# Properties

 Label 1352.1.g.a.339.1 Level $1352$ Weight $1$ Character 1352.339 Analytic conductor $0.675$ Analytic rank $0$ Dimension $2$ Projective image $D_{3}$ CM discriminant -104 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1352 = 2^{3} \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1352.g (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.674735897080$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 104) Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.104.1 Artin image: $C_4\times S_3$ Artin field: Galois closure of 12.0.43436029431808.1

## Embedding invariants

 Embedding label 339.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1352.339 Dual form 1352.1.g.a.339.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{10} +1.00000 q^{12} -1.00000 q^{14} -1.00000i q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000i q^{20} +1.00000i q^{21} -1.00000i q^{24} +1.00000 q^{27} +1.00000i q^{28} -1.00000 q^{30} -2.00000i q^{31} -1.00000i q^{32} -1.00000i q^{34} +1.00000 q^{35} -1.00000i q^{37} -1.00000 q^{40} +1.00000 q^{42} +1.00000 q^{43} -1.00000i q^{47} -1.00000 q^{48} -1.00000 q^{51} -1.00000i q^{54} +1.00000 q^{56} +1.00000i q^{60} -2.00000 q^{62} -1.00000 q^{64} -1.00000 q^{68} -1.00000i q^{70} +1.00000i q^{71} -1.00000 q^{74} +1.00000i q^{80} -1.00000 q^{81} -1.00000i q^{84} +1.00000i q^{85} -1.00000i q^{86} +2.00000i q^{93} -1.00000 q^{94} +1.00000i q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} - 2 q^{4}+O(q^{10})$$ 2 * q - 2 * q^3 - 2 * q^4 $$2 q - 2 q^{3} - 2 q^{4} + 2 q^{10} + 2 q^{12} - 2 q^{14} + 2 q^{16} + 2 q^{17} + 2 q^{27} - 2 q^{30} + 2 q^{35} - 2 q^{40} + 2 q^{42} + 2 q^{43} - 2 q^{48} - 2 q^{51} + 2 q^{56} - 4 q^{62} - 2 q^{64} - 2 q^{68} - 2 q^{74} - 2 q^{81} - 2 q^{94}+O(q^{100})$$ 2 * q - 2 * q^3 - 2 * q^4 + 2 * q^10 + 2 * q^12 - 2 * q^14 + 2 * q^16 + 2 * q^17 + 2 * q^27 - 2 * q^30 + 2 * q^35 - 2 * q^40 + 2 * q^42 + 2 * q^43 - 2 * q^48 - 2 * q^51 + 2 * q^56 - 4 * q^62 - 2 * q^64 - 2 * q^68 - 2 * q^74 - 2 * q^81 - 2 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$$.

 $$n$$ $$677$$ $$1015$$ $$1185$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ − 1.00000i − 1.00000i
$$3$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$4$$ −1.00000 −1.00000
$$5$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 1.00000i 1.00000i
$$7$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$8$$ 1.00000i 1.00000i
$$9$$ 0 0
$$10$$ 1.00000 1.00000
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 1.00000 1.00000
$$13$$ 0 0
$$14$$ −1.00000 −1.00000
$$15$$ − 1.00000i − 1.00000i
$$16$$ 1.00000 1.00000
$$17$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ − 1.00000i − 1.00000i
$$21$$ 1.00000i 1.00000i
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ − 1.00000i − 1.00000i
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000 1.00000
$$28$$ 1.00000i 1.00000i
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ −1.00000 −1.00000
$$31$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$32$$ − 1.00000i − 1.00000i
$$33$$ 0 0
$$34$$ − 1.00000i − 1.00000i
$$35$$ 1.00000 1.00000
$$36$$ 0 0
$$37$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −1.00000 −1.00000
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 1.00000 1.00000
$$43$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$48$$ −1.00000 −1.00000
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −1.00000 −1.00000
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ − 1.00000i − 1.00000i
$$55$$ 0 0
$$56$$ 1.00000 1.00000
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 1.00000i 1.00000i
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ −2.00000 −2.00000
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ −1.00000 −1.00000
$$69$$ 0 0
$$70$$ − 1.00000i − 1.00000i
$$71$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ −1.00000 −1.00000
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 1.00000i 1.00000i
$$81$$ −1.00000 −1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ − 1.00000i − 1.00000i
$$85$$ 1.00000i 1.00000i
$$86$$ − 1.00000i − 1.00000i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 2.00000i 2.00000i
$$94$$ −1.00000 −1.00000
$$95$$ 0 0
$$96$$ 1.00000i 1.00000i
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 1.00000i 1.00000i
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ −1.00000 −1.00000
$$106$$ 0 0
$$107$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$108$$ −1.00000 −1.00000
$$109$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$110$$ 0 0
$$111$$ 1.00000i 1.00000i
$$112$$ − 1.00000i − 1.00000i
$$113$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ − 1.00000i − 1.00000i
$$120$$ 1.00000 1.00000
$$121$$ −1.00000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 2.00000i 2.00000i
$$125$$ 1.00000i 1.00000i
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 1.00000i 1.00000i
$$129$$ −1.00000 −1.00000
$$130$$ 0 0
$$131$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 1.00000i 1.00000i
$$136$$ 1.00000i 1.00000i
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$140$$ −1.00000 −1.00000
$$141$$ 1.00000i 1.00000i
$$142$$ 1.00000 1.00000
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 1.00000i 1.00000i
$$149$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$150$$ 0 0
$$151$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 2.00000 2.00000
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 1.00000 1.00000
$$161$$ 0 0
$$162$$ 1.00000i 1.00000i
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ −1.00000 −1.00000
$$169$$ 0 0
$$170$$ 1.00000 1.00000
$$171$$ 0 0
$$172$$ −1.00000 −1.00000
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.00000 1.00000
$$186$$ 2.00000 2.00000
$$187$$ 0 0
$$188$$ 1.00000i 1.00000i
$$189$$ − 1.00000i − 1.00000i
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 1.00000 1.00000
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 1.00000 1.00000
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 1.00000i 1.00000i
$$211$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ 0 0
$$213$$ − 1.00000i − 1.00000i
$$214$$ − 2.00000i − 2.00000i
$$215$$ 1.00000i 1.00000i
$$216$$ 1.00000i 1.00000i
$$217$$ −2.00000 −2.00000
$$218$$ 1.00000 1.00000
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 1.00000 1.00000
$$223$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$224$$ −1.00000 −1.00000
$$225$$ 0 0
$$226$$ − 2.00000i − 2.00000i
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$234$$ 0 0
$$235$$ 1.00000 1.00000
$$236$$ 0 0
$$237$$ 0 0
$$238$$ −1.00000 −1.00000
$$239$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$240$$ − 1.00000i − 1.00000i
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 1.00000i 1.00000i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 2.00000 2.00000
$$249$$ 0 0
$$250$$ 1.00000 1.00000
$$251$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ − 1.00000i − 1.00000i
$$256$$ 1.00000 1.00000
$$257$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$258$$ 1.00000i 1.00000i
$$259$$ −1.00000 −1.00000
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 1.00000i 1.00000i
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 1.00000 1.00000
$$271$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$272$$ 1.00000 1.00000
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 1.00000i 1.00000i
$$279$$ 0 0
$$280$$ 1.00000i 1.00000i
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 1.00000 1.00000
$$283$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$284$$ − 1.00000i − 1.00000i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 1.00000 1.00000
$$297$$ 0 0
$$298$$ −2.00000 −2.00000
$$299$$ 0 0
$$300$$ 0 0
$$301$$ − 1.00000i − 1.00000i
$$302$$ −1.00000 −1.00000
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ − 2.00000i − 2.00000i
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ − 1.00000i − 1.00000i
$$321$$ −2.00000 −2.00000
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ − 1.00000i − 1.00000i
$$328$$ 0 0
$$329$$ −1.00000 −1.00000
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 2.00000 2.00000
$$335$$ 0 0
$$336$$ 1.00000i 1.00000i
$$337$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$338$$ 0 0
$$339$$ −2.00000 −2.00000
$$340$$ − 1.00000i − 1.00000i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ − 1.00000i − 1.00000i
$$344$$ 1.00000i 1.00000i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$348$$ 0 0
$$349$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ −1.00000 −1.00000
$$356$$ 0 0
$$357$$ 1.00000i 1.00000i
$$358$$ − 1.00000i − 1.00000i
$$359$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −1.00000 −1.00000
$$362$$ 0 0
$$363$$ 1.00000 1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ − 1.00000i − 1.00000i
$$371$$ 0 0
$$372$$ − 2.00000i − 2.00000i
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ − 1.00000i − 1.00000i
$$376$$ 1.00000 1.00000
$$377$$ 0 0
$$378$$ −1.00000 −1.00000
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ − 1.00000i − 1.00000i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 1.00000 1.00000
$$394$$ 1.00000 1.00000
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ − 1.00000i − 1.00000i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ − 1.00000i − 1.00000i
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 1.00000 1.00000
$$418$$ 0 0
$$419$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$420$$ 1.00000 1.00000
$$421$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$422$$ 1.00000i 1.00000i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ −1.00000 −1.00000
$$427$$ 0 0
$$428$$ −2.00000 −2.00000
$$429$$ 0 0
$$430$$ 1.00000 1.00000
$$431$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$432$$ 1.00000 1.00000
$$433$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$434$$ 2.00000i 2.00000i
$$435$$ 0 0
$$436$$ − 1.00000i − 1.00000i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ − 1.00000i − 1.00000i
$$445$$ 0 0
$$446$$ 1.00000 1.00000
$$447$$ 2.00000i 2.00000i
$$448$$ 1.00000i 1.00000i
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −2.00000 −2.00000
$$453$$ 1.00000i 1.00000i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ −1.00000 −1.00000
$$459$$ 1.00000 1.00000
$$460$$ 0 0
$$461$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$462$$ 0 0
$$463$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ −2.00000 −2.00000
$$466$$ − 1.00000i − 1.00000i
$$467$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ − 1.00000i − 1.00000i
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 1.00000i 1.00000i
$$477$$ 0 0
$$478$$ 1.00000 1.00000
$$479$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$480$$ −1.00000 −1.00000
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000 1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ − 2.00000i − 2.00000i
$$497$$ 1.00000 1.00000
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ − 1.00000i − 1.00000i
$$501$$ − 2.00000i − 2.00000i
$$502$$ 2.00000i 2.00000i
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$510$$ −1.00000 −1.00000
$$511$$ 0 0
$$512$$ − 1.00000i − 1.00000i
$$513$$ 0 0
$$514$$ − 1.00000i − 1.00000i
$$515$$ 0 0
$$516$$ 1.00000 1.00000
$$517$$ 0 0
$$518$$ 1.00000i 1.00000i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$524$$ 1.00000 1.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ − 2.00000i − 2.00000i
$$528$$ 0 0
$$529$$ 1.00000 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 2.00000i 2.00000i
$$536$$ 0 0
$$537$$ −1.00000 −1.00000
$$538$$ 0 0
$$539$$ 0 0
$$540$$ − 1.00000i − 1.00000i
$$541$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$542$$ −1.00000 −1.00000
$$543$$ 0 0
$$544$$ − 1.00000i − 1.00000i
$$545$$ −1.00000 −1.00000
$$546$$ 0 0
$$547$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −1.00000 −1.00000
$$556$$ 1.00000 1.00000
$$557$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 1.00000 1.00000
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$564$$ − 1.00000i − 1.00000i
$$565$$ 2.00000i 2.00000i
$$566$$ 2.00000i 2.00000i
$$567$$ 1.00000i 1.00000i
$$568$$ −1.00000 −1.00000
$$569$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$570$$ 0 0
$$571$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −1.00000 −1.00000
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ − 1.00000i − 1.00000i
$$592$$ − 1.00000i − 1.00000i
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 1.00000 1.00000
$$596$$ 2.00000i 2.00000i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ −1.00000 −1.00000
$$603$$ 0 0
$$604$$ 1.00000i 1.00000i
$$605$$ − 1.00000i − 1.00000i
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ −2.00000 −2.00000
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −1.00000 −1.00000
$$626$$ 1.00000i 1.00000i
$$627$$ 0 0
$$628$$ 0 0
$$629$$ − 1.00000i − 1.00000i
$$630$$ 0 0
$$631$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$632$$ 0 0
$$633$$ 1.00000 1.00000
$$634$$ −2.00000 −2.00000
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.00000 −1.00000
$$641$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$642$$ 2.00000i 2.00000i
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ − 1.00000i − 1.00000i
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ − 1.00000i − 1.00000i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 2.00000 2.00000
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ −1.00000 −1.00000
$$655$$ − 1.00000i − 1.00000i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 1.00000i 1.00000i
$$659$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$660$$ 0 0
$$661$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ − 2.00000i − 2.00000i
$$669$$ − 1.00000i − 1.00000i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.00000 1.00000
$$673$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$674$$ − 1.00000i − 1.00000i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 2.00000i 2.00000i
$$679$$ 0 0
$$680$$ −1.00000 −1.00000
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −1.00000 −1.00000
$$687$$ 1.00000i 1.00000i
$$688$$ 1.00000 1.00000
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 1.00000i 1.00000i
$$695$$ − 1.00000i − 1.00000i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −1.00000 −1.00000
$$699$$ −1.00000 −1.00000
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −1.00000 −1.00000
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$710$$ 1.00000i 1.00000i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 1.00000 1.00000
$$715$$ 0 0
$$716$$ −1.00000 −1.00000
$$717$$ − 1.00000i − 1.00000i
$$718$$ 2.00000 2.00000
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000i 1.00000i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ − 1.00000i − 1.00000i
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 1.00000 1.00000
$$732$$ 0 0
$$733$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ −1.00000 −1.00000
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$744$$ −2.00000 −2.00000
$$745$$ 2.00000 2.00000
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ − 2.00000i − 2.00000i
$$750$$ −1.00000 −1.00000
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ − 1.00000i − 1.00000i
$$753$$ 2.00000 2.00000
$$754$$ 0 0
$$755$$ 1.00000 1.00000
$$756$$ 1.00000i 1.00000i
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 1.00000 1.00000
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 1.00000 1.00000
$$767$$ 0 0
$$768$$ −1.00000 −1.00000
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ −1.00000 −1.00000
$$772$$ 0 0
$$773$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 1.00000 1.00000
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ − 1.00000i − 1.00000i
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ − 1.00000i − 1.00000i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ − 2.00000i − 2.00000i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 2.00000 2.00000
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ − 1.00000i − 1.00000i
$$800$$ 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
$$809$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$810$$ −1.00000 −1.00000
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 1.00000i 1.00000i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −1.00000 −1.00000
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ − 1.00000i − 1.00000i
$$835$$ −2.00000 −2.00000
$$836$$ 0 0
$$837$$ − 2.00000i − 2.00000i
$$838$$ 1.00000i 1.00000i
$$839$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ − 1.00000i − 1.00000i
$$841$$ 1.00000 1.00000
$$842$$ 1.00000 1.00000
$$843$$ 0 0
$$844$$ 1.00000 1.00000
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 1.00000i 1.00000i
$$848$$ 0 0
$$849$$ 2.00000 2.00000
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 1.00000i 1.00000i
$$853$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 2.00000i 2.00000i
$$857$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$860$$ − 1.00000i − 1.00000i
$$861$$ 0 0
$$862$$ 1.00000 1.00000
$$863$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$864$$ − 1.00000i − 1.00000i
$$865$$ 0 0
$$866$$ − 1.00000i − 1.00000i
$$867$$ 0 0
$$868$$ 2.00000 2.00000
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −1.00000 −1.00000
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 1.00000 1.00000
$$876$$ 0 0
$$877$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$878$$ 0 0
$$879$$ 1.00000i 1.00000i
$$880$$ 0 0
$$881$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$882$$ 0 0
$$883$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 1.00000i 1.00000i
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ −1.00000 −1.00000
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ − 1.00000i − 1.00000i
$$893$$ 0 0
$$894$$ 2.00000 2.00000
$$895$$ 1.00000i 1.00000i
$$896$$ 1.00000 1.00000
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 1.00000i 1.00000i
$$904$$ 2.00000i 2.00000i
$$905$$ 0 0
$$906$$ 1.00000 1.00000
$$907$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 1.00000i 1.00000i
$$917$$ 1.00000i 1.00000i
$$918$$ − 1.00000i − 1.00000i
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 1.00000 1.00000
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 2.00000 2.00000
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 2.00000i 2.00000i
$$931$$ 0 0
$$932$$ −1.00000 −1.00000
$$933$$ 0 0
$$934$$ 2.00000i 2.00000i
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$938$$ 0 0
$$939$$ 1.00000 1.00000
$$940$$ −1.00000 −1.00000
$$941$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 1.00000 1.00000
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 2.00000i 2.00000i
$$952$$ 1.00000 1.00000
$$953$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ − 1.00000i − 1.00000i
$$957$$ 0 0
$$958$$ −1.00000 −1.00000
$$959$$ 0 0
$$960$$ 1.00000i 1.00000i
$$961$$ −3.00000 −3.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$968$$ − 1.00000i − 1.00000i
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$972$$ 0 0
$$973$$ 1.00000i 1.00000i
$$974$$ −2.00000 −2.00000
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ − 1.00000i − 1.00000i
$$983$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$984$$ 0 0
$$985$$ −1.00000 −1.00000
$$986$$ 0 0
$$987$$ 1.00000 1.00000
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ −2.00000 −2.00000
$$993$$ 0 0
$$994$$ − 1.00000i − 1.00000i
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 0 0
$$999$$ − 1.00000i − 1.00000i
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1352.1.g.a.339.1 2
8.3 odd 2 inner 1352.1.g.a.339.2 2
13.2 odd 12 1352.1.p.b.147.1 2
13.3 even 3 1352.1.n.a.867.2 4
13.4 even 6 1352.1.n.a.315.2 4
13.5 odd 4 104.1.h.a.51.1 1
13.6 odd 12 1352.1.p.b.699.1 2
13.7 odd 12 1352.1.p.a.699.1 2
13.8 odd 4 104.1.h.b.51.1 yes 1
13.9 even 3 1352.1.n.a.315.1 4
13.10 even 6 1352.1.n.a.867.1 4
13.11 odd 12 1352.1.p.a.147.1 2
13.12 even 2 inner 1352.1.g.a.339.2 2
39.5 even 4 936.1.o.b.883.1 1
39.8 even 4 936.1.o.a.883.1 1
52.31 even 4 416.1.h.b.207.1 1
52.47 even 4 416.1.h.a.207.1 1
65.8 even 4 2600.1.b.a.1299.1 2
65.18 even 4 2600.1.b.b.1299.2 2
65.34 odd 4 2600.1.o.b.51.1 1
65.44 odd 4 2600.1.o.d.51.1 1
65.47 even 4 2600.1.b.a.1299.2 2
65.57 even 4 2600.1.b.b.1299.1 2
104.3 odd 6 1352.1.n.a.867.1 4
104.5 odd 4 416.1.h.a.207.1 1
104.11 even 12 1352.1.p.b.147.1 2
104.19 even 12 1352.1.p.a.699.1 2
104.21 odd 4 416.1.h.b.207.1 1
104.35 odd 6 1352.1.n.a.315.2 4
104.43 odd 6 1352.1.n.a.315.1 4
104.51 odd 2 CM 1352.1.g.a.339.1 2
104.59 even 12 1352.1.p.b.699.1 2
104.67 even 12 1352.1.p.a.147.1 2
104.75 odd 6 1352.1.n.a.867.2 4
104.83 even 4 104.1.h.b.51.1 yes 1
104.99 even 4 104.1.h.a.51.1 1
156.47 odd 4 3744.1.o.b.2287.1 1
156.83 odd 4 3744.1.o.a.2287.1 1
208.5 odd 4 3328.1.c.a.3327.2 2
208.21 odd 4 3328.1.c.e.3327.2 2
208.83 even 4 3328.1.c.e.3327.2 2
208.99 even 4 3328.1.c.a.3327.2 2
208.109 odd 4 3328.1.c.a.3327.1 2
208.125 odd 4 3328.1.c.e.3327.1 2
208.187 even 4 3328.1.c.e.3327.1 2
208.203 even 4 3328.1.c.a.3327.1 2
312.5 even 4 3744.1.o.b.2287.1 1
312.83 odd 4 936.1.o.a.883.1 1
312.125 even 4 3744.1.o.a.2287.1 1
312.203 odd 4 936.1.o.b.883.1 1
520.83 odd 4 2600.1.b.a.1299.1 2
520.99 even 4 2600.1.o.d.51.1 1
520.187 odd 4 2600.1.b.a.1299.2 2
520.203 odd 4 2600.1.b.b.1299.2 2
520.307 odd 4 2600.1.b.b.1299.1 2
520.499 even 4 2600.1.o.b.51.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
104.1.h.a.51.1 1 13.5 odd 4
104.1.h.a.51.1 1 104.99 even 4
104.1.h.b.51.1 yes 1 13.8 odd 4
104.1.h.b.51.1 yes 1 104.83 even 4
416.1.h.a.207.1 1 52.47 even 4
416.1.h.a.207.1 1 104.5 odd 4
416.1.h.b.207.1 1 52.31 even 4
416.1.h.b.207.1 1 104.21 odd 4
936.1.o.a.883.1 1 39.8 even 4
936.1.o.a.883.1 1 312.83 odd 4
936.1.o.b.883.1 1 39.5 even 4
936.1.o.b.883.1 1 312.203 odd 4
1352.1.g.a.339.1 2 1.1 even 1 trivial
1352.1.g.a.339.1 2 104.51 odd 2 CM
1352.1.g.a.339.2 2 8.3 odd 2 inner
1352.1.g.a.339.2 2 13.12 even 2 inner
1352.1.n.a.315.1 4 13.9 even 3
1352.1.n.a.315.1 4 104.43 odd 6
1352.1.n.a.315.2 4 13.4 even 6
1352.1.n.a.315.2 4 104.35 odd 6
1352.1.n.a.867.1 4 13.10 even 6
1352.1.n.a.867.1 4 104.3 odd 6
1352.1.n.a.867.2 4 13.3 even 3
1352.1.n.a.867.2 4 104.75 odd 6
1352.1.p.a.147.1 2 13.11 odd 12
1352.1.p.a.147.1 2 104.67 even 12
1352.1.p.a.699.1 2 13.7 odd 12
1352.1.p.a.699.1 2 104.19 even 12
1352.1.p.b.147.1 2 13.2 odd 12
1352.1.p.b.147.1 2 104.11 even 12
1352.1.p.b.699.1 2 13.6 odd 12
1352.1.p.b.699.1 2 104.59 even 12
2600.1.b.a.1299.1 2 65.8 even 4
2600.1.b.a.1299.1 2 520.83 odd 4
2600.1.b.a.1299.2 2 65.47 even 4
2600.1.b.a.1299.2 2 520.187 odd 4
2600.1.b.b.1299.1 2 65.57 even 4
2600.1.b.b.1299.1 2 520.307 odd 4
2600.1.b.b.1299.2 2 65.18 even 4
2600.1.b.b.1299.2 2 520.203 odd 4
2600.1.o.b.51.1 1 65.34 odd 4
2600.1.o.b.51.1 1 520.499 even 4
2600.1.o.d.51.1 1 65.44 odd 4
2600.1.o.d.51.1 1 520.99 even 4
3328.1.c.a.3327.1 2 208.109 odd 4
3328.1.c.a.3327.1 2 208.203 even 4
3328.1.c.a.3327.2 2 208.5 odd 4
3328.1.c.a.3327.2 2 208.99 even 4
3328.1.c.e.3327.1 2 208.125 odd 4
3328.1.c.e.3327.1 2 208.187 even 4
3328.1.c.e.3327.2 2 208.21 odd 4
3328.1.c.e.3327.2 2 208.83 even 4
3744.1.o.a.2287.1 1 156.83 odd 4
3744.1.o.a.2287.1 1 312.125 even 4
3744.1.o.b.2287.1 1 156.47 odd 4
3744.1.o.b.2287.1 1 312.5 even 4