# Properties

 Label 1200.1.z.a.1043.1 Level $1200$ Weight $1$ Character 1200.1043 Analytic conductor $0.599$ Analytic rank $0$ Dimension $2$ Projective image $D_{4}$ CM discriminant -15 Inner twists $4$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,1,Mod(107,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 1]))

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

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

chi := DirichletCharacter("1200.107");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1200.z (of order $$4$$, degree $$2$$, 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: $$0.598878015160$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{4}$$ Projective field: Galois closure of 4.2.153600.1

## Embedding invariants

 Embedding label 1043.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1200.1043 Dual form 1200.1.z.a.107.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{6} -1.00000 q^{8} -1.00000 q^{9} -1.00000i q^{12} +1.00000 q^{16} +(-1.00000 - 1.00000i) q^{17} +1.00000 q^{18} +(-1.00000 - 1.00000i) q^{19} +(1.00000 - 1.00000i) q^{23} +1.00000i q^{24} +1.00000i q^{27} -2.00000i q^{31} -1.00000 q^{32} +(1.00000 + 1.00000i) q^{34} -1.00000 q^{36} +(1.00000 + 1.00000i) q^{38} +(-1.00000 + 1.00000i) q^{46} +(1.00000 - 1.00000i) q^{47} -1.00000i q^{48} +1.00000i q^{49} +(-1.00000 + 1.00000i) q^{51} +2.00000i q^{53} -1.00000i q^{54} +(-1.00000 + 1.00000i) q^{57} +(-1.00000 - 1.00000i) q^{61} +2.00000i q^{62} +1.00000 q^{64} +(-1.00000 - 1.00000i) q^{68} +(-1.00000 - 1.00000i) q^{69} +1.00000 q^{72} +(-1.00000 - 1.00000i) q^{76} +1.00000 q^{81} +(1.00000 - 1.00000i) q^{92} -2.00000 q^{93} +(-1.00000 + 1.00000i) q^{94} +1.00000i q^{96} -1.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 2 * q^9 $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 2 q^{9} + 2 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{23} - 2 q^{32} + 2 q^{34} - 2 q^{36} + 2 q^{38} - 2 q^{46} + 2 q^{47} - 2 q^{51} - 2 q^{57} - 2 q^{61} + 2 q^{64} - 2 q^{68} - 2 q^{69} + 2 q^{72} - 2 q^{76} + 2 q^{81} + 2 q^{92} - 4 q^{93} - 2 q^{94}+O(q^{100})$$ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 2 * q^9 + 2 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^23 - 2 * q^32 + 2 * q^34 - 2 * q^36 + 2 * q^38 - 2 * q^46 + 2 * q^47 - 2 * q^51 - 2 * q^57 - 2 * q^61 + 2 * q^64 - 2 * q^68 - 2 * q^69 + 2 * q^72 - 2 * q^76 + 2 * q^81 + 2 * q^92 - 4 * q^93 - 2 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$577$$ $$751$$ $$901$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −1.00000
$$3$$ 1.00000i 1.00000i
$$4$$ 1.00000 1.00000
$$5$$ 0 0
$$6$$ 1.00000i 1.00000i
$$7$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$8$$ −1.00000 −1.00000
$$9$$ −1.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$12$$ 1.00000i 1.00000i
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$18$$ 1.00000 1.00000
$$19$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$24$$ 1.00000i 1.00000i
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000i 1.00000i
$$28$$ 0 0
$$29$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$30$$ 0 0
$$31$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$32$$ −1.00000 −1.00000
$$33$$ 0 0
$$34$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$35$$ 0 0
$$36$$ −1.00000 −1.00000
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$47$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$48$$ 1.00000i 1.00000i
$$49$$ 1.00000i 1.00000i
$$50$$ 0 0
$$51$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$52$$ 0 0
$$53$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 1.00000i 1.00000i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$58$$ 0 0
$$59$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$60$$ 0 0
$$61$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$62$$ 2.00000i 2.00000i
$$63$$ 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 1.00000i −1.00000 1.00000i
$$69$$ −1.00000 1.00000i −1.00000 1.00000i
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 1.00000 1.00000
$$73$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −1.00000 1.00000i −1.00000 1.00000i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 1.00000 1.00000i 1.00000 1.00000i
$$93$$ −2.00000 −2.00000
$$94$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$95$$ 0 0
$$96$$ 1.00000i 1.00000i
$$97$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$98$$ 1.00000i 1.00000i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$102$$ 1.00000 1.00000i 1.00000 1.00000i
$$103$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 2.00000i 2.00000i
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 1.00000i 1.00000i
$$109$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$114$$ 1.00000 1.00000i 1.00000 1.00000i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000i 1.00000i
$$122$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$123$$ 0 0
$$124$$ 2.00000i 2.00000i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$128$$ −1.00000 −1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$137$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$138$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$139$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ −1.00000 1.00000i −1.00000 1.00000i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 1.00000 1.00000
$$148$$ 0 0
$$149$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$150$$ 0 0
$$151$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$152$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$153$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 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
$$162$$ −1.00000 −1.00000
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$172$$ 0 0
$$173$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$180$$ 0 0
$$181$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$184$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$185$$ 0 0
$$186$$ 2.00000 2.00000
$$187$$ 0 0
$$188$$ 1.00000 1.00000i 1.00000 1.00000i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 1.00000i 1.00000i
$$193$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 1.00000i 1.00000i
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$212$$ 2.00000i 2.00000i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 1.00000i 1.00000i
$$217$$ 0 0
$$218$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.00000 1.00000i 1.00000 1.00000i
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$229$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 1.00000i 1.00000i
$$243$$ 1.00000i 1.00000i
$$244$$ −1.00000 1.00000i −1.00000 1.00000i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 2.00000i 2.00000i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −1.00000 1.00000i −1.00000 1.00000i
$$273$$ 0 0
$$274$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$275$$ 0 0
$$276$$ −1.00000 1.00000i −1.00000 1.00000i
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 1.00000 1.00000i 1.00000 1.00000i
$$279$$ 2.00000i 2.00000i
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000 1.00000
$$289$$ 1.00000i 1.00000i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$294$$ −1.00000 −1.00000
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −2.00000 −2.00000
$$303$$ 0 0
$$304$$ −1.00000 1.00000i −1.00000 1.00000i
$$305$$ 0 0
$$306$$ −1.00000 1.00000i −1.00000 1.00000i
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ −2.00000 −2.00000
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2.00000i 2.00000i
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −1.00000 1.00000i −1.00000 1.00000i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −1.00000 1.00000i −1.00000 1.00000i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$338$$ −1.00000 −1.00000
$$339$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −1.00000 1.00000i −1.00000 1.00000i
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −2.00000 −2.00000
$$347$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$348$$ 0 0
$$349$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$354$$ 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
$$361$$ 1.00000i 1.00000i
$$362$$ 1.00000 1.00000i 1.00000 1.00000i
$$363$$ 1.00000 1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 1.00000 1.00000i 1.00000 1.00000i
$$367$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$368$$ 1.00000 1.00000i 1.00000 1.00000i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.00000 −2.00000
$$373$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$384$$ 1.00000i 1.00000i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$390$$ 0 0
$$391$$ −2.00000 −2.00000
$$392$$ 1.00000i 1.00000i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 1.00000 1.00000i 1.00000 1.00000i
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ −1.00000 1.00000i −1.00000 1.00000i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 1.00000 1.00000i 1.00000 1.00000i
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$418$$ 0 0
$$419$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$420$$ 0 0
$$421$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$422$$ 1.00000 1.00000i 1.00000 1.00000i
$$423$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$424$$ 2.00000i 2.00000i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 1.00000i 1.00000i
$$433$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.00000 1.00000i 1.00000 1.00000i
$$437$$ −2.00000 −2.00000
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 1.00000i 1.00000i
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$453$$ 2.00000i 2.00000i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 1.00000 1.00000i 1.00000 1.00000i
$$457$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$458$$ −1.00000 1.00000i −1.00000 1.00000i
$$459$$ 1.00000 1.00000i 1.00000 1.00000i
$$460$$ 0 0
$$461$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$467$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 2.00000i 2.00000i
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000i 1.00000i
$$485$$ 0 0
$$486$$ 1.00000i 1.00000i
$$487$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$488$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 2.00000i 2.00000i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 1.00000 1.00000i 1.00000 1.00000i
$$502$$ 0 0
$$503$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 1.00000i 1.00000i
$$508$$ 0 0
$$509$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −1.00000
$$513$$ 1.00000 1.00000i 1.00000 1.00000i
$$514$$ −1.00000 1.00000i −1.00000 1.00000i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 2.00000i 2.00000i
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$527$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$528$$ 0 0
$$529$$ 1.00000i 1.00000i
$$530$$ 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
$$541$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$542$$ 0 0
$$543$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$544$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 1.00000 1.00000i 1.00000 1.00000i
$$549$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$557$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 2.00000i 2.00000i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ −1.00000 1.00000i −1.00000 1.00000i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1.00000 −1.00000
$$577$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$578$$ 1.00000i 1.00000i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 2.00000i 2.00000i
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 1.00000 1.00000
$$589$$ −2.00000 + 2.00000i −2.00000 + 2.00000i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 2.00000 2.00000
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$608$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$618$$ 0 0
$$619$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 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
$$633$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 2.00000 2.00000
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 2.00000i 2.00000i
$$647$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$648$$ −1.00000 −1.00000
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$654$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$660$$ 0 0
$$661$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$662$$ −1.00000 1.00000i −1.00000 1.00000i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 1.00000 1.00000
$$677$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$678$$ −1.00000 1.00000i −1.00000 1.00000i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$684$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.00000 1.00000i 1.00000 1.00000i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 1.00000 1.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$692$$ 2.00000 2.00000
$$693$$ 0 0
$$694$$ 2.00000i 2.00000i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$699$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$700$$ 0 0
$$701$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −1.00000 1.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −2.00000 2.00000i −2.00000 2.00000i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000i 1.00000i
$$723$$ 0 0
$$724$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$725$$ 0 0
$$726$$ −1.00000 −1.00000
$$727$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 $$0$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$744$$ 2.00000 2.00000
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 1.00000 1.00000i 1.00000 1.00000i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$767$$ 0 0
$$768$$ 1.00000i 1.00000i
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 1.00000 1.00000i 1.00000 1.00000i
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 2.00000 2.00000
$$783$$ 0 0
$$784$$ 1.00000i 1.00000i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 0 0
$$789$$ −1.00000 1.00000i −1.00000 1.00000i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ −2.00000 −2.00000
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0