# Properties

 Label 51.2.d.b.16.2 Level $51$ Weight $2$ Character 51.16 Analytic conductor $0.407$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$51 = 3 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 51.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.407237050309$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 16.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 51.16 Dual form 51.2.d.b.16.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -4.00000i q^{7} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -4.00000i q^{7} -3.00000 q^{8} -1.00000 q^{9} +4.00000i q^{11} -1.00000i q^{12} +2.00000 q^{13} -4.00000i q^{14} -1.00000 q^{16} +(1.00000 + 4.00000i) q^{17} -1.00000 q^{18} -4.00000 q^{19} +4.00000 q^{21} +4.00000i q^{22} -4.00000i q^{23} -3.00000i q^{24} +5.00000 q^{25} +2.00000 q^{26} -1.00000i q^{27} +4.00000i q^{28} -4.00000i q^{31} +5.00000 q^{32} -4.00000 q^{33} +(1.00000 + 4.00000i) q^{34} +1.00000 q^{36} +8.00000i q^{37} -4.00000 q^{38} +2.00000i q^{39} -8.00000i q^{41} +4.00000 q^{42} -4.00000 q^{43} -4.00000i q^{44} -4.00000i q^{46} -8.00000 q^{47} -1.00000i q^{48} -9.00000 q^{49} +5.00000 q^{50} +(-4.00000 + 1.00000i) q^{51} -2.00000 q^{52} +6.00000 q^{53} -1.00000i q^{54} +12.0000i q^{56} -4.00000i q^{57} -12.0000 q^{59} -8.00000i q^{61} -4.00000i q^{62} +4.00000i q^{63} +7.00000 q^{64} -4.00000 q^{66} +12.0000 q^{67} +(-1.00000 - 4.00000i) q^{68} +4.00000 q^{69} +12.0000i q^{71} +3.00000 q^{72} +8.00000i q^{74} +5.00000i q^{75} +4.00000 q^{76} +16.0000 q^{77} +2.00000i q^{78} -4.00000i q^{79} +1.00000 q^{81} -8.00000i q^{82} +12.0000 q^{83} -4.00000 q^{84} -4.00000 q^{86} -12.0000i q^{88} -10.0000 q^{89} -8.00000i q^{91} +4.00000i q^{92} +4.00000 q^{93} -8.00000 q^{94} +5.00000i q^{96} +16.0000i q^{97} -9.00000 q^{98} -4.00000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} - 2q^{4} - 6q^{8} - 2q^{9} + O(q^{10})$$ $$2q + 2q^{2} - 2q^{4} - 6q^{8} - 2q^{9} + 4q^{13} - 2q^{16} + 2q^{17} - 2q^{18} - 8q^{19} + 8q^{21} + 10q^{25} + 4q^{26} + 10q^{32} - 8q^{33} + 2q^{34} + 2q^{36} - 8q^{38} + 8q^{42} - 8q^{43} - 16q^{47} - 18q^{49} + 10q^{50} - 8q^{51} - 4q^{52} + 12q^{53} - 24q^{59} + 14q^{64} - 8q^{66} + 24q^{67} - 2q^{68} + 8q^{69} + 6q^{72} + 8q^{76} + 32q^{77} + 2q^{81} + 24q^{83} - 8q^{84} - 8q^{86} - 20q^{89} + 8q^{93} - 16q^{94} - 18q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$$.

 $$n$$ $$35$$ $$37$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107 0.353553 0.935414i $$-0.384973\pi$$
0.353553 + 0.935414i $$0.384973\pi$$
$$3$$ 1.00000i 0.577350i
$$4$$ −1.00000 −0.500000
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 1.00000i 0.408248i
$$7$$ 4.00000i 1.51186i −0.654654 0.755929i $$-0.727186\pi$$
0.654654 0.755929i $$-0.272814\pi$$
$$8$$ −3.00000 −1.06066
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 4.00000i 1.20605i 0.797724 + 0.603023i $$0.206037\pi$$
−0.797724 + 0.603023i $$0.793963\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 4.00000i 1.06904i
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 1.00000 + 4.00000i 0.242536 + 0.970143i
$$18$$ −1.00000 −0.235702
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ 0 0
$$21$$ 4.00000 0.872872
$$22$$ 4.00000i 0.852803i
$$23$$ 4.00000i 0.834058i −0.908893 0.417029i $$-0.863071\pi$$
0.908893 0.417029i $$-0.136929\pi$$
$$24$$ 3.00000i 0.612372i
$$25$$ 5.00000 1.00000
$$26$$ 2.00000 0.392232
$$27$$ 1.00000i 0.192450i
$$28$$ 4.00000i 0.755929i
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 4.00000i 0.718421i −0.933257 0.359211i $$-0.883046\pi$$
0.933257 0.359211i $$-0.116954\pi$$
$$32$$ 5.00000 0.883883
$$33$$ −4.00000 −0.696311
$$34$$ 1.00000 + 4.00000i 0.171499 + 0.685994i
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 8.00000i 1.31519i 0.753371 + 0.657596i $$0.228427\pi$$
−0.753371 + 0.657596i $$0.771573\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ 2.00000i 0.320256i
$$40$$ 0 0
$$41$$ 8.00000i 1.24939i −0.780869 0.624695i $$-0.785223\pi$$
0.780869 0.624695i $$-0.214777\pi$$
$$42$$ 4.00000 0.617213
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 4.00000i 0.603023i
$$45$$ 0 0
$$46$$ 4.00000i 0.589768i
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −9.00000 −1.28571
$$50$$ 5.00000 0.707107
$$51$$ −4.00000 + 1.00000i −0.560112 + 0.140028i
$$52$$ −2.00000 −0.277350
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ 0 0
$$56$$ 12.0000i 1.60357i
$$57$$ 4.00000i 0.529813i
$$58$$ 0 0
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ 8.00000i 1.02430i −0.858898 0.512148i $$-0.828850\pi$$
0.858898 0.512148i $$-0.171150\pi$$
$$62$$ 4.00000i 0.508001i
$$63$$ 4.00000i 0.503953i
$$64$$ 7.00000 0.875000
$$65$$ 0 0
$$66$$ −4.00000 −0.492366
$$67$$ 12.0000 1.46603 0.733017 0.680211i $$-0.238112\pi$$
0.733017 + 0.680211i $$0.238112\pi$$
$$68$$ −1.00000 4.00000i −0.121268 0.485071i
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ 12.0000i 1.42414i 0.702109 + 0.712069i $$0.252242\pi$$
−0.702109 + 0.712069i $$0.747758\pi$$
$$72$$ 3.00000 0.353553
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 8.00000i 0.929981i
$$75$$ 5.00000i 0.577350i
$$76$$ 4.00000 0.458831
$$77$$ 16.0000 1.82337
$$78$$ 2.00000i 0.226455i
$$79$$ 4.00000i 0.450035i −0.974355 0.225018i $$-0.927756\pi$$
0.974355 0.225018i $$-0.0722440\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 8.00000i 0.883452i
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ −4.00000 −0.436436
$$85$$ 0 0
$$86$$ −4.00000 −0.431331
$$87$$ 0 0
$$88$$ 12.0000i 1.27920i
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 8.00000i 0.838628i
$$92$$ 4.00000i 0.417029i
$$93$$ 4.00000 0.414781
$$94$$ −8.00000 −0.825137
$$95$$ 0 0
$$96$$ 5.00000i 0.510310i
$$97$$ 16.0000i 1.62455i 0.583272 + 0.812277i $$0.301772\pi$$
−0.583272 + 0.812277i $$0.698228\pi$$
$$98$$ −9.00000 −0.909137
$$99$$ 4.00000i 0.402015i
$$100$$ −5.00000 −0.500000
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ −4.00000 + 1.00000i −0.396059 + 0.0990148i
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ −6.00000 −0.588348
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 12.0000i 1.16008i −0.814587 0.580042i $$-0.803036\pi$$
0.814587 0.580042i $$-0.196964\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ 8.00000i 0.766261i 0.923694 + 0.383131i $$0.125154\pi$$
−0.923694 + 0.383131i $$0.874846\pi$$
$$110$$ 0 0
$$111$$ −8.00000 −0.759326
$$112$$ 4.00000i 0.377964i
$$113$$ 8.00000i 0.752577i −0.926503 0.376288i $$-0.877200\pi$$
0.926503 0.376288i $$-0.122800\pi$$
$$114$$ 4.00000i 0.374634i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ −12.0000 −1.10469
$$119$$ 16.0000 4.00000i 1.46672 0.366679i
$$120$$ 0 0
$$121$$ −5.00000 −0.454545
$$122$$ 8.00000i 0.724286i
$$123$$ 8.00000 0.721336
$$124$$ 4.00000i 0.359211i
$$125$$ 0 0
$$126$$ 4.00000i 0.356348i
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ −3.00000 −0.265165
$$129$$ 4.00000i 0.352180i
$$130$$ 0 0
$$131$$ 4.00000i 0.349482i 0.984614 + 0.174741i $$0.0559088\pi$$
−0.984614 + 0.174741i $$0.944091\pi$$
$$132$$ 4.00000 0.348155
$$133$$ 16.0000i 1.38738i
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ −3.00000 12.0000i −0.257248 1.02899i
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 4.00000 0.340503
$$139$$ 4.00000i 0.339276i 0.985506 + 0.169638i $$0.0542598\pi$$
−0.985506 + 0.169638i $$0.945740\pi$$
$$140$$ 0 0
$$141$$ 8.00000i 0.673722i
$$142$$ 12.0000i 1.00702i
$$143$$ 8.00000i 0.668994i
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 9.00000i 0.742307i
$$148$$ 8.00000i 0.657596i
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 5.00000i 0.408248i
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 12.0000 0.973329
$$153$$ −1.00000 4.00000i −0.0808452 0.323381i
$$154$$ 16.0000 1.28932
$$155$$ 0 0
$$156$$ 2.00000i 0.160128i
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ 4.00000i 0.318223i
$$159$$ 6.00000i 0.475831i
$$160$$ 0 0
$$161$$ −16.0000 −1.26098
$$162$$ 1.00000 0.0785674
$$163$$ 20.0000i 1.56652i 0.621694 + 0.783260i $$0.286445\pi$$
−0.621694 + 0.783260i $$0.713555\pi$$
$$164$$ 8.00000i 0.624695i
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ −12.0000 −0.925820
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ 4.00000 0.304997
$$173$$ 16.0000i 1.21646i −0.793762 0.608229i $$-0.791880\pi$$
0.793762 0.608229i $$-0.208120\pi$$
$$174$$ 0 0
$$175$$ 20.0000i 1.51186i
$$176$$ 4.00000i 0.301511i
$$177$$ 12.0000i 0.901975i
$$178$$ −10.0000 −0.749532
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ 8.00000i 0.594635i −0.954779 0.297318i $$-0.903908\pi$$
0.954779 0.297318i $$-0.0960920\pi$$
$$182$$ 8.00000i 0.592999i
$$183$$ 8.00000 0.591377
$$184$$ 12.0000i 0.884652i
$$185$$ 0 0
$$186$$ 4.00000 0.293294
$$187$$ −16.0000 + 4.00000i −1.17004 + 0.292509i
$$188$$ 8.00000 0.583460
$$189$$ −4.00000 −0.290957
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 7.00000i 0.505181i
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 16.0000i 1.14873i
$$195$$ 0 0
$$196$$ 9.00000 0.642857
$$197$$ 16.0000i 1.13995i 0.821661 + 0.569976i $$0.193048\pi$$
−0.821661 + 0.569976i $$0.806952\pi$$
$$198$$ 4.00000i 0.284268i
$$199$$ 20.0000i 1.41776i −0.705328 0.708881i $$-0.749200\pi$$
0.705328 0.708881i $$-0.250800\pi$$
$$200$$ −15.0000 −1.06066
$$201$$ 12.0000i 0.846415i
$$202$$ −6.00000 −0.422159
$$203$$ 0 0
$$204$$ 4.00000 1.00000i 0.280056 0.0700140i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 4.00000i 0.278019i
$$208$$ −2.00000 −0.138675
$$209$$ 16.0000i 1.10674i
$$210$$ 0 0
$$211$$ 4.00000i 0.275371i 0.990476 + 0.137686i $$0.0439664\pi$$
−0.990476 + 0.137686i $$0.956034\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ −12.0000 −0.822226
$$214$$ 12.0000i 0.820303i
$$215$$ 0 0
$$216$$ 3.00000i 0.204124i
$$217$$ −16.0000 −1.08615
$$218$$ 8.00000i 0.541828i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2.00000 + 8.00000i 0.134535 + 0.538138i
$$222$$ −8.00000 −0.536925
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 20.0000i 1.33631i
$$225$$ −5.00000 −0.333333
$$226$$ 8.00000i 0.532152i
$$227$$ 12.0000i 0.796468i −0.917284 0.398234i $$-0.869623\pi$$
0.917284 0.398234i $$-0.130377\pi$$
$$228$$ 4.00000i 0.264906i
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 16.0000i 1.05272i
$$232$$ 0 0
$$233$$ 8.00000i 0.524097i 0.965055 + 0.262049i $$0.0843981\pi$$
−0.965055 + 0.262049i $$0.915602\pi$$
$$234$$ −2.00000 −0.130744
$$235$$ 0 0
$$236$$ 12.0000 0.781133
$$237$$ 4.00000 0.259828
$$238$$ 16.0000 4.00000i 1.03713 0.259281i
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ 16.0000i 1.03065i −0.856995 0.515325i $$-0.827671\pi$$
0.856995 0.515325i $$-0.172329\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 1.00000i 0.0641500i
$$244$$ 8.00000i 0.512148i
$$245$$ 0 0
$$246$$ 8.00000 0.510061
$$247$$ −8.00000 −0.509028
$$248$$ 12.0000i 0.762001i
$$249$$ 12.0000i 0.760469i
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 4.00000i 0.251976i
$$253$$ 16.0000 1.00591
$$254$$ 8.00000 0.501965
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 4.00000i 0.249029i
$$259$$ 32.0000 1.98838
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 4.00000i 0.247121i
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 12.0000 0.738549
$$265$$ 0 0
$$266$$ 16.0000i 0.981023i
$$267$$ 10.0000i 0.611990i
$$268$$ −12.0000 −0.733017
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ −1.00000 4.00000i −0.0606339 0.242536i
$$273$$ 8.00000 0.484182
$$274$$ −10.0000 −0.604122
$$275$$ 20.0000i 1.20605i
$$276$$ −4.00000 −0.240772
$$277$$ 8.00000i 0.480673i −0.970690 0.240337i $$-0.922742\pi$$
0.970690 0.240337i $$-0.0772579\pi$$
$$278$$ 4.00000i 0.239904i
$$279$$ 4.00000i 0.239474i
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 8.00000i 0.476393i
$$283$$ 4.00000i 0.237775i 0.992908 + 0.118888i $$0.0379328\pi$$
−0.992908 + 0.118888i $$0.962067\pi$$
$$284$$ 12.0000i 0.712069i
$$285$$ 0 0
$$286$$ 8.00000i 0.473050i
$$287$$ −32.0000 −1.88890
$$288$$ −5.00000 −0.294628
$$289$$ −15.0000 + 8.00000i −0.882353 + 0.470588i
$$290$$ 0 0
$$291$$ −16.0000 −0.937937
$$292$$ 0 0
$$293$$ −10.0000 −0.584206 −0.292103 0.956387i $$-0.594355\pi$$
−0.292103 + 0.956387i $$0.594355\pi$$
$$294$$ 9.00000i 0.524891i
$$295$$ 0 0
$$296$$ 24.0000i 1.39497i
$$297$$ 4.00000 0.232104
$$298$$ 6.00000 0.347571
$$299$$ 8.00000i 0.462652i
$$300$$ 5.00000i 0.288675i
$$301$$ 16.0000i 0.922225i
$$302$$ 0 0
$$303$$ 6.00000i 0.344691i
$$304$$ 4.00000 0.229416
$$305$$ 0 0
$$306$$ −1.00000 4.00000i −0.0571662 0.228665i
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ −16.0000 −0.911685
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 12.0000i 0.680458i 0.940343 + 0.340229i $$0.110505\pi$$
−0.940343 + 0.340229i $$0.889495\pi$$
$$312$$ 6.00000i 0.339683i
$$313$$ 16.0000i 0.904373i −0.891923 0.452187i $$-0.850644\pi$$
0.891923 0.452187i $$-0.149356\pi$$
$$314$$ −2.00000 −0.112867
$$315$$ 0 0
$$316$$ 4.00000i 0.225018i
$$317$$ 32.0000i 1.79730i −0.438667 0.898650i $$-0.644549\pi$$
0.438667 0.898650i $$-0.355451\pi$$
$$318$$ 6.00000i 0.336463i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ −16.0000 −0.891645
$$323$$ −4.00000 16.0000i −0.222566 0.890264i
$$324$$ −1.00000 −0.0555556
$$325$$ 10.0000 0.554700
$$326$$ 20.0000i 1.10770i
$$327$$ −8.00000 −0.442401
$$328$$ 24.0000i 1.32518i
$$329$$ 32.0000i 1.76422i
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 8.00000i 0.438397i
$$334$$ 12.0000i 0.656611i
$$335$$ 0 0
$$336$$ −4.00000 −0.218218
$$337$$ 16.0000i 0.871576i −0.900049 0.435788i $$-0.856470\pi$$
0.900049 0.435788i $$-0.143530\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ 8.00000 0.434500
$$340$$ 0 0
$$341$$ 16.0000 0.866449
$$342$$ 4.00000 0.216295
$$343$$ 8.00000i 0.431959i
$$344$$ 12.0000 0.646997
$$345$$ 0 0
$$346$$ 16.0000i 0.860165i
$$347$$ 4.00000i 0.214731i 0.994220 + 0.107366i $$0.0342415\pi$$
−0.994220 + 0.107366i $$0.965758\pi$$
$$348$$ 0 0
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 20.0000i 1.06904i
$$351$$ 2.00000i 0.106752i
$$352$$ 20.0000i 1.06600i
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 12.0000i 0.637793i
$$355$$ 0 0
$$356$$ 10.0000 0.529999
$$357$$ 4.00000 + 16.0000i 0.211702 + 0.846810i
$$358$$ 4.00000 0.211407
$$359$$ 32.0000 1.68890 0.844448 0.535638i $$-0.179929\pi$$
0.844448 + 0.535638i $$0.179929\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 8.00000i 0.420471i
$$363$$ 5.00000i 0.262432i
$$364$$ 8.00000i 0.419314i
$$365$$ 0 0
$$366$$ 8.00000 0.418167
$$367$$ 12.0000i 0.626395i 0.949688 + 0.313197i $$0.101400\pi$$
−0.949688 + 0.313197i $$0.898600\pi$$
$$368$$ 4.00000i 0.208514i
$$369$$ 8.00000i 0.416463i
$$370$$ 0 0
$$371$$ 24.0000i 1.24602i
$$372$$ −4.00000 −0.207390
$$373$$ 26.0000 1.34623 0.673114 0.739538i $$-0.264956\pi$$
0.673114 + 0.739538i $$0.264956\pi$$
$$374$$ −16.0000 + 4.00000i −0.827340 + 0.206835i
$$375$$ 0 0
$$376$$ 24.0000 1.23771
$$377$$ 0 0
$$378$$ −4.00000 −0.205738
$$379$$ 20.0000i 1.02733i 0.857991 + 0.513665i $$0.171713\pi$$
−0.857991 + 0.513665i $$0.828287\pi$$
$$380$$ 0 0
$$381$$ 8.00000i 0.409852i
$$382$$ −8.00000 −0.409316
$$383$$ −16.0000 −0.817562 −0.408781 0.912633i $$-0.634046\pi$$
−0.408781 + 0.912633i $$0.634046\pi$$
$$384$$ 3.00000i 0.153093i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.00000 0.203331
$$388$$ 16.0000i 0.812277i
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 16.0000 4.00000i 0.809155 0.202289i
$$392$$ 27.0000 1.36371
$$393$$ −4.00000 −0.201773
$$394$$ 16.0000i 0.806068i
$$395$$ 0 0
$$396$$ 4.00000i 0.201008i
$$397$$ 8.00000i 0.401508i −0.979642 0.200754i $$-0.935661\pi$$
0.979642 0.200754i $$-0.0643393\pi$$
$$398$$ 20.0000i 1.00251i
$$399$$ −16.0000 −0.801002
$$400$$ −5.00000 −0.250000
$$401$$ 24.0000i 1.19850i −0.800561 0.599251i $$-0.795465\pi$$
0.800561 0.599251i $$-0.204535\pi$$
$$402$$ 12.0000i 0.598506i
$$403$$ 8.00000i 0.398508i
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −32.0000 −1.58618
$$408$$ 12.0000 3.00000i 0.594089 0.148522i
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 0 0
$$411$$ 10.0000i 0.493264i
$$412$$ 0 0
$$413$$ 48.0000i 2.36193i
$$414$$ 4.00000i 0.196589i
$$415$$ 0 0
$$416$$ 10.0000 0.490290
$$417$$ −4.00000 −0.195881
$$418$$ 16.0000i 0.782586i
$$419$$ 4.00000i 0.195413i 0.995215 + 0.0977064i $$0.0311506\pi$$
−0.995215 + 0.0977064i $$0.968849\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 4.00000i 0.194717i
$$423$$ 8.00000 0.388973
$$424$$ −18.0000 −0.874157
$$425$$ 5.00000 + 20.0000i 0.242536 + 0.970143i
$$426$$ −12.0000 −0.581402
$$427$$ −32.0000 −1.54859
$$428$$ 12.0000i 0.580042i
$$429$$ −8.00000 −0.386244
$$430$$ 0 0
$$431$$ 20.0000i 0.963366i −0.876346 0.481683i $$-0.840026\pi$$
0.876346 0.481683i $$-0.159974\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ −16.0000 −0.768025
$$435$$ 0 0
$$436$$ 8.00000i 0.383131i
$$437$$ 16.0000i 0.765384i
$$438$$ 0 0
$$439$$ 36.0000i 1.71819i −0.511819 0.859093i $$-0.671028\pi$$
0.511819 0.859093i $$-0.328972\pi$$
$$440$$ 0 0
$$441$$ 9.00000 0.428571
$$442$$ 2.00000 + 8.00000i 0.0951303 + 0.380521i
$$443$$ −20.0000 −0.950229 −0.475114 0.879924i $$-0.657593\pi$$
−0.475114 + 0.879924i $$0.657593\pi$$
$$444$$ 8.00000 0.379663
$$445$$ 0 0
$$446$$ 16.0000 0.757622
$$447$$ 6.00000i 0.283790i
$$448$$ 28.0000i 1.32288i
$$449$$ 8.00000i 0.377543i 0.982021 + 0.188772i $$0.0604506\pi$$
−0.982021 + 0.188772i $$0.939549\pi$$
$$450$$ −5.00000 −0.235702
$$451$$ 32.0000 1.50682
$$452$$ 8.00000i 0.376288i
$$453$$ 0 0
$$454$$ 12.0000i 0.563188i
$$455$$ 0 0
$$456$$ 12.0000i 0.561951i
$$457$$ 38.0000 1.77757 0.888783 0.458329i $$-0.151552\pi$$
0.888783 + 0.458329i $$0.151552\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 4.00000 1.00000i 0.186704 0.0466760i
$$460$$ 0 0
$$461$$ −34.0000 −1.58354 −0.791769 0.610821i $$-0.790840\pi$$
−0.791769 + 0.610821i $$0.790840\pi$$
$$462$$ 16.0000i 0.744387i
$$463$$ −40.0000 −1.85896 −0.929479 0.368875i $$-0.879743\pi$$
−0.929479 + 0.368875i $$0.879743\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 8.00000i 0.370593i
$$467$$ 4.00000 0.185098 0.0925490 0.995708i $$-0.470499\pi$$
0.0925490 + 0.995708i $$0.470499\pi$$
$$468$$ 2.00000 0.0924500
$$469$$ 48.0000i 2.21643i
$$470$$ 0 0
$$471$$ 2.00000i 0.0921551i
$$472$$ 36.0000 1.65703
$$473$$ 16.0000i 0.735681i
$$474$$ 4.00000 0.183726
$$475$$ −20.0000 −0.917663
$$476$$ −16.0000 + 4.00000i −0.733359 + 0.183340i
$$477$$ −6.00000 −0.274721
$$478$$ −8.00000 −0.365911
$$479$$ 12.0000i 0.548294i 0.961688 + 0.274147i $$0.0883955\pi$$
−0.961688 + 0.274147i $$0.911605\pi$$
$$480$$ 0 0
$$481$$ 16.0000i 0.729537i
$$482$$ 16.0000i 0.728780i
$$483$$ 16.0000i 0.728025i
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ 1.00000i 0.0453609i
$$487$$ 4.00000i 0.181257i −0.995885 0.0906287i $$-0.971112\pi$$
0.995885 0.0906287i $$-0.0288876\pi$$
$$488$$ 24.0000i 1.08643i
$$489$$ −20.0000 −0.904431
$$490$$ 0 0
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ −8.00000 −0.360668
$$493$$ 0 0
$$494$$ −8.00000 −0.359937
$$495$$ 0 0
$$496$$ 4.00000i 0.179605i
$$497$$ 48.0000 2.15309
$$498$$ 12.0000i 0.537733i
$$499$$ 36.0000i 1.61158i 0.592200 + 0.805791i $$0.298259\pi$$
−0.592200 + 0.805791i $$0.701741\pi$$
$$500$$ 0 0
$$501$$ −12.0000 −0.536120
$$502$$ 12.0000 0.535586
$$503$$ 12.0000i 0.535054i 0.963550 + 0.267527i $$0.0862064\pi$$
−0.963550 + 0.267527i $$0.913794\pi$$
$$504$$ 12.0000i 0.534522i
$$505$$ 0 0
$$506$$ 16.0000 0.711287
$$507$$ 9.00000i 0.399704i
$$508$$ −8.00000 −0.354943
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −11.0000 −0.486136
$$513$$ 4.00000i 0.176604i
$$514$$ −2.00000 −0.0882162
$$515$$ 0 0
$$516$$ 4.00000i 0.176090i
$$517$$ 32.0000i 1.40736i
$$518$$ 32.0000 1.40600
$$519$$ 16.0000 0.702322
$$520$$ 0 0
$$521$$ 24.0000i 1.05146i 0.850652 + 0.525730i $$0.176208\pi$$
−0.850652 + 0.525730i $$0.823792\pi$$
$$522$$ 0 0
$$523$$ −12.0000 −0.524723 −0.262362 0.964970i $$-0.584501\pi$$
−0.262362 + 0.964970i $$0.584501\pi$$
$$524$$ 4.00000i 0.174741i
$$525$$ 20.0000 0.872872
$$526$$ 24.0000 1.04645
$$527$$ 16.0000 4.00000i 0.696971 0.174243i
$$528$$ 4.00000 0.174078
$$529$$ 7.00000 0.304348
$$530$$ 0 0
$$531$$ 12.0000 0.520756
$$532$$ 16.0000i 0.693688i
$$533$$ 16.0000i 0.693037i
$$534$$ 10.0000i 0.432742i
$$535$$ 0 0
$$536$$ −36.0000 −1.55496
$$537$$ 4.00000i 0.172613i
$$538$$ 0 0
$$539$$ 36.0000i 1.55063i
$$540$$ 0 0
$$541$$ 40.0000i 1.71973i 0.510518 + 0.859867i $$0.329454\pi$$
−0.510518 + 0.859867i $$0.670546\pi$$
$$542$$ 0 0
$$543$$ 8.00000 0.343313
$$544$$ 5.00000 + 20.0000i 0.214373 + 0.857493i
$$545$$ 0 0
$$546$$ 8.00000 0.342368
$$547$$ 36.0000i 1.53925i 0.638497 + 0.769624i $$0.279557\pi$$
−0.638497 + 0.769624i $$0.720443\pi$$
$$548$$ 10.0000 0.427179
$$549$$ 8.00000i 0.341432i
$$550$$ 20.0000i 0.852803i
$$551$$ 0 0
$$552$$ −12.0000 −0.510754
$$553$$ −16.0000 −0.680389
$$554$$ 8.00000i 0.339887i
$$555$$ 0 0
$$556$$ 4.00000i 0.169638i
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 4.00000i 0.169334i
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ −4.00000 16.0000i −0.168880 0.675521i
$$562$$ 10.0000 0.421825
$$563$$ 44.0000 1.85438 0.927189 0.374593i $$-0.122217\pi$$
0.927189 + 0.374593i $$0.122217\pi$$
$$564$$ 8.00000i 0.336861i
$$565$$ 0 0
$$566$$ 4.00000i 0.168133i
$$567$$ 4.00000i 0.167984i
$$568$$ 36.0000i 1.51053i
$$569$$ 26.0000 1.08998 0.544988 0.838444i $$-0.316534\pi$$
0.544988 + 0.838444i $$0.316534\pi$$
$$570$$ 0 0
$$571$$ 20.0000i 0.836974i 0.908223 + 0.418487i $$0.137439\pi$$
−0.908223 + 0.418487i $$0.862561\pi$$
$$572$$ 8.00000i 0.334497i
$$573$$ 8.00000i 0.334205i
$$574$$ −32.0000 −1.33565
$$575$$ 20.0000i 0.834058i
$$576$$ −7.00000 −0.291667
$$577$$ 30.0000 1.24892 0.624458 0.781058i $$-0.285320\pi$$
0.624458 + 0.781058i $$0.285320\pi$$
$$578$$ −15.0000 + 8.00000i −0.623918 + 0.332756i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 48.0000i 1.99138i
$$582$$ −16.0000 −0.663221
$$583$$ 24.0000i 0.993978i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −10.0000 −0.413096
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 9.00000i 0.371154i
$$589$$ 16.0000i 0.659269i
$$590$$ 0 0
$$591$$ −16.0000 −0.658152
$$592$$ 8.00000i 0.328798i
$$593$$ −46.0000 −1.88899 −0.944497 0.328521i $$-0.893450\pi$$
−0.944497 + 0.328521i $$0.893450\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 20.0000 0.818546
$$598$$ 8.00000i 0.327144i
$$599$$ −8.00000 −0.326871 −0.163436 0.986554i $$-0.552258\pi$$
−0.163436 + 0.986554i $$0.552258\pi$$
$$600$$ 15.0000i 0.612372i
$$601$$ 16.0000i 0.652654i 0.945257 + 0.326327i $$0.105811\pi$$
−0.945257 + 0.326327i $$0.894189\pi$$
$$602$$ 16.0000i 0.652111i
$$603$$ −12.0000 −0.488678
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 6.00000i 0.243733i
$$607$$ 4.00000i 0.162355i −0.996700 0.0811775i $$-0.974132\pi$$
0.996700 0.0811775i $$-0.0258681\pi$$
$$608$$ −20.0000 −0.811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −16.0000 −0.647291
$$612$$ 1.00000 + 4.00000i 0.0404226 + 0.161690i
$$613$$ 6.00000 0.242338 0.121169 0.992632i $$-0.461336\pi$$
0.121169 + 0.992632i $$0.461336\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ 0 0
$$616$$ −48.0000 −1.93398
$$617$$ 24.0000i 0.966204i −0.875564 0.483102i $$-0.839510\pi$$
0.875564 0.483102i $$-0.160490\pi$$
$$618$$ 0 0
$$619$$ 36.0000i 1.44696i 0.690344 + 0.723481i $$0.257459\pi$$
−0.690344 + 0.723481i $$0.742541\pi$$
$$620$$ 0 0
$$621$$ −4.00000 −0.160514
$$622$$ 12.0000i 0.481156i
$$623$$ 40.0000i 1.60257i
$$624$$ 2.00000i 0.0800641i
$$625$$ 25.0000 1.00000
$$626$$ 16.0000i 0.639489i
$$627$$ 16.0000 0.638978
$$628$$ 2.00000 0.0798087
$$629$$ −32.0000 + 8.00000i −1.27592 + 0.318981i
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 12.0000i 0.477334i
$$633$$ −4.00000 −0.158986
$$634$$ 32.0000i 1.27088i
$$635$$ 0 0
$$636$$ 6.00000i 0.237915i
$$637$$ −18.0000 −0.713186
$$638$$ 0 0
$$639$$ 12.0000i 0.474713i
$$640$$ 0 0
$$641$$ 8.00000i 0.315981i 0.987441 + 0.157991i $$0.0505015\pi$$
−0.987441 + 0.157991i $$0.949498\pi$$
$$642$$ 12.0000 0.473602
$$643$$ 4.00000i 0.157745i 0.996885 + 0.0788723i $$0.0251319\pi$$
−0.996885 + 0.0788723i $$0.974868\pi$$
$$644$$ 16.0000 0.630488
$$645$$ 0 0
$$646$$ −4.00000 16.0000i −0.157378 0.629512i
$$647$$ 32.0000 1.25805 0.629025 0.777385i $$-0.283454\pi$$
0.629025 + 0.777385i $$0.283454\pi$$
$$648$$ −3.00000 −0.117851
$$649$$ 48.0000i 1.88416i
$$650$$ 10.0000 0.392232
$$651$$ 16.0000i 0.627089i
$$652$$ 20.0000i 0.783260i
$$653$$ 32.0000i 1.25226i −0.779720 0.626128i $$-0.784639\pi$$
0.779720 0.626128i $$-0.215361\pi$$
$$654$$ −8.00000 −0.312825
$$655$$ 0 0
$$656$$ 8.00000i 0.312348i
$$657$$ 0 0
$$658$$ 32.0000i 1.24749i
$$659$$ −4.00000 −0.155818 −0.0779089 0.996960i $$-0.524824\pi$$
−0.0779089 + 0.996960i $$0.524824\pi$$
$$660$$ 0 0
$$661$$ −42.0000 −1.63361 −0.816805 0.576913i $$-0.804257\pi$$
−0.816805 + 0.576913i $$0.804257\pi$$
$$662$$ −20.0000 −0.777322
$$663$$ −8.00000 + 2.00000i −0.310694 + 0.0776736i
$$664$$ −36.0000 −1.39707
$$665$$ 0 0
$$666$$ 8.00000i 0.309994i
$$667$$ 0 0
$$668$$ 12.0000i 0.464294i
$$669$$ 16.0000i 0.618596i
$$670$$ 0 0
$$671$$ 32.0000 1.23535
$$672$$ 20.0000 0.771517
$$673$$ 32.0000i 1.23351i 0.787155 + 0.616755i $$0.211553\pi$$
−0.787155 + 0.616755i $$0.788447\pi$$
$$674$$ 16.0000i 0.616297i
$$675$$ 5.00000i 0.192450i
$$676$$ 9.00000 0.346154
$$677$$ 48.0000i 1.84479i 0.386248 + 0.922395i $$0.373771\pi$$
−0.386248 + 0.922395i $$0.626229\pi$$
$$678$$ 8.00000 0.307238
$$679$$ 64.0000 2.45609
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 16.0000 0.612672
$$683$$ 12.0000i 0.459167i −0.973289 0.229584i $$-0.926264\pi$$
0.973289 0.229584i $$-0.0737364\pi$$
$$684$$ −4.00000 −0.152944
$$685$$ 0 0
$$686$$ 8.00000i 0.305441i
$$687$$ 10.0000i 0.381524i
$$688$$ 4.00000 0.152499
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ 20.0000i 0.760836i 0.924815 + 0.380418i $$0.124220\pi$$
−0.924815 + 0.380418i $$0.875780\pi$$
$$692$$ 16.0000i 0.608229i
$$693$$ −16.0000 −0.607790
$$694$$ 4.00000i 0.151838i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 32.0000 8.00000i 1.21209 0.303022i
$$698$$ −2.00000 −0.0757011
$$699$$ −8.00000 −0.302588
$$700$$ 20.0000i 0.755929i
$$701$$ 34.0000 1.28416 0.642081 0.766637i $$-0.278071\pi$$
0.642081 + 0.766637i $$0.278071\pi$$
$$702$$ 2.00000i 0.0754851i
$$703$$ 32.0000i 1.20690i
$$704$$ 28.0000i 1.05529i
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ 24.0000i 0.902613i
$$708$$ 12.0000i 0.450988i
$$709$$ 40.0000i 1.50223i −0.660171 0.751116i $$-0.729516\pi$$
0.660171 0.751116i $$-0.270484\pi$$
$$710$$ 0 0
$$711$$ 4.00000i 0.150012i
$$712$$ 30.0000 1.12430
$$713$$ −16.0000 −0.599205
$$714$$ 4.00000 + 16.0000i 0.149696 + 0.598785i
$$715$$ 0 0
$$716$$ −4.00000 −0.149487
$$717$$ 8.00000i 0.298765i
$$718$$ 32.0000 1.19423
$$719$$ 36.0000i 1.34257i −0.741198 0.671287i $$-0.765742\pi$$
0.741198 0.671287i $$-0.234258\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −3.00000 −0.111648
$$723$$ 16.0000 0.595046
$$724$$ 8.00000i 0.297318i
$$725$$ 0 0
$$726$$ 5.00000i 0.185567i
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 24.0000i 0.889499i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −4.00000 16.0000i −0.147945 0.591781i
$$732$$ −8.00000 −0.295689
$$733$$ −34.0000 −1.25582 −0.627909 0.778287i $$-0.716089\pi$$
−0.627909 + 0.778287i $$0.716089\pi$$
$$734$$ 12.0000i 0.442928i
$$735$$ 0 0
$$736$$ 20.0000i 0.737210i
$$737$$ 48.0000i 1.76810i
$$738$$ 8.00000i 0.294484i
$$739$$ −4.00000 −0.147142 −0.0735712 0.997290i $$-0.523440\pi$$
−0.0735712 + 0.997290i $$0.523440\pi$$
$$740$$ 0 0
$$741$$ 8.00000i 0.293887i
$$742$$ 24.0000i 0.881068i
$$743$$ 36.0000i 1.32071i −0.750953 0.660356i $$-0.770405\pi$$
0.750953 0.660356i $$-0.229595\pi$$
$$744$$ −12.0000 −0.439941
$$745$$ 0 0
$$746$$ 26.0000 0.951928
$$747$$ −12.0000 −0.439057
$$748$$ 16.0000 4.00000i 0.585018 0.146254i
$$749$$ −48.0000 −1.75388
$$750$$ 0 0
$$751$$ 20.0000i 0.729810i −0.931045 0.364905i $$-0.881101\pi$$
0.931045 0.364905i $$-0.118899\pi$$
$$752$$ 8.00000 0.291730
$$753$$ 12.0000i 0.437304i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 4.00000 0.145479
$$757$$ −38.0000 −1.38113 −0.690567 0.723269i $$-0.742639\pi$$
−0.690567 + 0.723269i $$0.742639\pi$$
$$758$$ 20.0000i 0.726433i
$$759$$ 16.0000i 0.580763i
$$760$$ 0 0
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 8.00000i 0.289809i
$$763$$ 32.0000 1.15848
$$764$$ 8.00000 0.289430
$$765$$ 0 0
$$766$$ −16.0000 −0.578103
$$767$$ −24.0000 −0.866590
$$768$$ 17.0000i 0.613435i
$$769$$ −34.0000 −1.22607 −0.613036 0.790055i $$-0.710052\pi$$
−0.613036 + 0.790055i $$0.710052\pi$$
$$770$$ 0 0
$$771$$ 2.00000i 0.0720282i
$$772$$ 0 0
$$773$$ −6.00000 −0.215805 −0.107903 0.994161i $$-0.534413\pi$$
−0.107903 + 0.994161i $$0.534413\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 20.0000i 0.718421i
$$776$$ 48.0000i 1.72310i
$$777$$ 32.0000i 1.14799i
$$778$$ −6.00000 −0.215110
$$779$$ 32.0000i 1.14652i
$$780$$ 0 0
$$781$$ −48.0000 −1.71758
$$782$$ 16.0000 4.00000i 0.572159 0.143040i
$$783$$ 0 0
$$784$$ 9.00000 0.321429
$$785$$ 0 0
$$786$$ −4.00000 −0.142675
$$787$$ 12.0000i 0.427754i −0.976861 0.213877i $$-0.931391\pi$$
0.976861 0.213877i $$-0.0686091\pi$$
$$788$$ 16.0000i 0.569976i
$$789$$ 24.0000i 0.854423i
$$790$$ 0 0
$$791$$ −32.0000 −1.13779
$$792$$ 12.0000i 0.426401i
$$793$$ 16.0000i 0.568177i
$$794$$ 8.00000i 0.283909i
$$795$$ 0 0
$$796$$ 20.0000i 0.708881i
$$797$$ −18.0000 −0.637593 −0.318796