# Properties

 Label 735.1.o.c.569.1 Level $735$ Weight $1$ Character 735.569 Analytic conductor $0.367$ Analytic rank $0$ Dimension $4$ Projective image $D_{4}$ CM discriminant -15 Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,1,Mod(569,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("735.569");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 735.o (of order $$6$$, degree $$2$$, 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: $$0.366812784285$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 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 4.2.15435.1 Artin image: $C_6\times D_8$ Artin field: Galois closure of $$\mathbb{Q}[x]/(x^{48} - \cdots)$$

## Embedding invariants

 Embedding label 569.1 Root $$0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 735.569 Dual form 735.1.o.c.704.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 1.22474i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.41421 q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.707107 + 1.22474i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.41421 q^{6} +(-0.500000 + 0.866025i) q^{9} +(0.707107 + 1.22474i) q^{10} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.707107 - 1.22474i) q^{18} +(0.707107 - 1.22474i) q^{19} -1.00000 q^{20} +(0.707107 - 1.22474i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(0.707107 - 1.22474i) q^{30} +(-0.707107 - 1.22474i) q^{31} +(0.707107 + 1.22474i) q^{32} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{45} +(1.00000 + 1.73205i) q^{46} -1.00000 q^{48} +1.41421 q^{50} +(0.707107 + 1.22474i) q^{53} +(-0.707107 + 1.22474i) q^{54} -1.41421 q^{57} +(0.500000 + 0.866025i) q^{60} +(-0.707107 + 1.22474i) q^{61} +2.00000 q^{62} -1.00000 q^{64} -1.41421 q^{69} +(-0.500000 + 0.866025i) q^{75} -1.41421 q^{76} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} -1.41421 q^{90} -1.41421 q^{92} +(-0.707107 + 1.22474i) q^{93} +(-0.707107 - 1.22474i) q^{95} +(0.707107 - 1.22474i) q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10})$$ 4 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^9 $$4 q - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{9} - 2 q^{12} - 4 q^{15} + 2 q^{16} - 4 q^{20} - 2 q^{25} + 4 q^{27} + 4 q^{36} + 4 q^{38} + 2 q^{45} + 4 q^{46} - 4 q^{48} + 2 q^{60} + 8 q^{62} - 4 q^{64} - 2 q^{75} - 2 q^{80} - 2 q^{81}+O(q^{100})$$ 4 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^9 - 2 * q^12 - 4 * q^15 + 2 * q^16 - 4 * q^20 - 2 * q^25 + 4 * q^27 + 4 * q^36 + 4 * q^38 + 2 * q^45 + 4 * q^46 - 4 * q^48 + 2 * q^60 + 8 * q^62 - 4 * q^64 - 2 * q^75 - 2 * q^80 - 2 * q^81

## Character values

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

 $$n$$ $$346$$ $$442$$ $$491$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$3$$ −0.500000 0.866025i −0.500000 0.866025i
$$4$$ −0.500000 0.866025i −0.500000 0.866025i
$$5$$ 0.500000 0.866025i 0.500000 0.866025i
$$6$$ 1.41421 1.41421
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$10$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$11$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$12$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −1.00000
$$16$$ 0.500000 0.866025i 0.500000 0.866025i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ −0.707107 1.22474i −0.707107 1.22474i
$$19$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$20$$ −1.00000 −1.00000
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.500000 0.866025i
$$26$$ 0 0
$$27$$ 1.00000 1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0.707107 1.22474i 0.707107 1.22474i
$$31$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$32$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$38$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$39$$ 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
$$45$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$46$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ −1.00000 −1.00000
$$49$$ 0 0
$$50$$ 1.41421 1.41421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$54$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.41421 −1.41421
$$58$$ 0 0
$$59$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$60$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$61$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$62$$ 2.00000 2.00000
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$68$$ 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 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$74$$ 0 0
$$75$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$76$$ −1.41421 −1.41421
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$80$$ −0.500000 0.866025i −0.500000 0.866025i
$$81$$ −0.500000 0.866025i −0.500000 0.866025i
$$82$$ 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 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ −1.41421 −1.41421
$$91$$ 0 0
$$92$$ −1.41421 −1.41421
$$93$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$94$$ 0 0
$$95$$ −0.707107 1.22474i −0.707107 1.22474i
$$96$$ 0.707107 1.22474i 0.707107 1.22474i
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$101$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −2.00000 −2.00000
$$107$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$108$$ −0.500000 0.866025i −0.500000 0.866025i
$$109$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$114$$ 1.00000 1.73205i 1.00000 1.73205i
$$115$$ −0.707107 1.22474i −0.707107 1.22474i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$122$$ −1.00000 1.73205i −1.00000 1.73205i
$$123$$ 0 0
$$124$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$125$$ −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 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.500000 0.866025i 0.500000 0.866025i
$$136$$ 0 0
$$137$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$138$$ 1.00000 1.73205i 1.00000 1.73205i
$$139$$ 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
$$144$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ −0.707107 1.22474i −0.707107 1.22474i
$$151$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.41421 −1.41421
$$156$$ 0 0
$$157$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$158$$ 0 0
$$159$$ 0.707107 1.22474i 0.707107 1.22474i
$$160$$ 1.41421 1.41421
$$161$$ 0 0
$$162$$ 1.41421 1.41421
$$163$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$172$$ 0 0
$$173$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$180$$ 0.500000 0.866025i 0.500000 0.866025i
$$181$$ −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
$$186$$ −1.00000 1.73205i −1.00000 1.73205i
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 2.00000 2.00000
$$191$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$193$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$198$$ 0 0
$$199$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$212$$ 0.707107 1.22474i 0.707107 1.22474i
$$213$$ 0 0
$$214$$ −1.00000 1.73205i −1.00000 1.73205i
$$215$$ 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
$$226$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$227$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$229$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$230$$ 2.00000 2.00000
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$241$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$242$$ −0.707107 1.22474i −0.707107 1.22474i
$$243$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$244$$ 1.41421 1.41421
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0.707107 1.22474i 0.707107 1.22474i
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.500000 0.866025i
$$257$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$264$$ 0 0
$$265$$ 1.41421 1.41421
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$270$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$271$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 2.00000 2.00000
$$275$$ 0 0
$$276$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$277$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$278$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$279$$ 1.41421 1.41421
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$284$$ 0 0
$$285$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.41421 −1.41421
$$289$$ 0.500000 0.866025i 0.500000 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$294$$ 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
$$304$$ −0.707107 1.22474i −0.707107 1.22474i
$$305$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1.00000 1.73205i 1.00000 1.73205i
$$311$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$312$$ 0 0
$$313$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$318$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$319$$ 0 0
$$320$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$321$$ 1.41421 1.41421
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 1.00000 1.73205i 1.00000 1.73205i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 1.41421 2.44949i 1.41421 2.44949i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$339$$ −0.707107 1.22474i −0.707107 1.22474i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −2.00000 −2.00000
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$346$$ 0 0
$$347$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$348$$ 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
$$353$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$360$$ 0 0
$$361$$ −0.500000 0.866025i −0.500000 0.866025i
$$362$$ 1.00000 1.73205i 1.00000 1.73205i
$$363$$ 1.00000 1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$367$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$368$$ −0.707107 1.22474i −0.707107 1.22474i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 1.41421 1.41421
$$373$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ 0 0
$$375$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$398$$ −2.00000 −2.00000
$$399$$ 0 0
$$400$$ −1.00000 −1.00000
$$401$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −1.00000 −1.00000
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$410$$ 0 0
$$411$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −2.00000 −2.00000
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −0.707107 1.22474i −0.707107 1.22474i
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 1.41421 2.44949i 1.41421 2.44949i
$$423$$ 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 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$432$$ 0.500000 0.866025i 0.500000 0.866025i
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.00000 1.73205i 1.00000 1.73205i
$$437$$ −1.00000 1.73205i −1.00000 1.73205i
$$438$$ 0 0
$$439$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$451$$ 0 0
$$452$$ −0.707107 1.22474i −0.707107 1.22474i
$$453$$ 0 0
$$454$$ −2.82843 −2.82843
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$458$$ −1.00000 1.73205i −1.00000 1.73205i
$$459$$ 0 0
$$460$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$466$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$467$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$468$$ 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 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ −0.707107 1.22474i −0.707107 1.22474i
$$481$$ 0 0
$$482$$ −2.00000 −2.00000
$$483$$ 0 0
$$484$$ 1.00000 1.00000
$$485$$ 0 0
$$486$$ −0.707107 1.22474i −0.707107 1.22474i
$$487$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$488$$ 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 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$500$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$501$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.500000 0.866025i −0.500000 0.866025i
$$508$$ 0 0
$$509$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.41421 1.41421
$$513$$ 0.707107 1.22474i 0.707107 1.22474i
$$514$$ −1.41421 2.44949i −1.41421 2.44949i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$522$$ 0 0
$$523$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 2.00000 2.00000
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.500000 0.866025i −0.500000 0.866025i
$$530$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ −1.00000 −1.00000
$$541$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$542$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$543$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$544$$ 0 0
$$545$$ 2.00000 2.00000
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$549$$ −0.707107 1.22474i −0.707107 1.22474i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.707107 1.22474i −0.707107 1.22474i
$$557$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$558$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$564$$ 0 0
$$565$$ 0.707107 1.22474i 0.707107 1.22474i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$570$$ −1.00000 1.73205i −1.00000 1.73205i
$$571$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.41421 −1.41421
$$576$$ 0.500000 0.866025i 0.500000 0.866025i
$$577$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$578$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −1.41421 + 2.44949i −1.41421 + 2.44949i
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ −2.00000 −2.00000
$$590$$ 0 0
$$591$$ −0.707107 1.22474i −0.707107 1.22474i
$$592$$ 0 0
$$593$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0.707107 1.22474i 0.707107 1.22474i
$$598$$ 0 0
$$599$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$600$$ 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
$$605$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$606$$ 0 0
$$607$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$608$$ 2.00000 2.00000
$$609$$ 0 0
$$610$$ −2.00000 −2.00000
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$618$$ 0 0
$$619$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$620$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$621$$ 0.707107 1.22474i 0.707107 1.22474i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$626$$ 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 + 1.73205i 1.00000 + 1.73205i
$$634$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$635$$ 0 0
$$636$$ −1.41421 −1.41421
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$642$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$654$$ 1.41421 + 2.44949i 1.41421 + 2.44949i
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$662$$ 1.41421 + 2.44949i 1.41421 + 2.44949i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −0.500000 0.866025i −0.500000 0.866025i
$$676$$ −0.500000 0.866025i −0.500000 0.866025i
$$677$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$678$$ 2.00000 2.00000
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.00000 1.73205i 1.00000 1.73205i
$$682$$ 0 0
$$683$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$684$$ 0.707107 1.22474i 0.707107 1.22474i
$$685$$ −1.41421 −1.41421
$$686$$ 0 0
$$687$$ 1.41421 1.41421
$$688$$ 0 0
$$689$$ 0 0
$$690$$ −1.00000 1.73205i −1.00000 1.73205i
$$691$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −2.00000 −2.00000
$$695$$ 0.707107 1.22474i 0.707107 1.22474i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 1.00000 1.73205i 1.00000 1.73205i
$$699$$ −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 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$710$$ 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 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$720$$ 1.00000 1.00000
$$721$$ 0 0
$$722$$ 1.41421 1.41421
$$723$$ 0.707107 1.22474i 0.707107 1.22474i
$$724$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$725$$ 0 0
$$726$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −0.707107 1.22474i −0.707107 1.22474i
$$733$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 2.00000 2.00000
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −1.41421 −1.41421
$$751$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 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 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$769$$ 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 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$774$$ 0 0
$$775$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$776$$ 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 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$788$$ −0.707107 1.22474i −0.707107 1.22474i
$$789$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −0.707107 1.22474i −0.707107 1.22474i
$$796$$ 0.707107 1.22474i 0.707107 1.22474i
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$