# Properties

 Modulus $6025$ Structure $$C_{240}\times C_{20}$$ Order $4800$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(6025)

pari: g = idealstar(,6025,2)

## Character group

 sage: G.order()  pari: g.no Order = 4800 sage: H.invariants()  pari: g.cyc Structure = $$C_{240}\times C_{20}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6025}(2652,\cdot)$, $\chi_{6025}(2176,\cdot)$

## First 32 of 4800 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{6025}(1,\cdot)$$ 6025.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6025}(2,\cdot)$$ 6025.ip 120 yes $$-1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{120}\right)$$
$$\chi_{6025}(3,\cdot)$$ 6025.hz 120 yes $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{6025}(4,\cdot)$$ 6025.gu 60 yes $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{6025}(6,\cdot)$$ 6025.dn 20 yes $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{6025}(7,\cdot)$$ 6025.jp 240 no $$1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{61}{240}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{227}{240}\right)$$
$$\chi_{6025}(8,\cdot)$$ 6025.er 40 yes $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{40}\right)$$
$$\chi_{6025}(9,\cdot)$$ 6025.gt 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{6025}(11,\cdot)$$ 6025.iu 240 yes $$-1$$ $$1$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{97}{240}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{23}{240}\right)$$
$$\chi_{6025}(12,\cdot)$$ 6025.hx 120 yes $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{73}{120}\right)$$
$$\chi_{6025}(13,\cdot)$$ 6025.jb 240 yes $$1$$ $$1$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{227}{240}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{240}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{61}{240}\right)$$
$$\chi_{6025}(14,\cdot)$$ 6025.jg 240 yes $$-1$$ $$1$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{71}{240}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{167}{240}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$
$$\chi_{6025}(16,\cdot)$$ 6025.ei 30 yes $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{6025}(17,\cdot)$$ 6025.hn 80 yes $$1$$ $$1$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{7}{80}\right)$$
$$\chi_{6025}(18,\cdot)$$ 6025.hw 120 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{120}\right)$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{89}{120}\right)$$
$$\chi_{6025}(19,\cdot)$$ 6025.iv 240 yes $$-1$$ $$1$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{61}{240}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{179}{240}\right)$$
$$\chi_{6025}(21,\cdot)$$ 6025.hj 80 yes $$-1$$ $$1$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{19}{80}\right)$$
$$\chi_{6025}(22,\cdot)$$ 6025.jn 240 yes $$1$$ $$1$$ $$e\left(\frac{7}{120}\right)$$ $$e\left(\frac{119}{120}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{239}{240}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{61}{240}\right)$$
$$\chi_{6025}(23,\cdot)$$ 6025.hn 80 yes $$1$$ $$1$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-i$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{49}{80}\right)$$
$$\chi_{6025}(24,\cdot)$$ 6025.ek 30 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$-1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{6025}(26,\cdot)$$ 6025.gz 80 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{33}{80}\right)$$
$$\chi_{6025}(27,\cdot)$$ 6025.fh 40 yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{6025}(28,\cdot)$$ 6025.hr 80 yes $$1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$-i$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{21}{80}\right)$$
$$\chi_{6025}(29,\cdot)$$ 6025.ic 120 yes $$1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$-1$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{120}\right)$$
$$\chi_{6025}(31,\cdot)$$ 6025.je 240 yes $$-1$$ $$1$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{37}{120}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$i$$ $$e\left(\frac{151}{240}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{31}{240}\right)$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{41}{240}\right)$$
$$\chi_{6025}(32,\cdot)$$ 6025.dq 24 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{24}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{6025}(33,\cdot)$$ 6025.hs 80 yes $$1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{31}{80}\right)$$
$$\chi_{6025}(34,\cdot)$$ 6025.jk 240 yes $$-1$$ $$1$$ $$e\left(\frac{119}{120}\right)$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{181}{240}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{133}{240}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{59}{240}\right)$$
$$\chi_{6025}(36,\cdot)$$ 6025.bb 10 yes $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{6025}(37,\cdot)$$ 6025.ix 240 yes $$1$$ $$1$$ $$e\left(\frac{29}{120}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$-i$$ $$e\left(\frac{133}{240}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{193}{240}\right)$$ $$e\left(\frac{119}{120}\right)$$ $$e\left(\frac{203}{240}\right)$$
$$\chi_{6025}(38,\cdot)$$ 6025.jm 240 yes $$1$$ $$1$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{203}{240}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{217}{240}\right)$$
$$\chi_{6025}(39,\cdot)$$ 6025.jk 240 yes $$-1$$ $$1$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{109}{240}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{157}{240}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{131}{240}\right)$$