Properties

 Label 799.1.c.c.798.2 Level $799$ Weight $1$ Character 799.798 Self dual yes Analytic conductor $0.399$ Analytic rank $0$ Dimension $4$ Projective image $D_{8}$ CM discriminant -799 Inner twists $4$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,1,Mod(798,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, 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("799.798");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$799 = 17 \cdot 47$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 799.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: yes Analytic conductor: $$0.398752945094$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{16})^+$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 4x^{2} + 2$$ x^4 - 4*x^2 + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{8}$$ Projective field: Galois closure of 8.2.8671400783.1

Embedding invariants

 Embedding label 798.2 Root $$-1.84776$$ of defining polynomial Character $$\chi$$ $$=$$ 799.798

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.41421 q^{2} +1.00000 q^{4} +1.84776 q^{5} +1.00000 q^{9} +O(q^{10})$$ $$q-1.41421 q^{2} +1.00000 q^{4} +1.84776 q^{5} +1.00000 q^{9} -2.61313 q^{10} +0.765367 q^{11} -1.00000 q^{16} -1.00000 q^{17} -1.41421 q^{18} +1.84776 q^{20} -1.08239 q^{22} -1.84776 q^{23} +2.41421 q^{25} -0.765367 q^{29} -0.765367 q^{31} +1.41421 q^{32} +1.41421 q^{34} +1.00000 q^{36} -1.84776 q^{41} +0.765367 q^{44} +1.84776 q^{45} +2.61313 q^{46} -1.00000 q^{47} +1.00000 q^{49} -3.41421 q^{50} +1.41421 q^{55} +1.08239 q^{58} +1.41421 q^{59} +1.08239 q^{62} -1.00000 q^{64} -1.00000 q^{68} +0.765367 q^{73} -1.84776 q^{80} +1.00000 q^{81} +2.61313 q^{82} -1.84776 q^{85} -2.61313 q^{90} -1.84776 q^{92} +1.41421 q^{94} -1.41421 q^{98} +0.765367 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{4} + 4 q^{9}+O(q^{10})$$ 4 * q + 4 * q^4 + 4 * q^9 $$4 q + 4 q^{4} + 4 q^{9} - 4 q^{16} - 4 q^{17} + 4 q^{25} + 4 q^{36} - 4 q^{47} + 4 q^{49} - 8 q^{50} - 4 q^{64} - 4 q^{68} + 4 q^{81}+O(q^{100})$$ 4 * q + 4 * q^4 + 4 * q^9 - 4 * q^16 - 4 * q^17 + 4 * q^25 + 4 * q^36 - 4 * q^47 + 4 * q^49 - 8 * q^50 - 4 * q^64 - 4 * q^68 + 4 * q^81

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$$.

 $$n$$ $$52$$ $$377$$ $$\chi(n)$$ $$-1$$ $$-1$$

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 $$0.750000\pi$$
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ 1.00000 1.00000
$$10$$ −2.61313 −2.61313
$$11$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.00000 −1.00000
$$17$$ −1.00000 −1.00000
$$18$$ −1.41421 −1.41421
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 1.84776 1.84776
$$21$$ 0 0
$$22$$ −1.08239 −1.08239
$$23$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$24$$ 0 0
$$25$$ 2.41421 2.41421
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$30$$ 0 0
$$31$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$32$$ 1.41421 1.41421
$$33$$ 0 0
$$34$$ 1.41421 1.41421
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0.765367 0.765367
$$45$$ 1.84776 1.84776
$$46$$ 2.61313 2.61313
$$47$$ −1.00000 −1.00000
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ −3.41421 −3.41421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 1.41421 1.41421
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.08239 1.08239
$$59$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 1.08239 1.08239
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ −1.00000 −1.00000
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ −1.84776 −1.84776
$$81$$ 1.00000 1.00000
$$82$$ 2.61313 2.61313
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −1.84776 −1.84776
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ −2.61313 −2.61313
$$91$$ 0 0
$$92$$ −1.84776 −1.84776
$$93$$ 0 0
$$94$$ 1.41421 1.41421
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ −1.41421 −1.41421
$$99$$ 0.765367 0.765367
$$100$$ 2.41421 2.41421
$$101$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$102$$ 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
$$106$$ 0 0
$$107$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$108$$ 0 0
$$109$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$110$$ −2.00000 −2.00000
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$114$$ 0 0
$$115$$ −3.41421 −3.41421
$$116$$ −0.765367 −0.765367
$$117$$ 0 0
$$118$$ −2.00000 −2.00000
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.414214 −0.414214
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −0.765367 −0.765367
$$125$$ 2.61313 2.61313
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −1.00000 −1.00000
$$145$$ −1.41421 −1.41421
$$146$$ −1.08239 −1.08239
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ −1.00000 −1.00000
$$154$$ 0 0
$$155$$ −1.41421 −1.41421
$$156$$ 0 0
$$157$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 2.61313 2.61313
$$161$$ 0 0
$$162$$ −1.41421 −1.41421
$$163$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$164$$ −1.84776 −1.84776
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 2.61313 2.61313
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.765367 −0.765367
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 1.84776 1.84776
$$181$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −0.765367 −0.765367
$$188$$ −1.00000 −1.00000
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$192$$ 0 0
$$193$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 1.00000 1.00000
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ −1.08239 −1.08239
$$199$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 2.00000 2.00000
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −3.41421 −3.41421
$$206$$ 2.00000 2.00000
$$207$$ −1.84776 −1.84776
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 1.08239 1.08239
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −1.08239 −1.08239
$$219$$ 0 0
$$220$$ 1.41421 1.41421
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 2.41421 2.41421
$$226$$ 1.08239 1.08239
$$227$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 4.82843 4.82843
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$234$$ 0 0
$$235$$ −1.84776 −1.84776
$$236$$ 1.41421 1.41421
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0.585786 0.585786
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1.84776 1.84776
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −3.69552 −3.69552
$$251$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$252$$ 0 0
$$253$$ −1.41421 −1.41421
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −0.765367 −0.765367
$$262$$ 0 0
$$263$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$272$$ 1.00000 1.00000
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.84776 1.84776
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 2.61313 2.61313
$$279$$ −0.765367 −0.765367
$$280$$ 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
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.41421 1.41421
$$289$$ 1.00000 1.00000
$$290$$ 2.00000 2.00000
$$291$$ 0 0
$$292$$ 0.765367 0.765367
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 2.61313 2.61313
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −2.00000 −2.00000
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 1.41421 1.41421
$$307$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 2.00000 2.00000
$$311$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$312$$ 0 0
$$313$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$314$$ −2.00000 −2.00000
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$318$$ 0 0
$$319$$ −0.585786 −0.585786
$$320$$ −1.84776 −1.84776
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ −2.61313 −2.61313
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −2.61313 −2.61313
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −1.41421 −1.41421
$$339$$ 0 0
$$340$$ −1.84776 −1.84776
$$341$$ −0.585786 −0.585786
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.08239 1.08239
$$353$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 2.61313 2.61313
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.41421 1.41421
$$366$$ 0 0
$$367$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$368$$ 1.84776 1.84776
$$369$$ −1.84776 −1.84776
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 1.08239 1.08239
$$375$$ 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
$$382$$ 2.00000 2.00000
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 1.08239 1.08239
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 1.84776 1.84776
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.765367 0.765367
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ −2.61313 −2.61313
$$399$$ 0 0
$$400$$ −2.41421 −2.41421
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −1.41421 −1.41421
$$405$$ 1.84776 1.84776
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 4.82843 4.82843
$$411$$ 0 0
$$412$$ −1.41421 −1.41421
$$413$$ 0 0
$$414$$ 2.61313 2.61313
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ −2.61313 −2.61313
$$423$$ −1.00000 −1.00000
$$424$$ 0 0
$$425$$ −2.41421 −2.41421
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.765367 −0.765367
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0.765367 0.765367
$$437$$ 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 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$450$$ −3.41421 −3.41421
$$451$$ −1.41421 −1.41421
$$452$$ −0.765367 −0.765367
$$453$$ 0 0
$$454$$ 2.61313 2.61313
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −3.41421 −3.41421
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0.765367 0.765367
$$465$$ 0 0
$$466$$ −1.08239 −1.08239
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 2.61313 2.61313
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −0.414214 −0.414214
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −2.61313 −2.61313
$$491$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0.765367 0.765367
$$494$$ 0 0
$$495$$ 1.41421 1.41421
$$496$$ 0.765367 0.765367
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$500$$ 2.61313 2.61313
$$501$$ 0 0
$$502$$ −2.00000 −2.00000
$$503$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$504$$ 0 0
$$505$$ −2.61313 −2.61313
$$506$$ 2.00000 2.00000
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.41421 −1.41421
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −2.61313 −2.61313
$$516$$ 0 0
$$517$$ −0.765367 −0.765367
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 1.08239 1.08239
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −2.00000 −2.00000
$$527$$ 0.765367 0.765367
$$528$$ 0 0
$$529$$ 2.41421 2.41421
$$530$$ 0 0
$$531$$ 1.41421 1.41421
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −1.41421 −1.41421
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0.765367 0.765367
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 2.00000 2.00000
$$543$$ 0 0
$$544$$ −1.41421 −1.41421
$$545$$ 1.41421 1.41421
$$546$$ 0 0
$$547$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ −2.61313 −2.61313
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −1.84776 −1.84776
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 1.08239 1.08239
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ −1.41421 −1.41421
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −4.46088 −4.46088
$$576$$ −1.00000 −1.00000
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ −1.41421 −1.41421
$$579$$ 0 0
$$580$$ −1.41421 −1.41421
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −3.69552 −3.69552
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 1.41421 1.41421
$$597$$ 0 0
$$598$$ 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
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −0.765367 −0.765367
$$606$$ 0 0
$$607$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −1.00000 −1.00000
$$613$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$614$$ −2.00000 −2.00000
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ −1.41421 −1.41421
$$621$$ 0 0
$$622$$ −1.08239 −1.08239
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 2.41421 2.41421
$$626$$ 2.61313 2.61313
$$627$$ 0 0
$$628$$ 1.41421 1.41421
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 2.61313 2.61313
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0.828427 0.828427
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$648$$ 0 0
$$649$$ 1.08239 1.08239
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 1.84776 1.84776
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 1.84776 1.84776
$$657$$ 0.765367 0.765367
$$658$$ 0 0
$$659$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$662$$ 2.00000 2.00000
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.41421 1.41421
$$668$$ 1.84776 1.84776
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 1.00000 1.00000
$$677$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0.828427 0.828427
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −3.41421 −3.41421
$$696$$ 0 0
$$697$$ 1.84776 1.84776
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −0.765367 −0.765367
$$705$$ 0 0
$$706$$ 2.00000 2.00000
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.41421 1.41421
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ −1.84776 −1.84776
$$721$$ 0 0
$$722$$ −1.41421 −1.41421
$$723$$ 0 0
$$724$$ −1.84776 −1.84776
$$725$$ −1.84776 −1.84776
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ −2.00000 −2.00000
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$734$$ −1.08239 −1.08239
$$735$$ 0 0
$$736$$ −2.61313 −2.61313
$$737$$ 0 0
$$738$$ 2.61313 2.61313
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$744$$ 0 0
$$745$$ 2.61313 2.61313
$$746$$ 0 0
$$747$$ 0 0
$$748$$ −0.765367 −0.765367
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$752$$ 1.00000 1.00000
$$753$$ 0 0
$$754$$ 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
$$761$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −1.41421 −1.41421
$$765$$ −1.84776 −1.84776
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −0.765367 −0.765367
$$773$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$774$$ 0 0
$$775$$ −1.84776 −1.84776
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −2.61313 −2.61313
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ 2.61313 2.61313
$$786$$ 0 0
$$787$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 1.84776 1.84776
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 1.00000 1.00000
$$800$$ 3.41421 3.41421
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0.585786 0.585786
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$810$$ −2.61313 −2.61313
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 3.41421 3.41421
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ −3.41421 −3.41421
$$821$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$822$$ 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 $$\pi$$
$$828$$ −1.84776 −1.84776
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1.00000 −1.00000
$$834$$ 0 0
$$835$$ 3.41421 3.41421
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −2.61313 −2.61313
$$839$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$840$$ 0 0
$$841$$ −0.414214 −0.414214
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 1.84776 1.84776
$$845$$ 1.84776 1.84776
$$846$$ 1.41421 1.41421
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 3.41421 3.41421
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ −1.41421 −1.41421
$$881$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$882$$ −1.41421 −1.41421
$$883$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0.765367 0.765367
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 2.61313 2.61313
$$899$$ 0.585786 0.585786
$$900$$ 2.41421 2.41421
$$901$$ 0 0
$$902$$ 2.00000 2.00000
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −3.41421 −3.41421
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ −1.84776 −1.84776
$$909$$ −1.41421 −1.41421
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −1.41421 −1.41421
$$928$$ −1.08239 −1.08239
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0.765367 0.765367
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −1.41421 −1.41421
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ −1.84776 −1.84776
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 3.41421 3.41421
$$944$$ −1.41421 −1.41421
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ −2.61313 −2.61313
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −0.414214 −0.414214
$$962$$ 0 0
$$963$$ −0.765367 −0.765367
$$964$$ 0 0
$$965$$ −1.41421 −1.41421
$$966$$ 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 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 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
$$980$$ 1.84776 1.84776
$$981$$ 0.765367 0.765367
$$982$$ 2.82843 2.82843
$$983$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −1.08239 −1.08239
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ −2.00000 −2.00000
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ −1.08239 −1.08239
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 3.41421 3.41421
$$996$$ 0 0
$$997$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$998$$ 2.61313 2.61313
$$999$$ 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 799.1.c.c.798.2 yes 4
17.16 even 2 inner 799.1.c.c.798.1 4
47.46 odd 2 inner 799.1.c.c.798.1 4
799.798 odd 2 CM 799.1.c.c.798.2 yes 4

By twisted newform
Twist Min Dim Char Parity Ord Type
799.1.c.c.798.1 4 17.16 even 2 inner
799.1.c.c.798.1 4 47.46 odd 2 inner
799.1.c.c.798.2 yes 4 1.1 even 1 trivial
799.1.c.c.798.2 yes 4 799.798 odd 2 CM