# Properties

 Label 95.1.d.b.94.1 Level $95$ Weight $1$ Character 95.94 Self dual yes Analytic conductor $0.047$ Analytic rank $0$ Dimension $2$ Projective image $D_{4}$ CM discriminant -95 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,1,Mod(94,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, 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("95.94");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$95 = 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 95.d (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: $$0.0474111762001$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{8})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - 2$$ x^2 - 2 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{4}$$ Projective field: Galois closure of 4.2.475.1 Artin image: $D_8$ Artin field: Galois closure of 8.2.4286875.1

## Embedding invariants

 Embedding label 94.1 Root $$1.41421$$ of defining polynomial Character $$\chi$$ $$=$$ 95.94

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.41421 q^{2} +1.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{9} +O(q^{10})$$ $$q-1.41421 q^{2} +1.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{9} +1.41421 q^{10} +1.41421 q^{12} -1.41421 q^{13} -1.41421 q^{15} -1.00000 q^{16} -1.41421 q^{18} -1.00000 q^{19} -1.00000 q^{20} +1.00000 q^{25} +2.00000 q^{26} +2.00000 q^{30} +1.41421 q^{32} +1.00000 q^{36} +1.41421 q^{37} +1.41421 q^{38} -2.00000 q^{39} -1.00000 q^{45} -1.41421 q^{48} +1.00000 q^{49} -1.41421 q^{50} -1.41421 q^{52} +1.41421 q^{53} -1.41421 q^{57} -1.41421 q^{60} -1.00000 q^{64} +1.41421 q^{65} -1.41421 q^{67} -2.00000 q^{74} +1.41421 q^{75} -1.00000 q^{76} +2.82843 q^{78} +1.00000 q^{80} -1.00000 q^{81} +1.41421 q^{90} +1.00000 q^{95} +2.00000 q^{96} +1.41421 q^{97} -1.41421 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10})$$ 2 * q + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^9 $$2 q + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{9} - 2 q^{16} - 2 q^{19} - 2 q^{20} + 2 q^{25} + 4 q^{26} + 4 q^{30} + 2 q^{36} - 4 q^{39} - 2 q^{45} + 2 q^{49} - 2 q^{64} - 4 q^{74} - 2 q^{76} + 2 q^{80} - 2 q^{81} + 2 q^{95} + 4 q^{96}+O(q^{100})$$ 2 * q + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^9 - 2 * q^16 - 2 * q^19 - 2 * q^20 + 2 * q^25 + 4 * q^26 + 4 * q^30 + 2 * q^36 - 4 * q^39 - 2 * q^45 + 2 * q^49 - 2 * q^64 - 4 * q^74 - 2 * q^76 + 2 * q^80 - 2 * q^81 + 2 * q^95 + 4 * q^96

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$77$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$3$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$4$$ 1.00000 1.00000
$$5$$ −1.00000 −1.00000
$$6$$ −2.00000 −2.00000
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ 1.00000 1.00000
$$10$$ 1.41421 1.41421
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 1.41421 1.41421
$$13$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$14$$ 0 0
$$15$$ −1.41421 −1.41421
$$16$$ −1.00000 −1.00000
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ −1.41421 −1.41421
$$19$$ −1.00000 −1.00000
$$20$$ −1.00000 −1.00000
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 1.00000 1.00000
$$26$$ 2.00000 2.00000
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 2.00000 2.00000
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.41421 1.41421
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$38$$ 1.41421 1.41421
$$39$$ −2.00000 −2.00000
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ −1.00000 −1.00000
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ −1.41421 −1.41421
$$49$$ 1.00000 1.00000
$$50$$ −1.41421 −1.41421
$$51$$ 0 0
$$52$$ −1.41421 −1.41421
$$53$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.41421 −1.41421
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ −1.41421 −1.41421
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 1.41421 1.41421
$$66$$ 0 0
$$67$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ −2.00000 −2.00000
$$75$$ 1.41421 1.41421
$$76$$ −1.00000 −1.00000
$$77$$ 0 0
$$78$$ 2.82843 2.82843
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 1.00000 1.00000
$$81$$ −1.00000 −1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 1.41421 1.41421
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 1.00000 1.00000
$$96$$ 2.00000 2.00000
$$97$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$98$$ −1.41421 −1.41421
$$99$$ 0 0
$$100$$ 1.00000 1.00000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −2.00000 −2.00000
$$107$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 2.00000 2.00000
$$112$$ 0 0
$$113$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$114$$ 2.00000 2.00000
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.41421 −1.41421
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.00000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −1.00000
$$126$$ 0 0
$$127$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ −2.00000 −2.00000
$$131$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.00000 2.00000
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 1.41421 1.41421
$$148$$ 1.41421 1.41421
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ −2.00000 −2.00000
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −2.00000 −2.00000
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 2.00000 2.00000
$$160$$ −1.41421 −1.41421
$$161$$ 0 0
$$162$$ 1.41421 1.41421
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ −1.00000 −1.00000
$$172$$ 0 0
$$173$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ −1.00000 −1.00000
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1.41421 −1.41421
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −1.41421 −1.41421
$$191$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$192$$ −1.41421 −1.41421
$$193$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$194$$ −2.00000 −2.00000
$$195$$ 2.00000 2.00000
$$196$$ 1.00000 1.00000
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ −2.00000 −2.00000
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 2.00000 2.00000
$$207$$ 0 0
$$208$$ 1.41421 1.41421
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 1.41421 1.41421
$$213$$ 0 0
$$214$$ 2.00000 2.00000
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −2.82843 −2.82843
$$223$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$224$$ 0 0
$$225$$ 1.00000 1.00000
$$226$$ 2.00000 2.00000
$$227$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$228$$ −1.41421 −1.41421
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 2.00000 2.00000
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$240$$ 1.41421 1.41421
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 1.41421 1.41421
$$243$$ −1.41421 −1.41421
$$244$$ 0 0
$$245$$ −1.00000 −1.00000
$$246$$ 0 0
$$247$$ 1.41421 1.41421
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 1.41421 1.41421
$$251$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −2.00000 −2.00000
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 1.41421 1.41421
$$261$$ 0 0
$$262$$ −2.82843 −2.82843
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ −1.41421 −1.41421
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1.41421 −1.41421
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 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 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ 1.41421 1.41421
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.41421 1.41421
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ 2.00000 2.00000
$$292$$ 0 0
$$293$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$294$$ −2.00000 −2.00000
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 1.41421 1.41421
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 1.00000 1.00000
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$308$$ 0 0
$$309$$ −2.00000 −2.00000
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$318$$ −2.82843 −2.82843
$$319$$ 0 0
$$320$$ 1.00000 1.00000
$$321$$ −2.00000 −2.00000
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.00000 −1.00000
$$325$$ −1.41421 −1.41421
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 1.41421 1.41421
$$334$$ −2.00000 −2.00000
$$335$$ 1.41421 1.41421
$$336$$ 0 0
$$337$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$338$$ −1.41421 −1.41421
$$339$$ −2.00000 −2.00000
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 1.41421 1.41421
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 2.00000 2.00000
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 0 0
$$363$$ −1.41421 −1.41421
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 2.00000 2.00000
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$374$$ 0 0
$$375$$ −1.41421 −1.41421
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 1.00000 1.00000
$$381$$ 2.00000 2.00000
$$382$$ 2.82843 2.82843
$$383$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.00000 −2.00000
$$387$$ 0 0
$$388$$ 1.41421 1.41421
$$389$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$390$$ −2.82843 −2.82843
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 2.82843 2.82843
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 2.82843 2.82843
$$399$$ 0 0
$$400$$ −1.00000 −1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 2.82843 2.82843
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 1.00000 1.00000
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −1.41421 −1.41421
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −2.00000 −2.00000
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −1.41421 −1.41421
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 1.00000 1.00000
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 2.00000 2.00000
$$445$$ 0 0
$$446$$ −2.00000 −2.00000
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ −1.41421 −1.41421
$$451$$ 0 0
$$452$$ −1.41421 −1.41421
$$453$$ 0 0
$$454$$ 2.00000 2.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ −1.41421 −1.41421
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −1.00000 −1.00000
$$476$$ 0 0
$$477$$ 1.41421 1.41421
$$478$$ −2.82843 −2.82843
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ −2.00000 −2.00000
$$481$$ −2.00000 −2.00000
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −1.00000 −1.00000
$$485$$ −1.41421 −1.41421
$$486$$ 2.00000 2.00000
$$487$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 1.41421 1.41421
$$491$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −2.00000 −2.00000
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −1.00000 −1.00000
$$501$$ 2.00000 2.00000
$$502$$ 2.82843 2.82843
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 1.41421 1.41421
$$508$$ 1.41421 1.41421
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.41421 −1.41421
$$513$$ 0 0
$$514$$ −2.00000 −2.00000
$$515$$ 1.41421 1.41421
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −2.00000 −2.00000
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$524$$ 2.00000 2.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 1.00000
$$530$$ 2.00000 2.00000
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 1.41421 1.41421
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −2.00000 −2.00000
$$556$$ 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
$$563$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$564$$ 0 0
$$565$$ 1.41421 1.41421
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ −2.00000 −2.00000
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ −2.82843 −2.82843
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1.00000 −1.00000
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ −1.41421 −1.41421
$$579$$ 2.00000 2.00000
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −2.82843 −2.82843
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 1.41421 1.41421
$$586$$ −2.00000 −2.00000
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 1.41421 1.41421
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.41421 −1.41421
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −2.82843 −2.82843
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ −1.41421 −1.41421
$$604$$ 0 0
$$605$$ 1.00000 1.00000
$$606$$ 0 0
$$607$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$608$$ −1.41421 −1.41421
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 2.00000 2.00000
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 2.82843 2.82843
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 2.00000 2.00000
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 2.00000 2.00000
$$635$$ −1.41421 −1.41421
$$636$$ 2.00000 2.00000
$$637$$ −1.41421 −1.41421
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 2.82843 2.82843
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 2.00000 2.00000
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ −2.00000 −2.00000
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 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
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −2.00000 −2.00000
$$667$$ 0 0
$$668$$ 1.41421 1.41421
$$669$$ 2.00000 2.00000
$$670$$ −2.00000 −2.00000
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$674$$ 2.00000 2.00000
$$675$$ 0 0
$$676$$ 1.00000 1.00000
$$677$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$678$$ 2.82843 2.82843
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −2.00000 −2.00000
$$682$$ 0 0
$$683$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$684$$ −1.00000 −1.00000
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −2.00000 −2.00000
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ −1.41421 −1.41421
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 2.82843 2.82843
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ −1.41421 −1.41421
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 2.82843 2.82843
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 1.00000 1.00000
$$721$$ 0 0
$$722$$ −1.41421 −1.41421
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 2.00000 2.00000
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ −1.41421 −1.41421
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$740$$ −1.41421 −1.41421
$$741$$ 2.00000 2.00000
$$742$$ 0 0
$$743$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −2.00000 −2.00000
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 2.00000 2.00000
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ −2.82843 −2.82843
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ −2.82843 −2.82843
$$763$$ 0 0
$$764$$ −2.00000 −2.00000
$$765$$ 0 0
$$766$$ 2.00000 2.00000
$$767$$ 0 0
$$768$$ 1.41421 1.41421
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ 2.00000 2.00000
$$772$$ 1.41421 1.41421
$$773$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −2.82843 −2.82843
$$779$$ 0 0
$$780$$ 2.00000 2.00000
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ 0 0
$$786$$ −4.00000 −4.00000
$$787$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −2.00000 −2.00000
$$796$$ −2.00000 −2.00000
$$797$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.41421 1.41421
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ −2.00000 −2.00000
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$810$$ −1.41421 −1.41421
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 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
$$821$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 1.41421 1.41421
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −1.41421 −1.41421
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −2.82843 −2.82843
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −1.00000 −1.00000
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −1.41421 −1.41421
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 1.00000 1.00000
$$856$$ 0 0
$$857$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$858$$ 0 0
$$859$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$864$$ 0 0
$$865$$ 1.41421 1.41421
$$866$$ 2.00000 2.00000
$$867$$ 1.41421 1.41421
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 2.00000 2.00000
$$872$$ 0 0
$$873$$ 1.41421 1.41421
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$878$$ 0 0
$$879$$ 2.00000 2.00000
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ −1.41421 −1.41421
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 1.41421 1.41421
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 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
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$908$$ −1.41421 −1.41421
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 1.41421 1.41421
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$920$$ 0 0
$$921$$ −2.00000 −2.00000
$$922$$ −2.82843 −2.82843
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 1.41421 1.41421
$$926$$ 0 0
$$927$$ −1.41421 −1.41421
$$928$$ 0 0
$$929$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ −1.00000 −1.00000
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 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
$$949$$ 0 0
$$950$$ 1.41421 1.41421
$$951$$ −2.00000 −2.00000
$$952$$ 0 0
$$953$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$954$$ −2.00000 −2.00000
$$955$$ 2.00000 2.00000
$$956$$ 2.00000 2.00000
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 1.41421 1.41421
$$961$$ 1.00000 1.00000
$$962$$ 2.82843 2.82843
$$963$$ −1.41421 −1.41421
$$964$$ 0 0
$$965$$ −1.41421 −1.41421
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 2.00000 2.00000
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ −1.41421 −1.41421
$$973$$ 0 0
$$974$$ 2.00000 2.00000
$$975$$ −2.00000 −2.00000
$$976$$ 0 0
$$977$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ −1.00000 −1.00000
$$981$$ 0 0
$$982$$ 2.82843 2.82843
$$983$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 1.41421 1.41421
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 2.00000 2.00000
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 0 0
$$999$$ 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 95.1.d.b.94.1 2
3.2 odd 2 855.1.g.c.379.2 2
4.3 odd 2 1520.1.m.b.1329.1 2
5.2 odd 4 475.1.c.b.151.1 2
5.3 odd 4 475.1.c.b.151.2 2
5.4 even 2 inner 95.1.d.b.94.2 yes 2
15.14 odd 2 855.1.g.c.379.1 2
19.2 odd 18 1805.1.o.b.984.1 12
19.3 odd 18 1805.1.o.b.694.2 12
19.4 even 9 1805.1.o.b.1029.1 12
19.5 even 9 1805.1.o.b.849.1 12
19.6 even 9 1805.1.o.b.1199.1 12
19.7 even 3 1805.1.h.b.654.2 4
19.8 odd 6 1805.1.h.b.69.1 4
19.9 even 9 1805.1.o.b.299.2 12
19.10 odd 18 1805.1.o.b.299.1 12
19.11 even 3 1805.1.h.b.69.2 4
19.12 odd 6 1805.1.h.b.654.1 4
19.13 odd 18 1805.1.o.b.1199.2 12
19.14 odd 18 1805.1.o.b.849.2 12
19.15 odd 18 1805.1.o.b.1029.2 12
19.16 even 9 1805.1.o.b.694.1 12
19.17 even 9 1805.1.o.b.984.2 12
19.18 odd 2 inner 95.1.d.b.94.2 yes 2
20.19 odd 2 1520.1.m.b.1329.2 2
57.56 even 2 855.1.g.c.379.1 2
76.75 even 2 1520.1.m.b.1329.2 2
95.4 even 18 1805.1.o.b.1029.2 12
95.9 even 18 1805.1.o.b.299.1 12
95.14 odd 18 1805.1.o.b.849.1 12
95.18 even 4 475.1.c.b.151.1 2
95.24 even 18 1805.1.o.b.849.2 12
95.29 odd 18 1805.1.o.b.299.2 12
95.34 odd 18 1805.1.o.b.1029.1 12
95.37 even 4 475.1.c.b.151.2 2
95.44 even 18 1805.1.o.b.1199.2 12
95.49 even 6 1805.1.h.b.69.1 4
95.54 even 18 1805.1.o.b.694.2 12
95.59 odd 18 1805.1.o.b.984.2 12
95.64 even 6 1805.1.h.b.654.1 4
95.69 odd 6 1805.1.h.b.654.2 4
95.74 even 18 1805.1.o.b.984.1 12
95.79 odd 18 1805.1.o.b.694.1 12
95.84 odd 6 1805.1.h.b.69.2 4
95.89 odd 18 1805.1.o.b.1199.1 12
95.94 odd 2 CM 95.1.d.b.94.1 2
285.284 even 2 855.1.g.c.379.2 2
380.379 even 2 1520.1.m.b.1329.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
95.1.d.b.94.1 2 1.1 even 1 trivial
95.1.d.b.94.1 2 95.94 odd 2 CM
95.1.d.b.94.2 yes 2 5.4 even 2 inner
95.1.d.b.94.2 yes 2 19.18 odd 2 inner
475.1.c.b.151.1 2 5.2 odd 4
475.1.c.b.151.1 2 95.18 even 4
475.1.c.b.151.2 2 5.3 odd 4
475.1.c.b.151.2 2 95.37 even 4
855.1.g.c.379.1 2 15.14 odd 2
855.1.g.c.379.1 2 57.56 even 2
855.1.g.c.379.2 2 3.2 odd 2
855.1.g.c.379.2 2 285.284 even 2
1520.1.m.b.1329.1 2 4.3 odd 2
1520.1.m.b.1329.1 2 380.379 even 2
1520.1.m.b.1329.2 2 20.19 odd 2
1520.1.m.b.1329.2 2 76.75 even 2
1805.1.h.b.69.1 4 19.8 odd 6
1805.1.h.b.69.1 4 95.49 even 6
1805.1.h.b.69.2 4 19.11 even 3
1805.1.h.b.69.2 4 95.84 odd 6
1805.1.h.b.654.1 4 19.12 odd 6
1805.1.h.b.654.1 4 95.64 even 6
1805.1.h.b.654.2 4 19.7 even 3
1805.1.h.b.654.2 4 95.69 odd 6
1805.1.o.b.299.1 12 19.10 odd 18
1805.1.o.b.299.1 12 95.9 even 18
1805.1.o.b.299.2 12 19.9 even 9
1805.1.o.b.299.2 12 95.29 odd 18
1805.1.o.b.694.1 12 19.16 even 9
1805.1.o.b.694.1 12 95.79 odd 18
1805.1.o.b.694.2 12 19.3 odd 18
1805.1.o.b.694.2 12 95.54 even 18
1805.1.o.b.849.1 12 19.5 even 9
1805.1.o.b.849.1 12 95.14 odd 18
1805.1.o.b.849.2 12 19.14 odd 18
1805.1.o.b.849.2 12 95.24 even 18
1805.1.o.b.984.1 12 19.2 odd 18
1805.1.o.b.984.1 12 95.74 even 18
1805.1.o.b.984.2 12 19.17 even 9
1805.1.o.b.984.2 12 95.59 odd 18
1805.1.o.b.1029.1 12 19.4 even 9
1805.1.o.b.1029.1 12 95.34 odd 18
1805.1.o.b.1029.2 12 19.15 odd 18
1805.1.o.b.1029.2 12 95.4 even 18
1805.1.o.b.1199.1 12 19.6 even 9
1805.1.o.b.1199.1 12 95.89 odd 18
1805.1.o.b.1199.2 12 19.13 odd 18
1805.1.o.b.1199.2 12 95.44 even 18