# Properties

 Label 735.1.f.c.344.1 Level $735$ Weight $1$ Character 735.344 Self dual yes Analytic conductor $0.367$ Analytic rank $0$ Dimension $2$ Projective image $D_{4}$ CM discriminant -15 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,1,Mod(344,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("735.344");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 735.f (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: $$0.366812784285$$ 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 4.2.15435.1 Artin image: $D_8$ Artin field: Galois closure of 8.2.8338372875.1

## Embedding invariants

 Embedding label 344.1 Root $$1.41421$$ of defining polynomial Character $$\chi$$ $$=$$ 735.344

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.41421 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.41421 q^{6} +1.00000 q^{9} +O(q^{10})$$ $$q-1.41421 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.41421 q^{6} +1.00000 q^{9} -1.41421 q^{10} -1.00000 q^{12} -1.00000 q^{15} -1.00000 q^{16} -1.41421 q^{18} -1.41421 q^{19} +1.00000 q^{20} +1.41421 q^{23} +1.00000 q^{25} -1.00000 q^{27} +1.41421 q^{30} +1.41421 q^{31} +1.41421 q^{32} +1.00000 q^{36} +2.00000 q^{38} +1.00000 q^{45} -2.00000 q^{46} +1.00000 q^{48} -1.41421 q^{50} +1.41421 q^{53} +1.41421 q^{54} +1.41421 q^{57} -1.00000 q^{60} +1.41421 q^{61} -2.00000 q^{62} -1.00000 q^{64} -1.41421 q^{69} -1.00000 q^{75} -1.41421 q^{76} -1.00000 q^{80} +1.00000 q^{81} -1.41421 q^{90} +1.41421 q^{92} -1.41421 q^{93} -1.41421 q^{95} -1.41421 q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^9 $$2 q - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{9} - 2 q^{12} - 2 q^{15} - 2 q^{16} + 2 q^{20} + 2 q^{25} - 2 q^{27} + 2 q^{36} + 4 q^{38} + 2 q^{45} - 4 q^{46} + 2 q^{48} - 2 q^{60} - 4 q^{62} - 2 q^{64} - 2 q^{75} - 2 q^{80} + 2 q^{81}+O(q^{100})$$ 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^9 - 2 * q^12 - 2 * q^15 - 2 * q^16 + 2 * q^20 + 2 * q^25 - 2 * q^27 + 2 * q^36 + 4 * q^38 + 2 * q^45 - 4 * q^46 + 2 * q^48 - 2 * q^60 - 4 * q^62 - 2 * q^64 - 2 * q^75 - 2 * q^80 + 2 * q^81

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$$.

 $$n$$ $$346$$ $$442$$ $$491$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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 $$0.750000\pi$$
$$3$$ −1.00000 −1.00000
$$4$$ 1.00000 1.00000
$$5$$ 1.00000 1.00000
$$6$$ 1.41421 1.41421
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 1.00000
$$10$$ −1.41421 −1.41421
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ −1.00000 −1.00000
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −1.00000
$$16$$ −1.00000 −1.00000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ −1.41421 −1.41421
$$19$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$20$$ 1.00000 1.00000
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$24$$ 0 0
$$25$$ 1.00000 1.00000
$$26$$ 0 0
$$27$$ −1.00000 −1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 1.41421 1.41421
$$31$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$32$$ 1.41421 1.41421
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 2.00000 2.00000
$$39$$ 0 0
$$40$$ 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
$$46$$ −2.00000 −2.00000
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 1.00000 1.00000
$$49$$ 0 0
$$50$$ −1.41421 −1.41421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$54$$ 1.41421 1.41421
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.41421 1.41421
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ −1.00000 −1.00000
$$61$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$62$$ −2.00000 −2.00000
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ −1.41421 −1.41421
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ −1.00000 −1.00000
$$76$$ −1.41421 −1.41421
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −1.00000 −1.00000
$$81$$ 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 $$\pi$$
$$90$$ −1.41421 −1.41421
$$91$$ 0 0
$$92$$ 1.41421 1.41421
$$93$$ −1.41421 −1.41421
$$94$$ 0 0
$$95$$ −1.41421 −1.41421
$$96$$ −1.41421 −1.41421
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1.00000 1.00000
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 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 $$0.750000\pi$$
$$108$$ −1.00000 −1.00000
$$109$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 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
$$115$$ 1.41421 1.41421
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ −2.00000 −2.00000
$$123$$ 0 0
$$124$$ 1.41421 1.41421
$$125$$ 1.00000 1.00000
$$126$$ 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
$$135$$ −1.00000 −1.00000
$$136$$ 0 0
$$137$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$138$$ 2.00000 2.00000
$$139$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 1.41421 1.41421
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1.41421 1.41421
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ −1.41421 −1.41421
$$160$$ 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
$$167$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ −1.41421 −1.41421
$$172$$ 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 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 1.00000 1.00000
$$181$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$182$$ 0 0
$$183$$ −1.41421 −1.41421
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 2.00000 2.00000
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 2.00000 2.00000
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 1.00000 1.00000
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$198$$ 0 0
$$199$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 1.41421 1.41421
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−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
$$218$$ 2.82843 2.82843
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 1.00000 1.00000
$$226$$ 2.00000 2.00000
$$227$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$228$$ 1.41421 1.41421
$$229$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$230$$ −2.00000 −2.00000
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 1.00000 1.00000
$$241$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$242$$ −1.41421 −1.41421
$$243$$ −1.00000 −1.00000
$$244$$ 1.41421 1.41421
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −1.41421 −1.41421
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$264$$ 0 0
$$265$$ 1.41421 1.41421
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 1.41421 1.41421
$$271$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 2.00000 2.00000
$$275$$ 0 0
$$276$$ −1.41421 −1.41421
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ −2.00000 −2.00000
$$279$$ 1.41421 1.41421
$$280$$ 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
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −1.00000 −1.00000
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 1.41421 1.41421
$$305$$ 1.41421 1.41421
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −2.00000 −2.00000
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 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 $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$318$$ 2.00000 2.00000
$$319$$ 0 0
$$320$$ −1.00000 −1.00000
$$321$$ 1.41421 1.41421
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 2.00000 2.00000
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −2.82843 −2.82843
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −1.41421 −1.41421
$$339$$ 1.41421 1.41421
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 2.00000 2.00000
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −1.41421 −1.41421
$$346$$ 0 0
$$347$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$348$$ 0 0
$$349$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$354$$ 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
$$362$$ 2.00000 2.00000
$$363$$ −1.00000 −1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 2.00000 2.00000
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ −1.41421 −1.41421
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −1.41421 −1.41421
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ −1.00000 −1.00000
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ −1.41421 −1.41421
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 2.00000 2.00000
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 2.00000 2.00000
$$399$$ 0 0
$$400$$ −1.00000 −1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 1.00000 1.00000
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$410$$ 0 0
$$411$$ 1.41421 1.41421
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −2.00000 −2.00000
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −1.41421 −1.41421
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 2.82843 2.82843
$$423$$ 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 $$\pi$$
$$432$$ 1.00000 1.00000
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −2.00000 −2.00000
$$437$$ −2.00000 −2.00000
$$438$$ 0 0
$$439$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 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
$$454$$ −2.82843 −2.82843
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ −2.00000 −2.00000
$$459$$ 0 0
$$460$$ 1.41421 1.41421
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ −1.41421 −1.41421
$$466$$ −2.00000 −2.00000
$$467$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −1.41421 −1.41421
$$476$$ 0 0
$$477$$ 1.41421 1.41421
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ −1.41421 −1.41421
$$481$$ 0 0
$$482$$ 2.00000 2.00000
$$483$$ 0 0
$$484$$ 1.00000 1.00000
$$485$$ 0 0
$$486$$ 1.41421 1.41421
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 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 0
$$495$$ 0 0
$$496$$ −1.41421 −1.41421
$$497$$ 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
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −1.00000 −1.00000
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.41421 −1.41421
$$513$$ 1.41421 1.41421
$$514$$ 2.82843 2.82843
$$515$$ 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 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 2.00000 2.00000
$$527$$ 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
$$540$$ −1.00000 −1.00000
$$541$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$542$$ 2.00000 2.00000
$$543$$ 1.41421 1.41421
$$544$$ 0 0
$$545$$ −2.00000 −2.00000
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ −1.41421 −1.41421
$$549$$ 1.41421 1.41421
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 1.41421 1.41421
$$557$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$558$$ −2.00000 −2.00000
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 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
$$571$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.41421 1.41421
$$576$$ −1.00000 −1.00000
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 1.41421 1.41421
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 2.82843 2.82843
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ −2.00000 −2.00000
$$590$$ 0 0
$$591$$ 1.41421 1.41421
$$592$$ 0 0
$$593$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 1.41421 1.41421
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 1.00000 1.00000
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ −2.00000 −2.00000
$$609$$ 0 0
$$610$$ −2.00000 −2.00000
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$618$$ 0 0
$$619$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$620$$ 1.41421 1.41421
$$621$$ −1.41421 −1.41421
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 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
$$633$$ 2.00000 2.00000
$$634$$ −2.00000 −2.00000
$$635$$ 0 0
$$636$$ −1.41421 −1.41421
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ −2.00000 −2.00000
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$654$$ −2.82843 −2.82843
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$662$$ 2.82843 2.82843
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 2.00000 2.00000
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −1.00000 −1.00000
$$676$$ 1.00000 1.00000
$$677$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$678$$ −2.00000 −2.00000
$$679$$ 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 $$0.250000\pi$$
$$684$$ −1.41421 −1.41421
$$685$$ −1.41421 −1.41421
$$686$$ 0 0
$$687$$ −1.41421 −1.41421
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 2.00000 2.00000
$$691$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −2.00000 −2.00000
$$695$$ 1.41421 1.41421
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 2.00000 2.00000
$$699$$ −1.41421 −1.41421
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 2.82843 2.82843
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2.00000 2.00000
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ −1.00000 −1.00000
$$721$$ 0 0
$$722$$ −1.41421 −1.41421
$$723$$ 1.41421 1.41421
$$724$$ −1.41421 −1.41421
$$725$$ 0 0
$$726$$ 1.41421 1.41421
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −1.41421 −1.41421
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 2.00000 2.00000
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 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
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 1.41421 1.41421
$$751$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$752$$ 0 0
$$753$$ 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
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −1.00000 −1.00000
$$769$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$770$$ 0 0
$$771$$ 2.00000 2.00000
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 1.41421 1.41421
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ −1.41421 −1.41421
$$789$$ 1.41421 1.41421
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −1.41421 −1.41421
$$796$$ −1.41421 −1.41421
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.41421 1.41421
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ −1.41421 −1.41421
$$811$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$812$$ 0 0
$$813$$ 1.41421 1.41421
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 2.00000 2.00000
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ −2.00000 −2.00000
$$823$$ 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 $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$828$$ 1.41421 1.41421
$$829$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 2.00000 2.00000
$$835$$ 2.00000 2.00000
$$836$$ 0 0
$$837$$ −1.41421 −1.41421
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ −2.00000 −2.00000
$$845$$ 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
$$855$$ −1.41421 −1.41421
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$864$$ −1.41421 −1.41421
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 1.00000 1.00000
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 2.82843 2.82843
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ −2.00000 −2.00000
$$879$$ 2.00000 2.00000
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 2.00000 2.00000
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 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
$$905$$ −1.41421 −1.41421
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ 2.00000 2.00000
$$909$$ 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
$$915$$ −1.41421 −1.41421
$$916$$ 1.41421 1.41421
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 2.00000 2.00000
$$931$$ 0 0
$$932$$ 1.41421 1.41421
$$933$$ 0 0
$$934$$ −2.82843 −2.82843
$$935$$ 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
$$947$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 2.00000 2.00000
$$951$$ −1.41421 −1.41421
$$952$$ 0 0
$$953$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$954$$ −2.00000 −2.00000
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 1.00000 1.00000
$$961$$ 1.00000 1.00000
$$962$$ 0 0
$$963$$ −1.41421 −1.41421
$$964$$ −1.41421 −1.41421
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ −1.00000 −1.00000
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ −1.41421 −1.41421
$$977$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −2.00000 −2.00000
$$982$$ 0 0
$$983$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ −1.41421 −1.41421
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$992$$ 2.00000 2.00000
$$993$$ 2.00000 2.00000
$$994$$ 0 0
$$995$$ −1.41421 −1.41421
$$996$$ 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 735.1.f.c.344.1 2
3.2 odd 2 735.1.f.d.344.2 yes 2
5.2 odd 4 3675.1.c.f.1226.2 4
5.3 odd 4 3675.1.c.f.1226.3 4
5.4 even 2 735.1.f.d.344.2 yes 2
7.2 even 3 735.1.o.d.704.2 4
7.3 odd 6 735.1.o.c.569.2 4
7.4 even 3 735.1.o.d.569.2 4
7.5 odd 6 735.1.o.c.704.2 4
7.6 odd 2 735.1.f.d.344.1 yes 2
15.2 even 4 3675.1.c.f.1226.3 4
15.8 even 4 3675.1.c.f.1226.2 4
15.14 odd 2 CM 735.1.f.c.344.1 2
21.2 odd 6 735.1.o.c.704.1 4
21.5 even 6 735.1.o.d.704.1 4
21.11 odd 6 735.1.o.c.569.1 4
21.17 even 6 735.1.o.d.569.1 4
21.20 even 2 inner 735.1.f.c.344.2 yes 2
35.2 odd 12 3675.1.u.f.851.1 8
35.3 even 12 3675.1.u.f.1451.2 8
35.4 even 6 735.1.o.c.569.1 4
35.9 even 6 735.1.o.c.704.1 4
35.12 even 12 3675.1.u.f.851.2 8
35.13 even 4 3675.1.c.f.1226.4 4
35.17 even 12 3675.1.u.f.1451.3 8
35.18 odd 12 3675.1.u.f.1451.1 8
35.19 odd 6 735.1.o.d.704.1 4
35.23 odd 12 3675.1.u.f.851.4 8
35.24 odd 6 735.1.o.d.569.1 4
35.27 even 4 3675.1.c.f.1226.1 4
35.32 odd 12 3675.1.u.f.1451.4 8
35.33 even 12 3675.1.u.f.851.3 8
35.34 odd 2 inner 735.1.f.c.344.2 yes 2
105.2 even 12 3675.1.u.f.851.4 8
105.17 odd 12 3675.1.u.f.1451.2 8
105.23 even 12 3675.1.u.f.851.1 8
105.32 even 12 3675.1.u.f.1451.1 8
105.38 odd 12 3675.1.u.f.1451.3 8
105.44 odd 6 735.1.o.d.704.2 4
105.47 odd 12 3675.1.u.f.851.3 8
105.53 even 12 3675.1.u.f.1451.4 8
105.59 even 6 735.1.o.c.569.2 4
105.62 odd 4 3675.1.c.f.1226.4 4
105.68 odd 12 3675.1.u.f.851.2 8
105.74 odd 6 735.1.o.d.569.2 4
105.83 odd 4 3675.1.c.f.1226.1 4
105.89 even 6 735.1.o.c.704.2 4
105.104 even 2 735.1.f.d.344.1 yes 2

By twisted newform
Twist Min Dim Char Parity Ord Type
735.1.f.c.344.1 2 1.1 even 1 trivial
735.1.f.c.344.1 2 15.14 odd 2 CM
735.1.f.c.344.2 yes 2 21.20 even 2 inner
735.1.f.c.344.2 yes 2 35.34 odd 2 inner
735.1.f.d.344.1 yes 2 7.6 odd 2
735.1.f.d.344.1 yes 2 105.104 even 2
735.1.f.d.344.2 yes 2 3.2 odd 2
735.1.f.d.344.2 yes 2 5.4 even 2
735.1.o.c.569.1 4 21.11 odd 6
735.1.o.c.569.1 4 35.4 even 6
735.1.o.c.569.2 4 7.3 odd 6
735.1.o.c.569.2 4 105.59 even 6
735.1.o.c.704.1 4 21.2 odd 6
735.1.o.c.704.1 4 35.9 even 6
735.1.o.c.704.2 4 7.5 odd 6
735.1.o.c.704.2 4 105.89 even 6
735.1.o.d.569.1 4 21.17 even 6
735.1.o.d.569.1 4 35.24 odd 6
735.1.o.d.569.2 4 7.4 even 3
735.1.o.d.569.2 4 105.74 odd 6
735.1.o.d.704.1 4 21.5 even 6
735.1.o.d.704.1 4 35.19 odd 6
735.1.o.d.704.2 4 7.2 even 3
735.1.o.d.704.2 4 105.44 odd 6
3675.1.c.f.1226.1 4 35.27 even 4
3675.1.c.f.1226.1 4 105.83 odd 4
3675.1.c.f.1226.2 4 5.2 odd 4
3675.1.c.f.1226.2 4 15.8 even 4
3675.1.c.f.1226.3 4 5.3 odd 4
3675.1.c.f.1226.3 4 15.2 even 4
3675.1.c.f.1226.4 4 35.13 even 4
3675.1.c.f.1226.4 4 105.62 odd 4
3675.1.u.f.851.1 8 35.2 odd 12
3675.1.u.f.851.1 8 105.23 even 12
3675.1.u.f.851.2 8 35.12 even 12
3675.1.u.f.851.2 8 105.68 odd 12
3675.1.u.f.851.3 8 35.33 even 12
3675.1.u.f.851.3 8 105.47 odd 12
3675.1.u.f.851.4 8 35.23 odd 12
3675.1.u.f.851.4 8 105.2 even 12
3675.1.u.f.1451.1 8 35.18 odd 12
3675.1.u.f.1451.1 8 105.32 even 12
3675.1.u.f.1451.2 8 35.3 even 12
3675.1.u.f.1451.2 8 105.17 odd 12
3675.1.u.f.1451.3 8 35.17 even 12
3675.1.u.f.1451.3 8 105.38 odd 12
3675.1.u.f.1451.4 8 35.32 odd 12
3675.1.u.f.1451.4 8 105.53 even 12