233$$ −15.0000 + 25.9808i −0.982683 + 1.70206i −0.330870 + 0.943676i $$0.607342\pi$$
−0.651813 + 0.758380i $$0.725991\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −1.50000 + 2.59808i −0.0976417 + 0.169120i
$$237$$ 0 0
$$238$$ 15.0000 5.19615i 0.972306 0.336817i
$$239$$ −21.0000 −1.35838 −0.679189 0.733964i $$-0.737668\pi$$
−0.679189 + 0.733964i $$0.737668\pi$$
$$240$$ 0 0
$$241$$ 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i $$-0.0622852\pi$$
−0.658838 + 0.752285i $$0.728952\pi$$
$$242$$ 0.500000 + 0.866025i 0.0321412 + 0.0556702i
$$243$$ 0 0
$$244$$ −7.00000 −0.448129
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −5.00000 + 8.66025i −0.318142 + 0.551039i
$$248$$ 4.00000 + 6.92820i 0.254000 + 0.439941i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ −6.00000 −0.377217
$$254$$ −6.50000 + 11.2583i −0.407846 + 0.706410i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 13.5000 23.3827i 0.842107 1.45857i −0.0460033 0.998941i $$-0.514648\pi$$
0.888110 0.459631i $$-0.152018\pi$$
$$258$$ 0 0
$$259$$ −1.00000 + 5.19615i −0.0621370 + 0.322873i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.00000 5.19615i −0.185341 0.321019i
$$263$$ −1.50000 2.59808i −0.0924940 0.160204i 0.816066 0.577959i $$-0.196151\pi$$
−0.908560 + 0.417755i $$0.862817\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 4.00000 + 3.46410i 0.245256 + 0.212398i
$$267$$ 0 0
$$268$$ 6.50000 11.2583i 0.397051 0.687712i
$$269$$ −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i $$-0.905416\pi$$
0.224523 0.974469i $$-0.427917\pi$$
$$270$$ 0 0
$$271$$ 12.5000 21.6506i 0.759321 1.31518i −0.183876 0.982949i $$-0.558865\pi$$
0.943197 0.332233i $$-0.107802\pi$$
$$272$$ −6.00000 −0.363803
$$273$$ 0 0
$$274$$ 15.0000 0.906183
$$275$$ 2.50000 4.33013i 0.150756 0.261116i
$$276$$ 0 0
$$277$$ 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i $$-0.157103\pi$$
−0.850613 + 0.525792i $$0.823769\pi$$
$$278$$ −2.00000 + 3.46410i −0.119952 + 0.207763i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i $$0.0601941\pi$$
−0.328291 + 0.944577i $$0.606473\pi$$
$$284$$ −6.00000 10.3923i −0.356034 0.616670i
$$285$$ 0 0
$$286$$ −5.00000 −0.295656
$$287$$ 15.0000 5.19615i 0.885422 0.306719i
$$288$$ 0 0
$$289$$ −9.50000 + 16.4545i −0.558824 + 0.967911i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 5.00000 8.66025i 0.292603 0.506803i
$$293$$ 18.0000 1.05157 0.525786 0.850617i $$-0.323771\pi$$
0.525786 + 0.850617i $$0.323771\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 1.00000 1.73205i 0.0581238 0.100673i
$$297$$ 0 0
$$298$$ 3.00000 + 5.19615i 0.173785 + 0.301005i
$$299$$ 15.0000 25.9808i 0.867472 1.50251i
$$300$$ 0 0
$$301$$ −10.0000 + 3.46410i −0.576390 + 0.199667i
$$302$$ 1.00000 0.0575435
$$303$$ 0 0
$$304$$ −1.00000 1.73205i −0.0573539 0.0993399i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 32.0000 1.82634 0.913168 0.407583i $$-0.133628\pi$$
0.913168 + 0.407583i $$0.133628\pi$$
$$308$$ −0.500000 + 2.59808i −0.0284901 + 0.148039i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i $$0.0715523\pi$$
−0.294384 + 0.955687i $$0.595114\pi$$
$$312$$ 0 0
$$313$$ 3.50000 6.06218i 0.197832 0.342655i −0.749993 0.661445i $$-0.769943\pi$$
0.947825 + 0.318791i $$0.103277\pi$$
$$314$$ 4.00000 0.225733
$$315$$ 0 0
$$316$$ −1.00000 −0.0562544
$$317$$ −12.0000 + 20.7846i −0.673987 + 1.16738i 0.302777 + 0.953062i $$0.402086\pi$$
−0.976764 + 0.214318i $$0.931247\pi$$
$$318$$ 0 0
$$319$$ 1.50000 + 2.59808i 0.0839839 + 0.145464i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −12.0000 10.3923i −0.668734 0.579141i
$$323$$ −12.0000 −0.667698
$$324$$ 0 0
$$325$$ 12.5000 + 21.6506i 0.693375 + 1.20096i
$$326$$ 8.50000 + 14.7224i 0.470771 + 0.815400i
$$327$$ 0 0
$$328$$ −6.00000 −0.331295
$$329$$ 3.00000 15.5885i 0.165395 0.859419i
$$330$$ 0 0
$$331$$ 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i $$-0.717040\pi$$
0.987504 + 0.157593i $$0.0503735\pi$$
$$332$$ 3.00000 + 5.19615i 0.164646 + 0.285176i
$$333$$ 0 0
$$334$$ −4.50000 + 7.79423i −0.246229 + 0.426481i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −22.0000 −1.19842 −0.599208 0.800593i $$-0.704518\pi$$
−0.599208 + 0.800593i $$0.704518\pi$$
$$338$$ 6.00000 10.3923i 0.326357 0.565267i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −4.00000 + 6.92820i −0.216612 + 0.375183i
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ 7.50000 + 12.9904i 0.403202 + 0.698367i
$$347$$ 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i $$-0.0622790\pi$$
−0.658824 + 0.752297i $$0.728946\pi$$
$$348$$ 0 0
$$349$$ −34.0000 −1.81998 −0.909989 0.414632i $$-0.863910\pi$$
−0.909989 + 0.414632i $$0.863910\pi$$
$$350$$ 12.5000 4.33013i 0.668153 0.231455i
$$351$$ 0 0
$$352$$ 0.500000 0.866025i 0.0266501 0.0461593i
$$353$$ 15.0000 + 25.9808i 0.798369 + 1.38282i 0.920677 + 0.390324i $$0.127637\pi$$
−0.122308 + 0.992492i $$0.539030\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 9.00000 0.475665
$$359$$ −4.50000 + 7.79423i −0.237501 + 0.411364i −0.959997 0.280012i $$-0.909662\pi$$
0.722496 + 0.691375i $$0.242995\pi$$
$$360$$ 0 0
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ −5.00000 + 8.66025i −0.262794 + 0.455173i
$$363$$ 0 0
$$364$$ −10.0000 8.66025i −0.524142 0.453921i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −19.0000 32.9090i −0.991792 1.71783i −0.606628 0.794986i $$-0.707478\pi$$
−0.385164 0.922848i $$-0.625855\pi$$
$$368$$ 3.00000 + 5.19615i 0.156386 + 0.270868i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −24.0000 20.7846i −1.24602 1.07908i
$$372$$ 0 0
$$373$$ −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i $$-0.925254\pi$$
0.687776 + 0.725923i $$0.258587\pi$$
$$374$$ −3.00000 5.19615i −0.155126 0.268687i
$$375$$ 0 0
$$376$$ −3.00000 + 5.19615i −0.154713 + 0.267971i
$$377$$ −15.0000 −0.772539
$$378$$ 0 0
$$379$$ −25.0000 −1.28416 −0.642082 0.766636i $$-0.721929\pi$$
−0.642082 + 0.766636i $$0.721929\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 9.00000 + 15.5885i 0.460480 + 0.797575i
$$383$$ 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i $$-0.734147\pi$$
0.977613 + 0.210411i $$0.0674801\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 22.0000 1.11977
$$387$$ 0 0
$$388$$ 6.50000 + 11.2583i 0.329988 + 0.571555i
$$389$$ 6.00000 + 10.3923i 0.304212 + 0.526911i 0.977086 0.212847i $$-0.0682735\pi$$
−0.672874 + 0.739758i $$0.734940\pi$$
$$390$$ 0 0
$$391$$ 36.0000 1.82060
$$392$$ −5.50000 + 4.33013i −0.277792 + 0.218704i
$$393$$ 0 0
$$394$$ 4.50000 7.79423i 0.226707 0.392668i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i $$-0.849316\pi$$
0.839840 + 0.542834i $$0.182649\pi$$
$$398$$ −14.0000 −0.701757
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ −4.50000 + 7.79423i −0.224719 + 0.389225i −0.956235 0.292599i $$-0.905480\pi$$
0.731516 + 0.681824i $$0.238813\pi$$
$$402$$ 0 0
$$403$$ −20.0000 34.6410i −0.996271 1.72559i
$$404$$ 1.50000 2.59808i 0.0746278 0.129259i
$$405$$ 0 0
$$406$$ −1.50000 + 7.79423i −0.0744438 + 0.386821i
$$407$$ 2.00000 0.0991363
$$408$$ 0 0
$$409$$ 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i $$-0.135136\pi$$
−0.812333 + 0.583193i $$0.801803\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −4.00000 −0.197066
$$413$$ −6.00000 5.19615i −0.295241 0.255686i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 2.50000 + 4.33013i 0.122573 + 0.212302i
$$417$$ 0 0
$$418$$ 1.00000 1.73205i 0.0489116 0.0847174i
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ −16.0000 −0.779792 −0.389896 0.920859i $$-0.627489\pi$$
−0.389896 + 0.920859i $$0.627489\pi$$
$$422$$ 13.0000 22.5167i 0.632830 1.09609i
$$423$$ 0 0
$$424$$ 6.00000 + 10.3923i 0.291386 + 0.504695i
$$425$$ −15.0000 + 25.9808i −0.727607 + 1.26025i
$$426$$ 0 0
$$427$$ 3.50000 18.1865i 0.169377 0.880108i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i $$-0.0490126\pi$$
−0.626907 + 0.779094i $$0.715679\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ −20.0000 + 6.92820i −0.960031 + 0.332564i
$$435$$ 0 0
$$436$$ −7.00000 + 12.1244i −0.335239 + 0.580651i
$$437$$ 6.00000 + 10.3923i 0.287019 + 0.497131i
$$438$$ 0 0
$$439$$ 9.50000 16.4545i 0.453410 0.785330i −0.545185 0.838316i $$-0.683541\pi$$
0.998595 + 0.0529862i $$0.0168739\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 30.0000 1.42695
$$443$$ 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i $$-0.741317\pi$$
0.972626 + 0.232377i $$0.0746503\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −5.00000 + 8.66025i −0.236757 + 0.410075i
$$447$$ 0 0
$$448$$ 2.50000 0.866025i 0.118114 0.0409159i
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ −3.00000 5.19615i −0.141264 0.244677i
$$452$$ 4.50000 + 7.79423i 0.211662 + 0.366610i
$$453$$ 0 0
$$454$$ −6.00000 −0.281594
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i $$-0.661289\pi$$
0.999857 0.0168929i $$-0.00537742\pi$$
$$458$$ 10.0000 + 17.3205i 0.467269 + 0.809334i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −39.0000 −1.81641 −0.908206 0.418524i $$-0.862547\pi$$
−0.908206 + 0.418524i $$0.862547\pi$$
$$462$$ 0 0
$$463$$ 26.0000 1.20832 0.604161 0.796862i $$-0.293508\pi$$
0.604161 + 0.796862i $$0.293508\pi$$
$$464$$ 1.50000 2.59808i 0.0696358 0.120613i
$$465$$ 0 0
$$466$$ 15.0000 + 25.9808i 0.694862 + 1.20354i
$$467$$ −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i $$-0.922888\pi$$
0.693153 + 0.720791i $$0.256221\pi$$
$$468$$ 0 0
$$469$$ 26.0000 + 22.5167i 1.20057 + 1.03972i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.50000 + 2.59808i 0.0690431 + 0.119586i
$$473$$ 2.00000 + 3.46410i 0.0919601 + 0.159280i
$$474$$ 0 0
$$475$$ −10.0000 −0.458831
$$476$$ 3.00000 15.5885i 0.137505 0.714496i
$$477$$ 0 0
$$478$$ −10.5000 + 18.1865i −0.480259 + 0.831833i
$$479$$ −1.50000 2.59808i −0.0685367 0.118709i 0.829721 0.558179i $$-0.188500\pi$$
−0.898257 + 0.439470i $$0.855166\pi$$
$$480$$ 0 0
$$481$$ −5.00000 + 8.66025i −0.227980 + 0.394874i
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 2.00000 + 3.46410i 0.0906287 + 0.156973i 0.907776 0.419456i $$-0.137779\pi$$
−0.817147 + 0.576429i $$0.804446\pi$$
$$488$$ −3.50000 + 6.06218i −0.158438 + 0.274422i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 30.0000 1.35388 0.676941 0.736038i $$-0.263305\pi$$
0.676941 + 0.736038i $$0.263305\pi$$
$$492$$ 0 0
$$493$$ −9.00000 15.5885i −0.405340 0.702069i
$$494$$ 5.00000 + 8.66025i 0.224961 + 0.389643i
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 30.0000 10.3923i 1.34568 0.466159i
$$498$$ 0 0
$$499$$ −4.00000 + 6.92820i −0.179065 + 0.310149i −0.941560 0.336844i $$-0.890640\pi$$
0.762496 + 0.646993i $$0.223974\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −6.00000 + 10.3923i −0.267793 + 0.463831i
$$503$$ −21.0000 −0.936344 −0.468172 0.883637i $$-0.655087\pi$$
−0.468172 + 0.883637i $$0.655087\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −3.00000 + 5.19615i −0.133366 + 0.230997i
$$507$$ 0 0
$$508$$ 6.50000 + 11.2583i 0.288391 + 0.499508i
$$509$$ 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i $$-0.790881\pi$$
0.924821 + 0.380402i $$0.124214\pi$$
$$510$$ 0 0
$$511$$ 20.0000 + 17.3205i 0.884748 + 0.766214i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −13.5000 23.3827i −0.595459 1.03137i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −6.00000 −0.263880
$$518$$ 4.00000 + 3.46410i 0.175750 + 0.152204i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i $$-0.295679\pi$$
−0.993011 + 0.118020i $$0.962345\pi$$
$$522$$ 0 0
$$523$$ 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i $$-0.719578\pi$$
0.986216 + 0.165460i $$0.0529109\pi$$
$$524$$ −6.00000 −0.262111
$$525$$ 0 0
$$526$$ −3.00000 −0.130806
$$527$$ 24.0000 41.5692i 1.04546 1.81078i
$$528$$ 0 0
$$529$$ −6.50000 11.2583i −0.282609 0.489493i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 5.00000 1.73205i 0.216777 0.0750939i
$$533$$ 30.0000 1.29944
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −6.50000 11.2583i −0.280757 0.486286i
$$537$$ 0 0
$$538$$ −24.0000 −1.03471
$$539$$ −6.50000 2.59808i −0.279975 0.111907i
$$540$$ 0 0
$$541$$ −2.50000 + 4.33013i −0.107483 + 0.186167i −0.914750 0.404020i $$-0.867613\pi$$
0.807267 + 0.590187i $$0.200946\pi$$
$$542$$ −12.5000 21.6506i −0.536921 0.929974i
$$543$$ 0 0
$$544$$ −3.00000 + 5.19615i −0.128624 + 0.222783i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ 7.50000 12.9904i 0.320384 0.554922i
$$549$$ 0 0
$$550$$ −2.50000 4.33013i −0.106600 0.184637i
$$551$$ 3.00000 5.19615i 0.127804 0.221364i
$$552$$ 0 0
$$553$$ 0.500000 2.59808i 0.0212622 0.110481i
$$554$$ 1.00000 0.0424859
$$555$$ 0 0
$$556$$ 2.00000 + 3.46410i 0.0848189 + 0.146911i
$$557$$ −3.00000 5.19615i −0.127114 0.220168i 0.795443 0.606028i $$-0.207238\pi$$
−0.922557 + 0.385860i $$0.873905\pi$$
$$558$$ 0 0
$$559$$ −20.0000 −0.845910
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 3.00000 5.19615i 0.126547 0.219186i
$$563$$ 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i $$-0.0428299\pi$$
−0.611656 + 0.791123i $$0.709497\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 22.0000 0.924729
$$567$$ 0 0
$$568$$ −12.0000 −0.503509
$$569$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$570$$ 0 0
$$571$$ −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i $$-0.304106\pi$$
−0.995788 + 0.0916910i $$0.970773\pi$$
$$572$$ −2.50000 + 4.33013i −0.104530 + 0.181052i
$$573$$ 0 0
$$574$$ 3.00000 15.5885i 0.125218 0.650650i
$$575$$ 30.0000 1.25109
$$576$$ 0 0
$$577$$ 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i $$-0.120121\pi$$
−0.783930 + 0.620850i $$0.786788\pi$$
$$578$$ 9.50000 + 16.4545i 0.395148 + 0.684416i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −15.0000 + 5.19615i −0.622305 + 0.215573i
$$582$$ 0 0
$$583$$ −6.00000 + 10.3923i −0.248495 + 0.430405i
$$584$$ −5.00000 8.66025i −0.206901 0.358364i
$$585$$ 0 0
$$586$$ 9.00000 15.5885i 0.371787 0.643953i
$$587$$ −9.00000 −0.371470 −0.185735 0.982600i $$-0.559467\pi$$
−0.185735 + 0.982600i $$0.559467\pi$$
$$588$$ 0 0
$$589$$ 16.0000 0.659269
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.00000 1.73205i −0.0410997 0.0711868i
$$593$$ 12.0000 20.7846i 0.492781 0.853522i −0.507184 0.861838i $$-0.669314\pi$$
0.999965 + 0.00831589i $$0.00264706\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ 0 0
$$598$$ −15.0000 25.9808i −0.613396 1.06243i
$$599$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ −2.00000 + 10.3923i −0.0815139 + 0.423559i
$$603$$ 0 0
$$604$$ 0.500000 0.866025i 0.0203447 0.0352381i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i $$-0.885242\pi$$
0.773358 + 0.633970i $$0.218576\pi$$
$$608$$ −2.00000 −0.0811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 15.0000 25.9808i 0.606835 1.05107i
$$612$$ 0 0
$$613$$ −13.0000 22.5167i −0.525065 0.909439i −0.999574 0.0291886i $$-0.990708\pi$$
0.474509 0.880251i $$-0.342626\pi$$
$$614$$ 16.0000 27.7128i 0.645707 1.11840i
$$615$$ 0 0
$$616$$ 2.00000 + 1.73205i 0.0805823 + 0.0697863i
$$617$$ −21.0000 −0.845428 −0.422714 0.906263i $$-0.638923\pi$$
−0.422714 + 0.906263i $$0.638923\pi$$
$$618$$ 0 0
$$619$$ −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i $$-0.821334\pi$$
−0.0376891 0.999290i $$-0.512000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 24.0000 0.962312
$$623$$ 3.00000 15.5885i 0.120192 0.624538i
$$624$$ 0 0
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ −3.50000 6.06218i −0.139888 0.242293i
$$627$$ 0 0
$$628$$ 2.00000 3.46410i 0.0798087 0.138233i
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ −0.500000 + 0.866025i −0.0198889 + 0.0344486i
$$633$$ 0 0
$$634$$ 12.0000 + 20.7846i 0.476581 + 0.825462i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 27.5000 21.6506i 1.08959 0.857829i
$$638$$ 3.00000 0.118771
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i $$-0.109788\pi$$
−0.763367 + 0.645966i $$0.776455\pi$$
$$642$$ 0 0
$$643$$ −19.0000 −0.749287 −0.374643 0.927169i $$-0.622235\pi$$
−0.374643 + 0.927169i $$0.622235\pi$$
$$644$$ −15.0000 + 5.19615i −0.591083 + 0.204757i
$$645$$ 0 0
$$646$$ −6.00000 + 10.3923i −0.236067 + 0.408880i
$$647$$ 18.0000 + 31.1769i 0.707653 + 1.22569i 0.965726 + 0.259565i $$0.0835793\pi$$
−0.258073 + 0.966126i $$0.583087\pi$$
$$648$$ 0 0
$$649$$ −1.50000 + 2.59808i −0.0588802 + 0.101983i
$$650$$ 25.0000 0.980581
$$651$$ 0 0
$$652$$ 17.0000 0.665771
$$653$$ −15.0000 + 25.9808i −0.586995 + 1.01671i 0.407628 + 0.913148i $$0.366356\pi$$
−0.994623 + 0.103558i $$0.966977\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −3.00000 + 5.19615i −0.117130 + 0.202876i
$$657$$ 0 0
$$658$$ −12.0000 10.3923i −0.467809 0.405134i
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ 17.0000 + 29.4449i 0.661223 + 1.14527i 0.980294 + 0.197542i $$0.0632958\pi$$
−0.319071 + 0.947731i $$0.603371\pi$$
$$662$$ −6.50000 11.2583i −0.252630 0.437567i
$$663$$ 0 0
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −9.00000 + 15.5885i −0.348481 + 0.603587i
$$668$$ 4.50000 + 7.79423i 0.174110 + 0.301568i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −7.00000 −0.270232
$$672$$ 0 0
$$673$$ −4.00000 −0.154189 −0.0770943 0.997024i $$-0.524564\pi$$
−0.0770943 + 0.997024i $$0.524564\pi$$
$$674$$ −11.0000 + 19.0526i −0.423704 + 0.733877i
$$675$$ 0 0
$$676$$ −6.00000 10.3923i −0.230769 0.399704i
$$677$$ 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i $$-0.534372\pi$$
0.914867 0.403755i $$-0.132295\pi$$
$$678$$ 0 0
$$679$$ −32.5000 + 11.2583i −1.24724 + 0.432055i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 4.00000 + 6.92820i 0.153168 + 0.265295i
$$683$$ −22.5000 38.9711i −0.860939 1.49119i −0.871024 0.491240i $$-0.836544\pi$$
0.0100856 0.999949i $$-0.496790\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −8.50000 16.4545i −0.324532 0.628235i
$$687$$ 0 0
$$688$$ 2.00000 3.46410i 0.0762493 0.132068i
$$689$$ −30.0000 51.9615i −1.14291 1.97958i
$$690$$ 0 0
$$691$$ −17.5000 + 30.3109i −0.665731 + 1.15308i 0.313355 + 0.949636i $$0.398547\pi$$
−0.979086 + 0.203445i $$0.934786\pi$$
$$692$$ 15.0000 0.570214
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 18.0000 + 31.1769i 0.681799 + 1.18091i
$$698$$ −17.0000 + 29.4449i −0.643459 + 1.11450i
$$699$$ 0 0
$$700$$ 2.50000 12.9904i 0.0944911 0.490990i
$$701$$ 3.00000 0.113308 0.0566542 0.998394i $$-0.481957\pi$$
0.0566542 + 0.998394i $$0.481957\pi$$
$$702$$ 0 0
$$703$$ −2.00000 3.46410i −0.0754314 0.130651i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ 30.0000 1.12906
$$707$$ 6.00000 + 5.19615i 0.225653 + 0.195421i
$$708$$ 0 0
$$709$$ 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i $$-0.773204\pi$$
0.944509 + 0.328484i $$0.106538\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −3.00000 + 5.19615i −0.112430 + 0.194734i
$$713$$ −48.0000 −1.79761
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 4.50000 7.79423i 0.168173 0.291284i
$$717$$ 0 0
$$718$$ 4.50000 + 7.79423i 0.167939 + 0.290878i
$$719$$ −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i $$-0.869021\pi$$
0.804648 + 0.593753i $$0.202354\pi$$
$$720$$ 0 0
$$721$$ 2.00000 10.3923i 0.0744839 0.387030i
$$722$$ 15.0000 0.558242
$$723$$ 0 0
$$724$$ 5.00000 + 8.66025i 0.185824 + 0.321856i
$$725$$ −7.50000 12.9904i −0.278543 0.482451i
$$726$$ 0 0
$$727$$ 50.0000 1.85440 0.927199 0.374570i $$-0.122210\pi$$
0.927199 + 0.374570i $$0.122210\pi$$
$$728$$ −12.5000 + 4.33013i −0.463281 + 0.160485i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −12.0000 20.7846i −0.443836 0.768747i
$$732$$ 0 0
$$733$$ 21.5000 37.2391i 0.794121 1.37546i −0.129275 0.991609i $$-0.541265\pi$$
0.923396 0.383849i $$-0.125402\pi$$
$$734$$ −38.0000 −1.40261
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 6.50000 11.2583i 0.239431 0.414706i
$$738$$ 0 0
$$739$$ −1.00000 1.73205i −0.0367856 0.0637145i 0.847046 0.531519i $$-0.178379\pi$$
−0.883832 + 0.467804i $$0.845045\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −30.0000 + 10.3923i −1.10133 + 0.381514i
$$743$$ 36.0000 1.32071 0.660356 0.750953i $$-0.270405\pi$$
0.660356 + 0.750953i $$0.270405\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 5.50000 + 9.52628i 0.201369 + 0.348782i
$$747$$ 0 0
$$748$$ −6.00000 −0.219382
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i $$-0.739038\pi$$
0.974265 + 0.225407i $$0.0723712\pi$$
$$752$$ 3.00000 + 5.19615i 0.109399 + 0.189484i
$$753$$ 0 0
$$754$$ −7.50000 + 12.9904i −0.273134 + 0.473082i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −10.0000 −0.363456 −0.181728 0.983349i $$-0.558169\pi$$
−0.181728 + 0.983349i $$0.558169\pi$$
$$758$$ −12.5000 + 21.6506i −0.454020 + 0.786386i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 15.0000 25.9808i 0.543750 0.941802i −0.454935 0.890525i $$-0.650337\pi$$
0.998684 0.0512772i $$-0.0163292\pi$$
$$762$$ 0 0
$$763$$ −28.0000 24.2487i −1.01367 0.877862i
$$764$$ 18.0000 0.651217
$$765$$ 0 0
$$766$$ −6.00000 10.3923i −0.216789 0.375489i
$$767$$ −7.50000 12.9904i −0.270809 0.469055i
$$768$$ 0 0
$$769$$ 2.00000 0.0721218 0.0360609 0.999350i $$-0.488519\pi$$
0.0360609 + 0.999350i $$0.488519\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 11.0000 19.0526i 0.395899 0.685717i
$$773$$ −12.0000 20.7846i −0.431610 0.747570i 0.565402 0.824815i $$-0.308721\pi$$
−0.997012 + 0.0772449i $$0.975388\pi$$
$$774$$ 0 0
$$775$$ 20.0000 34.6410i 0.718421 1.24434i
$$776$$ 13.0000 0.466673
$$777$$ 0 0
$$778$$ 12.0000 0.430221
$$779$$ −6.00000 + 10.3923i −0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ −6.00000 10.3923i −0.214697 0.371866i
$$782$$ 18.0000 31.1769i 0.643679 1.11488i
$$783$$ 0 0
$$784$$ 1.00000 + 6.92820i 0.0357143 + 0.247436i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −7.00000 12.1244i −0.249523 0.432187i 0.713871 0.700278i $$-0.246941\pi$$
−0.963394 + 0.268091i $$0.913607\pi$$
$$788$$ −4.50000 7.79423i −0.160306 0.277658i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −22.5000 + 7.79423i −0.800008 + 0.277131i
$$792$$ 0 0
$$793$$ 17.5000 30.3109i 0.621443 1.07637i
$$794$$ 1.00000 +