Properties

 Label 3800.1.b.b.949.2 Level $3800$ Weight $1$ Character 3800.949 Analytic conductor $1.896$ Analytic rank $0$ Dimension $2$ Projective image $D_{3}$ CM discriminant -152 Inner twists $4$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3800,1,Mod(949,3800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("3800.949");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3800 = 2^{3} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3800.b (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$1.89644704801$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 152) Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.152.1 Artin image: $C_4\times D_6$ Artin field: Galois closure of $$\mathbb{Q}[x]/(x^{24} - \cdots)$$

Embedding invariants

 Embedding label 949.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 3800.949 Dual form 3800.1.b.b.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{7} -1.00000i q^{8} -1.00000i q^{12} +1.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} -1.00000 q^{19} +1.00000 q^{21} +1.00000i q^{23} +1.00000 q^{24} -1.00000 q^{26} +1.00000i q^{27} +1.00000i q^{28} +1.00000 q^{29} +1.00000i q^{32} +1.00000 q^{34} +2.00000i q^{37} -1.00000i q^{38} -1.00000 q^{39} +1.00000i q^{42} -1.00000 q^{46} +2.00000i q^{47} +1.00000i q^{48} +1.00000 q^{51} -1.00000i q^{52} +1.00000i q^{53} -1.00000 q^{54} -1.00000 q^{56} -1.00000i q^{57} +1.00000i q^{58} +1.00000 q^{59} -1.00000 q^{64} -1.00000i q^{67} +1.00000i q^{68} -1.00000 q^{69} +1.00000i q^{73} -2.00000 q^{74} +1.00000 q^{76} -1.00000i q^{78} -1.00000 q^{81} -1.00000 q^{84} +1.00000i q^{87} +1.00000 q^{91} -1.00000i q^{92} -2.00000 q^{94} -1.00000 q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{4} - 2 q^{6}+O(q^{10})$$ 2 * q - 2 * q^4 - 2 * q^6 $$2 q - 2 q^{4} - 2 q^{6} + 2 q^{14} + 2 q^{16} - 2 q^{19} + 2 q^{21} + 2 q^{24} - 2 q^{26} + 2 q^{29} + 2 q^{34} - 2 q^{39} - 2 q^{46} + 2 q^{51} - 2 q^{54} - 2 q^{56} + 2 q^{59} - 2 q^{64} - 2 q^{69} - 4 q^{74} + 2 q^{76} - 2 q^{81} - 2 q^{84} + 2 q^{91} - 4 q^{94} - 2 q^{96}+O(q^{100})$$ 2 * q - 2 * q^4 - 2 * q^6 + 2 * q^14 + 2 * q^16 - 2 * q^19 + 2 * q^21 + 2 * q^24 - 2 * q^26 + 2 * q^29 + 2 * q^34 - 2 * q^39 - 2 * q^46 + 2 * q^51 - 2 * q^54 - 2 * q^56 + 2 * q^59 - 2 * q^64 - 2 * q^69 - 4 * q^74 + 2 * q^76 - 2 * q^81 - 2 * q^84 + 2 * q^91 - 4 * q^94 - 2 * q^96

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$951$$ $$1901$$ $$1977$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$-1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 1.00000i
$$3$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$4$$ −1.00000 −1.00000
$$5$$ 0 0
$$6$$ −1.00000 −1.00000
$$7$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$8$$ − 1.00000i − 1.00000i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ − 1.00000i − 1.00000i
$$13$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$14$$ 1.00000 1.00000
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −1.00000
$$20$$ 0 0
$$21$$ 1.00000 1.00000
$$22$$ 0 0
$$23$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 1.00000 1.00000
$$25$$ 0 0
$$26$$ −1.00000 −1.00000
$$27$$ 1.00000i 1.00000i
$$28$$ 1.00000i 1.00000i
$$29$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000i 1.00000i
$$33$$ 0 0
$$34$$ 1.00000 1.00000
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ − 1.00000i − 1.00000i
$$39$$ −1.00000 −1.00000
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 1.00000i 1.00000i
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −1.00000 −1.00000
$$47$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 1.00000i 1.00000i
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 1.00000 1.00000
$$52$$ − 1.00000i − 1.00000i
$$53$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$54$$ −1.00000 −1.00000
$$55$$ 0 0
$$56$$ −1.00000 −1.00000
$$57$$ − 1.00000i − 1.00000i
$$58$$ 1.00000i 1.00000i
$$59$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$68$$ 1.00000i 1.00000i
$$69$$ −1.00000 −1.00000
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$74$$ −2.00000 −2.00000
$$75$$ 0 0
$$76$$ 1.00000 1.00000
$$77$$ 0 0
$$78$$ − 1.00000i − 1.00000i
$$79$$ 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 $$0.5\pi$$
$$84$$ −1.00000 −1.00000
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.00000i 1.00000i
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 1.00000 1.00000
$$92$$ − 1.00000i − 1.00000i
$$93$$ 0 0
$$94$$ −2.00000 −2.00000
$$95$$ 0 0
$$96$$ −1.00000 −1.00000
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 1.00000i 1.00000i
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 1.00000 1.00000
$$105$$ 0 0
$$106$$ −1.00000 −1.00000
$$107$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$108$$ − 1.00000i − 1.00000i
$$109$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$110$$ 0 0
$$111$$ −2.00000 −2.00000
$$112$$ − 1.00000i − 1.00000i
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 1.00000 1.00000
$$115$$ 0 0
$$116$$ −1.00000 −1.00000
$$117$$ 0 0
$$118$$ 1.00000i 1.00000i
$$119$$ −1.00000 −1.00000
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ − 1.00000i − 1.00000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 1.00000i 1.00000i
$$134$$ 1.00000 1.00000
$$135$$ 0 0
$$136$$ −1.00000 −1.00000
$$137$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$138$$ − 1.00000i − 1.00000i
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ −2.00000 −2.00000
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −1.00000 −1.00000
$$147$$ 0 0
$$148$$ − 2.00000i − 2.00000i
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 1.00000i 1.00000i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 1.00000 1.00000
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ −1.00000 −1.00000
$$160$$ 0 0
$$161$$ 1.00000 1.00000
$$162$$ − 1.00000i − 1.00000i
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ − 1.00000i − 1.00000i
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$174$$ −1.00000 −1.00000
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 1.00000i 1.00000i
$$178$$ 0 0
$$179$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$182$$ 1.00000i 1.00000i
$$183$$ 0 0
$$184$$ 1.00000 1.00000
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ − 2.00000i − 2.00000i
$$189$$ 1.00000 1.00000
$$190$$ 0 0
$$191$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ − 1.00000i − 1.00000i
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$200$$ 0 0
$$201$$ 1.00000 1.00000
$$202$$ 0 0
$$203$$ − 1.00000i − 1.00000i
$$204$$ −1.00000 −1.00000
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 1.00000i 1.00000i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ − 1.00000i − 1.00000i
$$213$$ 0 0
$$214$$ 1.00000 1.00000
$$215$$ 0 0
$$216$$ 1.00000 1.00000
$$217$$ 0 0
$$218$$ 1.00000i 1.00000i
$$219$$ −1.00000 −1.00000
$$220$$ 0 0
$$221$$ 1.00000 1.00000
$$222$$ − 2.00000i − 2.00000i
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 1.00000 1.00000
$$225$$ 0 0
$$226$$ 0 0
$$227$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$228$$ 1.00000i 1.00000i
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ − 1.00000i − 1.00000i
$$233$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −1.00000 −1.00000
$$237$$ 0 0
$$238$$ − 1.00000i − 1.00000i
$$239$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 1.00000i 1.00000i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ − 1.00000i − 1.00000i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 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
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 2.00000 2.00000
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −1.00000 −1.00000
$$267$$ 0 0
$$268$$ 1.00000i 1.00000i
$$269$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$272$$ − 1.00000i − 1.00000i
$$273$$ 1.00000i 1.00000i
$$274$$ 1.00000 1.00000
$$275$$ 0 0
$$276$$ 1.00000 1.00000
$$277$$ 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 $$\pi$$
$$282$$ − 2.00000i − 2.00000i
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 0 0
$$292$$ − 1.00000i − 1.00000i
$$293$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 2.00000 2.00000
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −1.00000 −1.00000
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −1.00000 −1.00000
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 1.00000i 1.00000i
$$313$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$318$$ − 1.00000i − 1.00000i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 1.00000 1.00000
$$322$$ 1.00000i 1.00000i
$$323$$ 1.00000i 1.00000i
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 1.00000i 1.00000i
$$328$$ 0 0
$$329$$ 2.00000 2.00000
$$330$$ 0 0
$$331$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 1.00000 1.00000
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ − 1.00000i − 1.00000i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 2.00000 2.00000
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ − 1.00000i − 1.00000i
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −1.00000
$$352$$ 0 0
$$353$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$354$$ −1.00000 −1.00000
$$355$$ 0 0
$$356$$ 0 0
$$357$$ − 1.00000i − 1.00000i
$$358$$ − 2.00000i − 2.00000i
$$359$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 2.00000i 2.00000i
$$363$$ 1.00000i 1.00000i
$$364$$ −1.00000 −1.00000
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 1.00000i 1.00000i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1.00000 1.00000
$$372$$ 0 0
$$373$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 2.00000 2.00000
$$377$$ 1.00000i 1.00000i
$$378$$ 1.00000i 1.00000i
$$379$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ − 1.00000i − 1.00000i
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 1.00000 1.00000
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 1.00000 1.00000
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 1.00000i 1.00000i
$$399$$ −1.00000 −1.00000
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 1.00000i 1.00000i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 1.00000 1.00000
$$407$$ 0 0
$$408$$ − 1.00000i − 1.00000i
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 1.00000 1.00000
$$412$$ 0 0
$$413$$ − 1.00000i − 1.00000i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −1.00000 −1.00000
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$422$$ − 1.00000i − 1.00000i
$$423$$ 0 0
$$424$$ 1.00000 1.00000
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 1.00000i 1.00000i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 1.00000i 1.00000i
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.00000 −1.00000
$$437$$ − 1.00000i − 1.00000i
$$438$$ − 1.00000i − 1.00000i
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 1.00000i 1.00000i
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 2.00000 2.00000
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 1.00000i 1.00000i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 1.00000 1.00000
$$455$$ 0 0
$$456$$ −1.00000 −1.00000
$$457$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$458$$ 0 0
$$459$$ 1.00000 1.00000
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$464$$ 1.00000 1.00000
$$465$$ 0 0
$$466$$ 2.00000 2.00000
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ −1.00000 −1.00000
$$470$$ 0 0
$$471$$ 0 0
$$472$$ − 1.00000i − 1.00000i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 1.00000 1.00000
$$477$$ 0 0
$$478$$ 1.00000i 1.00000i
$$479$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ −2.00000 −2.00000
$$482$$ 0 0
$$483$$ 1.00000i 1.00000i
$$484$$ −1.00000 −1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ − 1.00000i − 1.00000i
$$494$$ 1.00000 1.00000
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 1.00000 1.00000
$$512$$ 1.00000i 1.00000i
$$513$$ − 1.00000i − 1.00000i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 2.00000i 2.00000i
$$519$$ 2.00000 2.00000
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 2.00000 2.00000
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 0 0
$$532$$ − 1.00000i − 1.00000i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −1.00000 −1.00000
$$537$$ − 2.00000i − 2.00000i
$$538$$ − 2.00000i − 2.00000i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ − 1.00000i − 1.00000i
$$543$$ 2.00000i 2.00000i
$$544$$ 1.00000 1.00000
$$545$$ 0 0
$$546$$ −1.00000 −1.00000
$$547$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 1.00000i 1.00000i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1.00000 −1.00000
$$552$$ 1.00000i 1.00000i
$$553$$ 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
$$563$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$564$$ 2.00000 2.00000
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1.00000i 1.00000i
$$568$$ 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
$$573$$ − 1.00000i − 1.00000i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 1.00000 1.00000
$$585$$ 0 0
$$586$$ −1.00000 −1.00000
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 2.00000i 2.00000i
$$593$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 1.00000i 1.00000i
$$598$$ − 1.00000i − 1.00000i
$$599$$ 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 0
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ − 1.00000i − 1.00000i
$$609$$ 1.00000 1.00000
$$610$$ 0 0
$$611$$ −2.00000 −2.00000
$$612$$ 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
$$617$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ −1.00000 −1.00000
$$622$$ − 1.00000i − 1.00000i
$$623$$ 0 0
$$624$$ −1.00000 −1.00000
$$625$$ 0 0
$$626$$ −1.00000 −1.00000
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 2.00000 2.00000
$$630$$ 0 0
$$631$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$632$$ 0 0
$$633$$ − 1.00000i − 1.00000i
$$634$$ 1.00000 1.00000
$$635$$ 0 0
$$636$$ 1.00000 1.00000
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 1.00000i 1.00000i
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ −1.00000 −1.00000
$$645$$ 0 0
$$646$$ −1.00000 −1.00000
$$647$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$648$$ 1.00000i 1.00000i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ −1.00000 −1.00000
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 2.00000i 2.00000i
$$659$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$660$$ 0 0
$$661$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$662$$ − 1.00000i − 1.00000i
$$663$$ 1.00000i 1.00000i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.00000i 1.00000i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.00000i 1.00000i
$$673$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.00000 1.00000
$$682$$ 0 0
$$683$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1.00000 1.00000
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1.00000 −1.00000
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 2.00000i 2.00000i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 1.00000 1.00000
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 2.00000 2.00000
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ − 1.00000i − 1.00000i
$$703$$ − 2.00000i − 2.00000i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −1.00000 −1.00000
$$707$$ 0 0
$$708$$ − 1.00000i − 1.00000i
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 1.00000 1.00000
$$715$$ 0 0
$$716$$ 2.00000 2.00000
$$717$$ 1.00000i 1.00000i
$$718$$ 1.00000i 1.00000i
$$719$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000i 1.00000i
$$723$$ 0 0
$$724$$ −2.00000 −2.00000
$$725$$ 0 0
$$726$$ −1.00000 −1.00000
$$727$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$728$$ − 1.00000i − 1.00000i
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ −2.00000 −2.00000
$$735$$ 0 0
$$736$$ −1.00000 −1.00000
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 1.00000 1.00000
$$742$$ 1.00000i 1.00000i
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −1.00000 −1.00000
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −1.00000 −1.00000
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 2.00000i 2.00000i
$$753$$ 0 0
$$754$$ −1.00000 −1.00000
$$755$$ 0 0
$$756$$ −1.00000 −1.00000
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 1.00000i 1.00000i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ − 1.00000i − 1.00000i
$$764$$ 1.00000 1.00000
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1.00000i 1.00000i
$$768$$ 1.00000i 1.00000i
$$769$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 2.00000i 2.00000i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 1.00000i 1.00000i
$$783$$ 1.00000i 1.00000i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$788$$ 0 0
$$789$$ 2.00000 2.00000
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −1.00000 −1.00000
$$797$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$798$$ − 1.00000i − 1.00000i
$$799$$ 2.00000 2.00000
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ −1.00000 −1.00000
$$805$$ 0 0
$$806$$ 0 0
$$807$$ − 2.00000i − 2.00000i
$$808$$ 0 0
$$809$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$810$$ 0 0
$$811$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$812$$ 1.00000i 1.00000i
$$813$$ − 1.00000i − 1.00000i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 1.00000 1.00000
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 1.00000i 1.00000i
$$823$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 1.00000 1.00000
$$827$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$828$$ 0 0
$$829$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ − 1.00000i − 1.00000i
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 0 0
$$842$$ − 1.00000i − 1.00000i
$$843$$ 0 0
$$844$$ 1.00000 1.00000
$$845$$ 0 0
$$846$$ 0 0
$$847$$ − 1.00000i − 1.00000i
$$848$$ 1.00000i 1.00000i
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −2.00000 −2.00000
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −1.00000 −1.00000
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ −1.00000 −1.00000
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 1.00000 1.00000
$$872$$ − 1.00000i − 1.00000i
$$873$$ 0 0
$$874$$ 1.00000 1.00000
$$875$$ 0 0
$$876$$ 1.00000 1.00000
$$877$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$878$$ 0 0
$$879$$ −1.00000 −1.00000
$$880$$ 0 0
$$881$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ −1.00000 −1.00000
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 2.00000i 2.00000i
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ − 2.00000i − 2.00000i
$$894$$ 0 0
$$895$$ 0 0
$$896$$ −1.00000 −1.00000
$$897$$ − 1.00000i − 1.00000i
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 1.00000 1.00000
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$908$$ 1.00000i 1.00000i
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ − 1.00000i − 1.00000i
$$913$$ 0 0
$$914$$ 1.00000 1.00000
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 1.00000i 1.00000i
$$919$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$920$$ 0 0
$$921$$ −2.00000 −2.00000
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 2.00000 2.00000
$$927$$ 0 0
$$928$$ 1.00000i 1.00000i
$$929$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 2.00000i 2.00000i
$$933$$ − 1.00000i − 1.00000i
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ − 1.00000i − 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$938$$ − 1.00000i − 1.00000i
$$939$$ −1.00000 −1.00000
$$940$$ 0 0
$$941$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 1.00000 1.00000
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ −1.00000 −1.00000
$$950$$ 0 0
$$951$$ 1.00000 1.00000
$$952$$ 1.00000i 1.00000i
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −1.00000 −1.00000
$$957$$ 0 0
$$958$$ − 2.00000i − 2.00000i
$$959$$ −1.00000 −1.00000
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ − 2.00000i − 2.00000i
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ −1.00000 −1.00000
$$967$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ − 1.00000i − 1.00000i
$$969$$ −1.00000 −1.00000
$$970$$ 0 0
$$971$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 1.00000 1.00000
$$987$$ 2.00000i 2.00000i
$$988$$ 1.00000i 1.00000i
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ − 1.00000i − 1.00000i
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 0 0
$$999$$ −2.00000 −2.00000
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 3800.1.b.b.949.2 2
5.2 odd 4 3800.1.o.a.1101.1 1
5.3 odd 4 152.1.g.b.37.1 yes 1
5.4 even 2 inner 3800.1.b.b.949.1 2
8.5 even 2 3800.1.b.a.949.1 2
15.8 even 4 1368.1.i.a.37.1 1
19.18 odd 2 3800.1.b.a.949.1 2
20.3 even 4 608.1.g.b.113.1 1
40.3 even 4 608.1.g.a.113.1 1
40.13 odd 4 152.1.g.a.37.1 1
40.29 even 2 3800.1.b.a.949.2 2
40.37 odd 4 3800.1.o.b.1101.1 1
95.3 even 36 2888.1.s.b.333.1 6
95.8 even 12 2888.1.l.b.69.1 2
95.13 even 36 2888.1.s.b.477.1 6
95.18 even 4 152.1.g.a.37.1 1
95.23 odd 36 2888.1.s.a.1029.1 6
95.28 odd 36 2888.1.s.a.1021.1 6
95.33 even 36 2888.1.s.b.2293.1 6
95.37 even 4 3800.1.o.b.1101.1 1
95.43 odd 36 2888.1.s.a.2293.1 6
95.48 even 36 2888.1.s.b.1021.1 6
95.53 even 36 2888.1.s.b.1029.1 6
95.63 odd 36 2888.1.s.a.477.1 6
95.68 odd 12 2888.1.l.a.69.1 2
95.73 odd 36 2888.1.s.a.333.1 6
95.78 even 36 2888.1.s.b.2789.1 6
95.83 odd 12 2888.1.l.a.293.1 2
95.88 even 12 2888.1.l.b.293.1 2
95.93 odd 36 2888.1.s.a.2789.1 6
95.94 odd 2 3800.1.b.a.949.2 2
120.53 even 4 1368.1.i.b.37.1 1
152.37 odd 2 CM 3800.1.b.b.949.2 2
285.113 odd 4 1368.1.i.b.37.1 1
380.303 odd 4 608.1.g.a.113.1 1
760.13 even 36 2888.1.s.a.477.1 6
760.37 even 4 3800.1.o.a.1101.1 1
760.53 even 36 2888.1.s.a.1029.1 6
760.93 odd 36 2888.1.s.b.2789.1 6
760.173 even 36 2888.1.s.a.2789.1 6
760.189 odd 2 inner 3800.1.b.b.949.1 2
760.213 odd 36 2888.1.s.b.1029.1 6
760.253 odd 36 2888.1.s.b.477.1 6
760.293 even 12 2888.1.l.a.69.1 2
760.333 even 36 2888.1.s.a.1021.1 6
760.373 even 12 2888.1.l.a.293.1 2
760.413 even 36 2888.1.s.a.2293.1 6
760.453 odd 36 2888.1.s.b.333.1 6
760.493 even 4 152.1.g.b.37.1 yes 1
760.573 even 36 2888.1.s.a.333.1 6
760.613 odd 36 2888.1.s.b.2293.1 6
760.653 odd 12 2888.1.l.b.293.1 2
760.683 odd 4 608.1.g.b.113.1 1
760.693 odd 36 2888.1.s.b.1021.1 6
760.733 odd 12 2888.1.l.b.69.1 2
2280.1253 odd 4 1368.1.i.a.37.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
152.1.g.a.37.1 1 40.13 odd 4
152.1.g.a.37.1 1 95.18 even 4
152.1.g.b.37.1 yes 1 5.3 odd 4
152.1.g.b.37.1 yes 1 760.493 even 4
608.1.g.a.113.1 1 40.3 even 4
608.1.g.a.113.1 1 380.303 odd 4
608.1.g.b.113.1 1 20.3 even 4
608.1.g.b.113.1 1 760.683 odd 4
1368.1.i.a.37.1 1 15.8 even 4
1368.1.i.a.37.1 1 2280.1253 odd 4
1368.1.i.b.37.1 1 120.53 even 4
1368.1.i.b.37.1 1 285.113 odd 4
2888.1.l.a.69.1 2 95.68 odd 12
2888.1.l.a.69.1 2 760.293 even 12
2888.1.l.a.293.1 2 95.83 odd 12
2888.1.l.a.293.1 2 760.373 even 12
2888.1.l.b.69.1 2 95.8 even 12
2888.1.l.b.69.1 2 760.733 odd 12
2888.1.l.b.293.1 2 95.88 even 12
2888.1.l.b.293.1 2 760.653 odd 12
2888.1.s.a.333.1 6 95.73 odd 36
2888.1.s.a.333.1 6 760.573 even 36
2888.1.s.a.477.1 6 95.63 odd 36
2888.1.s.a.477.1 6 760.13 even 36
2888.1.s.a.1021.1 6 95.28 odd 36
2888.1.s.a.1021.1 6 760.333 even 36
2888.1.s.a.1029.1 6 95.23 odd 36
2888.1.s.a.1029.1 6 760.53 even 36
2888.1.s.a.2293.1 6 95.43 odd 36
2888.1.s.a.2293.1 6 760.413 even 36
2888.1.s.a.2789.1 6 95.93 odd 36
2888.1.s.a.2789.1 6 760.173 even 36
2888.1.s.b.333.1 6 95.3 even 36
2888.1.s.b.333.1 6 760.453 odd 36
2888.1.s.b.477.1 6 95.13 even 36
2888.1.s.b.477.1 6 760.253 odd 36
2888.1.s.b.1021.1 6 95.48 even 36
2888.1.s.b.1021.1 6 760.693 odd 36
2888.1.s.b.1029.1 6 95.53 even 36
2888.1.s.b.1029.1 6 760.213 odd 36
2888.1.s.b.2293.1 6 95.33 even 36
2888.1.s.b.2293.1 6 760.613 odd 36
2888.1.s.b.2789.1 6 95.78 even 36
2888.1.s.b.2789.1 6 760.93 odd 36
3800.1.b.a.949.1 2 8.5 even 2
3800.1.b.a.949.1 2 19.18 odd 2
3800.1.b.a.949.2 2 40.29 even 2
3800.1.b.a.949.2 2 95.94 odd 2
3800.1.b.b.949.1 2 5.4 even 2 inner
3800.1.b.b.949.1 2 760.189 odd 2 inner
3800.1.b.b.949.2 2 1.1 even 1 trivial
3800.1.b.b.949.2 2 152.37 odd 2 CM
3800.1.o.a.1101.1 1 5.2 odd 4
3800.1.o.a.1101.1 1 760.37 even 4
3800.1.o.b.1101.1 1 40.37 odd 4
3800.1.o.b.1101.1 1 95.37 even 4