# Properties

 Modulus 4021 Structure $$C_{4020}$$ Order 4020

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4021)
pari: g = idealstar(,4021,2)

## Character group

 sage: G.order() pari: g.no Order = 4020 sage: H.invariants() pari: g.cyc Structure = $$C_{4020}$$ sage: H.gens() pari: g.gen Generators = $\chi_{4021}(2,\cdot)$

## First 32 of 4020 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
$$\chi_{4021}(1,\cdot)$$ 4021.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4021}(2,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{4020}\right)$$ $$e\left(\frac{746}{1005}\right)$$ $$e\left(\frac{1}{2010}\right)$$ $$e\left(\frac{131}{1005}\right)$$ $$e\left(\frac{199}{268}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{1340}\right)$$ $$e\left(\frac{487}{1005}\right)$$ $$e\left(\frac{35}{268}\right)$$ $$e\left(\frac{2557}{4020}\right)$$
$$\chi_{4021}(3,\cdot)$$ 4021.u 1005 Yes $$1$$ $$1$$ $$e\left(\frac{746}{1005}\right)$$ $$e\left(\frac{994}{1005}\right)$$ $$e\left(\frac{487}{1005}\right)$$ $$e\left(\frac{964}{1005}\right)$$ $$e\left(\frac{49}{67}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{76}{335}\right)$$ $$e\left(\frac{983}{1005}\right)$$ $$e\left(\frac{47}{67}\right)$$ $$e\left(\frac{32}{1005}\right)$$
$$\chi_{4021}(4,\cdot)$$ 4021.w 2010 Yes $$1$$ $$1$$ $$e\left(\frac{1}{2010}\right)$$ $$e\left(\frac{487}{1005}\right)$$ $$e\left(\frac{1}{1005}\right)$$ $$e\left(\frac{262}{1005}\right)$$ $$e\left(\frac{65}{134}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{670}\right)$$ $$e\left(\frac{974}{1005}\right)$$ $$e\left(\frac{35}{134}\right)$$ $$e\left(\frac{547}{2010}\right)$$
$$\chi_{4021}(5,\cdot)$$ 4021.u 1005 Yes $$1$$ $$1$$ $$e\left(\frac{131}{1005}\right)$$ $$e\left(\frac{964}{1005}\right)$$ $$e\left(\frac{262}{1005}\right)$$ $$e\left(\frac{304}{1005}\right)$$ $$e\left(\frac{6}{67}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{131}{335}\right)$$ $$e\left(\frac{923}{1005}\right)$$ $$e\left(\frac{29}{67}\right)$$ $$e\left(\frac{302}{1005}\right)$$
$$\chi_{4021}(6,\cdot)$$ 4021.p 268 Yes $$-1$$ $$1$$ $$e\left(\frac{199}{268}\right)$$ $$e\left(\frac{49}{67}\right)$$ $$e\left(\frac{65}{134}\right)$$ $$e\left(\frac{6}{67}\right)$$ $$e\left(\frac{127}{268}\right)$$ $$-i$$ $$e\left(\frac{61}{268}\right)$$ $$e\left(\frac{31}{67}\right)$$ $$e\left(\frac{223}{268}\right)$$ $$e\left(\frac{179}{268}\right)$$
$$\chi_{4021}(7,\cdot)$$ 4021.j 20 Yes $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-i$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{4021}(8,\cdot)$$ 4021.v 1340 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{1340}\right)$$ $$e\left(\frac{76}{335}\right)$$ $$e\left(\frac{1}{670}\right)$$ $$e\left(\frac{131}{335}\right)$$ $$e\left(\frac{61}{268}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{1340}\right)$$ $$e\left(\frac{152}{335}\right)$$ $$e\left(\frac{105}{268}\right)$$ $$e\left(\frac{1217}{1340}\right)$$
$$\chi_{4021}(9,\cdot)$$ 4021.u 1005 Yes $$1$$ $$1$$ $$e\left(\frac{487}{1005}\right)$$ $$e\left(\frac{983}{1005}\right)$$ $$e\left(\frac{974}{1005}\right)$$ $$e\left(\frac{923}{1005}\right)$$ $$e\left(\frac{31}{67}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{152}{335}\right)$$ $$e\left(\frac{961}{1005}\right)$$ $$e\left(\frac{27}{67}\right)$$ $$e\left(\frac{64}{1005}\right)$$
$$\chi_{4021}(10,\cdot)$$ 4021.p 268 Yes $$-1$$ $$1$$ $$e\left(\frac{35}{268}\right)$$ $$e\left(\frac{47}{67}\right)$$ $$e\left(\frac{35}{134}\right)$$ $$e\left(\frac{29}{67}\right)$$ $$e\left(\frac{223}{268}\right)$$ $$-i$$ $$e\left(\frac{105}{268}\right)$$ $$e\left(\frac{27}{67}\right)$$ $$e\left(\frac{151}{268}\right)$$ $$e\left(\frac{251}{268}\right)$$
$$\chi_{4021}(11,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{2557}{4020}\right)$$ $$e\left(\frac{32}{1005}\right)$$ $$e\left(\frac{547}{2010}\right)$$ $$e\left(\frac{302}{1005}\right)$$ $$e\left(\frac{179}{268}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1217}{1340}\right)$$ $$e\left(\frac{64}{1005}\right)$$ $$e\left(\frac{251}{268}\right)$$ $$e\left(\frac{1729}{4020}\right)$$
$$\chi_{4021}(12,\cdot)$$ 4021.w 2010 Yes $$1$$ $$1$$ $$e\left(\frac{1493}{2010}\right)$$ $$e\left(\frac{476}{1005}\right)$$ $$e\left(\frac{488}{1005}\right)$$ $$e\left(\frac{221}{1005}\right)$$ $$e\left(\frac{29}{134}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{153}{670}\right)$$ $$e\left(\frac{952}{1005}\right)$$ $$e\left(\frac{129}{134}\right)$$ $$e\left(\frac{611}{2010}\right)$$
$$\chi_{4021}(13,\cdot)$$ 4021.n 134 Yes $$1$$ $$1$$ $$e\left(\frac{103}{134}\right)$$ $$e\left(\frac{45}{67}\right)$$ $$e\left(\frac{36}{67}\right)$$ $$e\left(\frac{52}{67}\right)$$ $$e\left(\frac{59}{134}\right)$$ $$-1$$ $$e\left(\frac{41}{134}\right)$$ $$e\left(\frac{23}{67}\right)$$ $$e\left(\frac{73}{134}\right)$$ $$e\left(\frac{61}{134}\right)$$
$$\chi_{4021}(14,\cdot)$$ 4021.u 1005 Yes $$1$$ $$1$$ $$e\left(\frac{151}{1005}\right)$$ $$e\left(\frac{344}{1005}\right)$$ $$e\left(\frac{302}{1005}\right)$$ $$e\left(\frac{734}{1005}\right)$$ $$e\left(\frac{33}{67}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{151}{335}\right)$$ $$e\left(\frac{688}{1005}\right)$$ $$e\left(\frac{59}{67}\right)$$ $$e\left(\frac{187}{1005}\right)$$
$$\chi_{4021}(15,\cdot)$$ 4021.u 1005 Yes $$1$$ $$1$$ $$e\left(\frac{877}{1005}\right)$$ $$e\left(\frac{953}{1005}\right)$$ $$e\left(\frac{749}{1005}\right)$$ $$e\left(\frac{263}{1005}\right)$$ $$e\left(\frac{55}{67}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{207}{335}\right)$$ $$e\left(\frac{901}{1005}\right)$$ $$e\left(\frac{9}{67}\right)$$ $$e\left(\frac{334}{1005}\right)$$
$$\chi_{4021}(16,\cdot)$$ 4021.u 1005 Yes $$1$$ $$1$$ $$e\left(\frac{1}{1005}\right)$$ $$e\left(\frac{974}{1005}\right)$$ $$e\left(\frac{2}{1005}\right)$$ $$e\left(\frac{524}{1005}\right)$$ $$e\left(\frac{65}{67}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{335}\right)$$ $$e\left(\frac{943}{1005}\right)$$ $$e\left(\frac{35}{67}\right)$$ $$e\left(\frac{547}{1005}\right)$$
$$\chi_{4021}(17,\cdot)$$ 4021.s 670 Yes $$1$$ $$1$$ $$e\left(\frac{37}{670}\right)$$ $$e\left(\frac{264}{335}\right)$$ $$e\left(\frac{37}{335}\right)$$ $$e\left(\frac{314}{335}\right)$$ $$e\left(\frac{113}{134}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{111}{670}\right)$$ $$e\left(\frac{193}{335}\right)$$ $$e\left(\frac{133}{134}\right)$$ $$e\left(\frac{139}{670}\right)$$
$$\chi_{4021}(18,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{1949}{4020}\right)$$ $$e\left(\frac{724}{1005}\right)$$ $$e\left(\frac{1949}{2010}\right)$$ $$e\left(\frac{49}{1005}\right)$$ $$e\left(\frac{55}{268}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{609}{1340}\right)$$ $$e\left(\frac{443}{1005}\right)$$ $$e\left(\frac{143}{268}\right)$$ $$e\left(\frac{2813}{4020}\right)$$
$$\chi_{4021}(19,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{251}{4020}\right)$$ $$e\left(\frac{316}{1005}\right)$$ $$e\left(\frac{251}{2010}\right)$$ $$e\left(\frac{721}{1005}\right)$$ $$e\left(\frac{101}{268}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{251}{1340}\right)$$ $$e\left(\frac{632}{1005}\right)$$ $$e\left(\frac{209}{268}\right)$$ $$e\left(\frac{2627}{4020}\right)$$
$$\chi_{4021}(20,\cdot)$$ 4021.w 2010 Yes $$1$$ $$1$$ $$e\left(\frac{263}{2010}\right)$$ $$e\left(\frac{446}{1005}\right)$$ $$e\left(\frac{263}{1005}\right)$$ $$e\left(\frac{566}{1005}\right)$$ $$e\left(\frac{77}{134}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{263}{670}\right)$$ $$e\left(\frac{892}{1005}\right)$$ $$e\left(\frac{93}{134}\right)$$ $$e\left(\frac{1151}{2010}\right)$$
$$\chi_{4021}(21,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{3587}{4020}\right)$$ $$e\left(\frac{592}{1005}\right)$$ $$e\left(\frac{1577}{2010}\right)$$ $$e\left(\frac{562}{1005}\right)$$ $$e\left(\frac{129}{268}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{907}{1340}\right)$$ $$e\left(\frac{179}{1005}\right)$$ $$e\left(\frac{121}{268}\right)$$ $$e\left(\frac{2339}{4020}\right)$$
$$\chi_{4021}(22,\cdot)$$ 4021.w 2010 Yes $$1$$ $$1$$ $$e\left(\frac{1279}{2010}\right)$$ $$e\left(\frac{778}{1005}\right)$$ $$e\left(\frac{274}{1005}\right)$$ $$e\left(\frac{433}{1005}\right)$$ $$e\left(\frac{55}{134}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{609}{670}\right)$$ $$e\left(\frac{551}{1005}\right)$$ $$e\left(\frac{9}{134}\right)$$ $$e\left(\frac{133}{2010}\right)$$
$$\chi_{4021}(23,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{2371}{4020}\right)$$ $$e\left(\frac{971}{1005}\right)$$ $$e\left(\frac{361}{2010}\right)$$ $$e\left(\frac{56}{1005}\right)$$ $$e\left(\frac{149}{268}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1031}{1340}\right)$$ $$e\left(\frac{937}{1005}\right)$$ $$e\left(\frac{173}{268}\right)$$ $$e\left(\frac{487}{4020}\right)$$
$$\chi_{4021}(24,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{2987}{4020}\right)$$ $$e\left(\frac{217}{1005}\right)$$ $$e\left(\frac{977}{2010}\right)$$ $$e\left(\frac{352}{1005}\right)$$ $$e\left(\frac{257}{268}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{307}{1340}\right)$$ $$e\left(\frac{434}{1005}\right)$$ $$e\left(\frac{25}{268}\right)$$ $$e\left(\frac{3779}{4020}\right)$$
$$\chi_{4021}(25,\cdot)$$ 4021.u 1005 Yes $$1$$ $$1$$ $$e\left(\frac{262}{1005}\right)$$ $$e\left(\frac{923}{1005}\right)$$ $$e\left(\frac{524}{1005}\right)$$ $$e\left(\frac{608}{1005}\right)$$ $$e\left(\frac{12}{67}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{262}{335}\right)$$ $$e\left(\frac{841}{1005}\right)$$ $$e\left(\frac{58}{67}\right)$$ $$e\left(\frac{604}{1005}\right)$$
$$\chi_{4021}(26,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{3091}{4020}\right)$$ $$e\left(\frac{416}{1005}\right)$$ $$e\left(\frac{1081}{2010}\right)$$ $$e\left(\frac{911}{1005}\right)$$ $$e\left(\frac{49}{268}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{411}{1340}\right)$$ $$e\left(\frac{832}{1005}\right)$$ $$e\left(\frac{181}{268}\right)$$ $$e\left(\frac{367}{4020}\right)$$
$$\chi_{4021}(27,\cdot)$$ 4021.q 335 Yes $$1$$ $$1$$ $$e\left(\frac{76}{335}\right)$$ $$e\left(\frac{324}{335}\right)$$ $$e\left(\frac{152}{335}\right)$$ $$e\left(\frac{294}{335}\right)$$ $$e\left(\frac{13}{67}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{228}{335}\right)$$ $$e\left(\frac{313}{335}\right)$$ $$e\left(\frac{7}{67}\right)$$ $$e\left(\frac{32}{335}\right)$$
$$\chi_{4021}(28,\cdot)$$ 4021.t 804 Yes $$-1$$ $$1$$ $$e\left(\frac{121}{804}\right)$$ $$e\left(\frac{17}{201}\right)$$ $$e\left(\frac{121}{402}\right)$$ $$e\left(\frac{173}{201}\right)$$ $$e\left(\frac{63}{268}\right)$$ $$-i$$ $$e\left(\frac{121}{268}\right)$$ $$e\left(\frac{34}{201}\right)$$ $$e\left(\frac{3}{268}\right)$$ $$e\left(\frac{661}{804}\right)$$
$$\chi_{4021}(29,\cdot)$$ 4021.t 804 Yes $$-1$$ $$1$$ $$e\left(\frac{185}{804}\right)$$ $$e\left(\frac{124}{201}\right)$$ $$e\left(\frac{185}{402}\right)$$ $$e\left(\frac{115}{201}\right)$$ $$e\left(\frac{227}{268}\right)$$ $$-i$$ $$e\left(\frac{185}{268}\right)$$ $$e\left(\frac{47}{201}\right)$$ $$e\left(\frac{215}{268}\right)$$ $$e\left(\frac{293}{804}\right)$$
$$\chi_{4021}(30,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{3509}{4020}\right)$$ $$e\left(\frac{694}{1005}\right)$$ $$e\left(\frac{1499}{2010}\right)$$ $$e\left(\frac{394}{1005}\right)$$ $$e\left(\frac{151}{268}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{829}{1340}\right)$$ $$e\left(\frac{383}{1005}\right)$$ $$e\left(\frac{71}{268}\right)$$ $$e\left(\frac{3893}{4020}\right)$$
$$\chi_{4021}(31,\cdot)$$ 4021.x 4020 Yes $$-1$$ $$1$$ $$e\left(\frac{2353}{4020}\right)$$ $$e\left(\frac{608}{1005}\right)$$ $$e\left(\frac{343}{2010}\right)$$ $$e\left(\frac{713}{1005}\right)$$ $$e\left(\frac{51}{268}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1013}{1340}\right)$$ $$e\left(\frac{211}{1005}\right)$$ $$e\left(\frac{79}{268}\right)$$ $$e\left(\frac{2701}{4020}\right)$$
$$\chi_{4021}(32,\cdot)$$ 4021.t 804 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{804}\right)$$ $$e\left(\frac{143}{201}\right)$$ $$e\left(\frac{1}{402}\right)$$ $$e\left(\frac{131}{201}\right)$$ $$e\left(\frac{191}{268}\right)$$ $$-i$$ $$e\left(\frac{1}{268}\right)$$ $$e\left(\frac{85}{201}\right)$$ $$e\left(\frac{175}{268}\right)$$ $$e\left(\frac{145}{804}\right)$$