# Properties

 Modulus $3025$ Structure $$C_{10}\times C_{220}$$ Order $2200$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3025)

pari: g = idealstar(,3025,2)

## Character group

 sage: G.order()  pari: g.no Order = 2200 sage: H.invariants()  pari: g.cyc Structure = $$C_{10}\times C_{220}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3025}(727,\cdot)$, $\chi_{3025}(2301,\cdot)$

## First 32 of 2200 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$12$$ $$13$$ $$14$$
$$\chi_{3025}(1,\cdot)$$ 3025.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3025}(2,\cdot)$$ 3025.cx 220 yes $$1$$ $$1$$ $$e\left(\frac{13}{220}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{13}{110}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{69}{220}\right)$$ $$e\left(\frac{39}{220}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{59}{220}\right)$$ $$e\left(\frac{191}{220}\right)$$ $$e\left(\frac{41}{110}\right)$$
$$\chi_{3025}(3,\cdot)$$ 3025.bq 20 no $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$-1$$
$$\chi_{3025}(4,\cdot)$$ 3025.cj 110 yes $$1$$ $$1$$ $$e\left(\frac{13}{110}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{55}\right)$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{39}{110}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{59}{110}\right)$$ $$e\left(\frac{81}{110}\right)$$ $$e\left(\frac{41}{55}\right)$$
$$\chi_{3025}(6,\cdot)$$ 3025.cm 110 yes $$-1$$ $$1$$ $$e\left(\frac{23}{110}\right)$$ $$1$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{73}{110}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$1$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{48}{55}\right)$$
$$\chi_{3025}(7,\cdot)$$ 3025.cy 220 no $$1$$ $$1$$ $$e\left(\frac{69}{220}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{73}{110}\right)$$ $$e\left(\frac{153}{220}\right)$$ $$e\left(\frac{207}{220}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{39}{220}\right)$$ $$e\left(\frac{1}{110}\right)$$
$$\chi_{3025}(8,\cdot)$$ 3025.cx 220 yes $$1$$ $$1$$ $$e\left(\frac{39}{220}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{39}{110}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{207}{220}\right)$$ $$e\left(\frac{117}{220}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{177}{220}\right)$$ $$e\left(\frac{133}{220}\right)$$ $$e\left(\frac{13}{110}\right)$$
$$\chi_{3025}(9,\cdot)$$ 3025.bb 10 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$
$$\chi_{3025}(12,\cdot)$$ 3025.dc 220 yes $$-1$$ $$1$$ $$e\left(\frac{59}{220}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{59}{110}\right)$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{177}{220}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{151}{220}\right)$$ $$e\left(\frac{41}{220}\right)$$ $$e\left(\frac{27}{110}\right)$$
$$\chi_{3025}(13,\cdot)$$ 3025.dd 220 yes $$1$$ $$1$$ $$e\left(\frac{191}{220}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{81}{110}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{39}{220}\right)$$ $$e\left(\frac{133}{220}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{41}{220}\right)$$ $$e\left(\frac{173}{220}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{3025}(14,\cdot)$$ 3025.cd 110 yes $$1$$ $$1$$ $$e\left(\frac{41}{110}\right)$$ $$-1$$ $$e\left(\frac{41}{55}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{1}{110}\right)$$ $$e\left(\frac{13}{110}\right)$$ $$1$$ $$e\left(\frac{27}{110}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{55}\right)$$
$$\chi_{3025}(16,\cdot)$$ 3025.ca 55 yes $$1$$ $$1$$ $$e\left(\frac{13}{55}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{26}{55}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{14}{55}\right)$$ $$e\left(\frac{39}{55}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{26}{55}\right)$$ $$e\left(\frac{27}{55}\right)$$
$$\chi_{3025}(17,\cdot)$$ 3025.cv 220 yes $$1$$ $$1$$ $$e\left(\frac{21}{220}\right)$$ $$-i$$ $$e\left(\frac{21}{110}\right)$$ $$e\left(\frac{93}{110}\right)$$ $$e\left(\frac{81}{220}\right)$$ $$e\left(\frac{63}{220}\right)$$ $$-1$$ $$e\left(\frac{207}{220}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{51}{110}\right)$$
$$\chi_{3025}(18,\cdot)$$ 3025.cy 220 no $$1$$ $$1$$ $$e\left(\frac{79}{220}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{79}{110}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{3}{220}\right)$$ $$e\left(\frac{17}{220}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{169}{220}\right)$$ $$e\left(\frac{41}{110}\right)$$
$$\chi_{3025}(19,\cdot)$$ 3025.cp 110 yes $$-1$$ $$1$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{39}{110}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{53}{55}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{110}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{24}{55}\right)$$
$$\chi_{3025}(21,\cdot)$$ 3025.cg 110 yes $$-1$$ $$1$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{73}{110}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{55}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{28}{55}\right)$$
$$\chi_{3025}(23,\cdot)$$ 3025.dc 220 yes $$-1$$ $$1$$ $$e\left(\frac{41}{220}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{41}{110}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{123}{220}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{49}{220}\right)$$ $$e\left(\frac{159}{220}\right)$$ $$e\left(\frac{43}{110}\right)$$
$$\chi_{3025}(24,\cdot)$$ 3025.cq 110 no $$-1$$ $$1$$ $$e\left(\frac{18}{55}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{54}{55}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{34}{55}\right)$$
$$\chi_{3025}(26,\cdot)$$ 3025.bz 55 no $$1$$ $$1$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{27}{55}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{36}{55}\right)$$ $$e\left(\frac{23}{55}\right)$$
$$\chi_{3025}(27,\cdot)$$ 3025.bq 20 no $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-1$$
$$\chi_{3025}(28,\cdot)$$ 3025.de 220 yes $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{9}{110}\right)$$ $$e\left(\frac{71}{220}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{113}{220}\right)$$ $$e\left(\frac{201}{220}\right)$$ $$e\left(\frac{83}{110}\right)$$
$$\chi_{3025}(29,\cdot)$$ 3025.cp 110 yes $$-1$$ $$1$$ $$e\left(\frac{14}{55}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{28}{55}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{42}{55}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{89}{110}\right)$$ $$e\left(\frac{28}{55}\right)$$ $$e\left(\frac{46}{55}\right)$$
$$\chi_{3025}(31,\cdot)$$ 3025.bw 55 yes $$1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{26}{55}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{53}{55}\right)$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{36}{55}\right)$$
$$\chi_{3025}(32,\cdot)$$ 3025.bv 44 no $$1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$-i$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$-1$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{3025}(34,\cdot)$$ 3025.cl 110 yes $$1$$ $$1$$ $$e\left(\frac{17}{110}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{46}{55}\right)$$
$$\chi_{3025}(36,\cdot)$$ 3025.cb 55 yes $$1$$ $$1$$ $$e\left(\frac{23}{55}\right)$$ $$1$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{18}{55}\right)$$ $$e\left(\frac{14}{55}\right)$$ $$1$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{41}{55}\right)$$
$$\chi_{3025}(37,\cdot)$$ 3025.cz 220 yes $$-1$$ $$1$$ $$e\left(\frac{183}{220}\right)$$ $$-i$$ $$e\left(\frac{73}{110}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{203}{220}\right)$$ $$e\left(\frac{109}{220}\right)$$ $$-1$$ $$e\left(\frac{91}{220}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{83}{110}\right)$$
$$\chi_{3025}(38,\cdot)$$ 3025.db 220 yes $$-1$$ $$1$$ $$e\left(\frac{157}{220}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{21}{220}\right)$$ $$e\left(\frac{31}{220}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{61}{220}\right)$$ $$e\left(\frac{39}{220}\right)$$ $$e\left(\frac{89}{110}\right)$$
$$\chi_{3025}(39,\cdot)$$ 3025.cr 110 yes $$-1$$ $$1$$ $$e\left(\frac{1}{55}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{37}{110}\right)$$ $$e\left(\frac{13}{55}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{3025}(41,\cdot)$$ 3025.cs 110 yes $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{34}{55}\right)$$ $$e\left(\frac{101}{110}\right)$$ $$e\left(\frac{48}{55}\right)$$
$$\chi_{3025}(42,\cdot)$$ 3025.df 220 yes $$-1$$ $$1$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{79}{220}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{87}{220}\right)$$ $$e\left(\frac{109}{220}\right)$$ $$e\left(\frac{97}{110}\right)$$
$$\chi_{3025}(43,\cdot)$$ 3025.bv 44 no $$1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$i$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$-1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$