Properties

 Label 475.1.c.b.151.2 Level $475$ Weight $1$ Character 475.151 Analytic conductor $0.237$ 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] = [475,1,Mod(151,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("475.151");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 475.c (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: no Analytic conductor: $$0.237055881001$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-2})$$ 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: no (minimal twist has level 95) Projective image: $$D_{4}$$ Projective field: Galois closure of 4.2.475.1 Artin image: $\SD_{16}$ Artin field: Galois closure of 8.2.107171875.1

Embedding invariants

 Embedding label 151.2 Root $$-1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 475.151 Dual form 475.1.c.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.41421i q^{2} +1.41421i q^{3} -1.00000 q^{4} -2.00000 q^{6} -1.00000 q^{9} +O(q^{10})$$ $$q+1.41421i q^{2} +1.41421i q^{3} -1.00000 q^{4} -2.00000 q^{6} -1.00000 q^{9} -1.41421i q^{12} -1.41421i q^{13} -1.00000 q^{16} -1.41421i q^{18} +1.00000 q^{19} +2.00000 q^{26} -1.41421i q^{32} +1.00000 q^{36} -1.41421i q^{37} +1.41421i q^{38} +2.00000 q^{39} -1.41421i q^{48} -1.00000 q^{49} +1.41421i q^{52} +1.41421i q^{53} +1.41421i q^{57} +1.00000 q^{64} +1.41421i q^{67} +2.00000 q^{74} -1.00000 q^{76} +2.82843i q^{78} -1.00000 q^{81} +2.00000 q^{96} -1.41421i q^{97} -1.41421i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{4} - 4 q^{6} - 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^4 - 4 * q^6 - 2 * q^9 $$2 q - 2 q^{4} - 4 q^{6} - 2 q^{9} - 2 q^{16} + 2 q^{19} + 4 q^{26} + 2 q^{36} + 4 q^{39} - 2 q^{49} + 2 q^{64} + 4 q^{74} - 2 q^{76} - 2 q^{81} + 4 q^{96}+O(q^{100})$$ 2 * q - 2 * q^4 - 4 * q^6 - 2 * q^9 - 2 * q^16 + 2 * q^19 + 4 * q^26 + 2 * q^36 + 4 * q^39 - 2 * q^49 + 2 * q^64 + 4 * q^74 - 2 * q^76 - 2 * q^81 + 4 * q^96

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$-1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$3$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$4$$ −1.00000 −1.00000
$$5$$ 0 0
$$6$$ −2.00000 −2.00000
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ − 1.41421i − 1.41421i
$$13$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.00000 −1.00000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ − 1.41421i − 1.41421i
$$19$$ 1.00000 1.00000
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 2.00000 2.00000
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ − 1.41421i − 1.41421i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$38$$ 1.41421i 1.41421i
$$39$$ 2.00000 2.00000
$$40$$ 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 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ − 1.41421i − 1.41421i
$$49$$ −1.00000 −1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 1.41421i 1.41421i
$$53$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.41421i 1.41421i
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 2.00000 2.00000
$$75$$ 0 0
$$76$$ −1.00000 −1.00000
$$77$$ 0 0
$$78$$ 2.82843i 2.82843i
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 2.00000 2.00000
$$97$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$98$$ − 1.41421i − 1.41421i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −2.00000 −2.00000
$$107$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−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
$$113$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$114$$ −2.00000 −2.00000
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 1.41421i 1.41421i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.00000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 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
$$147$$ − 1.41421i − 1.41421i
$$148$$ 1.41421i 1.41421i
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ −2.00000 −2.00000
$$160$$ 0 0
$$161$$ 0 0
$$162$$ − 1.41421i − 1.41421i
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
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
$$173$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$192$$ 1.41421i 1.41421i
$$193$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$194$$ 2.00000 2.00000
$$195$$ 0 0
$$196$$ 1.00000 1.00000
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$200$$ 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
$$208$$ 1.41421i 1.41421i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ − 1.41421i − 1.41421i
$$213$$ 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
$$222$$ 2.82843i 2.82843i
$$223$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 2.00000 2.00000
$$227$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$228$$ − 1.41421i − 1.41421i
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ −2.00000 −2.00000
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ − 1.41421i − 1.41421i
$$243$$ − 1.41421i − 1.41421i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ − 1.41421i − 1.41421i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −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
$$257$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 2.82843i 2.82843i
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ − 1.41421i − 1.41421i
$$269$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.41421i 1.41421i
$$289$$ −1.00000 −1.00000
$$290$$ 0 0
$$291$$ 2.00000 2.00000
$$292$$ 0 0
$$293$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$294$$ 2.00000 2.00000
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −1.00000 −1.00000
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$318$$ − 2.82843i − 2.82843i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −2.00000 −2.00000
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ 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
$$333$$ 1.41421i 1.41421i
$$334$$ 2.00000 2.00000
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$338$$ − 1.41421i − 1.41421i
$$339$$ 2.00000 2.00000
$$340$$ 0 0
$$341$$ 0 0
$$342$$ − 1.41421i − 1.41421i
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 2.00000 2.00000
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 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
$$363$$ − 1.41421i − 1.41421i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$374$$ 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
$$381$$ 2.00000 2.00000
$$382$$ − 2.82843i − 2.82843i
$$383$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.00000 −2.00000
$$387$$ 0 0
$$388$$ 1.41421i 1.41421i
$$389$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 2.82843i 2.82843i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 2.82843i 2.82843i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ − 2.82843i − 2.82843i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 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
$$412$$ 1.41421i 1.41421i
$$413$$ 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 $$\pi$$
−1.00000 $$\pi$$
$$420$$ 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
$$428$$ − 1.41421i − 1.41421i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$434$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ −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 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 1.41421i 1.41421i
$$453$$ 0 0
$$454$$ −2.00000 −2.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ − 1.41421i − 1.41421i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ − 1.41421i − 1.41421i
$$478$$ − 2.82843i − 2.82843i
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −2.00000 −2.00000
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000 1.00000
$$485$$ 0 0
$$486$$ 2.00000 2.00000
$$487$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −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 $$0.5\pi$$
$$500$$ 0 0
$$501$$ 2.00000 2.00000
$$502$$ − 2.82843i − 2.82843i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ − 1.41421i − 1.41421i
$$508$$ 1.41421i 1.41421i
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.41421i 1.41421i
$$513$$ 0 0
$$514$$ 2.00000 2.00000
$$515$$ 0 0
$$516$$ 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
$$523$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$524$$ −2.00000 −2.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −1.00000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 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
$$547$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
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
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ − 2.82843i − 2.82843i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1.00000 −1.00000
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ − 1.41421i − 1.41421i
$$579$$ −2.00000 −2.00000
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 2.82843i 2.82843i
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −2.00000 −2.00000
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 1.41421i 1.41421i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.41421i 1.41421i
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 2.82843i 2.82843i
$$598$$ 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
$$603$$ − 1.41421i − 1.41421i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$608$$ − 1.41421i − 1.41421i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ −2.00000 −2.00000
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 2.82843i 2.82843i
$$619$$ 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
$$625$$ 0 0
$$626$$ 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
$$635$$ 0 0
$$636$$ 2.00000 2.00000
$$637$$ 1.41421i 1.41421i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ − 2.82843i − 2.82843i
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 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
$$668$$ 1.41421i 1.41421i
$$669$$ −2.00000 −2.00000
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$674$$ −2.00000 −2.00000
$$675$$ 0 0
$$676$$ 1.00000 1.00000
$$677$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$678$$ 2.82843i 2.82843i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −2.00000 −2.00000
$$682$$ 0 0
$$683$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$684$$ 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 $$0.5\pi$$
$$692$$ 1.41421i 1.41421i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 2.82843i 2.82843i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ − 1.41421i − 1.41421i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ − 2.82843i − 2.82843i
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.41421i 1.41421i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 2.00000 2.00000
$$727$$ 0 0 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
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$740$$ 0 0
$$741$$ 2.00000 2.00000
$$742$$ 0 0
$$743$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −2.00000 −2.00000
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ − 2.82843i − 2.82843i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 2.82843i 2.82843i
$$763$$ 0 0
$$764$$ 2.00000 2.00000
$$765$$ 0 0
$$766$$ 2.00000 2.00000
$$767$$ 0 0
$$768$$ 1.41421i 1.41421i
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ 2.00000 2.00000
$$772$$ − 1.41421i − 1.41421i
$$773$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ − 2.82843i − 2.82843i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 1.00000
$$785$$ 0 0
$$786$$ −4.00000 −4.00000
$$787$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
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
$$795$$ 0 0
$$796$$ −2.00000 −2.00000
$$797$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 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 $$0$$
1.00000 $$0$$
$$810$$ 0 0
$$811$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
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
$$832$$ − 1.41421i − 1.41421i
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ − 2.82843i − 2.82843i
$$839$$ 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
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ − 1.41421i − 1.41421i
$$849$$ 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
$$857$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$858$$ 0 0
$$859$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 2.00000 2.00000
$$867$$ − 1.41421i − 1.41421i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 2.00000 2.00000
$$872$$ 0 0
$$873$$ 1.41421i 1.41421i
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
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 $$0.5\pi$$
$$882$$ 1.41421i 1.41421i
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ − 1.41421i − 1.41421i
$$893$$ 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
$$907$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$908$$ − 1.41421i − 1.41421i
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ − 1.41421i − 1.41421i
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ −2.00000 −2.00000
$$922$$ 2.82843i 2.82843i
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 1.41421i 1.41421i
$$928$$ 0 0
$$929$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$930$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ −2.00000 −2.00000
$$952$$ 0 0
$$953$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$954$$ 2.00000 2.00000
$$955$$ 0 0
$$956$$ 2.00000 2.00000
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ − 2.82843i − 2.82843i
$$963$$ − 1.41421i − 1.41421i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 1.41421i 1.41421i
$$973$$ 0 0
$$974$$ −2.00000 −2.00000
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ − 2.82843i − 2.82843i
$$983$$ − 1.41421i − 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 1.41421i 1.41421i
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 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 475.1.c.b.151.2 2
5.2 odd 4 95.1.d.b.94.1 2
5.3 odd 4 95.1.d.b.94.2 yes 2
5.4 even 2 inner 475.1.c.b.151.1 2
15.2 even 4 855.1.g.c.379.2 2
15.8 even 4 855.1.g.c.379.1 2
19.18 odd 2 inner 475.1.c.b.151.1 2
20.3 even 4 1520.1.m.b.1329.2 2
20.7 even 4 1520.1.m.b.1329.1 2
95.2 even 36 1805.1.o.b.984.1 12
95.3 even 36 1805.1.o.b.694.1 12
95.7 odd 12 1805.1.h.b.654.2 4
95.8 even 12 1805.1.h.b.69.2 4
95.12 even 12 1805.1.h.b.654.1 4
95.13 even 36 1805.1.o.b.1199.1 12
95.17 odd 36 1805.1.o.b.984.2 12
95.18 even 4 95.1.d.b.94.1 2
95.22 even 36 1805.1.o.b.694.2 12
95.23 odd 36 1805.1.o.b.1029.2 12
95.27 even 12 1805.1.h.b.69.1 4
95.28 odd 36 1805.1.o.b.299.1 12
95.32 even 36 1805.1.o.b.1199.2 12
95.33 even 36 1805.1.o.b.849.1 12
95.37 even 4 95.1.d.b.94.2 yes 2
95.42 odd 36 1805.1.o.b.1029.1 12
95.43 odd 36 1805.1.o.b.849.2 12
95.47 odd 36 1805.1.o.b.299.2 12
95.48 even 36 1805.1.o.b.299.2 12
95.52 even 36 1805.1.o.b.849.2 12
95.53 even 36 1805.1.o.b.1029.1 12
95.62 odd 36 1805.1.o.b.849.1 12
95.63 odd 36 1805.1.o.b.1199.2 12
95.67 even 36 1805.1.o.b.299.1 12
95.68 odd 12 1805.1.h.b.69.1 4
95.72 even 36 1805.1.o.b.1029.2 12
95.73 odd 36 1805.1.o.b.694.2 12
95.78 even 36 1805.1.o.b.984.2 12
95.82 odd 36 1805.1.o.b.1199.1 12
95.83 odd 12 1805.1.h.b.654.1 4
95.87 odd 12 1805.1.h.b.69.2 4
95.88 even 12 1805.1.h.b.654.2 4
95.92 odd 36 1805.1.o.b.694.1 12
95.93 odd 36 1805.1.o.b.984.1 12
95.94 odd 2 CM 475.1.c.b.151.2 2
285.113 odd 4 855.1.g.c.379.2 2
285.227 odd 4 855.1.g.c.379.1 2
380.227 odd 4 1520.1.m.b.1329.2 2
380.303 odd 4 1520.1.m.b.1329.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
95.1.d.b.94.1 2 5.2 odd 4
95.1.d.b.94.1 2 95.18 even 4
95.1.d.b.94.2 yes 2 5.3 odd 4
95.1.d.b.94.2 yes 2 95.37 even 4
475.1.c.b.151.1 2 5.4 even 2 inner
475.1.c.b.151.1 2 19.18 odd 2 inner
475.1.c.b.151.2 2 1.1 even 1 trivial
475.1.c.b.151.2 2 95.94 odd 2 CM
855.1.g.c.379.1 2 15.8 even 4
855.1.g.c.379.1 2 285.227 odd 4
855.1.g.c.379.2 2 15.2 even 4
855.1.g.c.379.2 2 285.113 odd 4
1520.1.m.b.1329.1 2 20.7 even 4
1520.1.m.b.1329.1 2 380.303 odd 4
1520.1.m.b.1329.2 2 20.3 even 4
1520.1.m.b.1329.2 2 380.227 odd 4
1805.1.h.b.69.1 4 95.27 even 12
1805.1.h.b.69.1 4 95.68 odd 12
1805.1.h.b.69.2 4 95.8 even 12
1805.1.h.b.69.2 4 95.87 odd 12
1805.1.h.b.654.1 4 95.12 even 12
1805.1.h.b.654.1 4 95.83 odd 12
1805.1.h.b.654.2 4 95.7 odd 12
1805.1.h.b.654.2 4 95.88 even 12
1805.1.o.b.299.1 12 95.28 odd 36
1805.1.o.b.299.1 12 95.67 even 36
1805.1.o.b.299.2 12 95.47 odd 36
1805.1.o.b.299.2 12 95.48 even 36
1805.1.o.b.694.1 12 95.3 even 36
1805.1.o.b.694.1 12 95.92 odd 36
1805.1.o.b.694.2 12 95.22 even 36
1805.1.o.b.694.2 12 95.73 odd 36
1805.1.o.b.849.1 12 95.33 even 36
1805.1.o.b.849.1 12 95.62 odd 36
1805.1.o.b.849.2 12 95.43 odd 36
1805.1.o.b.849.2 12 95.52 even 36
1805.1.o.b.984.1 12 95.2 even 36
1805.1.o.b.984.1 12 95.93 odd 36
1805.1.o.b.984.2 12 95.17 odd 36
1805.1.o.b.984.2 12 95.78 even 36
1805.1.o.b.1029.1 12 95.42 odd 36
1805.1.o.b.1029.1 12 95.53 even 36
1805.1.o.b.1029.2 12 95.23 odd 36
1805.1.o.b.1029.2 12 95.72 even 36
1805.1.o.b.1199.1 12 95.13 even 36
1805.1.o.b.1199.1 12 95.82 odd 36
1805.1.o.b.1199.2 12 95.32 even 36
1805.1.o.b.1199.2 12 95.63 odd 36