Properties

 Label 3332.1.cc.c.135.2 Level $3332$ Weight $1$ Character 3332.135 Analytic conductor $1.663$ Analytic rank $0$ Dimension $24$ Projective image $D_{42}$ 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(135,3332)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 32, 21]))

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

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

chi := DirichletCharacter("3332.135");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3332.cc (of order $$42$$, degree $$12$$, 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: $$24$$ Relative dimension: $$2$$ over $$\Q(\zeta_{42})$$ Coefficient field: $$\Q(\zeta_{84})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1$$ x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{42}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{42} - \cdots)$$

Embedding invariants

 Embedding label 135.2 Root $$0.294755 - 0.955573i$$ of defining polynomial Character $$\chi$$ $$=$$ 3332.135 Dual form 3332.1.cc.c.543.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.826239 + 0.563320i) q^{2} +(0.997204 - 0.925270i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.302705 + 1.32624i) q^{6} +(-0.974928 + 0.222521i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.0635609 - 0.848162i) q^{9} +O(q^{10})$$ $$q+(-0.826239 + 0.563320i) q^{2} +(0.997204 - 0.925270i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.302705 + 1.32624i) q^{6} +(-0.974928 + 0.222521i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.0635609 - 0.848162i) q^{9} +(0.0841939 + 1.12349i) q^{11} +(-0.496990 - 1.26631i) q^{12} +(1.48883 + 0.716983i) q^{13} +(0.680173 - 0.733052i) q^{14} +(-0.733052 - 0.680173i) q^{16} +(-0.988831 - 0.149042i) q^{17} +(0.425270 + 0.736589i) q^{18} +(-0.766310 + 1.12397i) q^{21} +(-0.702449 - 0.880843i) q^{22} +(-0.858075 + 0.129334i) q^{23} +(1.12397 + 0.766310i) q^{24} +(0.826239 + 0.563320i) q^{25} +(-1.63402 + 0.246289i) q^{26} +(0.126766 + 0.158960i) q^{27} +(-0.149042 + 0.988831i) q^{28} +(0.974928 + 1.68862i) q^{31} +(0.988831 + 0.149042i) q^{32} +(1.12349 + 1.04245i) q^{33} +(0.900969 - 0.433884i) q^{34} +(-0.766310 - 0.369035i) q^{36} +(2.14807 - 0.662592i) q^{39} -1.36035i q^{42} +(1.07659 + 0.332083i) q^{44} +(0.636119 - 0.590232i) q^{46} -1.36035 q^{48} +(0.900969 - 0.433884i) q^{49} -1.00000 q^{50} +(-1.12397 + 0.766310i) q^{51} +(1.21135 - 1.12397i) q^{52} +(0.698220 - 1.77904i) q^{53} +(-0.194285 - 0.0599289i) q^{54} +(-0.433884 - 0.900969i) q^{56} +(-1.75676 - 0.846011i) q^{62} +(0.126766 + 0.841040i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-1.51550 - 0.228425i) q^{66} +(-0.500000 + 0.866025i) q^{68} +(-0.736007 + 0.922924i) q^{69} +(0.367554 + 0.460898i) q^{71} +(0.841040 - 0.126766i) q^{72} +(1.34515 - 0.202749i) q^{75} +(-0.332083 - 1.07659i) q^{77} +(-1.40157 + 1.75751i) q^{78} +(-0.997204 + 1.72721i) q^{79} +(1.11453 + 0.167989i) q^{81} +(0.766310 + 1.12397i) q^{84} +(-1.07659 + 0.332083i) q^{88} +(0.109562 - 1.46200i) q^{89} +(-1.61105 - 0.367711i) q^{91} +(-0.193096 + 0.846011i) q^{92} +(2.53464 + 0.781831i) q^{93} +(1.12397 - 0.766310i) q^{96} +(-0.500000 + 0.866025i) q^{98} +0.958252 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9}+O(q^{10})$$ 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9 $$24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{64} - 22 q^{66} - 12 q^{68} - 14 q^{69} - 4 q^{72} - 6 q^{77} + 30 q^{81} - 6 q^{84} + 2 q^{89} - 12 q^{98}+O(q^{100})$$ 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9 + 10 * q^13 + 2 * q^16 + 2 * q^17 + 10 * q^18 + 6 * q^21 + 2 * q^25 - 2 * q^26 - 2 * q^32 + 8 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^49 - 24 * q^50 + 2 * q^52 - 2 * q^53 - 4 * q^64 - 22 * q^66 - 12 * q^68 - 14 * q^69 - 4 * q^72 - 6 * q^77 + 30 * q^81 - 6 * q^84 + 2 * q^89 - 12 * q^98

Character values

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

 $$n$$ $$785$$ $$885$$ $$1667$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{16}{21}\right)$$ $$-1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.826239 + 0.563320i −0.826239 + 0.563320i
$$3$$ 0.997204 0.925270i 0.997204 0.925270i 1.00000i $$-0.5\pi$$
0.997204 + 0.0747301i $$0.0238095\pi$$
$$4$$ 0.365341 0.930874i 0.365341 0.930874i
$$5$$ 0 0 −0.955573 0.294755i $$-0.904762\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$6$$ −0.302705 + 1.32624i −0.302705 + 1.32624i
$$7$$ −0.974928 + 0.222521i −0.974928 + 0.222521i
$$8$$ 0.222521 + 0.974928i 0.222521 + 0.974928i
$$9$$ 0.0635609 0.848162i 0.0635609 0.848162i
$$10$$ 0 0
$$11$$ 0.0841939 + 1.12349i 0.0841939 + 1.12349i 0.866025 + 0.500000i $$0.166667\pi$$
−0.781831 + 0.623490i $$0.785714\pi$$
$$12$$ −0.496990 1.26631i −0.496990 1.26631i
$$13$$ 1.48883 + 0.716983i 1.48883 + 0.716983i 0.988831 0.149042i $$-0.0476190\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$14$$ 0.680173 0.733052i 0.680173 0.733052i
$$15$$ 0 0
$$16$$ −0.733052 0.680173i −0.733052 0.680173i
$$17$$ −0.988831 0.149042i −0.988831 0.149042i
$$18$$ 0.425270 + 0.736589i 0.425270 + 0.736589i
$$19$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$20$$ 0 0
$$21$$ −0.766310 + 1.12397i −0.766310 + 1.12397i
$$22$$ −0.702449 0.880843i −0.702449 0.880843i
$$23$$ −0.858075 + 0.129334i −0.858075 + 0.129334i −0.563320 0.826239i $$-0.690476\pi$$
−0.294755 + 0.955573i $$0.595238\pi$$
$$24$$ 1.12397 + 0.766310i 1.12397 + 0.766310i
$$25$$ 0.826239 + 0.563320i 0.826239 + 0.563320i
$$26$$ −1.63402 + 0.246289i −1.63402 + 0.246289i
$$27$$ 0.126766 + 0.158960i 0.126766 + 0.158960i
$$28$$ −0.149042 + 0.988831i −0.149042 + 0.988831i
$$29$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$30$$ 0 0
$$31$$ 0.974928 + 1.68862i 0.974928 + 1.68862i 0.680173 + 0.733052i $$0.261905\pi$$
0.294755 + 0.955573i $$0.404762\pi$$
$$32$$ 0.988831 + 0.149042i 0.988831 + 0.149042i
$$33$$ 1.12349 + 1.04245i 1.12349 + 1.04245i
$$34$$ 0.900969 0.433884i 0.900969 0.433884i
$$35$$ 0 0
$$36$$ −0.766310 0.369035i −0.766310 0.369035i
$$37$$ 0 0 −0.365341 0.930874i $$-0.619048\pi$$
0.365341 + 0.930874i $$0.380952\pi$$
$$38$$ 0 0
$$39$$ 2.14807 0.662592i 2.14807 0.662592i
$$40$$ 0 0
$$41$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$42$$ 1.36035i 1.36035i
$$43$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$44$$ 1.07659 + 0.332083i 1.07659 + 0.332083i
$$45$$ 0 0
$$46$$ 0.636119 0.590232i 0.636119 0.590232i
$$47$$ 0 0 0.826239 0.563320i $$-0.190476\pi$$
−0.826239 + 0.563320i $$0.809524\pi$$
$$48$$ −1.36035 −1.36035
$$49$$ 0.900969 0.433884i 0.900969 0.433884i
$$50$$ −1.00000 −1.00000
$$51$$ −1.12397 + 0.766310i −1.12397 + 0.766310i
$$52$$ 1.21135 1.12397i 1.21135 1.12397i
$$53$$ 0.698220 1.77904i 0.698220 1.77904i 0.0747301 0.997204i $$-0.476190\pi$$
0.623490 0.781831i $$-0.285714\pi$$
$$54$$ −0.194285 0.0599289i −0.194285 0.0599289i
$$55$$ 0 0
$$56$$ −0.433884 0.900969i −0.433884 0.900969i
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 0.955573 0.294755i $$-0.0952381\pi$$
−0.955573 + 0.294755i $$0.904762\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.365341 0.930874i $$-0.619048\pi$$
0.365341 + 0.930874i $$0.380952\pi$$
$$62$$ −1.75676 0.846011i −1.75676 0.846011i
$$63$$ 0.126766 + 0.841040i 0.126766 + 0.841040i
$$64$$ −0.900969 + 0.433884i −0.900969 + 0.433884i
$$65$$ 0 0
$$66$$ −1.51550 0.228425i −1.51550 0.228425i
$$67$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$68$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$69$$ −0.736007 + 0.922924i −0.736007 + 0.922924i
$$70$$ 0 0
$$71$$ 0.367554 + 0.460898i 0.367554 + 0.460898i 0.930874 0.365341i $$-0.119048\pi$$
−0.563320 + 0.826239i $$0.690476\pi$$
$$72$$ 0.841040 0.126766i 0.841040 0.126766i
$$73$$ 0 0 −0.826239 0.563320i $$-0.809524\pi$$
0.826239 + 0.563320i $$0.190476\pi$$
$$74$$ 0 0
$$75$$ 1.34515 0.202749i 1.34515 0.202749i
$$76$$ 0 0
$$77$$ −0.332083 1.07659i −0.332083 1.07659i
$$78$$ −1.40157 + 1.75751i −1.40157 + 1.75751i
$$79$$ −0.997204 + 1.72721i −0.997204 + 1.72721i −0.433884 + 0.900969i $$0.642857\pi$$
−0.563320 + 0.826239i $$0.690476\pi$$
$$80$$ 0 0
$$81$$ 1.11453 + 0.167989i 1.11453 + 0.167989i
$$82$$ 0 0
$$83$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$84$$ 0.766310 + 1.12397i 0.766310 + 1.12397i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −1.07659 + 0.332083i −1.07659 + 0.332083i
$$89$$ 0.109562 1.46200i 0.109562 1.46200i −0.623490 0.781831i $$-0.714286\pi$$
0.733052 0.680173i $$-0.238095\pi$$
$$90$$ 0 0
$$91$$ −1.61105 0.367711i −1.61105 0.367711i
$$92$$ −0.193096 + 0.846011i −0.193096 + 0.846011i
$$93$$ 2.53464 + 0.781831i 2.53464 + 0.781831i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 1.12397 0.766310i 1.12397 0.766310i
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$99$$ 0.958252 0.958252
$$100$$ 0.826239 0.563320i 0.826239 0.563320i
$$101$$ −1.32091 + 1.22563i −1.32091 + 1.22563i −0.365341 + 0.930874i $$0.619048\pi$$
−0.955573 + 0.294755i $$0.904762\pi$$
$$102$$ 0.496990 1.26631i 0.496990 1.26631i
$$103$$ 0 0 −0.955573 0.294755i $$-0.904762\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$104$$ −0.367711 + 1.61105i −0.367711 + 1.61105i
$$105$$ 0 0
$$106$$ 0.425270 + 1.86323i 0.425270 + 1.86323i
$$107$$ 0.139129 1.85654i 0.139129 1.85654i −0.294755 0.955573i $$-0.595238\pi$$
0.433884 0.900969i $$-0.357143\pi$$
$$108$$ 0.194285 0.0599289i 0.194285 0.0599289i
$$109$$ 0 0 −0.0747301 0.997204i $$-0.523810\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$113$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0.702749 1.21720i 0.702749 1.21720i
$$118$$ 0 0
$$119$$ 0.997204 0.0747301i 0.997204 0.0747301i
$$120$$ 0 0
$$121$$ −0.266310 + 0.0401398i −0.266310 + 0.0401398i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 1.92808 0.290611i 1.92808 0.290611i
$$125$$ 0 0
$$126$$ −0.578514 0.623490i −0.578514 0.623490i
$$127$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$128$$ 0.500000 0.866025i 0.500000 0.866025i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −0.636119 0.590232i −0.636119 0.590232i 0.294755 0.955573i $$-0.404762\pi$$
−0.930874 + 0.365341i $$0.880952\pi$$
$$132$$ 1.38084 0.664979i 1.38084 0.664979i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ −0.0747301 0.997204i −0.0747301 0.997204i
$$137$$ 1.40097 0.432142i 1.40097 0.432142i 0.500000 0.866025i $$-0.333333\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$138$$ 0.0882162 1.17716i 0.0882162 1.17716i
$$139$$ −0.443797 1.94440i −0.443797 1.94440i −0.294755 0.955573i $$-0.595238\pi$$
−0.149042 0.988831i $$-0.547619\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −0.563320 0.173761i −0.563320 0.173761i
$$143$$ −0.680173 + 1.73305i −0.680173 + 1.73305i
$$144$$ −0.623490 + 0.578514i −0.623490 + 0.578514i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0.496990 1.26631i 0.496990 1.26631i
$$148$$ 0 0
$$149$$ −1.21135 + 0.825886i −1.21135 + 0.825886i −0.988831 0.149042i $$-0.952381\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$150$$ −0.997204 + 0.925270i −0.997204 + 0.925270i
$$151$$ 0 0 0.365341 0.930874i $$-0.380952\pi$$
−0.365341 + 0.930874i $$0.619048\pi$$
$$152$$ 0 0
$$153$$ −0.189263 + 0.829215i −0.189263 + 0.829215i
$$154$$ 0.880843 + 0.702449i 0.880843 + 0.702449i
$$155$$ 0 0
$$156$$ 0.167989 2.24165i 0.167989 2.24165i
$$157$$ 0.142820 0.0440542i 0.142820 0.0440542i −0.222521 0.974928i $$-0.571429\pi$$
0.365341 + 0.930874i $$0.380952\pi$$
$$158$$ −0.149042 1.98883i −0.149042 1.98883i
$$159$$ −0.949820 2.42010i −0.949820 2.42010i
$$160$$ 0 0
$$161$$ 0.807782 0.317031i 0.807782 0.317031i
$$162$$ −1.01550 + 0.489040i −1.01550 + 0.489040i
$$163$$ 0 0 0.680173 0.733052i $$-0.261905\pi$$
−0.680173 + 0.733052i $$0.738095\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −0.185853 + 0.233052i −0.185853 + 0.233052i −0.866025 0.500000i $$-0.833333\pi$$
0.680173 + 0.733052i $$0.261905\pi$$
$$168$$ −1.26631 0.496990i −1.26631 0.496990i
$$169$$ 1.07906 + 1.35310i 1.07906 + 1.35310i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.988831 0.149042i $$-0.0476190\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$174$$ 0 0
$$175$$ −0.930874 0.365341i −0.930874 0.365341i
$$176$$ 0.702449 0.880843i 0.702449 0.880843i
$$177$$ 0 0
$$178$$ 0.733052 + 1.26968i 0.733052 + 1.26968i
$$179$$ 0 0 −0.988831 0.149042i $$-0.952381\pi$$
0.988831 + 0.149042i $$0.0476190\pi$$
$$180$$ 0 0
$$181$$ 0 0 0.900969 0.433884i $$-0.142857\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$182$$ 1.53825 0.603718i 1.53825 0.603718i
$$183$$ 0 0
$$184$$ −0.317031 0.807782i −0.317031 0.807782i
$$185$$ 0 0
$$186$$ −2.53464 + 0.781831i −2.53464 + 0.781831i
$$187$$ 0.0841939 1.12349i 0.0841939 1.12349i
$$188$$ 0 0
$$189$$ −0.158960 0.126766i −0.158960 0.126766i
$$190$$ 0 0
$$191$$ 0 0 −0.955573 0.294755i $$-0.904762\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$192$$ −0.496990 + 1.26631i −0.496990 + 1.26631i
$$193$$ 0 0 0.733052 0.680173i $$-0.238095\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −0.0747301 0.997204i −0.0747301 0.997204i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ −0.791745 + 0.539803i −0.791745 + 0.539803i
$$199$$ 0.432142 0.400969i 0.432142 0.400969i −0.433884 0.900969i $$-0.642857\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$200$$ −0.365341 + 0.930874i −0.365341 + 0.930874i
$$201$$ 0 0
$$202$$ 0.400969 1.75676i 0.400969 1.75676i
$$203$$ 0 0
$$204$$ 0.302705 + 1.32624i 0.302705 + 1.32624i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0.0551561 + 0.736007i 0.0551561 + 0.736007i
$$208$$ −0.603718 1.53825i −0.603718 1.53825i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.40881 0.678448i 1.40881 0.678448i 0.433884 0.900969i $$-0.357143\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$212$$ −1.40097 1.29991i −1.40097 1.29991i
$$213$$ 0.792981 + 0.119523i 0.792981 + 0.119523i
$$214$$ 0.930874 + 1.61232i 0.930874 + 1.61232i
$$215$$ 0 0
$$216$$ −0.126766 + 0.158960i −0.126766 + 0.158960i
$$217$$ −1.32624 1.42935i −1.32624 1.42935i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.36534 0.930874i −1.36534 0.930874i
$$222$$ 0 0
$$223$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$224$$ −0.997204 + 0.0747301i −0.997204 + 0.0747301i
$$225$$ 0.530303 0.664979i 0.530303 0.664979i
$$226$$ 0 0
$$227$$ 0.294755 + 0.510531i 0.294755 + 0.510531i 0.974928 0.222521i $$-0.0714286\pi$$
−0.680173 + 0.733052i $$0.738095\pi$$
$$228$$ 0 0
$$229$$ 0.914101 + 0.848162i 0.914101 + 0.848162i 0.988831 0.149042i $$-0.0476190\pi$$
−0.0747301 + 0.997204i $$0.523810\pi$$
$$230$$ 0 0
$$231$$ −1.32729 0.766310i −1.32729 0.766310i
$$232$$ 0 0
$$233$$ 0 0 −0.365341 0.930874i $$-0.619048\pi$$
0.365341 + 0.930874i $$0.380952\pi$$
$$234$$ 0.105033 + 1.40157i 0.105033 + 1.40157i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0.603718 + 2.64506i 0.603718 + 2.64506i
$$238$$ −0.781831 + 0.623490i −0.781831 + 0.623490i
$$239$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$240$$ 0 0
$$241$$ 0 0 0.365341 0.930874i $$-0.380952\pi$$
−0.365341 + 0.930874i $$0.619048\pi$$
$$242$$ 0.197424 0.183183i 0.197424 0.183183i
$$243$$ 1.09886 0.749192i 1.09886 0.749192i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −1.42935 + 1.32624i −1.42935 + 1.32624i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$252$$ 0.829215 + 0.189263i 0.829215 + 0.189263i
$$253$$ −0.217550 0.953150i −0.217550 0.953150i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0.0747301 + 0.997204i 0.0747301 + 0.997204i
$$257$$ 0.365341 + 0.930874i 0.365341 + 0.930874i 0.988831 + 0.149042i $$0.0476190\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0.858075 + 0.129334i 0.858075 + 0.129334i
$$263$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$264$$ −0.766310 + 1.32729i −0.766310 + 1.32729i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −1.24349 1.55929i −1.24349 1.55929i
$$268$$ 0 0
$$269$$ 0 0 −0.826239 0.563320i $$-0.809524\pi$$
0.826239 + 0.563320i $$0.190476\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.988831 0.149042i $$-0.0476190\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$272$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$273$$ −1.94677 + 1.12397i −1.94677 + 1.12397i
$$274$$ −0.914101 + 1.14625i −0.914101 + 1.14625i
$$275$$ −0.563320 + 0.975699i −0.563320 + 0.975699i
$$276$$ 0.590232 + 1.02231i 0.590232 + 1.02231i
$$277$$ 0 0 −0.988831 0.149042i $$-0.952381\pi$$
0.988831 + 0.149042i $$0.0476190\pi$$
$$278$$ 1.46200 + 1.35654i 1.46200 + 1.35654i
$$279$$ 1.49419 0.719566i 1.49419 0.719566i
$$280$$ 0 0
$$281$$ 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i $$-0.190476\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$282$$ 0 0
$$283$$ −0.0841939 1.12349i −0.0841939 1.12349i −0.866025 0.500000i $$-0.833333\pi$$
0.781831 0.623490i $$-0.214286\pi$$
$$284$$ 0.563320 0.173761i 0.563320 0.173761i
$$285$$ 0 0
$$286$$ −0.414278 1.81507i −0.414278 1.81507i
$$287$$ 0 0
$$288$$ 0.189263 0.829215i 0.189263 0.829215i
$$289$$ 0.955573 + 0.294755i 0.955573 + 0.294755i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0.149460 0.149460 0.0747301 0.997204i $$-0.476190\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$294$$ 0.302705 + 1.32624i 0.302705 + 1.32624i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −0.167917 + 0.155804i −0.167917 + 0.155804i
$$298$$ 0.535628 1.36476i 0.535628 1.36476i
$$299$$ −1.37026 0.422669i −1.37026 0.422669i
$$300$$ 0.302705 1.32624i 0.302705 1.32624i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −0.183183 + 2.44440i −0.183183 + 2.44440i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −0.310737 0.791745i −0.310737 0.791745i
$$307$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$308$$ −1.12349 0.0841939i −1.12349 0.0841939i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.71271 0.258149i −1.71271 0.258149i −0.781831 0.623490i $$-0.785714\pi$$
−0.930874 + 0.365341i $$0.880952\pi$$
$$312$$ 1.12397 + 1.94677i 1.12397 + 1.94677i
$$313$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$314$$ −0.0931869 + 0.116853i −0.0931869 + 0.116853i
$$315$$ 0 0
$$316$$ 1.24349 + 1.55929i 1.24349 + 1.55929i
$$317$$ 0 0 0.988831 0.149042i $$-0.0476190\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$318$$ 2.14807 + 1.46453i 2.14807 + 1.46453i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −1.57906 1.98008i −1.57906 1.98008i
$$322$$ −0.488831 + 0.716983i −0.488831 + 0.716983i
$$323$$ 0 0
$$324$$ 0.563561 0.976116i 0.563561 0.976116i
$$325$$ 0.826239 + 1.43109i 0.826239 + 1.43109i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.365341 0.930874i $$-0.619048\pi$$
0.365341 + 0.930874i $$0.380952\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0.0222759 0.297251i 0.0222759 0.297251i
$$335$$ 0 0
$$336$$ 1.32624 0.302705i 1.32624 0.302705i
$$337$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$338$$ −1.65379 0.510127i −1.65379 0.510127i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.81507 + 1.23749i −1.81507 + 1.23749i
$$342$$ 0 0
$$343$$ −0.781831 + 0.623490i −0.781831 + 0.623490i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −0.571270 + 1.45557i −0.571270 + 1.45557i 0.294755 + 0.955573i $$0.404762\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$348$$ 0 0
$$349$$ −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i $$0.285714\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$350$$ 0.974928 0.222521i 0.974928 0.222521i
$$351$$ 0.0747620 + 0.327554i 0.0747620 + 0.327554i
$$352$$ −0.0841939 + 1.12349i −0.0841939 + 1.12349i
$$353$$ −0.955573 + 0.294755i −0.955573 + 0.294755i −0.733052 0.680173i $$-0.761905\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −1.32091 0.636119i −1.32091 0.636119i
$$357$$ 0.925270 0.997204i 0.925270 0.997204i
$$358$$ 0 0
$$359$$ 0 0 −0.733052 0.680173i $$-0.761905\pi$$
0.733052 + 0.680173i $$0.238095\pi$$
$$360$$ 0 0
$$361$$ −0.500000 0.866025i −0.500000 0.866025i
$$362$$ 0 0
$$363$$ −0.228425 + 0.286436i −0.228425 + 0.286436i
$$364$$ −0.930874 + 1.36534i −0.930874 + 1.36534i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −1.53825 1.04876i −1.53825 1.04876i −0.974928 0.222521i $$-0.928571\pi$$
−0.563320 0.826239i $$-0.690476\pi$$
$$368$$ 0.716983 + 0.488831i 0.716983 + 0.488831i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −0.284841 + 1.88980i −0.284841 + 1.88980i
$$372$$ 1.65379 2.07379i 1.65379 2.07379i
$$373$$ 0.826239 1.43109i 0.826239 1.43109i −0.0747301 0.997204i $$-0.523810\pi$$
0.900969 0.433884i $$-0.142857\pi$$
$$374$$ 0.563320 + 0.975699i 0.563320 + 0.975699i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0.202749 + 0.0151939i 0.202749 + 0.0151939i
$$379$$ −1.56052 0.751509i −1.56052 0.751509i −0.563320 0.826239i $$-0.690476\pi$$
−0.997204 + 0.0747301i $$0.976190\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.0747301 0.997204i $$-0.476190\pi$$
−0.0747301 + 0.997204i $$0.523810\pi$$
$$384$$ −0.302705 1.32624i −0.302705 1.32624i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.44973 + 1.34515i −1.44973 + 1.34515i −0.623490 + 0.781831i $$0.714286\pi$$
−0.826239 + 0.563320i $$0.809524\pi$$
$$390$$ 0 0
$$391$$ 0.867767 0.867767
$$392$$ 0.623490 + 0.781831i 0.623490 + 0.781831i
$$393$$ −1.18046 −1.18046
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.350089 0.892012i 0.350089 0.892012i
$$397$$ 0 0 −0.955573 0.294755i $$-0.904762\pi$$
0.955573 + 0.294755i $$0.0952381\pi$$
$$398$$ −0.131178 + 0.574730i −0.131178 + 0.574730i
$$399$$ 0 0
$$400$$ −0.222521 0.974928i −0.222521 0.974928i
$$401$$ 0 0 0.0747301 0.997204i $$-0.476190\pi$$
−0.0747301 + 0.997204i $$0.523810\pi$$
$$402$$ 0 0
$$403$$ 0.240787 + 3.21308i 0.240787 + 3.21308i
$$404$$ 0.658322 + 1.67738i 0.658322 + 1.67738i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −0.997204 0.925270i −0.997204 0.925270i
$$409$$ −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i $$-0.857143\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$410$$ 0 0
$$411$$ 0.997204 1.72721i 0.997204 1.72721i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ −0.460180 0.577047i −0.460180 0.577047i
$$415$$ 0 0
$$416$$ 1.36534 + 0.930874i 1.36534 + 0.930874i
$$417$$ −2.24165 1.52833i −2.24165 1.52833i
$$418$$ 0 0
$$419$$ 1.24349 + 1.55929i 1.24349 + 1.55929i 0.680173 + 0.733052i $$0.261905\pi$$
0.563320 + 0.826239i $$0.309524\pi$$
$$420$$ 0 0
$$421$$ 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i $$-0.714286\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$422$$ −0.781831 + 1.35417i −0.781831 + 1.35417i
$$423$$ 0 0
$$424$$ 1.88980 + 0.284841i 1.88980 + 0.284841i
$$425$$ −0.733052 0.680173i −0.733052 0.680173i
$$426$$ −0.722521 + 0.347948i −0.722521 + 0.347948i
$$427$$ 0 0
$$428$$ −1.67738 0.807782i −1.67738 0.807782i
$$429$$ 0.925270 + 2.35755i 0.925270 + 2.35755i
$$430$$ 0 0
$$431$$ 1.65510 0.510531i 1.65510 0.510531i 0.680173 0.733052i $$-0.261905\pi$$
0.974928 + 0.222521i $$0.0714286\pi$$
$$432$$ 0.0151939 0.202749i 0.0151939 0.202749i
$$433$$ −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i $$-0.714286\pi$$
0.222521 0.974928i $$-0.428571\pi$$
$$434$$ 1.90097 + 0.433884i 1.90097 + 0.433884i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −1.64786 + 1.12349i −1.64786 + 1.12349i −0.781831 + 0.623490i $$0.785714\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ 0 0
$$441$$ −0.310737 0.791745i −0.310737 0.791745i
$$442$$ 1.65248 1.65248
$$443$$ 0 0 0.826239 0.563320i $$-0.190476\pi$$
−0.826239 + 0.563320i $$0.809524\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −0.443797 + 1.94440i −0.443797 + 1.94440i
$$448$$ 0.781831 0.623490i 0.781831 0.623490i
$$449$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$450$$ −0.0635609 + 0.848162i −0.0635609 + 0.848162i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −0.531130 0.255779i −0.531130 0.255779i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.32091 1.22563i −1.32091 1.22563i −0.955573 0.294755i $$-0.904762\pi$$
−0.365341 0.930874i $$-0.619048\pi$$
$$458$$ −1.23305 0.185853i −1.23305 0.185853i
$$459$$ −0.101659 0.176078i −0.101659 0.176078i
$$460$$ 0 0
$$461$$ 1.19158 1.49419i 1.19158 1.49419i 0.365341 0.930874i $$-0.380952\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$462$$ 1.52833 0.114533i 1.52833 0.114533i
$$463$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 0.988831 0.149042i $$-0.0476190\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$468$$ −0.876314 1.09886i −0.876314 1.09886i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0.101659 0.176078i 0.101659 0.176078i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ −1.98883 1.84537i −1.98883 1.84537i
$$475$$ 0 0
$$476$$ 0.294755 0.955573i 0.294755 0.955573i
$$477$$ −1.46453 0.705280i −1.46453 0.705280i
$$478$$ 0 0
$$479$$ −0.0648483 0.865341i −0.0648483 0.865341i −0.930874 0.365341i $$-0.880952\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0.512184 1.06356i 0.512184 1.06356i
$$484$$ −0.0599289 + 0.262566i −0.0599289 + 0.262566i
$$485$$ 0 0
$$486$$ −0.485888 + 1.23802i −0.485888 + 1.23802i
$$487$$ 1.26968 1.17809i 1.26968 1.17809i 0.294755 0.955573i $$-0.404762\pi$$
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
$$497$$ −0.460898 0.367554i −0.460898 0.367554i
$$498$$ 0 0
$$499$$ −0.149042 + 1.98883i −0.149042 + 1.98883i 1.00000i $$0.5\pi$$
−0.149042 + 0.988831i $$0.547619\pi$$
$$500$$ 0 0
$$501$$ 0.0303029 + 0.404364i 0.0303029 + 0.404364i
$$502$$ 0 0
$$503$$ −1.67738 0.807782i −1.67738 0.807782i −0.997204 0.0747301i $$-0.976190\pi$$
−0.680173 0.733052i $$-0.738095\pi$$
$$504$$ −0.791745 + 0.310737i −0.791745 + 0.310737i
$$505$$ 0 0
$$506$$ 0.716677 + 0.664979i 0.716677 + 0.664979i
$$507$$ 2.32803 + 0.350894i 2.32803 + 0.350894i
$$508$$ 0 0
$$509$$ 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i $$-0.476190\pi$$
0.826239 0.563320i $$-0.190476\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.623490 0.781831i −0.623490 0.781831i
$$513$$ 0 0
$$514$$ −0.826239 0.563320i −0.826239 0.563320i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$522$$ 0 0
$$523$$ 0 0 −0.733052 0.680173i $$-0.761905\pi$$
0.733052 + 0.680173i $$0.238095\pi$$
$$524$$ −0.781831 + 0.376510i −0.781831 + 0.376510i
$$525$$ −1.26631 + 0.496990i −1.26631 + 0.496990i
$$526$$ 0 0
$$527$$ −0.712362 1.81507i −0.712362 1.81507i
$$528$$ −0.114533 1.52833i −0.114533 1.52833i
$$529$$ −0.236007 + 0.0727985i −0.236007 + 0.0727985i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 1.90580 + 0.587862i 1.90580 + 0.587862i
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0.563320 + 0.975699i 0.563320 + 0.975699i
$$540$$ 0 0
$$541$$ 0 0 0.826239 0.563320i $$-0.190476\pi$$
−0.826239 + 0.563320i $$0.809524\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −0.955573 0.294755i −0.955573 0.294755i
$$545$$ 0 0
$$546$$ 0.975345 2.02532i 0.975345 2.02532i
$$547$$ 0.0663300 + 0.290611i 0.0663300 + 0.290611i 0.997204 0.0747301i $$-0.0238095\pi$$
−0.930874 + 0.365341i $$0.880952\pi$$
$$548$$ 0.109562 1.46200i 0.109562 1.46200i
$$549$$ 0 0
$$550$$ −0.0841939 1.12349i −0.0841939 1.12349i
$$551$$ 0 0
$$552$$ −1.06356 0.512184i −1.06356 0.512184i
$$553$$ 0.587862 1.90580i 0.587862 1.90580i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −1.97213 0.297251i −1.97213 0.297251i
$$557$$ 0.955573 + 1.65510i 0.955573 + 1.65510i 0.733052 + 0.680173i $$0.238095\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$558$$ −0.829215 + 1.43624i −0.829215 + 1.43624i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −0.955573 1.19825i −0.955573 1.19825i
$$562$$ −0.988831 + 0.149042i −0.988831 + 0.149042i
$$563$$ 0 0 −0.826239 0.563320i $$-0.809524\pi$$
0.826239 + 0.563320i $$0.190476\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0.702449 + 0.880843i 0.702449 + 0.880843i
$$567$$ −1.12397 + 0.0842299i −1.12397 + 0.0842299i
$$568$$ −0.367554 + 0.460898i −0.367554 + 0.460898i
$$569$$ −0.826239 + 1.43109i −0.826239 + 1.43109i 0.0747301 + 0.997204i $$0.476190\pi$$
−0.900969 + 0.433884i $$0.857143\pi$$
$$570$$ 0 0
$$571$$ 1.92808 + 0.290611i 1.92808 + 0.290611i 0.997204 0.0747301i $$-0.0238095\pi$$
0.930874 + 0.365341i $$0.119048\pi$$
$$572$$ 1.36476 + 1.26631i 1.36476 + 1.26631i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −0.781831 0.376510i −0.781831 0.376510i
$$576$$ 0.310737 + 0.791745i 0.310737 + 0.791745i
$$577$$ −0.0546039 0.728639i −0.0546039 0.728639i −0.955573 0.294755i $$-0.904762\pi$$
0.900969 0.433884i $$-0.142857\pi$$
$$578$$ −0.955573 + 0.294755i −0.955573 + 0.294755i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 2.05751 + 0.634659i 2.05751 + 0.634659i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −0.123490 + 0.0841939i −0.123490 + 0.0841939i
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ −0.997204 0.925270i −0.997204 0.925270i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0.698220 + 0.215372i 0.698220 + 0.215372i 0.623490 0.781831i $$-0.285714\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$594$$ 0.0509719 0.223322i 0.0509719 0.223322i
$$595$$ 0 0
$$596$$ 0.326239 + 1.42935i 0.326239 + 1.42935i
$$597$$ 0.0599289 0.799695i 0.0599289 0.799695i
$$598$$ 1.37026 0.422669i 1.37026 0.422669i
$$599$$ 0 0 −0.0747301 0.997204i $$-0.523810\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$600$$ 0.496990 + 1.26631i 0.496990 + 1.26631i
$$601$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ −1.22563 2.12285i −1.22563 2.12285i
$$607$$ 0.866025 1.50000i 0.866025 1.50000i 1.00000i $$-0.5\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0.702749 + 0.479126i 0.702749 + 0.479126i
$$613$$ −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i $$-0.857143\pi$$
−0.733052 0.680173i $$-0.761905\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0.975699 0.563320i 0.975699 0.563320i
$$617$$ 0 0 0.623490 0.781831i $$-0.285714\pi$$
−0.623490 + 0.781831i $$0.714286\pi$$
$$618$$ 0 0
$$619$$ −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$-0.5\pi$$
$$620$$ 0 0
$$621$$ −0.129334 0.120004i −0.129334 0.120004i
$$622$$ 1.56052 0.751509i 1.56052 0.751509i
$$623$$ 0.218511 + 1.44973i 0.218511 + 1.44973i
$$624$$ −2.02532 0.975345i −2.02532 0.975345i
$$625$$ 0.365341 + 0.930874i 0.365341 + 0.930874i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0.0111692 0.149042i 0.0111692 0.149042i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 0.222521 0.974928i $$-0.428571\pi$$
−0.222521 + 0.974928i $$0.571429\pi$$
$$632$$ −1.90580 0.587862i −1.90580 0.587862i
$$633$$ 0.777125 1.98008i 0.777125 1.98008i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ −2.59982 −2.59982
$$637$$ 1.65248 1.65248
$$638$$ 0 0
$$639$$ 0.414278 0.282450i 0.414278 0.282450i
$$640$$ 0 0
$$641$$ 0 0 0.365341 0.930874i $$-0.380952\pi$$
−0.365341 + 0.930874i $$0.619048\pi$$
$$642$$ 2.42010 + 0.746503i 2.42010 + 0.746503i
$$643$$ 0.0663300 0.290611i 0.0663300 0.290611i −0.930874 0.365341i $$-0.880952\pi$$
0.997204 + 0.0747301i $$0.0238095\pi$$
$$644$$ 0.867767i 0.867767i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.955573 0.294755i $$-0.0952381\pi$$
−0.955573 + 0.294755i $$0.904762\pi$$
$$648$$ 0.0842299 + 1.12397i 0.0842299 + 1.12397i
$$649$$ 0 0
$$650$$ −1.48883 0.716983i −1.48883 0.716983i
$$651$$ −2.64506 0.198220i −2.64506 0.198220i
$$652$$ 0 0
$$653$$ 0 0 −0.733052 0.680173i $$-0.761905\pi$$
0.733052 + 0.680173i $$0.238095\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 −0.623490 0.781831i $$-0.714286\pi$$
0.623490 + 0.781831i $$0.285714\pi$$
$$660$$ 0 0
$$661$$ −0.367711 0.250701i −0.367711 0.250701i 0.365341 0.930874i $$-0.380952\pi$$
−0.733052 + 0.680173i $$0.761905\pi$$
$$662$$ 0 0
$$663$$ −2.22283 + 0.335038i −2.22283 + 0.335038i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0.149042 + 0.258149i 0.149042 + 0.258149i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ −0.925270 + 0.997204i −0.925270 + 0.997204i
$$673$$ 0 0 −0.900969 0.433884i $$-0.857143\pi$$
0.900969 + 0.433884i $$0.142857\pi$$
$$674$$ 0 0
$$675$$ 0.0151939 + 0.202749i 0.0151939 + 0.202749i
$$676$$ 1.65379 0.510127i 1.65379 0.510127i
$$677$$ 0 0 0.0747301 0.997204i $$-0.476190\pi$$
−0.0747301 + 0.997204i $$0.523810\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0.766310 + 0.236375i 0.766310 + 0.236375i
$$682$$ 0.802576 2.04493i 0.802576 2.04493i
$$683$$ 0.432142 0.400969i 0.432142 0.400969i −0.433884 0.900969i $$-0.642857\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0.294755 0.955573i 0.294755 0.955573i
$$687$$ 1.69632 1.69632
$$688$$ 0 0
$$689$$ 2.31507 2.14807i 2.31507 2.14807i
$$690$$ 0 0
$$691$$ 1.86323 + 0.574730i 1.86323 + 0.574730i 0.997204 + 0.0747301i $$0.0238095\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$692$$ 0 0
$$693$$ −0.934227 + 0.213231i −0.934227 + 0.213231i
$$694$$ −0.347948 1.52446i −0.347948 1.52446i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −0.455573 1.16078i −0.455573 1.16078i
$$699$$ 0 0
$$700$$ −0.680173 + 0.733052i −0.680173 + 0.733052i
$$701$$ 1.72188 0.829215i 1.72188 0.829215i 0.733052 0.680173i $$-0.238095\pi$$
0.988831 0.149042i $$-0.0476190\pi$$
$$702$$ −0.246289 0.228523i −0.246289 0.228523i
$$703$$ 0 0
$$704$$ −0.563320 0.975699i −0.563320 0.975699i
$$705$$ 0 0
$$706$$ 0.623490 0.781831i 0.623490 0.781831i
$$707$$ 1.01507 1.48883i 1.01507 1.48883i
$$708$$ 0 0
$$709$$ 0 0 0.988831 0.149042i $$-0.0476190\pi$$
−0.988831 + 0.149042i $$0.952381\pi$$
$$710$$ 0 0
$$711$$ 1.40157 + 0.955573i 1.40157 + 0.955573i
$$712$$ 1.44973 0.218511i 1.44973 0.218511i
$$713$$ −1.05496 1.32288i −1.05496 1.32288i
$$714$$ −0.202749 + 1.34515i −0.202749 + 1.34515i
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −0.825886 0.766310i −0.825886 0.766310i 0.149042 0.988831i $$-0.452381\pi$$
−0.974928 + 0.222521i $$0.928571\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.900969 + 0.433884i 0.900969 + 0.433884i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0.0273785 0.365341i 0.0273785 0.365341i
$$727$$ 0 0 −0.222521 0.974928i $$-0.571429\pi$$
0.222521 + 0.974928i $$0.428571\pi$$
$$728$$ 1.65248i 1.65248i
$$729$$ 0.151777 0.664979i 0.151777 0.664979i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −0.826239 + 0.563320i −0.826239 + 0.563320i −0.900969 0.433884i $$-0.857143\pi$$
0.0747301 + 0.997204i $$0.476190\pi$$
$$734$$ 1.86175 1.86175
$$735$$ 0 0
$$736$$ −0.867767 −0.867767
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 0.365341 0.930874i $$-0.380952\pi$$
−0.365341 + 0.930874i $$0.619048\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −0.829215 1.72188i −0.829215 1.72188i
$$743$$ −0.302705 1.32624i −0.302705 1.32624i −0.866025 0.500000i $$-0.833333\pi$$
0.563320 0.826239i $$-0.309524\pi$$
$$744$$ −0.198220 + 2.64506i −0.198220 + 2.64506i
$$745$$ 0 0
$$746$$ 0.123490 + 1.64786i 0.123490 + 1.64786i
$$747$$ 0 0
$$748$$ −1.01507 0.488831i −1.01507 0.488831i
$$749$$ 0.277479 + 1.84095i 0.277479 + 1.84095i
$$750$$ 0 0
$$751$$ 1.46200 + 1.35654i 1.46200 + 1.35654i 0.781831 + 0.623490i $$0.214286\pi$$
0.680173 + 0.733052i $$0.261905\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −0.176078 + 0.101659i −0.176078 + 0.101659i
$$757$$ 0.623490 + 0.781831i 0.623490 + 0.781831i 0.988831 0.149042i $$-0.0476190\pi$$
−0.365341 + 0.930874i $$0.619048\pi$$
$$758$$ 1.71271 0.258149i 1.71271 0.258149i
$$759$$ −1.09886 0.749192i −1.09886 0.749192i
$$760$$ 0 0
$$761$$ −1.95557 + 0.294755i −1.95557 + 0.294755i −0.955573 + 0.294755i $$0.904762\pi$$
−1.00000 $$1.00000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0.997204 + 0.925270i 0.997204 + 0.925270i
$$769$$ −0.900969 + 0.433884i −0.900969 + 0.433884i −0.826239 0.563320i $$-0.809524\pi$$
−0.0747301 + 0.997204i $$0.523810\pi$$
$$770$$ 0 0
$$771$$ 1.22563 + 0.590232i 1.22563 + 0.590232i
$$772$$ 0 0
$$773$$ 0.147791 + 1.97213i 0.147791 + 1.97213i 0.222521 + 0.974928i $$0.428571\pi$$
−0.0747301 + 0.997204i $$0.523810\pi$$
$$774$$ 0 0
$$775$$ −0.145713 + 1.94440i −0.145713 + 1.94440i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0.440071 1.92808i 0.440071 1.92808i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −0.486868 + 0.451748i −0.486868 + 0.451748i
$$782$$ −0.716983 + 0.488831i −0.716983 + 0.488831i
$$783$$ 0 0
$$784$$ −0.955573 0.294755i −0.955573 0.294755i
$$785$$ 0 0
$$786$$ 0.975345 0.664979i 0.975345 0.664979i
$$787$$ 1.14625