# Properties

 Label 1296.3.q.b.593.1 Level $1296$ Weight $3$ Character 1296.593 Analytic conductor $35.313$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1296 = 2^{4} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1296.q (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$35.3134422611$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 12) Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

## Embedding invariants

 Embedding label 593.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1296.593 Dual form 1296.3.q.b.1025.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.73205i) q^{7} +O(q^{10})$$ $$q+(1.00000 - 1.73205i) q^{7} +(11.0000 + 19.0526i) q^{13} -26.0000 q^{19} +(-12.5000 + 21.6506i) q^{25} +(-23.0000 - 39.8372i) q^{31} +26.0000 q^{37} +(-11.0000 + 19.0526i) q^{43} +(22.5000 + 38.9711i) q^{49} +(-37.0000 + 64.0859i) q^{61} +(61.0000 + 105.655i) q^{67} -46.0000 q^{73} +(-71.0000 + 122.976i) q^{79} +44.0000 q^{91} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{7} + O(q^{10})$$ $$2q + 2q^{7} + 22q^{13} - 52q^{19} - 25q^{25} - 46q^{31} + 52q^{37} - 22q^{43} + 45q^{49} - 74q^{61} + 122q^{67} - 92q^{73} - 142q^{79} + 88q^{91} - 2q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1217$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$6$$ 0 0
$$7$$ 1.00000 1.73205i 0.142857 0.247436i −0.785714 0.618590i $$-0.787704\pi$$
0.928571 + 0.371154i $$0.121038\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ 0 0
$$13$$ 11.0000 + 19.0526i 0.846154 + 1.46558i 0.884615 + 0.466321i $$0.154421\pi$$
−0.0384615 + 0.999260i $$0.512246\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ −26.0000 −1.36842 −0.684211 0.729285i $$-0.739853\pi$$
−0.684211 + 0.729285i $$0.739853\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$30$$ 0 0
$$31$$ −23.0000 39.8372i −0.741935 1.28507i −0.951613 0.307299i $$-0.900575\pi$$
0.209677 0.977771i $$-0.432759\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 26.0000 0.702703 0.351351 0.936244i $$-0.385722\pi$$
0.351351 + 0.936244i $$0.385722\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$42$$ 0 0
$$43$$ −11.0000 + 19.0526i −0.255814 + 0.443083i −0.965116 0.261822i $$-0.915677\pi$$
0.709302 + 0.704904i $$0.249010\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$48$$ 0 0
$$49$$ 22.5000 + 38.9711i 0.459184 + 0.795329i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$60$$ 0 0
$$61$$ −37.0000 + 64.0859i −0.606557 + 1.05059i 0.385246 + 0.922814i $$0.374117\pi$$
−0.991803 + 0.127774i $$0.959217\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 61.0000 + 105.655i 0.910448 + 1.57694i 0.813433 + 0.581659i $$0.197596\pi$$
0.0970149 + 0.995283i $$0.469071\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −46.0000 −0.630137 −0.315068 0.949069i $$-0.602027\pi$$
−0.315068 + 0.949069i $$0.602027\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −71.0000 + 122.976i −0.898734 + 1.55665i −0.0696203 + 0.997574i $$0.522179\pi$$
−0.829114 + 0.559080i $$0.811155\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 44.0000 0.483516
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.00000 + 1.73205i −0.0103093 + 0.0178562i −0.871134 0.491045i $$-0.836615\pi$$
0.860825 + 0.508902i $$0.169948\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$102$$ 0 0
$$103$$ 97.0000 + 168.009i 0.941748 + 1.63115i 0.762136 + 0.647417i $$0.224151\pi$$
0.179612 + 0.983738i $$0.442516\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ −214.000 −1.96330 −0.981651 0.190684i $$-0.938929\pi$$
−0.981651 + 0.190684i $$0.938929\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −60.5000 104.789i −0.500000 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −146.000 −1.14961 −0.574803 0.818292i $$-0.694921\pi$$
−0.574803 + 0.818292i $$0.694921\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$132$$ 0 0
$$133$$ −26.0000 + 45.0333i −0.195489 + 0.338596i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ −11.0000 19.0526i −0.0791367 0.137069i 0.823741 0.566966i $$-0.191883\pi$$
−0.902878 + 0.429898i $$0.858550\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$150$$ 0 0
$$151$$ −143.000 + 247.683i −0.947020 + 1.64029i −0.195364 + 0.980731i $$0.562589\pi$$
−0.751656 + 0.659556i $$0.770744\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 59.0000 + 102.191i 0.375796 + 0.650898i 0.990446 0.137902i $$-0.0440359\pi$$
−0.614650 + 0.788800i $$0.710703\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 262.000 1.60736 0.803681 0.595060i $$-0.202872\pi$$
0.803681 + 0.595060i $$0.202872\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$168$$ 0 0
$$169$$ −157.500 + 272.798i −0.931953 + 1.61419i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ 0 0
$$175$$ 25.0000 + 43.3013i 0.142857 + 0.247436i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 314.000 1.73481 0.867403 0.497606i $$-0.165787\pi$$
0.867403 + 0.497606i $$0.165787\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ 0 0
$$193$$ 191.000 + 330.822i 0.989637 + 1.71410i 0.619171 + 0.785256i $$0.287469\pi$$
0.370466 + 0.928846i $$0.379198\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −386.000 −1.93970 −0.969849 0.243706i $$-0.921637\pi$$
−0.969849 + 0.243706i $$0.921637\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −83.0000 143.760i −0.393365 0.681328i 0.599526 0.800355i $$-0.295356\pi$$
−0.992891 + 0.119027i $$0.962022\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −92.0000 −0.423963
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 169.000 292.717i 0.757848 1.31263i −0.186099 0.982531i $$-0.559584\pi$$
0.943946 0.330099i $$-0.107082\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$228$$ 0 0
$$229$$ −13.0000 22.5167i −0.0567686 0.0983260i 0.836245 0.548357i $$-0.184746\pi$$
−0.893013 + 0.450031i $$0.851413\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$240$$ 0 0
$$241$$ 143.000 247.683i 0.593361 1.02773i −0.400415 0.916334i $$-0.631134\pi$$
0.993776 0.111397i $$-0.0355327\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −286.000 495.367i −1.15789 2.00553i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$258$$ 0 0
$$259$$ 26.0000 45.0333i 0.100386 0.173874i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ −242.000 −0.892989 −0.446494 0.894786i $$-0.647328\pi$$
−0.446494 + 0.894786i $$0.647328\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −61.0000 + 105.655i −0.220217 + 0.381426i −0.954874 0.297012i $$-0.904010\pi$$
0.734657 + 0.678439i $$0.237343\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$282$$ 0 0
$$283$$ 229.000 + 396.640i 0.809187 + 1.40155i 0.913428 + 0.407001i $$0.133426\pi$$
−0.104240 + 0.994552i $$0.533241\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 289.000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 22.0000 + 38.1051i 0.0730897 + 0.126595i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 358.000 1.16612 0.583062 0.812428i $$-0.301855\pi$$
0.583062 + 0.812428i $$0.301855\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$312$$ 0 0
$$313$$ 71.0000 122.976i 0.226837 0.392893i −0.730032 0.683413i $$-0.760495\pi$$
0.956869 + 0.290520i $$0.0938282\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −550.000 −1.69231
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 181.000 313.501i 0.546828 0.947134i −0.451662 0.892189i $$-0.649169\pi$$
0.998489 0.0549442i $$-0.0174981\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −241.000 417.424i −0.715134 1.23865i −0.962908 0.269830i $$-0.913033\pi$$
0.247774 0.968818i $$-0.420301\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 188.000 0.548105
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$348$$ 0 0
$$349$$ 251.000 434.745i 0.719198 1.24569i −0.242120 0.970246i $$-0.577843\pi$$
0.961318 0.275441i $$-0.0888238\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 315.000 0.872576
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −359.000 + 621.806i −0.978202 + 1.69429i −0.309264 + 0.950976i $$0.600083\pi$$
−0.668937 + 0.743319i $$0.733251\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −349.000 604.486i −0.935657 1.62061i −0.773458 0.633847i $$-0.781475\pi$$
−0.162198 0.986758i $$-0.551858\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 694.000 1.83113 0.915567 0.402165i $$-0.131742\pi$$
0.915567 + 0.402165i $$0.131742\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 362.000 0.911839 0.455919 0.890021i $$-0.349311\pi$$
0.455919 + 0.890021i $$0.349311\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$402$$ 0 0
$$403$$ 506.000 876.418i 1.25558 2.17473i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −313.000 542.132i −0.765281 1.32551i −0.940098 0.340905i $$-0.889267\pi$$
0.174817 0.984601i $$-0.444067\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$420$$ 0 0
$$421$$ 179.000 310.037i 0.425178 0.736430i −0.571259 0.820770i $$-0.693545\pi$$
0.996437 + 0.0843398i $$0.0268781\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 74.0000 + 128.172i 0.173302 + 0.300168i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ −862.000 −1.99076 −0.995381 0.0960028i $$-0.969394\pi$$
−0.995381 + 0.0960028i $$0.969394\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −47.0000 + 81.4064i −0.107062 + 0.185436i −0.914579 0.404408i $$-0.867478\pi$$
0.807517 + 0.589844i $$0.200811\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 407.000 704.945i 0.890591 1.54255i 0.0514223 0.998677i $$-0.483625\pi$$
0.839168 0.543872i $$-0.183042\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$462$$ 0 0
$$463$$ −263.000 455.529i −0.568035 0.983865i −0.996760 0.0804300i $$-0.974371\pi$$
0.428726 0.903435i $$-0.358963\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 244.000 0.520256
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 325.000 562.917i 0.684211 1.18509i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ 0 0
$$481$$ 286.000 + 495.367i 0.594595 + 1.02987i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −962.000 −1.97536 −0.987680 0.156489i $$-0.949982\pi$$
−0.987680 + 0.156489i $$0.949982\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 13.0000 + 22.5167i 0.0260521 + 0.0451236i 0.878758 0.477269i $$-0.158373\pi$$
−0.852705 + 0.522392i $$0.825040\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$510$$ 0 0
$$511$$ −46.0000 + 79.6743i −0.0900196 + 0.155918i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 982.000 1.87763 0.938815 0.344423i $$-0.111925\pi$$
0.938815 + 0.344423i $$0.111925\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −264.500 + 458.127i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 1034.00 1.91128 0.955638 0.294545i $$-0.0951680\pi$$
0.955638 + 0.294545i $$0.0951680\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 253.000 438.209i 0.462523 0.801113i −0.536563 0.843860i $$-0.680278\pi$$
0.999086 + 0.0427471i $$0.0136110\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 142.000 + 245.951i 0.256781 + 0.444758i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ −484.000 −0.865832
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$570$$ 0 0
$$571$$ −443.000 767.299i −0.775832 1.34378i −0.934326 0.356420i $$-0.883997\pi$$
0.158494 0.987360i $$-0.449336\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 962.000 1.66724 0.833622 0.552335i $$-0.186263\pi$$
0.833622 + 0.552335i $$0.186263\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$588$$ 0 0
$$589$$ 598.000 + 1035.77i 1.01528 + 1.75852i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$600$$ 0 0
$$601$$ 263.000 455.529i 0.437604 0.757952i −0.559900 0.828560i $$-0.689161\pi$$
0.997504 + 0.0706077i $$0.0224939\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −407.000 704.945i −0.670511 1.16136i −0.977759 0.209729i $$-0.932742\pi$$
0.307249 0.951629i $$-0.400592\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −1126.00 −1.83687 −0.918434 0.395574i $$-0.870546\pi$$
−0.918434 + 0.395574i $$0.870546\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$618$$ 0 0
$$619$$ −107.000 + 185.329i −0.172859 + 0.299401i −0.939418 0.342773i $$-0.888634\pi$$
0.766559 + 0.642174i $$0.221967\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −312.500 541.266i −0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −674.000 −1.06815 −0.534073 0.845438i $$-0.679339\pi$$
−0.534073 + 0.845438i $$0.679339\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −495.000 + 857.365i −0.777080 + 1.34594i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ 0 0
$$643$$ 157.000 + 271.932i 0.244168 + 0.422911i 0.961897 0.273411i $$-0.0881518\pi$$
−0.717729 + 0.696322i $$0.754819\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$660$$ 0 0
$$661$$ −61.0000 105.655i −0.0922844 0.159841i 0.816188 0.577787i $$-0.196084\pi$$
−0.908472 + 0.417946i $$0.862750\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −577.000 + 999.393i −0.857355 + 1.48498i 0.0170877 + 0.999854i $$0.494561\pi$$
−0.874443 + 0.485129i $$0.838773\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$678$$ 0 0
$$679$$ 2.00000 + 3.46410i 0.00294551 + 0.00510177i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −659.000 + 1141.42i −0.953690 + 1.65184i −0.216353 + 0.976315i $$0.569416\pi$$
−0.737337 + 0.675525i $$0.763917\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ −676.000 −0.961593
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 467.000 808.868i 0.658674 1.14086i −0.322285 0.946643i $$-0.604451\pi$$
0.980959 0.194214i $$-0.0622158\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 388.000 0.538141
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 241.000 417.424i 0.331499 0.574174i −0.651307 0.758815i $$-0.725779\pi$$
0.982806 + 0.184641i $$0.0591122\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −517.000 895.470i −0.705321 1.22165i −0.966576 0.256381i $$-0.917470\pi$$
0.261255 0.965270i $$-0.415864\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 1222.00 1.65359 0.826793 0.562506i $$-0.190163\pi$$
0.826793 + 0.562506i $$0.190163\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 601.000 + 1040.96i 0.800266 + 1.38610i 0.919441 + 0.393229i $$0.128642\pi$$
−0.119174 + 0.992873i $$0.538025\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −838.000 −1.10700 −0.553501 0.832849i $$-0.686708\pi$$
−0.553501 + 0.832849i $$0.686708\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$762$$ 0 0
$$763$$ −214.000 + 370.659i −0.280472 + 0.485791i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 767.000 + 1328.48i 0.997399 + 1.72755i 0.561118 + 0.827736i $$0.310371\pi$$
0.436281 + 0.899811i $$0.356295\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 1150.00 1.48387
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 781.000 + 1352.73i 0.992376 + 1.71885i 0.602922 + 0.797800i $$0.294003\pi$$
0.389454 + 0.921046i $$0.372664\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −1628.00 −2.05296
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ −1514.00 −1.86683