# Properties

 Label 1975.1.c.a.1974.2 Level $1975$ Weight $1$ Character 1975.1974 Analytic conductor $0.986$ Analytic rank $0$ Dimension $4$ Projective image $D_{5}$ CM discriminant -79 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1975,1,Mod(1974,1975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1975, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1975.1974");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1975 = 5^{2} \cdot 79$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1975.c (of order $$2$$, degree $$1$$, not 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: no Analytic conductor: $$0.985653399950$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 3x^{2} + 1$$ x^4 + 3*x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 79) Projective image: $$D_{5}$$ Projective field: Galois closure of 5.1.6241.1 Artin image: $C_4\times D_5$ Artin field: Galois closure of $$\mathbb{Q}[x]/(x^{20} - \cdots)$$

## Embedding invariants

 Embedding label 1974.2 Root $$0.618034i$$ of defining polynomial Character $$\chi$$ $$=$$ 1975.1974 Dual form 1975.1.c.a.1974.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-0.618034i q^{2} +0.618034 q^{4} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-0.618034i q^{2} +0.618034 q^{4} -1.00000i q^{8} -1.00000 q^{9} +0.618034 q^{11} +0.618034i q^{13} +0.618034i q^{18} +1.61803 q^{19} -0.381966i q^{22} -1.61803i q^{23} +0.381966 q^{26} +0.618034 q^{31} -1.00000i q^{32} -0.618034 q^{36} -1.00000i q^{38} +0.381966 q^{44} -1.00000 q^{46} -1.00000 q^{49} +0.381966i q^{52} -0.381966i q^{62} -0.618034 q^{64} +1.61803i q^{67} +1.00000i q^{72} -1.61803i q^{73} +1.00000 q^{76} -1.00000 q^{79} +1.00000 q^{81} +2.00000i q^{83} -0.618034i q^{88} -0.618034 q^{89} -1.00000i q^{92} +1.61803i q^{97} +0.618034i q^{98} -0.618034 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{4} - 4 q^{9}+O(q^{10})$$ 4 * q - 2 * q^4 - 4 * q^9 $$4 q - 2 q^{4} - 4 q^{9} - 2 q^{11} + 2 q^{19} + 6 q^{26} - 2 q^{31} + 2 q^{36} + 6 q^{44} - 4 q^{46} - 4 q^{49} + 2 q^{64} + 4 q^{76} - 4 q^{79} + 4 q^{81} + 2 q^{89} + 2 q^{99}+O(q^{100})$$ 4 * q - 2 * q^4 - 4 * q^9 - 2 * q^11 + 2 * q^19 + 6 * q^26 - 2 * q^31 + 2 * q^36 + 6 * q^44 - 4 * q^46 - 4 * q^49 + 2 * q^64 + 4 * q^76 - 4 * q^79 + 4 * q^81 + 2 * q^89 + 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1975\mathbb{Z}\right)^\times$$.

 $$n$$ $$951$$ $$1502$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 0.618034 0.618034
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ − 1.00000i − 1.00000i
$$9$$ −1.00000 −1.00000
$$10$$ 0 0
$$11$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$12$$ 0 0
$$13$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0.618034i 0.618034i
$$19$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ − 0.381966i − 0.381966i
$$23$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 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 $$0.400000\pi$$
$$32$$ − 1.00000i − 1.00000i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.618034 −0.618034
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ − 1.00000i − 1.00000i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0.381966 0.381966
$$45$$ 0 0
$$46$$ −1.00000 −1.00000
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0.381966i 0.381966i
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 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 $$\pi$$
$$62$$ − 0.381966i − 0.381966i
$$63$$ 0 0
$$64$$ −0.618034 −0.618034
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 1.00000i 1.00000i
$$73$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$74$$ 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
$$83$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ − 0.618034i − 0.618034i
$$89$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ − 1.00000i − 1.00000i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$98$$ 0.618034i 0.618034i
$$99$$ −0.618034 −0.618034
$$100$$ 0 0
$$101$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0.618034 0.618034
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ − 0.618034i − 0.618034i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.618034 −0.618034
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0.381966 0.381966
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ − 0.618034i − 0.618034i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0.381966i 0.381966i
$$144$$ 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 $$0.800000\pi$$
$$152$$ − 1.61803i − 1.61803i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0.618034i 0.618034i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ − 0.618034i − 0.618034i
$$163$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 1.23607 1.23607
$$167$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$168$$ 0 0
$$169$$ 0.618034 0.618034
$$170$$ 0 0
$$171$$ −1.61803 −1.61803
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0.381966i 0.381966i
$$179$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 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
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 1.00000 1.00000
$$195$$ 0 0
$$196$$ −0.618034 −0.618034
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0.381966i 0.381966i
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ − 0.381966i − 0.381966i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 1.61803i 1.61803i
$$208$$ 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 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ −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 $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$240$$ 0 0
$$241$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$242$$ 0.381966i 0.381966i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.00000i 1.00000i
$$248$$ − 0.618034i − 0.618034i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ − 1.00000i − 1.00000i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −1.00000 −1.00000
$$257$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 1.00000i 1.00000i
$$263$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 1.00000i 1.00000i
$$269$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$278$$ 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
$$283$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0.236068 0.236068
$$287$$ 0 0
$$288$$ 1.00000i 1.00000i
$$289$$ −1.00000 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ − 1.00000i − 1.00000i
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 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
$$302$$ 1.00000i 1.00000i
$$303$$ 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
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −0.618034 −0.618034
$$317$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0.618034 0.618034
$$325$$ 0 0
$$326$$ 0.381966 0.381966
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 1.23607i 1.23607i
$$333$$ 0 0
$$334$$ −0.381966 −0.381966
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$338$$ − 0.381966i − 0.381966i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0.381966 0.381966
$$342$$ 1.00000i 1.00000i
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ − 0.618034i − 0.618034i
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −0.381966 −0.381966
$$357$$ 0 0
$$358$$ 1.23607i 1.23607i
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.61803 1.61803
$$362$$ − 0.381966i − 0.381966i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 1.00000i 1.00000i
$$389$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.00000i 1.00000i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −0.381966 −0.381966
$$397$$ − 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0.381966i 0.381966i
$$404$$ 0.381966 0.381966
$$405$$ 0 0
$$406$$ 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
$$415$$ 0 0
$$416$$ 0.618034 0.618034
$$417$$ 0 0
$$418$$ − 0.618034i − 0.618034i
$$419$$ 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
$$433$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ − 2.61803i − 2.61803i
$$438$$ 0 0
$$439$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$440$$ 0 0
$$441$$ 1.00000 1.00000
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 1.23607 1.23607
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$468$$ − 0.381966i − 0.381966i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ − 1.00000i − 1.00000i
$$479$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ − 0.381966i − 0.381966i
$$483$$ 0 0
$$484$$ −0.381966 −0.381966
$$485$$ 0 0
$$486$$ 0 0
$$487$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0.618034 0.618034
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −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
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$524$$ −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
$$538$$ − 1.00000i − 1.00000i
$$539$$ −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
$$547$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 1.00000 1.00000
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$558$$ 0.381966i 0.381966i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 1.00000i 1.00000i
$$563$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 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 $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$570$$ 0 0
$$571$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$572$$ 0.236068i 0.236068i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0.618034 0.618034
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 0.618034i 0.618034i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −1.61803 −1.61803
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 1.00000 1.00000
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ − 0.618034i − 0.618034i
$$599$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ − 1.61803i − 1.61803i
$$604$$ −1.00000 −1.00000
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ − 1.61803i − 1.61803i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 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 $$\pi$$
$$632$$ 1.00000i 1.00000i
$$633$$ 0 0
$$634$$ −1.23607 −1.23607
$$635$$ 0 0
$$636$$ 0 0
$$637$$ − 0.618034i − 0.618034i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$642$$ 0 0
$$643$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ − 1.00000i − 1.00000i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0.381966i 0.381966i
$$653$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 1.61803i 1.61803i
$$658$$ 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
$$668$$ − 0.381966i − 0.381966i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$674$$ 1.00000 1.00000
$$675$$ 0 0
$$676$$ 0.381966 0.381966
$$677$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ − 0.236068i − 0.236068i
$$683$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$684$$ −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
$$712$$ 0.618034i 0.618034i
$$713$$ − 1.00000i − 1.00000i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −1.23607 −1.23607
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ − 1.00000i − 1.00000i
$$723$$ 0 0
$$724$$ 0.381966 0.381966
$$725$$ 0 0
$$726$$ 0 0
$$727$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$734$$ −0.381966 −0.381966
$$735$$ 0 0
$$736$$ −1.61803 −1.61803
$$737$$ 1.00000i 1.00000i
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ − 2.00000i − 2.00000i
$$748$$ 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
$$755$$ 0 0
$$756$$ 0 0
$$757$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −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
$$773$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 1.61803 1.61803
$$777$$ 0 0
$$778$$ 0.381966i 0.381966i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0.618034i 0.618034i
$$793$$ 0 0
$$794$$ −1.23607 −1.23607
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0.618034 0.618034
$$802$$ 0 0
$$803$$ − 1.00000i − 1.00000i
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0.236068 0.236068
$$807$$ 0 0
$$808$$ − 0.618034i − 0.618034i
$$809$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$810$$ 0 0
$$811$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 1.00000i 1.00000i
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ − 0.381966i − 0.381966i
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0.618034 0.618034
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 1.00000i 1.00000i
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 1.00000i 1.00000i
$$863$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 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
$$873$$ − 1.61803i − 1.61803i
$$874$$ −1.61803 −1.61803
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$878$$ − 1.00000i − 1.00000i
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ − 0.618034i − 0.618034i
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0.618034 0.618034
$$892$$ 1.23607i 1.23607i
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$908$$ 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
$$913$$ 1.23607i 1.23607i
$$914$$ −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 $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$920$$ 0 0
$$921$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 1.00000 1.00000
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 1.00000 1.00000
$$957$$ 0 0
$$958$$ 1.23607i 1.23607i
$$959$$ 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
$$967$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$968$$ 0.618034i 0.618034i
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ −0.381966 −0.381966
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0.618034i 0.618034i
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ − 0.618034i − 0.618034i
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$998$$ 0.381966i 0.381966i
$$999$$ 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 1975.1.c.a.1974.2 4
5.2 odd 4 79.1.b.a.78.2 2
5.3 odd 4 1975.1.d.c.1026.1 2
5.4 even 2 inner 1975.1.c.a.1974.3 4
15.2 even 4 711.1.d.b.631.1 2
20.7 even 4 1264.1.e.a.1105.1 2
35.2 odd 12 3871.1.m.c.3791.1 4
35.12 even 12 3871.1.m.b.3791.1 4
35.17 even 12 3871.1.m.b.1500.1 4
35.27 even 4 3871.1.c.c.2843.2 2
35.32 odd 12 3871.1.m.c.1500.1 4
79.78 odd 2 CM 1975.1.c.a.1974.2 4
395.78 even 4 1975.1.d.c.1026.1 2
395.157 even 4 79.1.b.a.78.2 2
395.394 odd 2 inner 1975.1.c.a.1974.3 4
1185.947 odd 4 711.1.d.b.631.1 2
1580.947 odd 4 1264.1.e.a.1105.1 2
2765.157 odd 12 3871.1.m.b.1500.1 4
2765.552 odd 4 3871.1.c.c.2843.2 2
2765.947 even 12 3871.1.m.c.3791.1 4
2765.1342 odd 12 3871.1.m.b.3791.1 4
2765.2132 even 12 3871.1.m.c.1500.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
79.1.b.a.78.2 2 5.2 odd 4
79.1.b.a.78.2 2 395.157 even 4
711.1.d.b.631.1 2 15.2 even 4
711.1.d.b.631.1 2 1185.947 odd 4
1264.1.e.a.1105.1 2 20.7 even 4
1264.1.e.a.1105.1 2 1580.947 odd 4
1975.1.c.a.1974.2 4 1.1 even 1 trivial
1975.1.c.a.1974.2 4 79.78 odd 2 CM
1975.1.c.a.1974.3 4 5.4 even 2 inner
1975.1.c.a.1974.3 4 395.394 odd 2 inner
1975.1.d.c.1026.1 2 5.3 odd 4
1975.1.d.c.1026.1 2 395.78 even 4
3871.1.c.c.2843.2 2 35.27 even 4
3871.1.c.c.2843.2 2 2765.552 odd 4
3871.1.m.b.1500.1 4 35.17 even 12
3871.1.m.b.1500.1 4 2765.157 odd 12
3871.1.m.b.3791.1 4 35.12 even 12
3871.1.m.b.3791.1 4 2765.1342 odd 12
3871.1.m.c.1500.1 4 35.32 odd 12
3871.1.m.c.1500.1 4 2765.2132 even 12
3871.1.m.c.3791.1 4 35.2 odd 12
3871.1.m.c.3791.1 4 2765.947 even 12