# Properties

 Label 79.1.b.a.78.2 Level $79$ Weight $1$ Character 79.78 Self dual yes Analytic conductor $0.039$ Analytic rank $0$ Dimension $2$ Projective image $D_{5}$ CM discriminant -79 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [79,1,Mod(78,79)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(79, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("79.78");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$79$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 79.b (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: $$0.0394261359980$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{5}$$ Projective field: Galois closure of 5.1.6241.1 Artin image: $D_5$ Artin field: Galois closure of 5.1.6241.1

## Embedding invariants

 Embedding label 78.2 Root $$1.61803$$ of defining polynomial Character $$\chi$$ $$=$$ 79.78

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+0.618034 q^{2} -0.618034 q^{4} -1.61803 q^{5} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+0.618034 q^{2} -0.618034 q^{4} -1.61803 q^{5} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +0.618034 q^{11} +0.618034 q^{13} +0.618034 q^{18} -1.61803 q^{19} +1.00000 q^{20} +0.381966 q^{22} -1.61803 q^{23} +1.61803 q^{25} +0.381966 q^{26} +0.618034 q^{31} +1.00000 q^{32} -0.618034 q^{36} -1.00000 q^{38} +1.61803 q^{40} -0.381966 q^{44} -1.61803 q^{45} -1.00000 q^{46} +1.00000 q^{49} +1.00000 q^{50} -0.381966 q^{52} -1.00000 q^{55} +0.381966 q^{62} +0.618034 q^{64} -1.00000 q^{65} -1.61803 q^{67} -1.00000 q^{72} -1.61803 q^{73} +1.00000 q^{76} +1.00000 q^{79} +1.00000 q^{81} +2.00000 q^{83} -0.618034 q^{88} +0.618034 q^{89} -1.00000 q^{90} +1.00000 q^{92} +2.61803 q^{95} -1.61803 q^{97} +0.618034 q^{98} +0.618034 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} + q^{4} - q^{5} - 2 q^{8} + 2 q^{9}+O(q^{10})$$ 2 * q - q^2 + q^4 - q^5 - 2 * q^8 + 2 * q^9 $$2 q - q^{2} + q^{4} - q^{5} - 2 q^{8} + 2 q^{9} - 2 q^{10} - q^{11} - q^{13} - q^{18} - q^{19} + 2 q^{20} + 3 q^{22} - q^{23} + q^{25} + 3 q^{26} - q^{31} + 2 q^{32} + q^{36} - 2 q^{38} + q^{40} - 3 q^{44} - q^{45} - 2 q^{46} + 2 q^{49} + 2 q^{50} - 3 q^{52} - 2 q^{55} + 3 q^{62} - q^{64} - 2 q^{65} - q^{67} - 2 q^{72} - q^{73} + 2 q^{76} + 2 q^{79} + 2 q^{81} + 4 q^{83} + q^{88} - q^{89} - 2 q^{90} + 2 q^{92} + 3 q^{95} - q^{97} - q^{98} - q^{99}+O(q^{100})$$ 2 * q - q^2 + q^4 - q^5 - 2 * q^8 + 2 * q^9 - 2 * q^10 - q^11 - q^13 - q^18 - q^19 + 2 * q^20 + 3 * q^22 - q^23 + q^25 + 3 * q^26 - q^31 + 2 * q^32 + q^36 - 2 * q^38 + q^40 - 3 * q^44 - q^45 - 2 * q^46 + 2 * q^49 + 2 * q^50 - 3 * q^52 - 2 * q^55 + 3 * q^62 - q^64 - 2 * q^65 - q^67 - 2 * q^72 - q^73 + 2 * q^76 + 2 * q^79 + 2 * q^81 + 4 * q^83 + q^88 - q^89 - 2 * q^90 + 2 * q^92 + 3 * q^95 - q^97 - q^98 - q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/79\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ −0.618034 −0.618034
$$5$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ −1.00000 −1.00000
$$9$$ 1.00000 1.00000
$$10$$ −1.00000 −1.00000
$$11$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$12$$ 0 0
$$13$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0.618034 0.618034
$$19$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$20$$ 1.00000 1.00000
$$21$$ 0 0
$$22$$ 0.381966 0.381966
$$23$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$24$$ 0 0
$$25$$ 1.61803 1.61803
$$26$$ 0.381966 0.381966
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$32$$ 1.00000 1.00000
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.618034 −0.618034
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ −1.00000 −1.00000
$$39$$ 0 0
$$40$$ 1.61803 1.61803
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ −0.381966 −0.381966
$$45$$ −1.61803 −1.61803
$$46$$ −1.00000 −1.00000
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ 1.00000 1.00000
$$51$$ 0 0
$$52$$ −0.381966 −0.381966
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ −1.00000 −1.00000
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0.381966 0.381966
$$63$$ 0 0
$$64$$ 0.618034 0.618034
$$65$$ −1.00000 −1.00000
$$66$$ 0 0
$$67$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ −1.00000 −1.00000
$$73$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 1.00000 1.00000
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1.00000 1.00000
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ 0 0
$$83$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −0.618034 −0.618034
$$89$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$90$$ −1.00000 −1.00000
$$91$$ 0 0
$$92$$ 1.00000 1.00000
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 2.61803 2.61803
$$96$$ 0 0
$$97$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$98$$ 0.618034 0.618034
$$99$$ 0.618034 0.618034
$$100$$ −1.00000 −1.00000
$$101$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ −0.618034 −0.618034
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ −0.618034 −0.618034
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 2.61803 2.61803
$$116$$ 0 0
$$117$$ 0.618034 0.618034
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.618034 −0.618034
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −0.381966 −0.381966
$$125$$ −1.00000 −1.00000
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −0.618034 −0.618034
$$129$$ 0 0
$$130$$ −0.618034 −0.618034
$$131$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −1.00000 −1.00000
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0.381966 0.381966
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −1.00000 −1.00000
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$152$$ 1.61803 1.61803
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.00000 −1.00000
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0.618034 0.618034
$$159$$ 0 0
$$160$$ −1.61803 −1.61803
$$161$$ 0 0
$$162$$ 0.618034 0.618034
$$163$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 1.23607 1.23607
$$167$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$168$$ 0 0
$$169$$ −0.618034 −0.618034
$$170$$ 0 0
$$171$$ −1.61803 −1.61803
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0.381966 0.381966
$$179$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$180$$ 1.00000 1.00000
$$181$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 1.61803 1.61803
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 1.61803 1.61803
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ −1.00000 −1.00000
$$195$$ 0 0
$$196$$ −0.618034 −0.618034
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0.381966 0.381966
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ −1.61803 −1.61803
$$201$$ 0 0
$$202$$ 0.381966 0.381966
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1.61803 −1.61803
$$208$$ 0 0
$$209$$ −1.00000 −1.00000
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0.618034 0.618034
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$224$$ 0 0
$$225$$ 1.61803 1.61803
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 1.61803 1.61803
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0.381966 0.381966
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$240$$ 0 0
$$241$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$242$$ −0.381966 −0.381966
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1.61803 −1.61803
$$246$$ 0 0
$$247$$ −1.00000 −1.00000
$$248$$ −0.618034 −0.618034
$$249$$ 0 0
$$250$$ −0.618034 −0.618034
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ −1.00000 −1.00000
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −1.00000 −1.00000
$$257$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0.618034 0.618034
$$261$$ 0 0
$$262$$ −1.00000 −1.00000
$$263$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 1.00000 1.00000
$$269$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.00000 1.00000
$$276$$ 0 0
$$277$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$278$$ 0 0
$$279$$ 0.618034 0.618034
$$280$$ 0 0
$$281$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$282$$ 0 0
$$283$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0.236068 0.236068
$$287$$ 0 0
$$288$$ 1.00000 1.00000
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 1.00000 1.00000
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −1.00000 −1.00000
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −1.00000 −1.00000
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −0.618034 −0.618034
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −0.618034 −0.618034
$$317$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −1.00000 −1.00000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.618034 −0.618034
$$325$$ 1.00000 1.00000
$$326$$ 0.381966 0.381966
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ −1.23607 −1.23607
$$333$$ 0 0
$$334$$ 0.381966 0.381966
$$335$$ 2.61803 2.61803
$$336$$ 0 0
$$337$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$338$$ −0.381966 −0.381966
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0.381966 0.381966
$$342$$ −1.00000 −1.00000
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0.618034 0.618034
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −0.381966 −0.381966
$$357$$ 0 0
$$358$$ 1.23607 1.23607
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 1.61803 1.61803
$$361$$ 1.61803 1.61803
$$362$$ 0.381966 0.381966
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.61803 2.61803
$$366$$ 0 0
$$367$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ −1.61803 −1.61803
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 1.00000 1.00000
$$389$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.00000 −1.00000
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −1.61803 −1.61803
$$396$$ −0.381966 −0.381966
$$397$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0.381966 0.381966
$$404$$ −0.381966 −0.381966
$$405$$ −1.61803 −1.61803
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −1.00000 −1.00000
$$415$$ −3.23607 −3.23607
$$416$$ 0.618034 0.618034
$$417$$ 0 0
$$418$$ −0.618034 −0.618034
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$432$$ 0 0
$$433$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 2.61803 2.61803
$$438$$ 0 0
$$439$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$440$$ 1.00000 1.00000
$$441$$ 1.00000 1.00000
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ −1.00000 −1.00000
$$446$$ 1.23607 1.23607
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 1.00000 1.00000
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −1.61803 −1.61803
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$468$$ −0.381966 −0.381966
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −2.61803 −2.61803
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −1.00000 −1.00000
$$479$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.381966 0.381966
$$483$$ 0 0
$$484$$ 0.381966 0.381966
$$485$$ 2.61803 2.61803
$$486$$ 0 0
$$487$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −1.00000 −1.00000
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −0.618034 −0.618034
$$495$$ −1.00000 −1.00000
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$500$$ 0.618034 0.618034
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ −1.00000 −1.00000
$$506$$ −0.618034 −0.618034
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0.381966 0.381966
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 1.00000 1.00000
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$524$$ 1.00000 1.00000
$$525$$ 0 0
$$526$$ 0.381966 0.381966
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.61803 1.61803
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 1.61803 1.61803
$$537$$ 0 0
$$538$$ −1.00000 −1.00000
$$539$$ 0.618034 0.618034
$$540$$ 0 0
$$541$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0.618034 0.618034
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −1.00000 −1.00000
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$558$$ 0.381966 0.381966
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −1.00000 −1.00000
$$563$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0.381966 0.381966
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$570$$ 0 0
$$571$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$572$$ −0.236068 −0.236068
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −2.61803 −2.61803
$$576$$ 0.618034 0.618034
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0.618034 0.618034
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 1.61803 1.61803
$$585$$ −1.00000 −1.00000
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ −1.00000 −1.00000
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ −0.618034 −0.618034
$$599$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ −1.61803 −1.61803
$$604$$ 1.00000 1.00000
$$605$$ 1.00000 1.00000
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ −1.61803 −1.61803
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0.618034 0.618034
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0.381966 0.381966
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ −1.00000 −1.00000
$$633$$ 0 0
$$634$$ 1.23607 1.23607
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0.618034 0.618034
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 1.00000 1.00000
$$641$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$642$$ 0 0
$$643$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ −1.00000 −1.00000
$$649$$ 0 0
$$650$$ 0.618034 0.618034
$$651$$ 0 0
$$652$$ −0.381966 −0.381966
$$653$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$654$$ 0 0
$$655$$ 2.61803 2.61803
$$656$$ 0 0
$$657$$ −1.61803 −1.61803
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ −2.00000 −2.00000
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −0.381966 −0.381966
$$669$$ 0 0
$$670$$ 1.61803 1.61803
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ −1.00000 −1.00000
$$675$$ 0 0
$$676$$ 0.381966 0.381966
$$677$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0.236068 0.236068
$$683$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$684$$ 1.00000 1.00000
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −1.00000 −1.00000
$$695$$ 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
$$703$$ 0 0
$$704$$ 0.381966 0.381966
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 1.00000 1.00000
$$712$$ −0.618034 −0.618034
$$713$$ −1.00000 −1.00000
$$714$$ 0 0
$$715$$ −0.618034 −0.618034
$$716$$ −1.23607 −1.23607
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000 1.00000
$$723$$ 0 0
$$724$$ −0.381966 −0.381966
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 1.61803 1.61803
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$734$$ 0.381966 0.381966
$$735$$ 0 0
$$736$$ −1.61803 −1.61803
$$737$$ −1.00000 −1.00000
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 2.00000 2.00000
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 2.61803 2.61803
$$756$$ 0 0
$$757$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ −2.61803 −2.61803
$$761$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0.381966 0.381966
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$774$$ 0 0
$$775$$ 1.00000 1.00000
$$776$$ 1.61803 1.61803
$$777$$ 0 0
$$778$$ 0.381966 0.381966
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ −1.00000 −1.00000
$$791$$ 0 0
$$792$$ −0.618034 −0.618034
$$793$$ 0 0
$$794$$ 1.23607 1.23607
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.61803 1.61803
$$801$$ 0.618034 0.618034
$$802$$ 0 0
$$803$$ −1.00000 −1.00000
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0.236068 0.236068
$$807$$ 0 0
$$808$$ −0.618034 −0.618034
$$809$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$810$$ −1.00000 −1.00000
$$811$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −1.00000 −1.00000
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 1.00000 1.00000
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ −2.00000 −2.00000
$$831$$ 0 0
$$832$$ 0.381966 0.381966
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −1.00000 −1.00000
$$836$$ 0.618034 0.618034
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ −1.00000 −1.00000
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 1.00000 1.00000
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 2.61803 2.61803
$$856$$ 0 0
$$857$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −1.00000 −1.00000
$$863$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −1.00000 −1.00000
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0.618034 0.618034
$$870$$ 0 0
$$871$$ −1.00000 −1.00000
$$872$$ 0 0
$$873$$ −1.61803 −1.61803
$$874$$ 1.61803 1.61803
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$878$$ −1.00000 −1.00000
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0.618034 0.618034
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ −0.618034 −0.618034
$$891$$ 0.618034 0.618034
$$892$$ −1.23607 −1.23607
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −3.23607 −3.23607
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ −1.00000 −1.00000
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −1.00000 −1.00000
$$906$$ 0 0
$$907$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$908$$ 0 0
$$909$$ 0.618034 0.618034
$$910$$ 0 0
$$911$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$912$$ 0 0
$$913$$ 1.23607 1.23607
$$914$$ 0.381966 0.381966
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$920$$ −2.61803 −2.61803
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ −1.61803 −1.61803
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0.381966 0.381966
$$935$$ 0 0
$$936$$ −0.618034 −0.618034
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ −1.00000 −1.00000
$$950$$ −1.61803 −1.61803
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 1.00000 1.00000
$$957$$ 0 0
$$958$$ 1.23607 1.23607
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −0.618034 −0.618034
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −0.381966 −0.381966
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$968$$ 0.618034 0.618034
$$969$$ 0 0
$$970$$ 1.61803 1.61803
$$971$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0.381966 0.381966
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0.381966 0.381966
$$980$$ 1.00000 1.00000
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0.618034 0.618034
$$989$$ 0 0
$$990$$ −0.618034 −0.618034
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0.618034 0.618034
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$998$$ 0.381966 0.381966
$$999$$ 0 0
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 79.1.b.a.78.2 2
3.2 odd 2 711.1.d.b.631.1 2
4.3 odd 2 1264.1.e.a.1105.1 2
5.2 odd 4 1975.1.c.a.1974.3 4
5.3 odd 4 1975.1.c.a.1974.2 4
5.4 even 2 1975.1.d.c.1026.1 2
7.2 even 3 3871.1.m.c.3791.1 4
7.3 odd 6 3871.1.m.b.1500.1 4
7.4 even 3 3871.1.m.c.1500.1 4
7.5 odd 6 3871.1.m.b.3791.1 4
7.6 odd 2 3871.1.c.c.2843.2 2
79.78 odd 2 CM 79.1.b.a.78.2 2
237.236 even 2 711.1.d.b.631.1 2
316.315 even 2 1264.1.e.a.1105.1 2
395.78 even 4 1975.1.c.a.1974.2 4
395.157 even 4 1975.1.c.a.1974.3 4
395.394 odd 2 1975.1.d.c.1026.1 2
553.157 even 6 3871.1.m.b.1500.1 4
553.236 even 6 3871.1.m.b.3791.1 4
553.394 odd 6 3871.1.m.c.3791.1 4
553.473 odd 6 3871.1.m.c.1500.1 4
553.552 even 2 3871.1.c.c.2843.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
79.1.b.a.78.2 2 1.1 even 1 trivial
79.1.b.a.78.2 2 79.78 odd 2 CM
711.1.d.b.631.1 2 3.2 odd 2
711.1.d.b.631.1 2 237.236 even 2
1264.1.e.a.1105.1 2 4.3 odd 2
1264.1.e.a.1105.1 2 316.315 even 2
1975.1.c.a.1974.2 4 5.3 odd 4
1975.1.c.a.1974.2 4 395.78 even 4
1975.1.c.a.1974.3 4 5.2 odd 4
1975.1.c.a.1974.3 4 395.157 even 4
1975.1.d.c.1026.1 2 5.4 even 2
1975.1.d.c.1026.1 2 395.394 odd 2
3871.1.c.c.2843.2 2 7.6 odd 2
3871.1.c.c.2843.2 2 553.552 even 2
3871.1.m.b.1500.1 4 7.3 odd 6
3871.1.m.b.1500.1 4 553.157 even 6
3871.1.m.b.3791.1 4 7.5 odd 6
3871.1.m.b.3791.1 4 553.236 even 6
3871.1.m.c.1500.1 4 7.4 even 3
3871.1.m.c.1500.1 4 553.473 odd 6
3871.1.m.c.3791.1 4 7.2 even 3
3871.1.m.c.3791.1 4 553.394 odd 6