# Properties

 Label 3479.1.g.e.1206.3 Level $3479$ Weight $1$ Character 3479.1206 Analytic conductor $1.736$ Analytic rank $0$ Dimension $6$ Projective image $D_{7}$ CM discriminant -71 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3479,1,Mod(851,3479)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3479, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("3479.851");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3479 = 7^{2} \cdot 71$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3479.g (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: $$1.73624717895$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{6})$$ Coefficient field: 6.0.64827.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1$$ x^6 - x^5 + 3*x^4 + 5*x^2 - 2*x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 71) Projective image: $$D_{7}$$ Projective field: Galois closure of 7.1.357911.1 Artin image: $C_3\times D_7$ Artin field: Galois closure of 21.3.31095511042786085990206459319.1

## Embedding invariants

 Embedding label 1206.3 Root $$-0.623490 + 1.07992i$$ of defining polynomial Character $$\chi$$ $$=$$ 3479.1206 Dual form 3479.1.g.e.851.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.900969 - 1.56052i) q^{2} +(0.222521 + 0.385418i) q^{3} +(-1.12349 - 1.94594i) q^{4} +(-0.623490 + 1.07992i) q^{5} +0.801938 q^{6} -2.24698 q^{8} +(0.400969 - 0.694498i) q^{9} +O(q^{10})$$ $$q+(0.900969 - 1.56052i) q^{2} +(0.222521 + 0.385418i) q^{3} +(-1.12349 - 1.94594i) q^{4} +(-0.623490 + 1.07992i) q^{5} +0.801938 q^{6} -2.24698 q^{8} +(0.400969 - 0.694498i) q^{9} +(1.12349 + 1.94594i) q^{10} +(0.500000 - 0.866025i) q^{12} -0.554958 q^{15} +(-0.900969 + 1.56052i) q^{16} +(-0.722521 - 1.25144i) q^{18} +(0.900969 - 1.56052i) q^{19} +2.80194 q^{20} +(-0.500000 - 0.866025i) q^{24} +(-0.277479 - 0.480608i) q^{25} +0.801938 q^{27} -0.445042 q^{29} +(-0.500000 + 0.866025i) q^{30} +(0.500000 + 0.866025i) q^{32} -1.80194 q^{36} +(0.900969 - 1.56052i) q^{37} +(-1.62349 - 2.81197i) q^{38} +(1.40097 - 2.42655i) q^{40} +1.24698 q^{43} +(0.500000 + 0.866025i) q^{45} -0.801938 q^{48} -1.00000 q^{50} +(0.722521 - 1.25144i) q^{54} +0.801938 q^{57} +(-0.400969 + 0.694498i) q^{58} +(0.623490 + 1.07992i) q^{60} +1.00000 q^{71} +(-0.900969 + 1.56052i) q^{72} +(-0.623490 - 1.07992i) q^{73} +(-1.62349 - 2.81197i) q^{74} +(0.123490 - 0.213891i) q^{75} -4.04892 q^{76} +(-0.623490 + 1.07992i) q^{79} +(-1.12349 - 1.94594i) q^{80} +(-0.222521 - 0.385418i) q^{81} -1.80194 q^{83} +(1.12349 - 1.94594i) q^{86} +(-0.0990311 - 0.171527i) q^{87} +(0.222521 - 0.385418i) q^{89} +1.80194 q^{90} +(1.12349 + 1.94594i) q^{95} +(-0.222521 + 0.385418i) q^{96} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + q^{2} + q^{3} - 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10})$$ 6 * q + q^2 + q^3 - 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 $$6 q + q^{2} + q^{3} - 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 3 q^{12} - 4 q^{15} - q^{16} - 4 q^{18} + q^{19} + 8 q^{20} - 3 q^{24} - 2 q^{25} - 4 q^{27} - 2 q^{29} - 3 q^{30} + 3 q^{32} - 2 q^{36} + q^{37} - 5 q^{38} + 4 q^{40} - 2 q^{43} + 3 q^{45} + 4 q^{48} - 6 q^{50} + 4 q^{54} - 4 q^{57} + 2 q^{58} - q^{60} + 6 q^{71} - q^{72} + q^{73} - 5 q^{74} - 4 q^{75} - 6 q^{76} + q^{79} - 2 q^{80} - q^{81} - 2 q^{83} + 2 q^{86} - 5 q^{87} + q^{89} + 2 q^{90} + 2 q^{95} - q^{96}+O(q^{100})$$ 6 * q + q^2 + q^3 - 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 + 2 * q^10 + 3 * q^12 - 4 * q^15 - q^16 - 4 * q^18 + q^19 + 8 * q^20 - 3 * q^24 - 2 * q^25 - 4 * q^27 - 2 * q^29 - 3 * q^30 + 3 * q^32 - 2 * q^36 + q^37 - 5 * q^38 + 4 * q^40 - 2 * q^43 + 3 * q^45 + 4 * q^48 - 6 * q^50 + 4 * q^54 - 4 * q^57 + 2 * q^58 - q^60 + 6 * q^71 - q^72 + q^73 - 5 * q^74 - 4 * q^75 - 6 * q^76 + q^79 - 2 * q^80 - q^81 - 2 * q^83 + 2 * q^86 - 5 * q^87 + q^89 + 2 * q^90 + 2 * q^95 - q^96

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3479\mathbb{Z}\right)^\times$$.

 $$n$$ $$640$$ $$1569$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i $$-0.476190\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$3$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$4$$ −1.12349 1.94594i −1.12349 1.94594i
$$5$$ −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i $$0.380952\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$6$$ 0.801938 0.801938
$$7$$ 0 0
$$8$$ −2.24698 −2.24698
$$9$$ 0.400969 0.694498i 0.400969 0.694498i
$$10$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$11$$ 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
$$15$$ −0.554958 −0.554958
$$16$$ −0.900969 + 1.56052i −0.900969 + 1.56052i
$$17$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$18$$ −0.722521 1.25144i −0.722521 1.25144i
$$19$$ 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i $$-0.476190\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$20$$ 2.80194 2.80194
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ −0.500000 0.866025i −0.500000 0.866025i
$$25$$ −0.277479 0.480608i −0.277479 0.480608i
$$26$$ 0 0
$$27$$ 0.801938 0.801938
$$28$$ 0 0
$$29$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$30$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$31$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$32$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −1.80194 −1.80194
$$37$$ 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i $$-0.476190\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$38$$ −1.62349 2.81197i −1.62349 2.81197i
$$39$$ 0 0
$$40$$ 1.40097 2.42655i 1.40097 2.42655i
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$44$$ 0 0
$$45$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$46$$ 0 0
$$47$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$48$$ −0.801938 −0.801938
$$49$$ 0 0
$$50$$ −1.00000 −1.00000
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$54$$ 0.722521 1.25144i 0.722521 1.25144i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0.801938 0.801938
$$58$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$59$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$60$$ 0.623490 + 1.07992i 0.623490 + 1.07992i
$$61$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 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
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.00000 1.00000
$$72$$ −0.900969 + 1.56052i −0.900969 + 1.56052i
$$73$$ −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i $$-0.952381\pi$$
0.365341 0.930874i $$-0.380952\pi$$
$$74$$ −1.62349 2.81197i −1.62349 2.81197i
$$75$$ 0.123490 0.213891i 0.123490 0.213891i
$$76$$ −4.04892 −4.04892
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i $$0.380952\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$80$$ −1.12349 1.94594i −1.12349 1.94594i
$$81$$ −0.222521 0.385418i −0.222521 0.385418i
$$82$$ 0 0
$$83$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.12349 1.94594i 1.12349 1.94594i
$$87$$ −0.0990311 0.171527i −0.0990311 0.171527i
$$88$$ 0 0
$$89$$ 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i $$-0.761905\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$90$$ 1.80194 1.80194
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$96$$ −0.222521 + 0.385418i −0.222521 + 0.385418i
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −0.623490 + 1.07992i −0.623490 + 1.07992i
$$101$$ 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i $$0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$102$$ 0 0
$$103$$ 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i $$-0.761905\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ −0.900969 1.56052i −0.900969 1.56052i
$$109$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$110$$ 0 0
$$111$$ 0.801938 0.801938
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0.722521 1.25144i 0.722521 1.25144i
$$115$$ 0 0
$$116$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 1.24698 1.24698
$$121$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −0.554958 −0.554958
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$129$$ 0.277479 + 0.480608i 0.277479 + 0.480608i
$$130$$ 0 0
$$131$$ −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i $$0.380952\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$136$$ 0 0
$$137$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0.900969 1.56052i 0.900969 1.56052i
$$143$$ 0 0
$$144$$ 0.722521 + 1.25144i 0.722521 + 1.25144i
$$145$$ 0.277479 0.480608i 0.277479 0.480608i
$$146$$ −2.24698 −2.24698
$$147$$ 0 0
$$148$$ −4.04892 −4.04892
$$149$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ −0.222521 0.385418i −0.222521 0.385418i
$$151$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$152$$ −2.02446 + 3.50647i −2.02446 + 3.50647i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$158$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$159$$ 0 0
$$160$$ −1.24698 −1.24698
$$161$$ 0 0
$$162$$ −0.801938 −0.801938
$$163$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −1.62349 + 2.81197i −1.62349 + 2.81197i
$$167$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ −0.722521 1.25144i −0.722521 1.25144i
$$172$$ −1.40097 2.42655i −1.40097 2.42655i
$$173$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ −0.356896 −0.356896
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −0.400969 0.694498i −0.400969 0.694498i
$$179$$ −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i $$-0.952381\pi$$
0.365341 0.930874i $$-0.380952\pi$$
$$180$$ 1.12349 1.94594i 1.12349 1.94594i
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 4.04892 4.04892
$$191$$ 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i $$-0.761905\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$192$$ 0 0
$$193$$ 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
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i $$0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$200$$ 0.623490 + 1.07992i 0.623490 + 1.07992i
$$201$$ 0 0
$$202$$ 3.24698 3.24698
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −0.400969 0.694498i −0.400969 0.694498i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0.222521 + 0.385418i 0.222521 + 0.385418i
$$214$$ 1.80194 + 3.12105i 1.80194 + 3.12105i
$$215$$ −0.777479 + 1.34663i −0.777479 + 1.34663i
$$216$$ −1.80194 −1.80194
$$217$$ 0 0
$$218$$ 0.801938 0.801938
$$219$$ 0.277479 0.480608i 0.277479 0.480608i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0.722521 1.25144i 0.722521 1.25144i
$$223$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$224$$ 0 0
$$225$$ −0.445042 −0.445042
$$226$$ 0 0
$$227$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ −0.900969 1.56052i −0.900969 1.56052i
$$229$$ −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i $$0.380952\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 1.00000 1.00000
$$233$$ 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i $$-0.476190\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −0.554958 −0.554958
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0.500000 0.866025i 0.500000 0.866025i
$$241$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$242$$ 0.900969 + 1.56052i 0.900969 + 1.56052i
$$243$$ 0.500000 0.866025i 0.500000 0.866025i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −0.400969 0.694498i −0.400969 0.694498i
$$250$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$251$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.900969 + 1.56052i 0.900969 + 1.56052i
$$257$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 1.00000 1.00000
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −0.178448 + 0.309081i −0.178448 + 0.309081i
$$262$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$263$$ −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i $$-0.952381\pi$$
0.365341 0.930874i $$-0.380952\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0.198062 0.198062
$$268$$ 0 0
$$269$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$270$$ 0.900969 + 1.56052i 0.900969 + 1.56052i
$$271$$ 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i $$-0.761905\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i $$0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 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 $$0.333333\pi$$
$$284$$ −1.12349 1.94594i −1.12349 1.94594i
$$285$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0.801938 0.801938
$$289$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$290$$ −0.500000 0.866025i −0.500000 0.866025i
$$291$$ 0 0
$$292$$ −1.40097 + 2.42655i −1.40097 + 2.42655i
$$293$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −2.02446 + 3.50647i −2.02446 + 3.50647i
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.554958 −0.554958
$$301$$ 0 0
$$302$$ 0.801938 0.801938
$$303$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$304$$ 1.62349 + 2.81197i 1.62349 + 2.81197i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0.198062 0.198062
$$310$$ 0 0
$$311$$ 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i $$0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$312$$ 0 0
$$313$$ 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i $$-0.476190\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$314$$ 0.801938 0.801938
$$315$$ 0 0
$$316$$ 2.80194 2.80194
$$317$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −0.890084 −0.890084
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −0.0990311 + 0.171527i −0.0990311 + 0.171527i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 2.02446 + 3.50647i 2.02446 + 3.50647i
$$333$$ −0.722521 1.25144i −0.722521 1.25144i
$$334$$ 1.12349 1.94594i 1.12349 1.94594i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0.900969 1.56052i 0.900969 1.56052i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −2.60388 −2.60388
$$343$$ 0 0
$$344$$ −2.80194 −2.80194
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$348$$ −0.222521 + 0.385418i −0.222521 + 0.385418i
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$354$$ 0 0
$$355$$ −0.623490 + 1.07992i −0.623490 + 1.07992i
$$356$$ −1.00000 −1.00000
$$357$$ 0 0
$$358$$ −2.24698 −2.24698
$$359$$ −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i $$0.380952\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$360$$ −1.12349 1.94594i −1.12349 1.94594i
$$361$$ −1.12349 1.94594i −1.12349 1.94594i
$$362$$ 0 0
$$363$$ −0.445042 −0.445042
$$364$$ 0 0
$$365$$ 1.55496 1.55496
$$366$$ 0 0
$$367$$ −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i $$-0.952381\pi$$
0.365341 0.930874i $$-0.380952\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 4.04892 4.04892
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i $$0.380952\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$374$$ 0 0
$$375$$ −0.123490 0.213891i −0.123490 0.213891i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$380$$ 2.52446 4.37249i 2.52446 4.37249i
$$381$$ 0 0
$$382$$ −0.400969 0.694498i −0.400969 0.694498i
$$383$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$384$$ −0.445042 −0.445042
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0.500000 0.866025i 0.500000 0.866025i
$$388$$ 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
$$393$$ −0.554958 −0.554958
$$394$$ 0 0
$$395$$ −0.777479 1.34663i −0.777479 1.34663i
$$396$$ 0 0
$$397$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$398$$ 3.24698 3.24698
$$399$$ 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
$$404$$ 2.02446 3.50647i 2.02446 3.50647i
$$405$$ 0.554958 0.554958
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −1.00000 −1.00000
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 1.12349 1.94594i 1.12349 1.94594i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0.801938 0.801938
$$427$$ 0 0
$$428$$ 4.49396 4.49396
$$429$$ 0 0
$$430$$ 1.40097 + 2.42655i 1.40097 + 2.42655i
$$431$$ 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i $$0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$432$$ −0.722521 + 1.25144i −0.722521 + 1.25144i
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0.246980 0.246980
$$436$$ 0.500000 0.866025i 0.500000 0.866025i
$$437$$ 0 0
$$438$$ −0.500000 0.866025i −0.500000 0.866025i
$$439$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ −0.900969 1.56052i −0.900969 1.56052i
$$445$$ 0.277479 + 0.480608i 0.277479 + 0.480608i
$$446$$ −1.62349 + 2.81197i −1.62349 + 2.81197i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −0.0990311 + 0.171527i −0.0990311 + 0.171527i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ −1.80194 −1.80194
$$457$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$458$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$464$$ 0.400969 0.694498i 0.400969 0.694498i
$$465$$ 0 0
$$466$$ −1.62349 2.81197i −1.62349 2.81197i
$$467$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −0.0990311 + 0.171527i −0.0990311 + 0.171527i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$475$$ −1.00000 −1.00000
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ −0.277479 0.480608i −0.277479 0.480608i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 2.24698 2.24698
$$485$$ 0 0
$$486$$ −0.900969 1.56052i −0.900969 1.56052i
$$487$$ 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
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −1.44504 −1.44504
$$499$$ 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i $$-0.761905\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$500$$ 0.623490 + 1.07992i 0.623490 + 1.07992i
$$501$$ 0.277479 + 0.480608i 0.277479 + 0.480608i
$$502$$ −1.62349 + 2.81197i −1.62349 + 2.81197i
$$503$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$504$$ 0 0
$$505$$ −2.24698 −2.24698
$$506$$ 0 0
$$507$$ 0.222521 + 0.385418i 0.222521 + 0.385418i
$$508$$ 0 0
$$509$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 2.24698 2.24698
$$513$$ 0.722521 1.25144i 0.722521 1.25144i
$$514$$ 0 0
$$515$$ 0.277479 + 0.480608i 0.277479 + 0.480608i
$$516$$ 0.623490 1.07992i 0.623490 1.07992i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i $$-0.952381\pi$$
0.365341 0.930874i $$-0.380952\pi$$
$$522$$ 0.321552 + 0.556945i 0.321552 + 0.556945i
$$523$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$524$$ 2.80194 2.80194
$$525$$ 0 0
$$526$$ −2.24698 −2.24698
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.500000 0.866025i −0.500000 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0.178448 0.309081i 0.178448 0.309081i
$$535$$ −1.24698 2.15983i −1.24698 2.15983i
$$536$$ 0 0
$$537$$ 0.277479 0.480608i 0.277479 0.480608i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 2.24698 2.24698
$$541$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$542$$ −0.400969 0.694498i −0.400969 0.694498i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −0.554958 −0.554958
$$546$$ 0 0
$$547$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 3.24698 3.24698
$$555$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$556$$ 0 0
$$557$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −2.24698 −2.24698
$$569$$ −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i $$0.380952\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$570$$ 0.900969 + 1.56052i 0.900969 + 1.56052i
$$571$$ 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i $$0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$572$$ 0 0
$$573$$ 0.198062 0.198062
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i $$-0.952381\pi$$
0.365341 0.930874i $$-0.380952\pi$$
$$578$$ 0.900969 + 1.56052i 0.900969 + 1.56052i
$$579$$ 0 0
$$580$$ −1.24698 −1.24698
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 1.40097 + 2.42655i 1.40097 + 2.42655i
$$585$$ 0 0
$$586$$ 1.80194 3.12105i 1.80194 3.12105i
$$587$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.62349 + 2.81197i 1.62349 + 2.81197i
$$593$$ 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i $$-0.761905\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$598$$ 0 0
$$599$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$600$$ −0.277479 + 0.480608i −0.277479 + 0.480608i
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0.500000 0.866025i 0.500000 0.866025i
$$605$$ −0.623490 1.07992i −0.623490 1.07992i
$$606$$ 0.722521 + 1.25144i 0.722521 + 1.25144i
$$607$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$608$$ 1.80194 1.80194
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$618$$ 0.178448 0.309081i 0.178448 0.309081i
$$619$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 3.24698 3.24698
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0.623490 1.07992i 0.623490 1.07992i
$$626$$ −1.62349 2.81197i −1.62349 2.81197i
$$627$$ 0 0
$$628$$ 0.500000 0.866025i 0.500000 0.866025i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 1.40097 2.42655i 1.40097 2.42655i
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0.400969 0.694498i 0.400969 0.694498i
$$640$$ −0.623490 1.07992i −0.623490 1.07992i
$$641$$ 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i $$0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$642$$ −0.801938 + 1.38900i −0.801938 + 1.38900i
$$643$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$644$$ 0 0
$$645$$ −0.692021 −0.692021
$$646$$ 0 0
$$647$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$648$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$654$$ 0.178448 + 0.309081i 0.178448 + 0.309081i
$$655$$ −0.777479 1.34663i −0.777479 1.34663i
$$656$$ 0 0
$$657$$ −1.00000 −1.00000
$$658$$ 0 0
$$659$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 4.04892 4.04892
$$665$$ 0 0
$$666$$ −2.60388 −2.60388
$$667$$ 0 0
$$668$$ −1.40097 2.42655i −1.40097 2.42655i
$$669$$ −0.400969 0.694498i −0.400969 0.694498i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −0.222521 0.385418i −0.222521 0.385418i
$$676$$ −1.12349 1.94594i −1.12349 1.94594i
$$677$$ 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i $$-0.761905\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$684$$ −1.62349 + 2.81197i −1.62349 + 2.81197i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −0.554958 −0.554958
$$688$$ −1.12349 + 1.94594i −1.12349 + 1.94594i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0.222521 + 0.385418i 0.222521 + 0.385418i
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0.801938 0.801938
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ −1.62349 2.81197i −1.62349 2.81197i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$710$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$711$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$712$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −1.40097 + 2.42655i −1.40097 + 2.42655i
$$717$$ 0 0
$$718$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$719$$ 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i $$-0.476190\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$720$$ −1.80194 −1.80194
$$721$$ 0 0
$$722$$ −4.04892 −4.04892
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0.123490 + 0.213891i 0.123490 + 0.213891i
$$726$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 1.40097 2.42655i 1.40097 2.42655i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$734$$ −2.24698 −2.24698
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 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 $$-0.666667\pi$$
$$740$$ 2.52446 4.37249i 2.52446 4.37249i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 1.12349 + 1.94594i 1.12349 + 1.94594i
$$747$$ −0.722521 + 1.25144i −0.722521 + 1.25144i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −0.445042 −0.445042
$$751$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 0 0
$$753$$ −0.400969 0.694498i −0.400969 0.694498i
$$754$$ 0 0
$$755$$ −0.554958 −0.554958
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$759$$ 0 0
$$760$$ −2.52446 4.37249i −2.52446 4.37249i
$$761$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −1.00000 −1.00000
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −0.400969 + 0.694498i −0.400969 + 0.694498i
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$774$$ −0.900969 1.56052i −0.900969 1.56052i
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −0.356896 −0.356896
$$784$$ 0 0
$$785$$ −0.554958 −0.554958
$$786$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$787$$ 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i $$-0.0952381\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$788$$ 0 0
$$789$$ 0.277479 0.480608i 0.277479 0.480608i
$$790$$ −2.80194 −2.80194
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 2.02446 3.50647i 2.02446 3.50647i
$$797$$ −1.80194 −1.80194 </