# Properties

 Modulus 2011 Structure $$C_{2010}$$ Order 2010

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(2011)

pari: g = idealstar(,2011,2)

## Character group

 sage: G.order()  pari: g.no Order = 2010 sage: H.invariants()  pari: g.cyc Structure = $$C_{2010}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2011}(3,\cdot)$

## First 32 of 2010 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
$$\chi_{2011}(1,\cdot)$$ 2011.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2011}(2,\cdot)$$ 2011.m 402 yes $$-1$$ $$1$$ $$e\left(\frac{347}{402}\right)$$ $$e\left(\frac{49}{402}\right)$$ $$e\left(\frac{146}{201}\right)$$ $$e\left(\frac{164}{201}\right)$$ $$e\left(\frac{66}{67}\right)$$ $$e\left(\frac{103}{402}\right)$$ $$e\left(\frac{79}{134}\right)$$ $$e\left(\frac{49}{201}\right)$$ $$e\left(\frac{91}{134}\right)$$ $$e\left(\frac{161}{402}\right)$$
$$\chi_{2011}(3,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{49}{402}\right)$$ $$e\left(\frac{1}{2010}\right)$$ $$e\left(\frac{49}{201}\right)$$ $$e\left(\frac{512}{1005}\right)$$ $$e\left(\frac{41}{335}\right)$$ $$e\left(\frac{1807}{2010}\right)$$ $$e\left(\frac{49}{134}\right)$$ $$e\left(\frac{1}{1005}\right)$$ $$e\left(\frac{423}{670}\right)$$ $$e\left(\frac{1037}{2010}\right)$$
$$\chi_{2011}(4,\cdot)$$ 2011.k 201 yes $$1$$ $$1$$ $$e\left(\frac{146}{201}\right)$$ $$e\left(\frac{49}{201}\right)$$ $$e\left(\frac{91}{201}\right)$$ $$e\left(\frac{127}{201}\right)$$ $$e\left(\frac{65}{67}\right)$$ $$e\left(\frac{103}{201}\right)$$ $$e\left(\frac{12}{67}\right)$$ $$e\left(\frac{98}{201}\right)$$ $$e\left(\frac{24}{67}\right)$$ $$e\left(\frac{161}{201}\right)$$
$$\chi_{2011}(5,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{164}{201}\right)$$ $$e\left(\frac{512}{1005}\right)$$ $$e\left(\frac{127}{201}\right)$$ $$e\left(\frac{683}{1005}\right)$$ $$e\left(\frac{109}{335}\right)$$ $$e\left(\frac{584}{1005}\right)$$ $$e\left(\frac{30}{67}\right)$$ $$e\left(\frac{19}{1005}\right)$$ $$e\left(\frac{166}{335}\right)$$ $$e\left(\frac{304}{1005}\right)$$
$$\chi_{2011}(6,\cdot)$$ 2011.l 335 yes $$1$$ $$1$$ $$e\left(\frac{66}{67}\right)$$ $$e\left(\frac{41}{335}\right)$$ $$e\left(\frac{65}{67}\right)$$ $$e\left(\frac{109}{335}\right)$$ $$e\left(\frac{36}{335}\right)$$ $$e\left(\frac{52}{335}\right)$$ $$e\left(\frac{64}{67}\right)$$ $$e\left(\frac{82}{335}\right)$$ $$e\left(\frac{104}{335}\right)$$ $$e\left(\frac{307}{335}\right)$$
$$\chi_{2011}(7,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{103}{402}\right)$$ $$e\left(\frac{1807}{2010}\right)$$ $$e\left(\frac{103}{201}\right)$$ $$e\left(\frac{584}{1005}\right)$$ $$e\left(\frac{52}{335}\right)$$ $$e\left(\frac{1009}{2010}\right)$$ $$e\left(\frac{103}{134}\right)$$ $$e\left(\frac{802}{1005}\right)$$ $$e\left(\frac{561}{670}\right)$$ $$e\left(\frac{539}{2010}\right)$$
$$\chi_{2011}(8,\cdot)$$ 2011.j 134 yes $$-1$$ $$1$$ $$e\left(\frac{79}{134}\right)$$ $$e\left(\frac{49}{134}\right)$$ $$e\left(\frac{12}{67}\right)$$ $$e\left(\frac{30}{67}\right)$$ $$e\left(\frac{64}{67}\right)$$ $$e\left(\frac{103}{134}\right)$$ $$e\left(\frac{103}{134}\right)$$ $$e\left(\frac{49}{67}\right)$$ $$e\left(\frac{5}{134}\right)$$ $$e\left(\frac{27}{134}\right)$$
$$\chi_{2011}(9,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{49}{201}\right)$$ $$e\left(\frac{1}{1005}\right)$$ $$e\left(\frac{98}{201}\right)$$ $$e\left(\frac{19}{1005}\right)$$ $$e\left(\frac{82}{335}\right)$$ $$e\left(\frac{802}{1005}\right)$$ $$e\left(\frac{49}{67}\right)$$ $$e\left(\frac{2}{1005}\right)$$ $$e\left(\frac{88}{335}\right)$$ $$e\left(\frac{32}{1005}\right)$$
$$\chi_{2011}(10,\cdot)$$ 2011.n 670 yes $$-1$$ $$1$$ $$e\left(\frac{91}{134}\right)$$ $$e\left(\frac{423}{670}\right)$$ $$e\left(\frac{24}{67}\right)$$ $$e\left(\frac{166}{335}\right)$$ $$e\left(\frac{104}{335}\right)$$ $$e\left(\frac{561}{670}\right)$$ $$e\left(\frac{5}{134}\right)$$ $$e\left(\frac{88}{335}\right)$$ $$e\left(\frac{117}{670}\right)$$ $$e\left(\frac{471}{670}\right)$$
$$\chi_{2011}(11,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{161}{402}\right)$$ $$e\left(\frac{1037}{2010}\right)$$ $$e\left(\frac{161}{201}\right)$$ $$e\left(\frac{304}{1005}\right)$$ $$e\left(\frac{307}{335}\right)$$ $$e\left(\frac{539}{2010}\right)$$ $$e\left(\frac{27}{134}\right)$$ $$e\left(\frac{32}{1005}\right)$$ $$e\left(\frac{471}{670}\right)$$ $$e\left(\frac{19}{2010}\right)$$
$$\chi_{2011}(12,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{341}{402}\right)$$ $$e\left(\frac{491}{2010}\right)$$ $$e\left(\frac{140}{201}\right)$$ $$e\left(\frac{142}{1005}\right)$$ $$e\left(\frac{31}{335}\right)$$ $$e\left(\frac{827}{2010}\right)$$ $$e\left(\frac{73}{134}\right)$$ $$e\left(\frac{491}{1005}\right)$$ $$e\left(\frac{663}{670}\right)$$ $$e\left(\frac{637}{2010}\right)$$
$$\chi_{2011}(13,\cdot)$$ 2011.l 335 yes $$1$$ $$1$$ $$e\left(\frac{15}{67}\right)$$ $$e\left(\frac{323}{335}\right)$$ $$e\left(\frac{30}{67}\right)$$ $$e\left(\frac{107}{335}\right)$$ $$e\left(\frac{63}{335}\right)$$ $$e\left(\frac{91}{335}\right)$$ $$e\left(\frac{45}{67}\right)$$ $$e\left(\frac{311}{335}\right)$$ $$e\left(\frac{182}{335}\right)$$ $$e\left(\frac{286}{335}\right)$$
$$\chi_{2011}(14,\cdot)$$ 2011.l 335 yes $$1$$ $$1$$ $$e\left(\frac{8}{67}\right)$$ $$e\left(\frac{7}{335}\right)$$ $$e\left(\frac{16}{67}\right)$$ $$e\left(\frac{133}{335}\right)$$ $$e\left(\frac{47}{335}\right)$$ $$e\left(\frac{254}{335}\right)$$ $$e\left(\frac{24}{67}\right)$$ $$e\left(\frac{14}{335}\right)$$ $$e\left(\frac{173}{335}\right)$$ $$e\left(\frac{224}{335}\right)$$
$$\chi_{2011}(15,\cdot)$$ 2011.m 402 yes $$-1$$ $$1$$ $$e\left(\frac{377}{402}\right)$$ $$e\left(\frac{205}{402}\right)$$ $$e\left(\frac{176}{201}\right)$$ $$e\left(\frac{38}{201}\right)$$ $$e\left(\frac{30}{67}\right)$$ $$e\left(\frac{193}{402}\right)$$ $$e\left(\frac{109}{134}\right)$$ $$e\left(\frac{4}{201}\right)$$ $$e\left(\frac{17}{134}\right)$$ $$e\left(\frac{329}{402}\right)$$
$$\chi_{2011}(16,\cdot)$$ 2011.k 201 yes $$1$$ $$1$$ $$e\left(\frac{91}{201}\right)$$ $$e\left(\frac{98}{201}\right)$$ $$e\left(\frac{182}{201}\right)$$ $$e\left(\frac{53}{201}\right)$$ $$e\left(\frac{63}{67}\right)$$ $$e\left(\frac{5}{201}\right)$$ $$e\left(\frac{24}{67}\right)$$ $$e\left(\frac{196}{201}\right)$$ $$e\left(\frac{48}{67}\right)$$ $$e\left(\frac{121}{201}\right)$$
$$\chi_{2011}(17,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{119}{402}\right)$$ $$e\left(\frac{347}{2010}\right)$$ $$e\left(\frac{119}{201}\right)$$ $$e\left(\frac{784}{1005}\right)$$ $$e\left(\frac{157}{335}\right)$$ $$e\left(\frac{1919}{2010}\right)$$ $$e\left(\frac{119}{134}\right)$$ $$e\left(\frac{347}{1005}\right)$$ $$e\left(\frac{51}{670}\right)$$ $$e\left(\frac{49}{2010}\right)$$
$$\chi_{2011}(18,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{43}{402}\right)$$ $$e\left(\frac{247}{2010}\right)$$ $$e\left(\frac{43}{201}\right)$$ $$e\left(\frac{839}{1005}\right)$$ $$e\left(\frac{77}{335}\right)$$ $$e\left(\frac{109}{2010}\right)$$ $$e\left(\frac{43}{134}\right)$$ $$e\left(\frac{247}{1005}\right)$$ $$e\left(\frac{631}{670}\right)$$ $$e\left(\frac{869}{2010}\right)$$
$$\chi_{2011}(19,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{305}{402}\right)$$ $$e\left(\frac{1163}{2010}\right)$$ $$e\left(\frac{104}{201}\right)$$ $$e\left(\frac{496}{1005}\right)$$ $$e\left(\frac{113}{335}\right)$$ $$e\left(\frac{1091}{2010}\right)$$ $$e\left(\frac{37}{134}\right)$$ $$e\left(\frac{158}{1005}\right)$$ $$e\left(\frac{169}{670}\right)$$ $$e\left(\frac{31}{2010}\right)$$
$$\chi_{2011}(20,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{109}{201}\right)$$ $$e\left(\frac{757}{1005}\right)$$ $$e\left(\frac{17}{201}\right)$$ $$e\left(\frac{313}{1005}\right)$$ $$e\left(\frac{99}{335}\right)$$ $$e\left(\frac{94}{1005}\right)$$ $$e\left(\frac{42}{67}\right)$$ $$e\left(\frac{509}{1005}\right)$$ $$e\left(\frac{286}{335}\right)$$ $$e\left(\frac{104}{1005}\right)$$
$$\chi_{2011}(21,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{76}{201}\right)$$ $$e\left(\frac{904}{1005}\right)$$ $$e\left(\frac{152}{201}\right)$$ $$e\left(\frac{91}{1005}\right)$$ $$e\left(\frac{93}{335}\right)$$ $$e\left(\frac{403}{1005}\right)$$ $$e\left(\frac{9}{67}\right)$$ $$e\left(\frac{803}{1005}\right)$$ $$e\left(\frac{157}{335}\right)$$ $$e\left(\frac{788}{1005}\right)$$
$$\chi_{2011}(22,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{53}{201}\right)$$ $$e\left(\frac{641}{1005}\right)$$ $$e\left(\frac{106}{201}\right)$$ $$e\left(\frac{119}{1005}\right)$$ $$e\left(\frac{302}{335}\right)$$ $$e\left(\frac{527}{1005}\right)$$ $$e\left(\frac{53}{67}\right)$$ $$e\left(\frac{277}{1005}\right)$$ $$e\left(\frac{128}{335}\right)$$ $$e\left(\frac{412}{1005}\right)$$
$$\chi_{2011}(23,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{47}{201}\right)$$ $$e\left(\frac{83}{1005}\right)$$ $$e\left(\frac{94}{201}\right)$$ $$e\left(\frac{572}{1005}\right)$$ $$e\left(\frac{106}{335}\right)$$ $$e\left(\frac{236}{1005}\right)$$ $$e\left(\frac{47}{67}\right)$$ $$e\left(\frac{166}{1005}\right)$$ $$e\left(\frac{269}{335}\right)$$ $$e\left(\frac{646}{1005}\right)$$
$$\chi_{2011}(24,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{143}{201}\right)$$ $$e\left(\frac{368}{1005}\right)$$ $$e\left(\frac{85}{201}\right)$$ $$e\left(\frac{962}{1005}\right)$$ $$e\left(\frac{26}{335}\right)$$ $$e\left(\frac{671}{1005}\right)$$ $$e\left(\frac{9}{67}\right)$$ $$e\left(\frac{736}{1005}\right)$$ $$e\left(\frac{224}{335}\right)$$ $$e\left(\frac{721}{1005}\right)$$
$$\chi_{2011}(25,\cdot)$$ 2011.o 1005 yes $$1$$ $$1$$ $$e\left(\frac{127}{201}\right)$$ $$e\left(\frac{19}{1005}\right)$$ $$e\left(\frac{53}{201}\right)$$ $$e\left(\frac{361}{1005}\right)$$ $$e\left(\frac{218}{335}\right)$$ $$e\left(\frac{163}{1005}\right)$$ $$e\left(\frac{60}{67}\right)$$ $$e\left(\frac{38}{1005}\right)$$ $$e\left(\frac{332}{335}\right)$$ $$e\left(\frac{608}{1005}\right)$$
$$\chi_{2011}(26,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{35}{402}\right)$$ $$e\left(\frac{173}{2010}\right)$$ $$e\left(\frac{35}{201}\right)$$ $$e\left(\frac{136}{1005}\right)$$ $$e\left(\frac{58}{335}\right)$$ $$e\left(\frac{1061}{2010}\right)$$ $$e\left(\frac{35}{134}\right)$$ $$e\left(\frac{173}{1005}\right)$$ $$e\left(\frac{149}{670}\right)$$ $$e\left(\frac{511}{2010}\right)$$
$$\chi_{2011}(27,\cdot)$$ 2011.n 670 yes $$-1$$ $$1$$ $$e\left(\frac{49}{134}\right)$$ $$e\left(\frac{1}{670}\right)$$ $$e\left(\frac{49}{67}\right)$$ $$e\left(\frac{177}{335}\right)$$ $$e\left(\frac{123}{335}\right)$$ $$e\left(\frac{467}{670}\right)$$ $$e\left(\frac{13}{134}\right)$$ $$e\left(\frac{1}{335}\right)$$ $$e\left(\frac{599}{670}\right)$$ $$e\left(\frac{367}{670}\right)$$
$$\chi_{2011}(28,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{395}{402}\right)$$ $$e\left(\frac{287}{2010}\right)$$ $$e\left(\frac{194}{201}\right)$$ $$e\left(\frac{214}{1005}\right)$$ $$e\left(\frac{42}{335}\right)$$ $$e\left(\frac{29}{2010}\right)$$ $$e\left(\frac{127}{134}\right)$$ $$e\left(\frac{287}{1005}\right)$$ $$e\left(\frac{131}{670}\right)$$ $$e\left(\frac{139}{2010}\right)$$
$$\chi_{2011}(29,\cdot)$$ 2011.p 2010 yes $$-1$$ $$1$$ $$e\left(\frac{331}{402}\right)$$ $$e\left(\frac{97}{2010}\right)$$ $$e\left(\frac{130}{201}\right)$$ $$e\left(\frac{419}{1005}\right)$$ $$e\left(\frac{292}{335}\right)$$ $$e\left(\frac{409}{2010}\right)$$ $$e\left(\frac{63}{134}\right)$$ $$e\left(\frac{97}{1005}\right)$$ $$e\left(\frac{161}{670}\right)$$ $$e\left(\frac{89}{2010}\right)$$
$$\chi_{2011}(30,\cdot)$$ 2011.k 201 yes $$1$$ $$1$$ $$e\left(\frac{161}{201}\right)$$ $$e\left(\frac{127}{201}\right)$$ $$e\left(\frac{121}{201}\right)$$ $$e\left(\frac{1}{201}\right)$$ $$e\left(\frac{29}{67}\right)$$ $$e\left(\frac{148}{201}\right)$$ $$e\left(\frac{27}{67}\right)$$ $$e\left(\frac{53}{201}\right)$$ $$e\left(\frac{54}{67}\right)$$ $$e\left(\frac{44}{201}\right)$$
$$\chi_{2011}(31,\cdot)$$ 2011.l 335 yes $$1$$ $$1$$ $$e\left(\frac{46}{67}\right)$$ $$e\left(\frac{258}{335}\right)$$ $$e\left(\frac{25}{67}\right)$$ $$e\left(\frac{212}{335}\right)$$ $$e\left(\frac{153}{335}\right)$$ $$e\left(\frac{221}{335}\right)$$ $$e\left(\frac{4}{67}\right)$$ $$e\left(\frac{181}{335}\right)$$ $$e\left(\frac{107}{335}\right)$$ $$e\left(\frac{216}{335}\right)$$
$$\chi_{2011}(32,\cdot)$$ 2011.m 402 yes $$-1$$ $$1$$ $$e\left(\frac{127}{402}\right)$$ $$e\left(\frac{245}{402}\right)$$ $$e\left(\frac{127}{201}\right)$$ $$e\left(\frac{16}{201}\right)$$ $$e\left(\frac{62}{67}\right)$$ $$e\left(\frac{113}{402}\right)$$ $$e\left(\frac{127}{134}\right)$$ $$e\left(\frac{44}{201}\right)$$ $$e\left(\frac{53}{134}\right)$$ $$e\left(\frac{1}{402}\right)$$