# Properties

 Modulus $2601$ Structure $$C_{816}\times C_{2}$$ Order $1632$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2601)

pari: g = idealstar(,2601,2)

## Character group

 sage: G.order()  pari: g.no Order = 1632 sage: H.invariants()  pari: g.cyc Structure = $$C_{816}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2601}(290,\cdot)$, $\chi_{2601}(2026,\cdot)$

## First 32 of 1632 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.

Character Orbit Order Primitive $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{2601}(1,\cdot)$$ 2601.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2601}(2,\cdot)$$ 2601.bl 408 yes $$-1$$ $$1$$ $$e\left(\frac{181}{204}\right)$$ $$e\left(\frac{79}{102}\right)$$ $$e\left(\frac{325}{408}\right)$$ $$e\left(\frac{383}{408}\right)$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{93}{136}\right)$$ $$e\left(\frac{95}{408}\right)$$ $$e\left(\frac{25}{102}\right)$$ $$e\left(\frac{337}{408}\right)$$ $$e\left(\frac{28}{51}\right)$$
$$\chi_{2601}(4,\cdot)$$ 2601.bg 204 yes $$1$$ $$1$$ $$e\left(\frac{79}{102}\right)$$ $$e\left(\frac{28}{51}\right)$$ $$e\left(\frac{121}{204}\right)$$ $$e\left(\frac{179}{204}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{25}{68}\right)$$ $$e\left(\frac{95}{204}\right)$$ $$e\left(\frac{25}{51}\right)$$ $$e\left(\frac{133}{204}\right)$$ $$e\left(\frac{5}{51}\right)$$
$$\chi_{2601}(5,\cdot)$$ 2601.bn 816 yes $$1$$ $$1$$ $$e\left(\frac{325}{408}\right)$$ $$e\left(\frac{121}{204}\right)$$ $$e\left(\frac{787}{816}\right)$$ $$e\left(\frac{677}{816}\right)$$ $$e\left(\frac{53}{136}\right)$$ $$e\left(\frac{207}{272}\right)$$ $$e\left(\frac{161}{816}\right)$$ $$e\left(\frac{139}{204}\right)$$ $$e\left(\frac{511}{816}\right)$$ $$e\left(\frac{19}{102}\right)$$
$$\chi_{2601}(7,\cdot)$$ 2601.bm 816 yes $$-1$$ $$1$$ $$e\left(\frac{383}{408}\right)$$ $$e\left(\frac{179}{204}\right)$$ $$e\left(\frac{677}{816}\right)$$ $$e\left(\frac{811}{816}\right)$$ $$e\left(\frac{111}{136}\right)$$ $$e\left(\frac{209}{272}\right)$$ $$e\left(\frac{631}{816}\right)$$ $$e\left(\frac{5}{204}\right)$$ $$e\left(\frac{761}{816}\right)$$ $$e\left(\frac{77}{102}\right)$$
$$\chi_{2601}(8,\cdot)$$ 2601.bf 136 no $$-1$$ $$1$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{53}{136}\right)$$ $$e\left(\frac{111}{136}\right)$$ $$e\left(\frac{67}{68}\right)$$ $$e\left(\frac{7}{136}\right)$$ $$e\left(\frac{95}{136}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{65}{136}\right)$$ $$e\left(\frac{11}{17}\right)$$
$$\chi_{2601}(10,\cdot)$$ 2601.bi 272 no $$-1$$ $$1$$ $$e\left(\frac{93}{136}\right)$$ $$e\left(\frac{25}{68}\right)$$ $$e\left(\frac{207}{272}\right)$$ $$e\left(\frac{209}{272}\right)$$ $$e\left(\frac{7}{136}\right)$$ $$e\left(\frac{121}{272}\right)$$ $$e\left(\frac{117}{272}\right)$$ $$e\left(\frac{63}{68}\right)$$ $$e\left(\frac{123}{272}\right)$$ $$e\left(\frac{25}{34}\right)$$
$$\chi_{2601}(11,\cdot)$$ 2601.bn 816 yes $$1$$ $$1$$ $$e\left(\frac{95}{408}\right)$$ $$e\left(\frac{95}{204}\right)$$ $$e\left(\frac{161}{816}\right)$$ $$e\left(\frac{631}{816}\right)$$ $$e\left(\frac{95}{136}\right)$$ $$e\left(\frac{117}{272}\right)$$ $$e\left(\frac{91}{816}\right)$$ $$e\left(\frac{185}{204}\right)$$ $$e\left(\frac{5}{816}\right)$$ $$e\left(\frac{95}{102}\right)$$
$$\chi_{2601}(13,\cdot)$$ 2601.bg 204 yes $$1$$ $$1$$ $$e\left(\frac{25}{102}\right)$$ $$e\left(\frac{25}{51}\right)$$ $$e\left(\frac{139}{204}\right)$$ $$e\left(\frac{5}{204}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{63}{68}\right)$$ $$e\left(\frac{185}{204}\right)$$ $$e\left(\frac{46}{51}\right)$$ $$e\left(\frac{55}{204}\right)$$ $$e\left(\frac{50}{51}\right)$$
$$\chi_{2601}(14,\cdot)$$ 2601.bn 816 yes $$1$$ $$1$$ $$e\left(\frac{337}{408}\right)$$ $$e\left(\frac{133}{204}\right)$$ $$e\left(\frac{511}{816}\right)$$ $$e\left(\frac{761}{816}\right)$$ $$e\left(\frac{65}{136}\right)$$ $$e\left(\frac{123}{272}\right)$$ $$e\left(\frac{5}{816}\right)$$ $$e\left(\frac{55}{204}\right)$$ $$e\left(\frac{619}{816}\right)$$ $$e\left(\frac{31}{102}\right)$$
$$\chi_{2601}(16,\cdot)$$ 2601.bd 102 yes $$1$$ $$1$$ $$e\left(\frac{28}{51}\right)$$ $$e\left(\frac{5}{51}\right)$$ $$e\left(\frac{19}{102}\right)$$ $$e\left(\frac{77}{102}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{95}{102}\right)$$ $$e\left(\frac{50}{51}\right)$$ $$e\left(\frac{31}{102}\right)$$ $$e\left(\frac{10}{51}\right)$$
$$\chi_{2601}(19,\cdot)$$ 2601.be 136 no $$1$$ $$1$$ $$e\left(\frac{53}{68}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{107}{136}\right)$$ $$e\left(\frac{133}{136}\right)$$ $$e\left(\frac{23}{68}\right)$$ $$e\left(\frac{77}{136}\right)$$ $$e\left(\frac{25}{136}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{103}{136}\right)$$ $$e\left(\frac{2}{17}\right)$$
$$\chi_{2601}(20,\cdot)$$ 2601.bn 816 yes $$1$$ $$1$$ $$e\left(\frac{233}{408}\right)$$ $$e\left(\frac{29}{204}\right)$$ $$e\left(\frac{455}{816}\right)$$ $$e\left(\frac{577}{816}\right)$$ $$e\left(\frac{97}{136}\right)$$ $$e\left(\frac{35}{272}\right)$$ $$e\left(\frac{541}{816}\right)$$ $$e\left(\frac{35}{204}\right)$$ $$e\left(\frac{227}{816}\right)$$ $$e\left(\frac{29}{102}\right)$$
$$\chi_{2601}(22,\cdot)$$ 2601.bm 816 yes $$-1$$ $$1$$ $$e\left(\frac{49}{408}\right)$$ $$e\left(\frac{49}{204}\right)$$ $$e\left(\frac{811}{816}\right)$$ $$e\left(\frac{581}{816}\right)$$ $$e\left(\frac{49}{136}\right)$$ $$e\left(\frac{31}{272}\right)$$ $$e\left(\frac{281}{816}\right)$$ $$e\left(\frac{31}{204}\right)$$ $$e\left(\frac{679}{816}\right)$$ $$e\left(\frac{49}{102}\right)$$
$$\chi_{2601}(23,\cdot)$$ 2601.bn 816 yes $$1$$ $$1$$ $$e\left(\frac{247}{408}\right)$$ $$e\left(\frac{43}{204}\right)$$ $$e\left(\frac{745}{816}\right)$$ $$e\left(\frac{335}{816}\right)$$ $$e\left(\frac{111}{136}\right)$$ $$e\left(\frac{141}{272}\right)$$ $$e\left(\frac{563}{816}\right)$$ $$e\left(\frac{73}{204}\right)$$ $$e\left(\frac{13}{816}\right)$$ $$e\left(\frac{43}{102}\right)$$
$$\chi_{2601}(25,\cdot)$$ 2601.bk 408 yes $$1$$ $$1$$ $$e\left(\frac{121}{204}\right)$$ $$e\left(\frac{19}{102}\right)$$ $$e\left(\frac{379}{408}\right)$$ $$e\left(\frac{269}{408}\right)$$ $$e\left(\frac{53}{68}\right)$$ $$e\left(\frac{71}{136}\right)$$ $$e\left(\frac{161}{408}\right)$$ $$e\left(\frac{37}{102}\right)$$ $$e\left(\frac{103}{408}\right)$$ $$e\left(\frac{19}{51}\right)$$
$$\chi_{2601}(26,\cdot)$$ 2601.bf 136 no $$-1$$ $$1$$ $$e\left(\frac{9}{68}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{65}{136}\right)$$ $$e\left(\frac{131}{136}\right)$$ $$e\left(\frac{27}{68}\right)$$ $$e\left(\frac{83}{136}\right)$$ $$e\left(\frac{19}{136}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{13}{136}\right)$$ $$e\left(\frac{9}{17}\right)$$
$$\chi_{2601}(28,\cdot)$$ 2601.bi 272 no $$-1$$ $$1$$ $$e\left(\frac{97}{136}\right)$$ $$e\left(\frac{29}{68}\right)$$ $$e\left(\frac{115}{272}\right)$$ $$e\left(\frac{237}{272}\right)$$ $$e\left(\frac{19}{136}\right)$$ $$e\left(\frac{37}{272}\right)$$ $$e\left(\frac{65}{272}\right)$$ $$e\left(\frac{35}{68}\right)$$ $$e\left(\frac{159}{272}\right)$$ $$e\left(\frac{29}{34}\right)$$
$$\chi_{2601}(29,\cdot)$$ 2601.bn 816 yes $$1$$ $$1$$ $$e\left(\frac{197}{408}\right)$$ $$e\left(\frac{197}{204}\right)$$ $$e\left(\frac{59}{816}\right)$$ $$e\left(\frac{733}{816}\right)$$ $$e\left(\frac{61}{136}\right)$$ $$e\left(\frac{151}{272}\right)$$ $$e\left(\frac{601}{816}\right)$$ $$e\left(\frac{83}{204}\right)$$ $$e\left(\frac{311}{816}\right)$$ $$e\left(\frac{95}{102}\right)$$
$$\chi_{2601}(31,\cdot)$$ 2601.bm 816 yes $$-1$$ $$1$$ $$e\left(\frac{253}{408}\right)$$ $$e\left(\frac{49}{204}\right)$$ $$e\left(\frac{199}{816}\right)$$ $$e\left(\frac{377}{816}\right)$$ $$e\left(\frac{117}{136}\right)$$ $$e\left(\frac{235}{272}\right)$$ $$e\left(\frac{77}{816}\right)$$ $$e\left(\frac{31}{204}\right)$$ $$e\left(\frac{67}{816}\right)$$ $$e\left(\frac{49}{102}\right)$$
$$\chi_{2601}(32,\cdot)$$ 2601.bl 408 yes $$-1$$ $$1$$ $$e\left(\frac{89}{204}\right)$$ $$e\left(\frac{89}{102}\right)$$ $$e\left(\frac{401}{408}\right)$$ $$e\left(\frac{283}{408}\right)$$ $$e\left(\frac{21}{68}\right)$$ $$e\left(\frac{57}{136}\right)$$ $$e\left(\frac{67}{408}\right)$$ $$e\left(\frac{23}{102}\right)$$ $$e\left(\frac{53}{408}\right)$$ $$e\left(\frac{38}{51}\right)$$
$$\chi_{2601}(35,\cdot)$$ 2601.v 34 no $$-1$$ $$1$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{7}{34}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{33}{34}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{16}{17}\right)$$
$$\chi_{2601}(37,\cdot)$$ 2601.bi 272 no $$-1$$ $$1$$ $$e\left(\frac{15}{136}\right)$$ $$e\left(\frac{15}{68}\right)$$ $$e\left(\frac{165}{272}\right)$$ $$e\left(\frac{139}{272}\right)$$ $$e\left(\frac{45}{136}\right)$$ $$e\left(\frac{195}{272}\right)$$ $$e\left(\frac{247}{272}\right)$$ $$e\left(\frac{65}{68}\right)$$ $$e\left(\frac{169}{272}\right)$$ $$e\left(\frac{15}{34}\right)$$
$$\chi_{2601}(38,\cdot)$$ 2601.m 12 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2601}(40,\cdot)$$ 2601.x 48 no $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2601}(41,\cdot)$$ 2601.bn 816 yes $$1$$ $$1$$ $$e\left(\frac{115}{408}\right)$$ $$e\left(\frac{115}{204}\right)$$ $$e\left(\frac{109}{816}\right)$$ $$e\left(\frac{635}{816}\right)$$ $$e\left(\frac{115}{136}\right)$$ $$e\left(\frac{113}{272}\right)$$ $$e\left(\frac{239}{816}\right)$$ $$e\left(\frac{181}{204}\right)$$ $$e\left(\frac{49}{816}\right)$$ $$e\left(\frac{13}{102}\right)$$
$$\chi_{2601}(43,\cdot)$$ 2601.bk 408 yes $$1$$ $$1$$ $$e\left(\frac{109}{204}\right)$$ $$e\left(\frac{7}{102}\right)$$ $$e\left(\frac{247}{408}\right)$$ $$e\left(\frac{185}{408}\right)$$ $$e\left(\frac{41}{68}\right)$$ $$e\left(\frac{19}{136}\right)$$ $$e\left(\frac{317}{408}\right)$$ $$e\left(\frac{19}{102}\right)$$ $$e\left(\frac{403}{408}\right)$$ $$e\left(\frac{7}{51}\right)$$
$$\chi_{2601}(44,\cdot)$$ 2601.bj 272 no $$1$$ $$1$$ $$e\left(\frac{1}{136}\right)$$ $$e\left(\frac{1}{68}\right)$$ $$e\left(\frac{215}{272}\right)$$ $$e\left(\frac{177}{272}\right)$$ $$e\left(\frac{3}{136}\right)$$ $$e\left(\frac{217}{272}\right)$$ $$e\left(\frac{157}{272}\right)$$ $$e\left(\frac{27}{68}\right)$$ $$e\left(\frac{179}{272}\right)$$ $$e\left(\frac{1}{34}\right)$$
$$\chi_{2601}(46,\cdot)$$ 2601.bi 272 no $$-1$$ $$1$$ $$e\left(\frac{67}{136}\right)$$ $$e\left(\frac{67}{68}\right)$$ $$e\left(\frac{193}{272}\right)$$ $$e\left(\frac{95}{272}\right)$$ $$e\left(\frac{65}{136}\right)$$ $$e\left(\frac{55}{272}\right)$$ $$e\left(\frac{251}{272}\right)$$ $$e\left(\frac{41}{68}\right)$$ $$e\left(\frac{229}{272}\right)$$ $$e\left(\frac{33}{34}\right)$$
$$\chi_{2601}(47,\cdot)$$ 2601.bh 204 yes $$-1$$ $$1$$ $$e\left(\frac{1}{51}\right)$$ $$e\left(\frac{2}{51}\right)$$ $$e\left(\frac{5}{204}\right)$$ $$e\left(\frac{133}{204}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{3}{68}\right)$$ $$e\left(\frac{127}{204}\right)$$ $$e\left(\frac{20}{51}\right)$$ $$e\left(\frac{137}{204}\right)$$ $$e\left(\frac{4}{51}\right)$$
$$\chi_{2601}(49,\cdot)$$ 2601.bk 408 yes $$1$$ $$1$$ $$e\left(\frac{179}{204}\right)$$ $$e\left(\frac{77}{102}\right)$$ $$e\left(\frac{269}{408}\right)$$ $$e\left(\frac{403}{408}\right)$$ $$e\left(\frac{43}{68}\right)$$ $$e\left(\frac{73}{136}\right)$$ $$e\left(\frac{223}{408}\right)$$ $$e\left(\frac{5}{102}\right)$$ $$e\left(\frac{353}{408}\right)$$ $$e\left(\frac{26}{51}\right)$$
$$\chi_{2601}(50,\cdot)$$ 2601.bc 102 yes $$-1$$ $$1$$ $$e\left(\frac{49}{102}\right)$$ $$e\left(\frac{49}{51}\right)$$ $$e\left(\frac{37}{51}\right)$$ $$e\left(\frac{61}{102}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{7}{34}\right)$$ $$e\left(\frac{32}{51}\right)$$ $$e\left(\frac{31}{51}\right)$$ $$e\left(\frac{4}{51}\right)$$ $$e\left(\frac{47}{51}\right)$$