# Properties

 Label 3332.1.be.b.1359.1 Level $3332$ Weight $1$ Character 3332.1359 Analytic conductor $1.663$ Analytic rank $0$ Dimension $6$ Projective image $D_{7}$ CM discriminant -68 Inner twists $4$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(407,3332)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 10, 7]))

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

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

chi := DirichletCharacter("3332.407");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.be (of order $$14$$, degree $$6$$, 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: $$1.66288462209$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: $$\Q(\zeta_{14})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{7}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{7} - \cdots)$$

## Embedding invariants

 Embedding label 1359.1 Root $$0.900969 - 0.433884i$$ of defining polynomial Character $$\chi$$ $$=$$ 3332.1359 Dual form 3332.1.be.b.407.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.222521 - 0.974928i) q^{2} +(0.777479 + 0.974928i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.777479 - 0.974928i) q^{6} +(0.623490 + 0.781831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.123490 + 0.541044i) q^{9} +O(q^{10})$$ $$q+(-0.222521 - 0.974928i) q^{2} +(0.777479 + 0.974928i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.777479 - 0.974928i) q^{6} +(0.623490 + 0.781831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.123490 + 0.541044i) q^{9} +(0.0990311 + 0.433884i) q^{11} +(-1.12349 - 0.541044i) q^{12} +(0.0990311 + 0.433884i) q^{13} +(0.623490 - 0.781831i) q^{14} +(0.623490 - 0.781831i) q^{16} +(-0.900969 - 0.433884i) q^{17} +0.554958 q^{18} +(-0.277479 + 1.21572i) q^{21} +(0.400969 - 0.193096i) q^{22} +(0.400969 - 0.193096i) q^{23} +(-0.277479 + 1.21572i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(0.400969 - 0.193096i) q^{26} +(0.500000 - 0.240787i) q^{27} +(-0.900969 - 0.433884i) q^{28} +1.24698 q^{31} +(-0.900969 - 0.433884i) q^{32} +(-0.346011 + 0.433884i) q^{33} +(-0.222521 + 0.974928i) q^{34} +(-0.123490 - 0.541044i) q^{36} +(-0.346011 + 0.433884i) q^{39} +1.24698 q^{42} +(-0.277479 - 0.347948i) q^{44} +(-0.277479 - 0.347948i) q^{46} +1.24698 q^{48} +(-0.222521 + 0.974928i) q^{49} +1.00000 q^{50} +(-0.277479 - 1.21572i) q^{51} +(-0.277479 - 0.347948i) q^{52} +(-1.12349 + 0.541044i) q^{53} +(-0.346011 - 0.433884i) q^{54} +(-0.222521 + 0.974928i) q^{56} +(-0.277479 - 1.21572i) q^{62} +(-0.500000 + 0.240787i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(0.500000 + 0.240787i) q^{66} +1.00000 q^{68} +(0.500000 + 0.240787i) q^{69} +(-1.12349 + 0.541044i) q^{71} +(-0.500000 + 0.240787i) q^{72} +(-1.12349 + 0.541044i) q^{75} +(-0.277479 + 0.347948i) q^{77} +(0.500000 + 0.240787i) q^{78} -0.445042 q^{79} +(1.12349 + 0.541044i) q^{81} +(-0.277479 - 1.21572i) q^{84} +(-0.277479 + 0.347948i) q^{88} +(-0.277479 + 1.21572i) q^{89} +(-0.277479 + 0.347948i) q^{91} +(-0.277479 + 0.347948i) q^{92} +(0.969501 + 1.21572i) q^{93} +(-0.277479 - 1.21572i) q^{96} +1.00000 q^{98} -0.246980 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - q^{2} + 5 q^{3} - q^{4} + 5 q^{6} - q^{7} - q^{8} + 4 q^{9}+O(q^{10})$$ 6 * q - q^2 + 5 * q^3 - q^4 + 5 * q^6 - q^7 - q^8 + 4 * q^9 $$6 q - q^{2} + 5 q^{3} - q^{4} + 5 q^{6} - q^{7} - q^{8} + 4 q^{9} + 5 q^{11} - 2 q^{12} + 5 q^{13} - q^{14} - q^{16} - q^{17} + 4 q^{18} - 2 q^{21} - 2 q^{22} - 2 q^{23} - 2 q^{24} - q^{25} - 2 q^{26} + 3 q^{27} - q^{28} - 2 q^{31} - q^{32} + 3 q^{33} - q^{34} + 4 q^{36} + 3 q^{39} - 2 q^{42} - 2 q^{44} - 2 q^{46} - 2 q^{48} - q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} + 3 q^{54} - q^{56} - 2 q^{62} - 3 q^{63} - q^{64} + 3 q^{66} + 6 q^{68} + 3 q^{69} - 2 q^{71} - 3 q^{72} - 2 q^{75} - 2 q^{77} + 3 q^{78} - 2 q^{79} + 2 q^{81} - 2 q^{84} - 2 q^{88} - 2 q^{89} - 2 q^{91} - 2 q^{92} - 4 q^{93} - 2 q^{96} + 6 q^{98} + 8 q^{99}+O(q^{100})$$ 6 * q - q^2 + 5 * q^3 - q^4 + 5 * q^6 - q^7 - q^8 + 4 * q^9 + 5 * q^11 - 2 * q^12 + 5 * q^13 - q^14 - q^16 - q^17 + 4 * q^18 - 2 * q^21 - 2 * q^22 - 2 * q^23 - 2 * q^24 - q^25 - 2 * q^26 + 3 * q^27 - q^28 - 2 * q^31 - q^32 + 3 * q^33 - q^34 + 4 * q^36 + 3 * q^39 - 2 * q^42 - 2 * q^44 - 2 * q^46 - 2 * q^48 - q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 + 3 * q^54 - q^56 - 2 * q^62 - 3 * q^63 - q^64 + 3 * q^66 + 6 * q^68 + 3 * q^69 - 2 * q^71 - 3 * q^72 - 2 * q^75 - 2 * q^77 + 3 * q^78 - 2 * q^79 + 2 * q^81 - 2 * q^84 - 2 * q^88 - 2 * q^89 - 2 * q^91 - 2 * q^92 - 4 * q^93 - 2 * q^96 + 6 * q^98 + 8 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$885$$ $$1667$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.222521 0.974928i −0.222521 0.974928i
$$3$$ 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 $$0$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$4$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$5$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$6$$ 0.777479 0.974928i 0.777479 0.974928i
$$7$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$8$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$9$$ −0.123490 + 0.541044i −0.123490 + 0.541044i
$$10$$ 0 0
$$11$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 $$0$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$12$$ −1.12349 0.541044i −1.12349 0.541044i
$$13$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 $$0$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$14$$ 0.623490 0.781831i 0.623490 0.781831i
$$15$$ 0 0
$$16$$ 0.623490 0.781831i 0.623490 0.781831i
$$17$$ −0.900969 0.433884i −0.900969 0.433884i
$$18$$ 0.554958 0.554958
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ −0.277479 + 1.21572i −0.277479 + 1.21572i
$$22$$ 0.400969 0.193096i 0.400969 0.193096i
$$23$$ 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$24$$ −0.277479 + 1.21572i −0.277479 + 1.21572i
$$25$$ −0.222521 + 0.974928i −0.222521 + 0.974928i
$$26$$ 0.400969 0.193096i 0.400969 0.193096i
$$27$$ 0.500000 0.240787i 0.500000 0.240787i
$$28$$ −0.900969 0.433884i −0.900969 0.433884i
$$29$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$30$$ 0 0
$$31$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$32$$ −0.900969 0.433884i −0.900969 0.433884i
$$33$$ −0.346011 + 0.433884i −0.346011 + 0.433884i
$$34$$ −0.222521 + 0.974928i −0.222521 + 0.974928i
$$35$$ 0 0
$$36$$ −0.123490 0.541044i −0.123490 0.541044i
$$37$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$38$$ 0 0
$$39$$ −0.346011 + 0.433884i −0.346011 + 0.433884i
$$40$$ 0 0
$$41$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$42$$ 1.24698 1.24698
$$43$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$44$$ −0.277479 0.347948i −0.277479 0.347948i
$$45$$ 0 0
$$46$$ −0.277479 0.347948i −0.277479 0.347948i
$$47$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$48$$ 1.24698 1.24698
$$49$$ −0.222521 + 0.974928i −0.222521 + 0.974928i
$$50$$ 1.00000 1.00000
$$51$$ −0.277479 1.21572i −0.277479 1.21572i
$$52$$ −0.277479 0.347948i −0.277479 0.347948i
$$53$$ −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i $$-0.857143\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$54$$ −0.346011 0.433884i −0.346011 0.433884i
$$55$$ 0 0
$$56$$ −0.222521 + 0.974928i −0.222521 + 0.974928i
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$62$$ −0.277479 1.21572i −0.277479 1.21572i
$$63$$ −0.500000 + 0.240787i −0.500000 + 0.240787i
$$64$$ −0.222521 + 0.974928i −0.222521 + 0.974928i
$$65$$ 0 0
$$66$$ 0.500000 + 0.240787i 0.500000 + 0.240787i
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 1.00000 1.00000
$$69$$ 0.500000 + 0.240787i 0.500000 + 0.240787i
$$70$$ 0 0
$$71$$ −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i $$-0.857143\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$72$$ −0.500000 + 0.240787i −0.500000 + 0.240787i
$$73$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$74$$ 0 0
$$75$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$76$$ 0 0
$$77$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$78$$ 0.500000 + 0.240787i 0.500000 + 0.240787i
$$79$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$80$$ 0 0
$$81$$ 1.12349 + 0.541044i 1.12349 + 0.541044i
$$82$$ 0 0
$$83$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$84$$ −0.277479 1.21572i −0.277479 1.21572i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$89$$ −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i $$0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$90$$ 0 0
$$91$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$92$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$93$$ 0.969501 + 1.21572i 0.969501 + 1.21572i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −0.277479 1.21572i −0.277479 1.21572i
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 1.00000 1.00000
$$99$$ −0.246980 −0.246980
$$100$$ −0.222521 0.974928i −0.222521 0.974928i
$$101$$ −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i $$-0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$102$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$103$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$104$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$105$$ 0 0
$$106$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$107$$ 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$108$$ −0.346011 + 0.433884i −0.346011 + 0.433884i
$$109$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 1.00000 1.00000
$$113$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −0.246980 −0.246980
$$118$$ 0 0
$$119$$ −0.222521 0.974928i −0.222521 0.974928i
$$120$$ 0 0
$$121$$ 0.722521 0.347948i 0.722521 0.347948i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$125$$ 0 0
$$126$$ 0.346011 + 0.433884i 0.346011 + 0.433884i
$$127$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$128$$ 1.00000 1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$132$$ 0.123490 0.541044i 0.123490 0.541044i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ −0.222521 0.974928i −0.222521 0.974928i
$$137$$ 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i $$-0.571429\pi$$
1.00000 $$0$$
$$138$$ 0.123490 0.541044i 0.123490 0.541044i
$$139$$ −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i $$-0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$143$$ −0.178448 + 0.0859360i −0.178448 + 0.0859360i
$$144$$ 0.346011 + 0.433884i 0.346011 + 0.433884i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$148$$ 0 0
$$149$$ −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$150$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$151$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$152$$ 0 0
$$153$$ 0.346011 0.433884i 0.346011 0.433884i
$$154$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$155$$ 0 0
$$156$$ 0.123490 0.541044i 0.123490 0.541044i
$$157$$ −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$158$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$159$$ −1.40097 0.674671i −1.40097 0.674671i
$$160$$ 0 0
$$161$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$162$$ 0.277479 1.21572i 0.277479 1.21572i
$$163$$ 1.24698 1.56366i 1.24698 1.56366i 0.623490 0.781831i $$-0.285714\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 $$0$$
0.623490 + 0.781831i $$0.285714\pi$$
$$168$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$169$$ 0.722521 0.347948i 0.722521 0.347948i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$174$$ 0 0
$$175$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$176$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$177$$ 0 0
$$178$$ 1.24698 1.24698
$$179$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$180$$ 0 0
$$181$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$182$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$183$$ 0 0
$$184$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$185$$ 0 0
$$186$$ 0.969501 1.21572i 0.969501 1.21572i
$$187$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$188$$ 0 0
$$189$$ 0.500000 + 0.240787i 0.500000 + 0.240787i
$$190$$ 0 0
$$191$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$192$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$193$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −0.222521 0.974928i −0.222521 0.974928i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0.0549581 + 0.240787i 0.0549581 + 0.240787i
$$199$$ 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 $$0$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$200$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$201$$ 0 0
$$202$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$203$$ 0 0
$$204$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0.0549581 + 0.240787i 0.0549581 + 0.240787i
$$208$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$212$$ 0.777479 0.974928i 0.777479 0.974928i
$$213$$ −1.40097 0.674671i −1.40097 0.674671i
$$214$$ −1.80194 −1.80194
$$215$$ 0 0
$$216$$ 0.500000 + 0.240787i 0.500000 + 0.240787i
$$217$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$222$$ 0 0
$$223$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$224$$ −0.222521 0.974928i −0.222521 0.974928i
$$225$$ −0.500000 0.240787i −0.500000 0.240787i
$$226$$ 0 0
$$227$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$228$$ 0 0
$$229$$ −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i $$0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$230$$ 0 0
$$231$$ −0.554958 −0.554958
$$232$$ 0 0
$$233$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$234$$ 0.0549581 + 0.240787i 0.0549581 + 0.240787i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −0.346011 0.433884i −0.346011 0.433884i
$$238$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$239$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$240$$ 0 0
$$241$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$242$$ −0.500000 0.626980i −0.500000 0.626980i
$$243$$ 0.222521 + 0.974928i 0.222521 + 0.974928i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$252$$ 0.346011 0.433884i 0.346011 0.433884i
$$253$$ 0.123490 + 0.154851i 0.123490 + 0.154851i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.222521 0.974928i −0.222521 0.974928i
$$257$$ −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 0.433884i $$-0.857143\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ −0.554958 −0.554958
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −1.40097 + 0.674671i −1.40097 + 0.674671i
$$268$$ 0 0
$$269$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$272$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$273$$ −0.554958 −0.554958
$$274$$ −1.12349 0.541044i −1.12349 0.541044i
$$275$$ −0.445042 −0.445042
$$276$$ −0.554958 −0.554958
$$277$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$278$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$279$$ −0.153989 + 0.674671i −0.153989 + 0.674671i
$$280$$ 0 0
$$281$$ −0.445042 1.94986i −0.445042 1.94986i −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$282$$ 0 0
$$283$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 $$0$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$284$$ 0.777479 0.974928i 0.777479 0.974928i
$$285$$ 0 0
$$286$$ 0.123490 + 0.154851i 0.123490 + 0.154851i
$$287$$ 0 0
$$288$$ 0.346011 0.433884i 0.346011 0.433884i
$$289$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$294$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0.153989 + 0.193096i 0.153989 + 0.193096i
$$298$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$299$$ 0.123490 + 0.154851i 0.123490 + 0.154851i
$$300$$ 0.777479 0.974928i 0.777479 0.974928i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0.123490 0.541044i 0.123490 0.541044i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −0.500000 0.240787i −0.500000 0.240787i
$$307$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$308$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 0.433884i $$-0.857143\pi$$
$$312$$ −0.554958 −0.554958
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$315$$ 0 0
$$316$$ 0.400969 0.193096i 0.400969 0.193096i
$$317$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$318$$ −0.346011 + 1.51597i −0.346011 + 1.51597i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 2.02446 0.974928i 2.02446 0.974928i
$$322$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$323$$ 0 0
$$324$$ −1.24698 −1.24698
$$325$$ −0.445042 −0.445042
$$326$$ −1.80194 0.867767i −1.80194 0.867767i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0.400969 1.75676i 0.400969 1.75676i
$$335$$ 0 0
$$336$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$337$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$338$$ −0.500000 0.626980i −0.500000 0.626980i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$342$$ 0 0
$$343$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i $$-0.285714\pi$$
1.00000 $$0$$
$$348$$ 0 0
$$349$$ −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i $$0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$350$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$351$$ 0.153989 + 0.193096i 0.153989 + 0.193096i
$$352$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$353$$ 1.24698 1.56366i 1.24698 1.56366i 0.623490 0.781831i $$-0.285714\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −0.277479 1.21572i −0.277479 1.21572i
$$357$$ 0.777479 0.974928i 0.777479 0.974928i
$$358$$ 0 0
$$359$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 0 0
$$363$$ 0.900969 + 0.433884i 0.900969 + 0.433884i
$$364$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$368$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −1.12349 0.541044i −1.12349 0.541044i
$$372$$ −1.40097 0.674671i −1.40097 0.674671i
$$373$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$374$$ −0.445042 −0.445042
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0.123490 0.541044i 0.123490 0.541044i
$$379$$ −0.445042 1.94986i −0.445042 1.94986i −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$384$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i $$-0.857143\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$390$$ 0 0
$$391$$ −0.445042 −0.445042
$$392$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$393$$ −0.554958 −0.554958
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.222521 0.107160i 0.222521 0.107160i
$$397$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$398$$ 0.777479 0.974928i 0.777479 0.974928i
$$399$$ 0 0
$$400$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$401$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$402$$ 0 0
$$403$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$404$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0.777479 0.974928i 0.777479 0.974928i
$$409$$ −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i $$-0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$410$$ 0 0
$$411$$ 1.55496 1.55496
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0.222521 0.107160i 0.222521 0.107160i
$$415$$ 0 0
$$416$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$417$$ 0.123490 0.541044i 0.123490 0.541044i
$$418$$ 0 0
$$419$$ 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$420$$ 0 0
$$421$$ −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i $$-0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$422$$ −1.80194 −1.80194
$$423$$ 0 0
$$424$$ −1.12349 0.541044i −1.12349 0.541044i
$$425$$ 0.623490 0.781831i 0.623490 0.781831i
$$426$$ −0.346011 + 1.51597i −0.346011 + 1.51597i
$$427$$ 0 0
$$428$$ 0.400969 + 1.75676i 0.400969 + 1.75676i
$$429$$ −0.222521 0.107160i −0.222521 0.107160i
$$430$$ 0 0
$$431$$ 1.24698 1.56366i 1.24698 1.56366i 0.623490 0.781831i $$-0.285714\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$432$$ 0.123490 0.541044i 0.123490 0.541044i
$$433$$ −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i $$-0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$434$$ 0.777479 0.974928i 0.777479 0.974928i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 $$0$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$440$$ 0 0
$$441$$ −0.500000 0.240787i −0.500000 0.240787i
$$442$$ −0.445042 −0.445042
$$443$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0.969501 1.21572i 0.969501 1.21572i
$$448$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$449$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$450$$ −0.123490 + 0.541044i −0.123490 + 0.541044i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −0.277479 1.21572i −0.277479 1.21572i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$458$$ 1.62349 + 0.781831i 1.62349 + 0.781831i
$$459$$ −0.554958 −0.554958
$$460$$ 0 0
$$461$$ −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i $$-0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$462$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$463$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$468$$ 0.222521 0.107160i 0.222521 0.107160i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −0.554958 −0.554958
$$472$$ 0 0
$$473$$ 0 0
$$474$$ −0.346011 + 0.433884i −0.346011 + 0.433884i
$$475$$ 0 0
$$476$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$477$$ −0.153989 0.674671i −0.153989 0.674671i
$$478$$ 0 0
$$479$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 $$0$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$484$$ −0.500000 + 0.626980i −0.500000 + 0.626980i
$$485$$ 0 0
$$486$$ 0.900969 0.433884i 0.900969 0.433884i
$$487$$ 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i $$0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$488$$ 0 0
$$489$$ 2.49396 2.49396
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0.777479 0.974928i 0.777479 0.974928i
$$497$$ −1.12349 0.541044i −1.12349 0.541044i
$$498$$ 0 0
$$499$$ 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i $$-0.857143\pi$$
1.00000 $$0$$
$$500$$ 0 0
$$501$$ 0.500000 + 2.19064i 0.500000 + 2.19064i
$$502$$ 0 0
$$503$$ 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i $$0.285714\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$504$$ −0.500000 0.240787i −0.500000 0.240787i
$$505$$ 0 0
$$506$$ 0.123490 0.154851i 0.123490 0.154851i
$$507$$ 0.900969 + 0.433884i 0.900969 + 0.433884i
$$508$$ 0 0
$$509$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$513$$ 0 0
$$514$$ −0.445042 + 1.94986i −0.445042 + 1.94986i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$524$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$525$$ −1.12349 0.541044i −1.12349 0.541044i
$$526$$ 0 0
$$527$$ −1.12349 0.541044i −1.12349 0.541044i
$$528$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$529$$ −0.500000 + 0.626980i −0.500000 + 0.626980i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0.969501 + 1.21572i 0.969501 + 1.21572i
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −0.445042 −0.445042
$$540$$ 0 0
$$541$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$545$$ 0 0
$$546$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$547$$ −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i $$-0.857143\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$548$$ −0.277479 + 1.21572i −0.277479 + 1.21572i
$$549$$ 0 0
$$550$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$551$$ 0 0
$$552$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$553$$ −0.277479 0.347948i −0.277479 0.347948i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0.400969 + 0.193096i 0.400969 + 0.193096i
$$557$$ 1.24698 1.24698 0.623490 0.781831i $$-0.285714\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$558$$ 0.692021 0.692021
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0.500000 0.240787i 0.500000 0.240787i
$$562$$ −1.80194 + 0.867767i −1.80194 + 0.867767i
$$563$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0.400969 0.193096i 0.400969 0.193096i
$$567$$ 0.277479 + 1.21572i 0.277479 + 1.21572i
$$568$$ −1.12349 0.541044i −1.12349 0.541044i
$$569$$ −0.445042 −0.445042 −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$570$$ 0 0
$$571$$ −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i $$-0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$572$$ 0.123490 0.154851i 0.123490 0.154851i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$576$$ −0.500000 0.240787i −0.500000 0.240787i
$$577$$ 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i $$0.285714\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$578$$ 0.623490 0.781831i 0.623490 0.781831i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −0.346011 0.433884i −0.346011 0.433884i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0.777479 0.974928i 0.777479 0.974928i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i $$-0.857143\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$594$$ 0.153989 0.193096i 0.153989 0.193096i
$$595$$ 0 0
$$596$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$597$$ −0.346011 + 1.51597i −0.346011 + 1.51597i
$$598$$ 0.123490 0.154851i 0.123490 0.154851i
$$599$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$600$$ −1.12349 0.541044i −1.12349 0.541044i
$$601$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ −0.554958 −0.554958
$$607$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −0.123490 + 0.541044i −0.123490 + 0.541044i
$$613$$ 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ −0.445042 −0.445042
$$617$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$618$$ 0 0
$$619$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$620$$ 0 0
$$621$$ 0.153989 0.193096i 0.153989 0.193096i
$$622$$ −0.445042 + 1.94986i −0.445042 + 1.94986i
$$623$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$624$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$625$$ −0.900969 0.433884i −0.900969 0.433884i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$632$$ −0.277479 0.347948i −0.277479 0.347948i
$$633$$ 2.02446 0.974928i 2.02446 0.974928i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 1.55496 1.55496
$$637$$ −0.445042 −0.445042
$$638$$ 0 0
$$639$$ −0.153989 0.674671i −0.153989 0.674671i
$$640$$ 0 0
$$641$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$642$$ −1.40097 1.75676i −1.40097 1.75676i
$$643$$ −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i $$0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$644$$ −0.445042 −0.445042
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$648$$ 0.277479 + 1.21572i 0.277479 + 1.21572i
$$649$$ 0 0
$$650$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$651$$ −0.346011 + 1.51597i −0.346011 + 1.51597i
$$652$$ −0.445042 + 1.94986i −0.445042 + 1.94986i
$$653$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$660$$ 0 0
$$661$$ −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i $$0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$662$$ 0 0
$$663$$ 0.500000 0.240787i 0.500000 0.240787i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −1.80194 −1.80194
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0.777479 0.974928i 0.777479 0.974928i
$$673$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$674$$ 0 0
$$675$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$676$$ −0.500000 + 0.626980i −0.500000 + 0.626980i
$$677$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0.969501 + 1.21572i 0.969501 + 1.21572i
$$682$$ 0.500000 0.240787i 0.500000 0.240787i
$$683$$ 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 $$0$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$687$$ −2.24698 −2.24698
$$688$$ 0 0
$$689$$ −0.346011 0.433884i −0.346011 0.433884i
$$690$$ 0 0
$$691$$ 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 $$0$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$692$$ 0 0
$$693$$ −0.153989 0.193096i −0.153989 0.193096i
$$694$$ −1.12349 1.40881i −1.12349 1.40881i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 1.62349 + 0.781831i 1.62349 + 0.781831i
$$699$$ 0 0
$$700$$ 0.623490 0.781831i 0.623490 0.781831i
$$701$$ −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i $$0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$702$$ 0.153989 0.193096i 0.153989 0.193096i
$$703$$ 0 0
$$704$$ −0.445042 −0.445042
$$705$$ 0 0
$$706$$ −1.80194 0.867767i −1.80194 0.867767i
$$707$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$708$$ 0 0
$$709$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$710$$ 0 0
$$711$$ 0.0549581 0.240787i 0.0549581 0.240787i
$$712$$ −1.12349 + 0.541044i −1.12349 + 0.541044i
$$713$$ 0.500000 0.240787i 0.500000 0.240787i
$$714$$ −1.12349 0.541044i −1.12349 0.541044i
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −0.222521 0.974928i −0.222521 0.974928i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0.222521 0.974928i 0.222521 0.974928i
$$727$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$728$$ −0.445042 −0.445042
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −0.445042 1.94986i −0.445042 1.94986i −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$734$$ −1.80194 −1.80194
$$735$$ 0 0
$$736$$ −0.445042 −0.445042
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −0.277479 + 1.21572i −0.277479 + 1.21572i
$$743$$ 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 $$0$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$744$$ −0.346011 + 1.51597i −0.346011 + 1.51597i
$$745$$ 0 0
$$746$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$747$$ 0 0
$$748$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$749$$ 1.62349 0.781831i 1.62349 0.781831i
$$750$$ 0 0
$$751$$ −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −0.554958 −0.554958
$$757$$ −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i $$0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$758$$ −1.80194 + 0.867767i −1.80194 + 0.867767i
$$759$$ −0.0549581 + 0.240787i −0.0549581 + 0.240787i
$$760$$ 0 0
$$761$$ 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i $$-0.285714\pi$$
1.00000 $$0$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.777479 0.974928i 0.777479 0.974928i
$$769$$ −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i $$0.571429\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$770$$ 0 0
$$771$$ −0.554958 2.43143i −0.554958 2.43143i
$$772$$ 0 0
$$773$$ 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i $$0.285714\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$774$$ 0 0
$$775$$ −0.277479 + 1.21572i −0.277479 + 1.21572i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −1.12349 + 1.40881i −1.12349 + 1.40881i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −0.346011 0.433884i −0.346011 0.433884i
$$782$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$783$$ 0 0
$$784$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$785$$ 0 0
$$786$$ 0.123490 + 0.541044i 0.123490 + 0.541044i
$$787$$ −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i $$-0.857143\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$