# Properties

 Label 3800.1.o.e.1101.2 Level $3800$ Weight $1$ Character 3800.1101 Self dual yes Analytic conductor $1.896$ Analytic rank $0$ Dimension $3$ Projective image $D_{9}$ CM discriminant -152 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3800,1,Mod(1101,3800)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3800.1101");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3800 = 2^{3} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3800.o (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$1.89644704801$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: $$\Q(\zeta_{18})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{3} - 3x - 1$$ x^3 - 3*x - 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{9}$$ Projective field: Galois closure of 9.1.8340544000000.1

## Embedding invariants

 Embedding label 1101.2 Root $$1.87939$$ of defining polynomial Character $$\chi$$ $$=$$ 3800.1101

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} +0.347296 q^{6} +1.87939 q^{7} +1.00000 q^{8} -0.879385 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} +0.347296 q^{6} +1.87939 q^{7} +1.00000 q^{8} -0.879385 q^{9} +0.347296 q^{12} +1.53209 q^{13} +1.87939 q^{14} +1.00000 q^{16} -1.53209 q^{17} -0.879385 q^{18} -1.00000 q^{19} +0.652704 q^{21} -0.347296 q^{23} +0.347296 q^{24} +1.53209 q^{26} -0.652704 q^{27} +1.87939 q^{28} -1.53209 q^{29} +1.00000 q^{32} -1.53209 q^{34} -0.879385 q^{36} -1.00000 q^{37} -1.00000 q^{38} +0.532089 q^{39} +0.652704 q^{42} -0.347296 q^{46} +1.00000 q^{47} +0.347296 q^{48} +2.53209 q^{49} -0.532089 q^{51} +1.53209 q^{52} -1.87939 q^{53} -0.652704 q^{54} +1.87939 q^{56} -0.347296 q^{57} -1.53209 q^{58} -0.347296 q^{59} -1.65270 q^{63} +1.00000 q^{64} -1.87939 q^{67} -1.53209 q^{68} -0.120615 q^{69} -0.879385 q^{72} -0.347296 q^{73} -1.00000 q^{74} -1.00000 q^{76} +0.532089 q^{78} +0.652704 q^{81} +0.652704 q^{84} -0.532089 q^{87} +2.87939 q^{91} -0.347296 q^{92} +1.00000 q^{94} +0.347296 q^{96} +2.53209 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 3 q^{2} + 3 q^{4} + 3 q^{8} + 3 q^{9}+O(q^{10})$$ 3 * q + 3 * q^2 + 3 * q^4 + 3 * q^8 + 3 * q^9 $$3 q + 3 q^{2} + 3 q^{4} + 3 q^{8} + 3 q^{9} + 3 q^{16} + 3 q^{18} - 3 q^{19} + 3 q^{21} - 3 q^{27} + 3 q^{32} + 3 q^{36} - 3 q^{37} - 3 q^{38} - 3 q^{39} + 3 q^{42} + 3 q^{47} + 3 q^{49} + 3 q^{51} - 3 q^{54} - 6 q^{63} + 3 q^{64} - 6 q^{69} + 3 q^{72} - 3 q^{74} - 3 q^{76} - 3 q^{78} + 3 q^{81} + 3 q^{84} + 3 q^{87} + 3 q^{91} + 3 q^{94} + 3 q^{98}+O(q^{100})$$ 3 * q + 3 * q^2 + 3 * q^4 + 3 * q^8 + 3 * q^9 + 3 * q^16 + 3 * q^18 - 3 * q^19 + 3 * q^21 - 3 * q^27 + 3 * q^32 + 3 * q^36 - 3 * q^37 - 3 * q^38 - 3 * q^39 + 3 * q^42 + 3 * q^47 + 3 * q^49 + 3 * q^51 - 3 * q^54 - 6 * q^63 + 3 * q^64 - 6 * q^69 + 3 * q^72 - 3 * q^74 - 3 * q^76 - 3 * q^78 + 3 * q^81 + 3 * q^84 + 3 * q^87 + 3 * q^91 + 3 * q^94 + 3 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$951$$ $$1901$$ $$1977$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.00000
$$3$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 0 0
$$6$$ 0.347296 0.347296
$$7$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$8$$ 1.00000 1.00000
$$9$$ −0.879385 −0.879385
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0.347296 0.347296
$$13$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$14$$ 1.87939 1.87939
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$18$$ −0.879385 −0.879385
$$19$$ −1.00000 −1.00000
$$20$$ 0 0
$$21$$ 0.652704 0.652704
$$22$$ 0 0
$$23$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$24$$ 0.347296 0.347296
$$25$$ 0 0
$$26$$ 1.53209 1.53209
$$27$$ −0.652704 −0.652704
$$28$$ 1.87939 1.87939
$$29$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000 1.00000
$$33$$ 0 0
$$34$$ −1.53209 −1.53209
$$35$$ 0 0
$$36$$ −0.879385 −0.879385
$$37$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$38$$ −1.00000 −1.00000
$$39$$ 0.532089 0.532089
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0.652704 0.652704
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −0.347296 −0.347296
$$47$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$48$$ 0.347296 0.347296
$$49$$ 2.53209 2.53209
$$50$$ 0 0
$$51$$ −0.532089 −0.532089
$$52$$ 1.53209 1.53209
$$53$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$54$$ −0.652704 −0.652704
$$55$$ 0 0
$$56$$ 1.87939 1.87939
$$57$$ −0.347296 −0.347296
$$58$$ −1.53209 −1.53209
$$59$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ −1.65270 −1.65270
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$68$$ −1.53209 −1.53209
$$69$$ −0.120615 −0.120615
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ −0.879385 −0.879385
$$73$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$74$$ −1.00000 −1.00000
$$75$$ 0 0
$$76$$ −1.00000 −1.00000
$$77$$ 0 0
$$78$$ 0.532089 0.532089
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 0.652704 0.652704
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0.652704 0.652704
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −0.532089 −0.532089
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 2.87939 2.87939
$$92$$ −0.347296 −0.347296
$$93$$ 0 0
$$94$$ 1.00000 1.00000
$$95$$ 0 0
$$96$$ 0.347296 0.347296
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 2.53209 2.53209
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ −0.532089 −0.532089
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 1.53209 1.53209
$$105$$ 0 0
$$106$$ −1.87939 −1.87939
$$107$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$108$$ −0.652704 −0.652704
$$109$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$110$$ 0 0
$$111$$ −0.347296 −0.347296
$$112$$ 1.87939 1.87939
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ −0.347296 −0.347296
$$115$$ 0 0
$$116$$ −1.53209 −1.53209
$$117$$ −1.34730 −1.34730
$$118$$ −0.347296 −0.347296
$$119$$ −2.87939 −2.87939
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ −1.65270 −1.65270
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 1.00000 1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ −1.87939 −1.87939
$$134$$ −1.87939 −1.87939
$$135$$ 0 0
$$136$$ −1.53209 −1.53209
$$137$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$138$$ −0.120615 −0.120615
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0.347296 0.347296
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.879385 −0.879385
$$145$$ 0 0
$$146$$ −0.347296 −0.347296
$$147$$ 0.879385 0.879385
$$148$$ −1.00000 −1.00000
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ −1.00000 −1.00000
$$153$$ 1.34730 1.34730
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0.532089 0.532089
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ −0.652704 −0.652704
$$160$$ 0 0
$$161$$ −0.652704 −0.652704
$$162$$ 0.652704 0.652704
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0.652704 0.652704
$$169$$ 1.34730 1.34730
$$170$$ 0 0
$$171$$ 0.879385 0.879385
$$172$$ 0 0
$$173$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ −0.532089 −0.532089
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −0.120615 −0.120615
$$178$$ 0 0
$$179$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$180$$ 0 0
$$181$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$182$$ 2.87939 2.87939
$$183$$ 0 0
$$184$$ −0.347296 −0.347296
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 1.00000 1.00000
$$189$$ −1.22668 −1.22668
$$190$$ 0 0
$$191$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$192$$ 0.347296 0.347296
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 2.53209 2.53209
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$200$$ 0 0
$$201$$ −0.652704 −0.652704
$$202$$ 0 0
$$203$$ −2.87939 −2.87939
$$204$$ −0.532089 −0.532089
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0.305407 0.305407
$$208$$ 1.53209 1.53209
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$212$$ −1.87939 −1.87939
$$213$$ 0 0
$$214$$ 1.53209 1.53209
$$215$$ 0 0
$$216$$ −0.652704 −0.652704
$$217$$ 0 0
$$218$$ 1.87939 1.87939
$$219$$ −0.120615 −0.120615
$$220$$ 0 0
$$221$$ −2.34730 −2.34730
$$222$$ −0.347296 −0.347296
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 1.87939 1.87939
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$228$$ −0.347296 −0.347296
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −1.53209 −1.53209
$$233$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$234$$ −1.34730 −1.34730
$$235$$ 0 0
$$236$$ −0.347296 −0.347296
$$237$$ 0 0
$$238$$ −2.87939 −2.87939
$$239$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 1.00000 1.00000
$$243$$ 0.879385 0.879385
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.53209 −1.53209
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ −1.65270 −1.65270
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ −1.87939 −1.87939
$$260$$ 0 0
$$261$$ 1.34730 1.34730
$$262$$ 0 0
$$263$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −1.87939 −1.87939
$$267$$ 0 0
$$268$$ −1.87939 −1.87939
$$269$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$270$$ 0 0
$$271$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$272$$ −1.53209 −1.53209
$$273$$ 1.00000 1.00000
$$274$$ 1.87939 1.87939
$$275$$ 0 0
$$276$$ −0.120615 −0.120615
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0.347296 0.347296
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −0.879385 −0.879385
$$289$$ 1.34730 1.34730
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −0.347296 −0.347296
$$293$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$294$$ 0.879385 0.879385
$$295$$ 0 0
$$296$$ −1.00000 −1.00000
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −0.532089 −0.532089
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −1.00000 −1.00000
$$305$$ 0 0
$$306$$ 1.34730 1.34730
$$307$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$312$$ 0.532089 0.532089
$$313$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$318$$ −0.652704 −0.652704
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0.532089 0.532089
$$322$$ −0.652704 −0.652704
$$323$$ 1.53209 1.53209
$$324$$ 0.652704 0.652704
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0.652704 0.652704
$$328$$ 0 0
$$329$$ 1.87939 1.87939
$$330$$ 0 0
$$331$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$332$$ 0 0
$$333$$ 0.879385 0.879385
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0.652704 0.652704
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 1.34730 1.34730
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.879385 0.879385
$$343$$ 2.87939 2.87939
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −1.00000 −1.00000
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ −0.532089 −0.532089
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −1.00000
$$352$$ 0 0
$$353$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$354$$ −0.120615 −0.120615
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −1.00000 −1.00000
$$358$$ 1.00000 1.00000
$$359$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 1.00000 1.00000
$$363$$ 0.347296 0.347296
$$364$$ 2.87939 2.87939
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$368$$ −0.347296 −0.347296
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −3.53209 −3.53209
$$372$$ 0 0
$$373$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 1.00000 1.00000
$$377$$ −2.34730 −2.34730
$$378$$ −1.22668 −1.22668
$$379$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0.347296 0.347296
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0.347296 0.347296
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0.532089 0.532089
$$392$$ 2.53209 2.53209
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ −1.87939 −1.87939
$$399$$ −0.652704 −0.652704
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ −0.652704 −0.652704
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −2.87939 −2.87939
$$407$$ 0 0
$$408$$ −0.532089 −0.532089
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0.652704 0.652704
$$412$$ 0 0
$$413$$ −0.652704 −0.652704
$$414$$ 0.305407 0.305407
$$415$$ 0 0
$$416$$ 1.53209 1.53209
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$422$$ −0.347296 −0.347296
$$423$$ −0.879385 −0.879385
$$424$$ −1.87939 −1.87939
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 1.53209 1.53209
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ −0.652704 −0.652704
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.87939 1.87939
$$437$$ 0.347296 0.347296
$$438$$ −0.120615 −0.120615
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ −2.22668 −2.22668
$$442$$ −2.34730 −2.34730
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ −0.347296 −0.347296
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 1.87939 1.87939
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −1.87939 −1.87939
$$455$$ 0 0
$$456$$ −0.347296 −0.347296
$$457$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$458$$ 0 0
$$459$$ 1.00000 1.00000
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$464$$ −1.53209 −1.53209
$$465$$ 0 0
$$466$$ 1.00000 1.00000
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ −1.34730 −1.34730
$$469$$ −3.53209 −3.53209
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −0.347296 −0.347296
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −2.87939 −2.87939
$$477$$ 1.65270 1.65270
$$478$$ 0.347296 0.347296
$$479$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ 0 0
$$481$$ −1.53209 −1.53209
$$482$$ 0 0
$$483$$ −0.226682 −0.226682
$$484$$ 1.00000 1.00000
$$485$$ 0 0
$$486$$ 0.879385 0.879385
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 2.34730 2.34730
$$494$$ −1.53209 −1.53209
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$504$$ −1.65270 −1.65270
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.467911 0.467911
$$508$$ 0 0
$$509$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$510$$ 0 0
$$511$$ −0.652704 −0.652704
$$512$$ 1.00000 1.00000
$$513$$ 0.652704 0.652704
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −1.87939 −1.87939
$$519$$ −0.347296 −0.347296
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 1.34730 1.34730
$$523$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −2.00000 −2.00000
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.879385 −0.879385
$$530$$ 0 0
$$531$$ 0.305407 0.305407
$$532$$ −1.87939 −1.87939
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −1.87939 −1.87939
$$537$$ 0.347296 0.347296
$$538$$ 1.00000 1.00000
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0.347296 0.347296
$$543$$ 0.347296 0.347296
$$544$$ −1.53209 −1.53209
$$545$$ 0 0
$$546$$ 1.00000 1.00000
$$547$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$548$$ 1.87939 1.87939
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1.53209 1.53209
$$552$$ −0.120615 −0.120615
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0.347296 0.347296
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1.22668 1.22668
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0.120615 0.120615
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.879385 −0.879385
$$577$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$578$$ 1.34730 1.34730
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −0.347296 −0.347296
$$585$$ 0 0
$$586$$ 1.53209 1.53209
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0.879385 0.879385
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.00000 −1.00000
$$593$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −0.652704 −0.652704
$$598$$ −0.532089 −0.532089
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 1.65270 1.65270
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ −1.00000 −1.00000
$$609$$ −1.00000 −1.00000
$$610$$ 0 0
$$611$$ 1.53209 1.53209
$$612$$ 1.34730 1.34730
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ −1.00000 −1.00000
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0.226682 0.226682
$$622$$ −1.87939 −1.87939
$$623$$ 0 0
$$624$$ 0.532089 0.532089
$$625$$ 0 0
$$626$$ −1.53209 −1.53209
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1.53209 1.53209
$$630$$ 0 0
$$631$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$632$$ 0 0
$$633$$ −0.120615 −0.120615
$$634$$ 0.347296 0.347296
$$635$$ 0 0
$$636$$ −0.652704 −0.652704
$$637$$ 3.87939 3.87939
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0.532089 0.532089
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ −0.652704 −0.652704
$$645$$ 0 0
$$646$$ 1.53209 1.53209
$$647$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$648$$ 0.652704 0.652704
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0.652704 0.652704
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0.305407 0.305407
$$658$$ 1.87939 1.87939
$$659$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$660$$ 0 0
$$661$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$662$$ −1.53209 −1.53209
$$663$$ −0.815207 −0.815207
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0.879385 0.879385
$$667$$ 0.532089 0.532089
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0.652704 0.652704
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 1.34730 1.34730
$$677$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −0.652704 −0.652704
$$682$$ 0 0
$$683$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$684$$ 0.879385 0.879385
$$685$$ 0 0
$$686$$ 2.87939 2.87939
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −2.87939 −2.87939
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ −1.00000 −1.00000
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ −0.532089 −0.532089
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0.347296 0.347296
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ −1.00000 −1.00000
$$703$$ 1.00000 1.00000
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 1.87939 1.87939
$$707$$ 0 0
$$708$$ −0.120615 −0.120615
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ −1.00000 −1.00000
$$715$$ 0 0
$$716$$ 1.00000 1.00000
$$717$$ 0.120615 0.120615
$$718$$ 1.53209 1.53209
$$719$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000 1.00000
$$723$$ 0 0
$$724$$ 1.00000 1.00000
$$725$$ 0 0
$$726$$ 0.347296 0.347296
$$727$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$728$$ 2.87939 2.87939
$$729$$ −0.347296 −0.347296
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ −2.00000 −2.00000
$$735$$ 0 0
$$736$$ −0.347296 −0.347296
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ −0.532089 −0.532089
$$742$$ −3.53209 −3.53209
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0.347296 0.347296
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 2.87939 2.87939
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 1.00000 1.00000
$$753$$ 0 0
$$754$$ −2.34730 −2.34730
$$755$$ 0 0
$$756$$ −1.22668 −1.22668
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 1.87939 1.87939
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$762$$ 0 0
$$763$$ 3.53209 3.53209
$$764$$ 0.347296 0.347296
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −0.532089 −0.532089
$$768$$ 0.347296 0.347296
$$769$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −0.652704 −0.652704
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0.532089 0.532089
$$783$$ 1.00000 1.00000
$$784$$ 2.53209 2.53209
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$788$$ 0 0
$$789$$ −0.694593 −0.694593
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −1.87939 −1.87939
$$797$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$798$$ −0.652704 −0.652704
$$799$$ −1.53209 −1.53209
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ −0.652704 −0.652704
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0.347296 0.347296
$$808$$ 0 0
$$809$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$810$$ 0 0
$$811$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$812$$ −2.87939 −2.87939
$$813$$ 0.120615 0.120615
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −0.532089 −0.532089
$$817$$ 0 0
$$818$$ 0 0
$$819$$ −2.53209 −2.53209
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0.652704 0.652704
$$823$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ −0.652704 −0.652704
$$827$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$828$$ 0.305407 0.305407
$$829$$ −0.347296 −0.347296 −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 1.53209 1.53209
$$833$$ −3.87939 −3.87939
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 1.34730 1.34730
$$842$$ −0.347296 −0.347296
$$843$$ 0 0
$$844$$ −0.347296 −0.347296
$$845$$ 0 0
$$846$$ −0.879385 −0.879385
$$847$$ 1.87939 1.87939
$$848$$ −1.87939 −1.87939
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0.347296 0.347296
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 1.53209 1.53209
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ −0.652704 −0.652704
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0.467911 0.467911
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −2.87939 −2.87939
$$872$$ 1.87939 1.87939
$$873$$ 0 0
$$874$$ 0.347296 0.347296
$$875$$ 0 0
$$876$$ −0.120615 −0.120615
$$877$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$878$$ 0 0
$$879$$ 0.532089 0.532089
$$880$$ 0 0
$$881$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$882$$ −2.22668 −2.22668
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ −2.34730 −2.34730
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ −0.347296 −0.347296
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −1.00000 −1.00000
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 1.87939 1.87939
$$897$$ −0.184793 −0.184793
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 2.87939 2.87939
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −1.87939 −1.87939 −0.939693 0.342020i $$-0.888889\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$908$$ −1.87939 −1.87939
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ −0.347296 −0.347296
$$913$$ 0 0
$$914$$ −1.53209 −1.53209
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 1.00000 1.00000
$$919$$ 1.53209 1.53209 0.766044 0.642788i $$-0.222222\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$920$$ 0 0
$$921$$ −0.347296 −0.347296
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 1.00000 1.00000
$$927$$ 0 0
$$928$$ −1.53209 −1.53209
$$929$$ 0.347296 0.347296 0.173648 0.984808i $$-0.444444\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$930$$ 0 0
$$931$$ −2.53209 −2.53209
$$932$$ 1.00000 1.00000
$$933$$ −0.652704 −0.652704
$$934$$ 0 0
$$935$$ 0 0
$$936$$ −1.34730 −1.34730
$$937$$ −1.53209 −1.53209 −0.766044 0.642788i $$-0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$938$$ −3.53209 −3.53209
$$939$$ −0.532089 −0.532089
$$940$$ 0 0
$$941$$ 1.87939 1.87939 0.939693 0.342020i $$-0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −0.347296 −0.347296
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ −0.532089 −0.532089
$$950$$ 0 0
$$951$$ 0.120615 0.120615
$$952$$ −2.87939 −2.87939
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 1.65270 1.65270
$$955$$ 0 0
$$956$$ 0.347296 0.347296
$$957$$ 0 0
$$958$$ −1.00000 −1.00000
$$959$$ 3.53209 3.53209
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ −1.53209 −1.53209
$$963$$ −1.34730 −1.34730
$$964$$ 0 0
$$965$$ 0 0
$$966$$ −0.226682 −0.226682
$$967$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$968$$ 1.00000 1.00000
$$969$$ 0.532089 0.532089
$$970$$ 0 0
$$971$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$972$$ 0.879385 0.879385
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −1.65270 −1.65270
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 2.34730 2.34730
$$987$$ 0.652704 0.652704
$$988$$ −1.53209 −1.53209
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ −0.532089 −0.532089
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 0 0
$$999$$ 0.652704 0.652704
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 3800.1.o.e.1101.2 yes 3
5.2 odd 4 3800.1.b.d.949.5 6
5.3 odd 4 3800.1.b.d.949.2 6
5.4 even 2 3800.1.o.c.1101.2 3
8.5 even 2 3800.1.o.d.1101.2 yes 3
19.18 odd 2 3800.1.o.d.1101.2 yes 3
40.13 odd 4 3800.1.b.c.949.5 6
40.29 even 2 3800.1.o.f.1101.2 yes 3
40.37 odd 4 3800.1.b.c.949.2 6
95.18 even 4 3800.1.b.c.949.5 6
95.37 even 4 3800.1.b.c.949.2 6
95.94 odd 2 3800.1.o.f.1101.2 yes 3
152.37 odd 2 CM 3800.1.o.e.1101.2 yes 3
760.37 even 4 3800.1.b.d.949.5 6
760.189 odd 2 3800.1.o.c.1101.2 3
760.493 even 4 3800.1.b.d.949.2 6

By twisted newform
Twist Min Dim Char Parity Ord Type
3800.1.b.c.949.2 6 40.37 odd 4
3800.1.b.c.949.2 6 95.37 even 4
3800.1.b.c.949.5 6 40.13 odd 4
3800.1.b.c.949.5 6 95.18 even 4
3800.1.b.d.949.2 6 5.3 odd 4
3800.1.b.d.949.2 6 760.493 even 4
3800.1.b.d.949.5 6 5.2 odd 4
3800.1.b.d.949.5 6 760.37 even 4
3800.1.o.c.1101.2 3 5.4 even 2
3800.1.o.c.1101.2 3 760.189 odd 2
3800.1.o.d.1101.2 yes 3 8.5 even 2
3800.1.o.d.1101.2 yes 3 19.18 odd 2
3800.1.o.e.1101.2 yes 3 1.1 even 1 trivial
3800.1.o.e.1101.2 yes 3 152.37 odd 2 CM
3800.1.o.f.1101.2 yes 3 40.29 even 2
3800.1.o.f.1101.2 yes 3 95.94 odd 2