# Properties

 Label 3332.1.be.c.1835.2 Level $3332$ Weight $1$ Character 3332.1835 Analytic conductor $1.663$ Analytic rank $0$ Dimension $12$ Projective image $D_{14}$ CM discriminant -68 Inner twists $8$

# Related objects

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: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{14})$$ Coefficient field: $$\Q(\zeta_{28})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$$ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{14}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{14} - \cdots)$$

## Embedding invariants

 Embedding label 1835.2 Root $$-0.433884 - 0.900969i$$ of defining polynomial Character $$\chi$$ $$=$$ 3332.1835 Dual form 3332.1.be.c.3263.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.900969 - 0.433884i) q^{2} +(0.433884 - 1.90097i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.433884 - 1.90097i) q^{6} +(0.974928 + 0.222521i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.52446 - 1.21572i) q^{9} +O(q^{10})$$ $$q+(0.900969 - 0.433884i) q^{2} +(0.433884 - 1.90097i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.433884 - 1.90097i) q^{6} +(0.974928 + 0.222521i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.52446 - 1.21572i) q^{9} +(0.781831 - 0.376510i) q^{11} +(-1.21572 - 1.52446i) q^{12} +(-1.62349 + 0.781831i) q^{13} +(0.974928 - 0.222521i) q^{14} +(-0.222521 - 0.974928i) q^{16} +(0.623490 + 0.781831i) q^{17} -2.80194 q^{18} +(0.846011 - 1.75676i) q^{21} +(0.541044 - 0.678448i) q^{22} +(-0.541044 + 0.678448i) q^{23} +(-1.75676 - 0.846011i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-1.12349 + 1.40881i) q^{26} +(-2.19064 + 2.74698i) q^{27} +(0.781831 - 0.623490i) q^{28} +1.94986 q^{31} +(-0.623490 - 0.781831i) q^{32} +(-0.376510 - 1.64960i) q^{33} +(0.900969 + 0.433884i) q^{34} +(-2.52446 + 1.21572i) q^{36} +(0.781831 + 3.42543i) q^{39} -1.94986i q^{42} +(0.193096 - 0.846011i) q^{44} +(-0.193096 + 0.846011i) q^{46} -1.94986 q^{48} +(0.900969 + 0.433884i) q^{49} -1.00000 q^{50} +(1.75676 - 0.846011i) q^{51} +(-0.400969 + 1.75676i) q^{52} +(-0.277479 + 0.347948i) q^{53} +(-0.781831 + 3.42543i) q^{54} +(0.433884 - 0.900969i) q^{56} +(1.75676 - 0.846011i) q^{62} +(-2.19064 - 1.74698i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.05496 - 1.32288i) q^{66} +1.00000 q^{68} +(1.05496 + 1.32288i) q^{69} +(1.21572 - 1.52446i) q^{71} +(-1.74698 + 2.19064i) q^{72} +(-1.21572 + 1.52446i) q^{75} +(0.846011 - 0.193096i) q^{77} +(2.19064 + 2.74698i) q^{78} +0.867767 q^{79} +(2.52446 + 3.16557i) q^{81} +(-0.846011 - 1.75676i) q^{84} +(-0.193096 - 0.846011i) q^{88} +(-0.400969 - 0.193096i) q^{89} +(-1.75676 + 0.400969i) q^{91} +(0.193096 + 0.846011i) q^{92} +(0.846011 - 3.70662i) q^{93} +(-1.75676 + 0.846011i) q^{96} +1.00000 q^{98} -2.43143 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 2 q^{2} - 2 q^{4} + 2 q^{8} - 12 q^{9}+O(q^{10})$$ 12 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 - 12 * q^9 $$12 q + 2 q^{2} - 2 q^{4} + 2 q^{8} - 12 q^{9} - 10 q^{13} - 2 q^{16} - 2 q^{17} - 16 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 14 q^{33} + 2 q^{34} - 12 q^{36} + 2 q^{49} - 12 q^{50} + 4 q^{52} - 4 q^{53} - 2 q^{64} - 14 q^{66} + 12 q^{68} + 14 q^{69} - 2 q^{72} + 12 q^{81} + 4 q^{89} + 12 q^{98}+O(q^{100})$$ 12 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 - 12 * q^9 - 10 * q^13 - 2 * q^16 - 2 * q^17 - 16 * q^18 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 14 * q^33 + 2 * q^34 - 12 * q^36 + 2 * q^49 - 12 * q^50 + 4 * q^52 - 4 * q^53 - 2 * q^64 - 14 * q^66 + 12 * q^68 + 14 * q^69 - 2 * q^72 + 12 * q^81 + 4 * q^89 + 12 * q^98

## Character values

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

 $$n$$ $$785$$ $$885$$ $$1667$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{4}{7}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.900969 0.433884i 0.900969 0.433884i
$$3$$ 0.433884 1.90097i 0.433884 1.90097i 1.00000i $$-0.5\pi$$
0.433884 0.900969i $$-0.357143\pi$$
$$4$$ 0.623490 0.781831i 0.623490 0.781831i
$$5$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$6$$ −0.433884 1.90097i −0.433884 1.90097i
$$7$$ 0.974928 + 0.222521i 0.974928 + 0.222521i
$$8$$ 0.222521 0.974928i 0.222521 0.974928i
$$9$$ −2.52446 1.21572i −2.52446 1.21572i
$$10$$ 0 0
$$11$$ 0.781831 0.376510i 0.781831 0.376510i 1.00000i $$-0.5\pi$$
0.781831 + 0.623490i $$0.214286\pi$$
$$12$$ −1.21572 1.52446i −1.21572 1.52446i
$$13$$ −1.62349 + 0.781831i −1.62349 + 0.781831i −0.623490 + 0.781831i $$0.714286\pi$$
−1.00000 $$1.00000\pi$$
$$14$$ 0.974928 0.222521i 0.974928 0.222521i
$$15$$ 0 0
$$16$$ −0.222521 0.974928i −0.222521 0.974928i
$$17$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$18$$ −2.80194 −2.80194
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0.846011 1.75676i 0.846011 1.75676i
$$22$$ 0.541044 0.678448i 0.541044 0.678448i
$$23$$ −0.541044 + 0.678448i −0.541044 + 0.678448i −0.974928 0.222521i $$-0.928571\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$24$$ −1.75676 0.846011i −1.75676 0.846011i
$$25$$ −0.900969 0.433884i −0.900969 0.433884i
$$26$$ −1.12349 + 1.40881i −1.12349 + 1.40881i
$$27$$ −2.19064 + 2.74698i −2.19064 + 2.74698i
$$28$$ 0.781831 0.623490i 0.781831 0.623490i
$$29$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$30$$ 0 0
$$31$$ 1.94986 1.94986 0.974928 0.222521i $$-0.0714286\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$32$$ −0.623490 0.781831i −0.623490 0.781831i
$$33$$ −0.376510 1.64960i −0.376510 1.64960i
$$34$$ 0.900969 + 0.433884i 0.900969 + 0.433884i
$$35$$ 0 0
$$36$$ −2.52446 + 1.21572i −2.52446 + 1.21572i
$$37$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$38$$ 0 0
$$39$$ 0.781831 + 3.42543i 0.781831 + 3.42543i
$$40$$ 0 0
$$41$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$42$$ 1.94986i 1.94986i
$$43$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$44$$ 0.193096 0.846011i 0.193096 0.846011i
$$45$$ 0 0
$$46$$ −0.193096 + 0.846011i −0.193096 + 0.846011i
$$47$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$48$$ −1.94986 −1.94986
$$49$$ 0.900969 + 0.433884i 0.900969 + 0.433884i
$$50$$ −1.00000 −1.00000
$$51$$ 1.75676 0.846011i 1.75676 0.846011i
$$52$$ −0.400969 + 1.75676i −0.400969 + 1.75676i
$$53$$ −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$54$$ −0.781831 + 3.42543i −0.781831 + 3.42543i
$$55$$ 0 0
$$56$$ 0.433884 0.900969i 0.433884 0.900969i
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$62$$ 1.75676 0.846011i 1.75676 0.846011i
$$63$$ −2.19064 1.74698i −2.19064 1.74698i
$$64$$ −0.900969 0.433884i −0.900969 0.433884i
$$65$$ 0 0
$$66$$ −1.05496 1.32288i −1.05496 1.32288i
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 1.00000 1.00000
$$69$$ 1.05496 + 1.32288i 1.05496 + 1.32288i
$$70$$ 0 0
$$71$$ 1.21572 1.52446i 1.21572 1.52446i 0.433884 0.900969i $$-0.357143\pi$$
0.781831 0.623490i $$-0.214286\pi$$
$$72$$ −1.74698 + 2.19064i −1.74698 + 2.19064i
$$73$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$74$$ 0 0
$$75$$ −1.21572 + 1.52446i −1.21572 + 1.52446i
$$76$$ 0 0
$$77$$ 0.846011 0.193096i 0.846011 0.193096i
$$78$$ 2.19064 + 2.74698i 2.19064 + 2.74698i
$$79$$ 0.867767 0.867767 0.433884 0.900969i $$-0.357143\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$80$$ 0 0
$$81$$ 2.52446 + 3.16557i 2.52446 + 3.16557i
$$82$$ 0 0
$$83$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$84$$ −0.846011 1.75676i −0.846011 1.75676i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −0.193096 0.846011i −0.193096 0.846011i
$$89$$ −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i $$-0.428571\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$90$$ 0 0
$$91$$ −1.75676 + 0.400969i −1.75676 + 0.400969i
$$92$$ 0.193096 + 0.846011i 0.193096 + 0.846011i
$$93$$ 0.846011 3.70662i 0.846011 3.70662i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.75676 + 0.846011i −1.75676 + 0.846011i
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 1.00000 1.00000
$$99$$ −2.43143 −2.43143
$$100$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$101$$ −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i $$0.428571\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$102$$ 1.21572 1.52446i 1.21572 1.52446i
$$103$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$104$$ 0.400969 + 1.75676i 0.400969 + 1.75676i
$$105$$ 0 0
$$106$$ −0.0990311 + 0.433884i −0.0990311 + 0.433884i
$$107$$ −1.40881 0.678448i −1.40881 0.678448i −0.433884 0.900969i $$-0.642857\pi$$
−0.974928 + 0.222521i $$0.928571\pi$$
$$108$$ 0.781831 + 3.42543i 0.781831 + 3.42543i
$$109$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 1.00000i 1.00000i
$$113$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 5.04892 5.04892
$$118$$ 0 0
$$119$$ 0.433884 + 0.900969i 0.433884 + 0.900969i
$$120$$ 0 0
$$121$$ −0.153989 + 0.193096i −0.153989 + 0.193096i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 1.21572 1.52446i 1.21572 1.52446i
$$125$$ 0 0
$$126$$ −2.73169 0.623490i −2.73169 0.623490i
$$127$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$128$$ −1.00000 −1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0.193096 + 0.846011i 0.193096 + 0.846011i 0.974928 + 0.222521i $$0.0714286\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$132$$ −1.52446 0.734141i −1.52446 0.734141i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0.900969 0.433884i 0.900969 0.433884i
$$137$$ −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i $$-0.142857\pi$$
−1.00000 $$\pi$$
$$138$$ 1.52446 + 0.734141i 1.52446 + 0.734141i
$$139$$ −0.193096 + 0.846011i −0.193096 + 0.846011i 0.781831 + 0.623490i $$0.214286\pi$$
−0.974928 + 0.222521i $$0.928571\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0.433884 1.90097i 0.433884 1.90097i
$$143$$ −0.974928 + 1.22252i −0.974928 + 1.22252i
$$144$$ −0.623490 + 2.73169i −0.623490 + 2.73169i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 1.21572 1.52446i 1.21572 1.52446i
$$148$$ 0 0
$$149$$ 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i $$-0.571429\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$150$$ −0.433884 + 1.90097i −0.433884 + 1.90097i
$$151$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$152$$ 0 0
$$153$$ −0.623490 2.73169i −0.623490 2.73169i
$$154$$ 0.678448 0.541044i 0.678448 0.541044i
$$155$$ 0 0
$$156$$ 3.16557 + 1.52446i 3.16557 + 1.52446i
$$157$$ 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i $$0.285714\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$158$$ 0.781831 0.376510i 0.781831 0.376510i
$$159$$ 0.541044 + 0.678448i 0.541044 + 0.678448i
$$160$$ 0 0
$$161$$ −0.678448 + 0.541044i −0.678448 + 0.541044i
$$162$$ 3.64795 + 1.75676i 3.64795 + 1.75676i
$$163$$ 0 0 0.974928 0.222521i $$-0.0714286\pi$$
−0.974928 + 0.222521i $$0.928571\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0.974928 + 1.22252i 0.974928 + 1.22252i 0.974928 + 0.222521i $$0.0714286\pi$$
1.00000i $$0.5\pi$$
$$168$$ −1.52446 1.21572i −1.52446 1.21572i
$$169$$ 1.40097 1.75676i 1.40097 1.75676i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$174$$ 0 0
$$175$$ −0.781831 0.623490i −0.781831 0.623490i
$$176$$ −0.541044 0.678448i −0.541044 0.678448i
$$177$$ 0 0
$$178$$ −0.445042 −0.445042
$$179$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$180$$ 0 0
$$181$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$182$$ −1.40881 + 1.12349i −1.40881 + 1.12349i
$$183$$ 0 0
$$184$$ 0.541044 + 0.678448i 0.541044 + 0.678448i
$$185$$ 0 0
$$186$$ −0.846011 3.70662i −0.846011 3.70662i
$$187$$ 0.781831 + 0.376510i 0.781831 + 0.376510i
$$188$$ 0 0
$$189$$ −2.74698 + 2.19064i −2.74698 + 2.19064i
$$190$$ 0 0
$$191$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$192$$ −1.21572 + 1.52446i −1.21572 + 1.52446i
$$193$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0.900969 0.433884i 0.900969 0.433884i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ −2.19064 + 1.05496i −2.19064 + 1.05496i
$$199$$ 0.433884 1.90097i 0.433884 1.90097i 1.00000i $$-0.5\pi$$
0.433884 0.900969i $$-0.357143\pi$$
$$200$$ −0.623490 + 0.781831i −0.623490 + 0.781831i
$$201$$ 0 0
$$202$$ 0.400969 + 1.75676i 0.400969 + 1.75676i
$$203$$ 0 0
$$204$$ 0.433884 1.90097i 0.433884 1.90097i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 2.19064 1.05496i 2.19064 1.05496i
$$208$$ 1.12349 + 1.40881i 1.12349 + 1.40881i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.40881 0.678448i −1.40881 0.678448i −0.433884 0.900969i $$-0.642857\pi$$
−0.974928 + 0.222521i $$0.928571\pi$$
$$212$$ 0.0990311 + 0.433884i 0.0990311 + 0.433884i
$$213$$ −2.37047 2.97247i −2.37047 2.97247i
$$214$$ −1.56366 −1.56366
$$215$$ 0 0
$$216$$ 2.19064 + 2.74698i 2.19064 + 2.74698i
$$217$$ 1.90097 + 0.433884i 1.90097 + 0.433884i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.62349 0.781831i −1.62349 0.781831i
$$222$$ 0 0
$$223$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$224$$ −0.433884 0.900969i −0.433884 0.900969i
$$225$$ 1.74698 + 2.19064i 1.74698 + 2.19064i
$$226$$ 0 0
$$227$$ −1.94986 −1.94986 −0.974928 0.222521i $$-0.928571\pi$$
−0.974928 + 0.222521i $$0.928571\pi$$
$$228$$ 0 0
$$229$$ 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i $$0.142857\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$230$$ 0 0
$$231$$ 1.69202i 1.69202i
$$232$$ 0 0
$$233$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$234$$ 4.54892 2.19064i 4.54892 2.19064i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0.376510 1.64960i 0.376510 1.64960i
$$238$$ 0.781831 + 0.623490i 0.781831 + 0.623490i
$$239$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$240$$ 0 0
$$241$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$242$$ −0.0549581 + 0.240787i −0.0549581 + 0.240787i
$$243$$ 3.94740 1.90097i 3.94740 1.90097i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0.433884 1.90097i 0.433884 1.90097i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$252$$ −2.73169 + 0.623490i −2.73169 + 0.623490i
$$253$$ −0.167563 + 0.734141i −0.167563 + 0.734141i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$257$$ −1.24698 1.56366i −1.24698 1.56366i −0.623490 0.781831i $$-0.714286\pi$$
−0.623490 0.781831i $$-0.714286\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0.541044 + 0.678448i 0.541044 + 0.678448i
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ −1.69202 −1.69202
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.541044 + 0.678448i −0.541044 + 0.678448i
$$268$$ 0 0
$$269$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$272$$ 0.623490 0.781831i 0.623490 0.781831i
$$273$$ 3.51352i 3.51352i
$$274$$ −0.277479 0.347948i −0.277479 0.347948i
$$275$$ −0.867767 −0.867767
$$276$$ 1.69202 1.69202
$$277$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$278$$ 0.193096 + 0.846011i 0.193096 + 0.846011i
$$279$$ −4.92233 2.37047i −4.92233 2.37047i
$$280$$ 0 0
$$281$$ −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i $$0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$282$$ 0 0
$$283$$ −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i $$-0.785714\pi$$
1.00000i $$0.5\pi$$
$$284$$ −0.433884 1.90097i −0.433884 1.90097i
$$285$$ 0 0
$$286$$ −0.347948 + 1.52446i −0.347948 + 1.52446i
$$287$$ 0 0
$$288$$ 0.623490 + 2.73169i 0.623490 + 2.73169i
$$289$$ −0.222521 + 0.974928i −0.222521 + 0.974928i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$294$$ 0.433884 1.90097i 0.433884 1.90097i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −0.678448 + 2.97247i −0.678448 + 2.97247i
$$298$$ 0.277479 0.347948i 0.277479 0.347948i
$$299$$ 0.347948 1.52446i 0.347948 1.52446i
$$300$$ 0.433884 + 1.90097i 0.433884 + 1.90097i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 3.16557 + 1.52446i 3.16557 + 1.52446i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −1.74698 2.19064i −1.74698 2.19064i
$$307$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$308$$ 0.376510 0.781831i 0.376510 0.781831i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 0.781831 0.623490i $$-0.214286\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$312$$ 3.51352 3.51352
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 1.12349 + 1.40881i 1.12349 + 1.40881i
$$315$$ 0 0
$$316$$ 0.541044 0.678448i 0.541044 0.678448i
$$317$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$318$$ 0.781831 + 0.376510i 0.781831 + 0.376510i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −1.90097 + 2.38374i −1.90097 + 2.38374i
$$322$$ −0.376510 + 0.781831i −0.376510 + 0.781831i
$$323$$ 0 0
$$324$$ 4.04892 4.04892
$$325$$ 1.80194 1.80194
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 1.40881 + 0.678448i 1.40881 + 0.678448i
$$335$$ 0 0
$$336$$ −1.90097 0.433884i −1.90097 0.433884i
$$337$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$338$$ 0.500000 2.19064i 0.500000 2.19064i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.52446 0.734141i 1.52446 0.734141i
$$342$$ 0 0
$$343$$ 0.781831 + 0.623490i 0.781831 + 0.623490i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.974928 1.22252i 0.974928 1.22252i 1.00000i $$-0.5\pi$$
0.974928 0.222521i $$-0.0714286\pi$$
$$348$$ 0 0
$$349$$ −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i $$-0.857143\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$350$$ −0.974928 0.222521i −0.974928 0.222521i
$$351$$ 1.40881 6.17241i 1.40881 6.17241i
$$352$$ −0.781831 0.376510i −0.781831 0.376510i
$$353$$ −0.445042 1.94986i −0.445042 1.94986i −0.222521 0.974928i $$-0.571429\pi$$
−0.222521 0.974928i $$-0.571429\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −0.400969 + 0.193096i −0.400969 + 0.193096i
$$357$$ 1.90097 0.433884i 1.90097 0.433884i
$$358$$ 0 0
$$359$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 0 0
$$363$$ 0.300257 + 0.376510i 0.300257 + 0.376510i
$$364$$ −0.781831 + 1.62349i −0.781831 + 1.62349i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.40881 + 0.678448i 1.40881 + 0.678448i 0.974928 0.222521i $$-0.0714286\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$368$$ 0.781831 + 0.376510i 0.781831 + 0.376510i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −0.347948 + 0.277479i −0.347948 + 0.277479i
$$372$$ −2.37047 2.97247i −2.37047 2.97247i
$$373$$ 1.80194 1.80194 0.900969 0.433884i $$-0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$374$$ 0.867767 0.867767
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ −1.52446 + 3.16557i −1.52446 + 3.16557i
$$379$$ 0 0 −0.433884 0.900969i $$-0.642857\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$384$$ −0.433884 + 1.90097i −0.433884 + 1.90097i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0.277479 1.21572i 0.277479 1.21572i −0.623490 0.781831i $$-0.714286\pi$$
0.900969 0.433884i $$-0.142857\pi$$
$$390$$ 0 0
$$391$$ −0.867767 −0.867767
$$392$$ 0.623490 0.781831i 0.623490 0.781831i
$$393$$ 1.69202 1.69202
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −1.51597 + 1.90097i −1.51597 + 1.90097i
$$397$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$398$$ −0.433884 1.90097i −0.433884 1.90097i
$$399$$ 0 0
$$400$$ −0.222521 + 0.974928i −0.222521 + 0.974928i
$$401$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$402$$ 0 0
$$403$$ −3.16557 + 1.52446i −3.16557 + 1.52446i
$$404$$ 1.12349 + 1.40881i 1.12349 + 1.40881i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −0.433884 1.90097i −0.433884 1.90097i
$$409$$ −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i $$-0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$410$$ 0 0
$$411$$ −0.867767 −0.867767
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 1.51597 1.90097i 1.51597 1.90097i
$$415$$ 0 0
$$416$$ 1.62349 + 0.781831i 1.62349 + 0.781831i
$$417$$ 1.52446 + 0.734141i 1.52446 + 0.734141i
$$418$$ 0 0
$$419$$ 0.541044 0.678448i 0.541044 0.678448i −0.433884 0.900969i $$-0.642857\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$420$$ 0 0
$$421$$ 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i $$-0.142857\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$422$$ −1.56366 −1.56366
$$423$$ 0 0
$$424$$ 0.277479 + 0.347948i 0.277479 + 0.347948i
$$425$$ −0.222521 0.974928i −0.222521 0.974928i
$$426$$ −3.42543 1.64960i −3.42543 1.64960i
$$427$$ 0 0
$$428$$ −1.40881 + 0.678448i −1.40881 + 0.678448i
$$429$$ 1.90097 + 2.38374i 1.90097 + 2.38374i
$$430$$ 0 0
$$431$$ 0 0 0.974928 0.222521i $$-0.0714286\pi$$
−0.974928 + 0.222521i $$0.928571\pi$$
$$432$$ 3.16557 + 1.52446i 3.16557 + 1.52446i
$$433$$ −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i $$0.428571\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$434$$ 1.90097 0.433884i 1.90097 0.433884i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0.781831 0.376510i 0.781831 0.376510i 1.00000i $$-0.5\pi$$
0.781831 + 0.623490i $$0.214286\pi$$
$$440$$ 0 0
$$441$$ −1.74698 2.19064i −1.74698 2.19064i
$$442$$ −1.80194 −1.80194
$$443$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −0.193096 0.846011i −0.193096 0.846011i
$$448$$ −0.781831 0.623490i −0.781831 0.623490i
$$449$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$450$$ 2.52446 + 1.21572i 2.52446 + 1.21572i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −1.75676 + 0.846011i −1.75676 + 0.846011i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i $$-0.714286\pi$$
0.222521 0.974928i $$-0.428571\pi$$
$$458$$ 0.777479 + 0.974928i 0.777479 + 0.974928i
$$459$$ −3.51352 −3.51352
$$460$$ 0 0
$$461$$ −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i $$-0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$462$$ −0.734141 1.52446i −0.734141 1.52446i
$$463$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$468$$ 3.14795 3.94740i 3.14795 3.94740i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 3.51352 3.51352
$$472$$ 0 0
$$473$$ 0 0
$$474$$ −0.376510 1.64960i −0.376510 1.64960i
$$475$$ 0 0
$$476$$ 0.974928 + 0.222521i 0.974928 + 0.222521i
$$477$$ 1.12349 0.541044i 1.12349 0.541044i
$$478$$ 0 0
$$479$$ −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i $$-0.785714\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0.734141 + 1.52446i 0.734141 + 1.52446i
$$484$$ 0.0549581 + 0.240787i 0.0549581 + 0.240787i
$$485$$ 0 0
$$486$$ 2.73169 3.42543i 2.73169 3.42543i
$$487$$ 0 0 −0.974928 0.222521i $$-0.928571\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$488$$ 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
$$496$$ −0.433884 1.90097i −0.433884 1.90097i
$$497$$ 1.52446 1.21572i 1.52446 1.21572i
$$498$$ 0 0
$$499$$ 0.781831 + 0.376510i 0.781831 + 0.376510i 0.781831 0.623490i $$-0.214286\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ 2.74698 1.32288i 2.74698 1.32288i
$$502$$ 0 0
$$503$$ −1.40881 + 0.678448i −1.40881 + 0.678448i −0.974928 0.222521i $$-0.928571\pi$$
−0.433884 + 0.900969i $$0.642857\pi$$
$$504$$ −2.19064 + 1.74698i −2.19064 + 1.74698i
$$505$$ 0 0
$$506$$ 0.167563 + 0.734141i 0.167563 + 0.734141i
$$507$$ −2.73169 3.42543i −2.73169 3.42543i
$$508$$ 0 0
$$509$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.623490 + 0.781831i −0.623490 + 0.781831i
$$513$$ 0 0
$$514$$ −1.80194 0.867767i −1.80194 0.867767i
$$515$$ 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 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$524$$ 0.781831 + 0.376510i 0.781831 + 0.376510i
$$525$$ −1.52446 + 1.21572i −1.52446 + 1.21572i
$$526$$ 0 0
$$527$$ 1.21572 + 1.52446i 1.21572 + 1.52446i
$$528$$ −1.52446 + 0.734141i −1.52446 + 0.734141i
$$529$$ 0.0549581 + 0.240787i 0.0549581 + 0.240787i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −0.193096 + 0.846011i −0.193096 + 0.846011i
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0.867767 0.867767
$$540$$ 0 0
$$541$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0.222521 0.974928i 0.222521 0.974928i
$$545$$ 0 0
$$546$$ 1.52446 + 3.16557i 1.52446 + 3.16557i
$$547$$ −0.347948 + 1.52446i −0.347948 + 1.52446i 0.433884 + 0.900969i $$0.357143\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$548$$ −0.400969 0.193096i −0.400969 0.193096i
$$549$$ 0 0
$$550$$ −0.781831 + 0.376510i −0.781831 + 0.376510i
$$551$$ 0 0
$$552$$ 1.52446 0.734141i 1.52446 0.734141i
$$553$$ 0.846011 + 0.193096i 0.846011 + 0.193096i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0.541044 + 0.678448i 0.541044 + 0.678448i
$$557$$ 0.445042 0.445042 0.222521 0.974928i $$-0.428571\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$558$$ −5.46337 −5.46337
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 1.05496 1.32288i 1.05496 1.32288i
$$562$$ −1.24698 + 1.56366i −1.24698 + 1.56366i
$$563$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −0.541044 + 0.678448i −0.541044 + 0.678448i
$$567$$ 1.75676 + 3.64795i 1.75676 + 3.64795i
$$568$$ −1.21572 1.52446i −1.21572 1.52446i
$$569$$ −1.80194 −1.80194 −0.900969 0.433884i $$-0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$570$$ 0 0
$$571$$ 1.21572 + 1.52446i 1.21572 + 1.52446i 0.781831 + 0.623490i $$0.214286\pi$$
0.433884 + 0.900969i $$0.357143\pi$$
$$572$$ 0.347948 + 1.52446i 0.347948 + 1.52446i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0.781831 0.376510i 0.781831 0.376510i
$$576$$ 1.74698 + 2.19064i 1.74698 + 2.19064i
$$577$$ 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i $$-0.428571\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$578$$ 0.222521 + 0.974928i 0.222521 + 0.974928i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −0.0859360 + 0.376510i −0.0859360 + 0.376510i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −1.62349 + 0.781831i −1.62349 + 0.781831i
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ −0.433884 1.90097i −0.433884 1.90097i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i $$0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$594$$ 0.678448 + 2.97247i 0.678448 + 2.97247i
$$595$$ 0 0
$$596$$ 0.0990311 0.433884i 0.0990311 0.433884i
$$597$$ −3.42543 1.64960i −3.42543 1.64960i
$$598$$ −0.347948 1.52446i −0.347948 1.52446i
$$599$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$600$$ 1.21572 + 1.52446i 1.21572 + 1.52446i
$$601$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 3.51352 3.51352
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −2.52446 1.21572i −2.52446 1.21572i
$$613$$ −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i $$-0.571429\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0.867767i 0.867767i
$$617$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ −0.678448 2.97247i −0.678448 2.97247i
$$622$$ 0 0
$$623$$ −0.347948 0.277479i −0.347948 0.277479i
$$624$$ 3.16557 1.52446i 3.16557 1.52446i
$$625$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 1.62349 + 0.781831i 1.62349 + 0.781831i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$632$$ 0.193096 0.846011i 0.193096 0.846011i
$$633$$ −1.90097 + 2.38374i −1.90097 + 2.38374i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0.867767 0.867767
$$637$$ −1.80194 −1.80194
$$638$$ 0 0
$$639$$ −4.92233 + 2.37047i −4.92233 + 2.37047i
$$640$$ 0 0
$$641$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$642$$ −0.678448 + 2.97247i −0.678448 + 2.97247i
$$643$$ −0.347948 1.52446i −0.347948 1.52446i −0.781831 0.623490i $$-0.785714\pi$$
0.433884 0.900969i $$-0.357143\pi$$
$$644$$ 0.867767i 0.867767i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$648$$ 3.64795 1.75676i 3.64795 1.75676i
$$649$$ 0 0
$$650$$ 1.62349 0.781831i 1.62349 0.781831i
$$651$$ 1.64960 3.42543i 1.64960 3.42543i
$$652$$ 0 0
$$653$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$660$$ 0 0
$$661$$ 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i $$-0.285714\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$662$$ 0 0
$$663$$ −2.19064 + 2.74698i −2.19064 + 2.74698i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 1.56366 1.56366
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ −1.90097 + 0.433884i −1.90097 + 0.433884i
$$673$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$674$$ 0 0
$$675$$ 3.16557 1.52446i 3.16557 1.52446i
$$676$$ −0.500000 2.19064i −0.500000 2.19064i
$$677$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −0.846011 + 3.70662i −0.846011 + 3.70662i
$$682$$ 1.05496 1.32288i 1.05496 1.32288i
$$683$$ 0.433884 1.90097i 0.433884 1.90097i 1.00000i $$-0.5\pi$$
0.433884 0.900969i $$-0.357143\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0.974928 + 0.222521i 0.974928 + 0.222521i
$$687$$ 2.43143 2.43143
$$688$$ 0 0
$$689$$ 0.178448 0.781831i 0.178448 0.781831i
$$690$$ 0 0
$$691$$ 0.433884 1.90097i 0.433884 1.90097i 1.00000i $$-0.5\pi$$
0.433884 0.900969i $$-0.357143\pi$$
$$692$$ 0 0
$$693$$ −2.37047 0.541044i −2.37047 0.541044i
$$694$$ 0.347948 1.52446i 0.347948 1.52446i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −0.777479 0.974928i −0.777479 0.974928i
$$699$$ 0 0
$$700$$ −0.974928 + 0.222521i −0.974928 + 0.222521i
$$701$$ −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i $$-0.428571\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$702$$ −1.40881 6.17241i −1.40881 6.17241i
$$703$$ 0 0
$$704$$ −0.867767 −0.867767
$$705$$ 0 0
$$706$$ −1.24698 1.56366i −1.24698 1.56366i
$$707$$ −0.781831 + 1.62349i −0.781831 + 1.62349i
$$708$$ 0 0
$$709$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$710$$ 0 0
$$711$$ −2.19064 1.05496i −2.19064 1.05496i
$$712$$ −0.277479 + 0.347948i −0.277479 + 0.347948i
$$713$$ −1.05496 + 1.32288i −1.05496 + 1.32288i
$$714$$ 1.52446 1.21572i 1.52446 1.21572i
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0.193096 + 0.846011i 0.193096 + 0.846011i 0.974928 + 0.222521i $$0.0714286\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.900969 0.433884i 0.900969 0.433884i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0.433884 + 0.208947i 0.433884 + 0.208947i
$$727$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$728$$ 1.80194i 1.80194i
$$729$$ −1.00000 4.38129i −1.00000 4.38129i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i $$0.857143\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$734$$ 1.56366 1.56366
$$735$$ 0 0
$$736$$ 0.867767 0.867767
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −0.193096 + 0.400969i −0.193096 + 0.400969i
$$743$$ −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i $$0.5\pi$$
−0.433884 + 0.900969i $$0.642857\pi$$
$$744$$ −3.42543 1.64960i −3.42543 1.64960i
$$745$$ 0 0
$$746$$ 1.62349 0.781831i 1.62349 0.781831i
$$747$$ 0 0
$$748$$ 0.781831 0.376510i 0.781831 0.376510i
$$749$$ −1.22252 0.974928i −1.22252 0.974928i
$$750$$ 0 0
$$751$$ 0.193096 + 0.846011i 0.193096 + 0.846011i 0.974928 + 0.222521i $$0.0714286\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 3.51352i 3.51352i
$$757$$ −1.24698 + 1.56366i −1.24698 + 1.56366i −0.623490 + 0.781831i $$0.714286\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$758$$ 0 0
$$759$$ 1.32288 + 0.637063i 1.32288 + 0.637063i
$$760$$ 0 0
$$761$$ −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i $$0.428571\pi$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.433884 + 1.90097i 0.433884 + 1.90097i
$$769$$ 1.80194 + 0.867767i 1.80194 + 0.867767i 0.900969 + 0.433884i $$0.142857\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$770$$ 0 0
$$771$$ −3.51352 + 1.69202i −3.51352 + 1.69202i
$$772$$ 0 0
$$773$$ 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i $$-0.428571\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$774$$ 0 0
$$775$$ −1.75676 0.846011i −1.75676 0.846011i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −0.277479 1.21572i −0.277479 1.21572i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0.376510 1.64960i 0.376510 1.64960i
$$782$$ −0.781831 + 0.376510i −0.781831 + 0.376510i
$$783$$ 0 0
$$784$$ 0.222521 0.974928i 0.222521 0.974928i
$$785$$ 0 0
$$786$$ 1.52446 0.734141i 1.52446 0.734141i
$$787$$ −0.347948 + 1.52446i −0.347948 + 1.52446i 0.433884 + 0.900969i $$0.357143\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$788$$ 0 0
$$789$$ 0