# Properties

 Modulus 4025 Structure $$C_{660}\times C_{2}\times C_{2}$$ Order 2640

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4025)

pari: g = idealstar(,4025,2)

## Character group

 sage: G.order()  pari: g.no Order = 2640 sage: H.invariants()  pari: g.cyc Structure = $$C_{660}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4025}(488,\cdot)$, $\chi_{4025}(1126,\cdot)$, $\chi_{4025}(2276,\cdot)$

## First 32 of 2640 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 6 8 9 11 12 13 16
$$\chi_{4025}(1,\cdot)$$ 4025.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4025}(2,\cdot)$$ 4025.dq 660 yes $$-1$$ $$1$$ $$e\left(\frac{593}{660}\right)$$ $$e\left(\frac{91}{660}\right)$$ $$e\left(\frac{263}{330}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{153}{220}\right)$$ $$e\left(\frac{91}{330}\right)$$ $$e\left(\frac{157}{165}\right)$$ $$e\left(\frac{617}{660}\right)$$ $$e\left(\frac{49}{220}\right)$$ $$e\left(\frac{98}{165}\right)$$
$$\chi_{4025}(3,\cdot)$$ 4025.do 660 yes $$1$$ $$1$$ $$e\left(\frac{91}{660}\right)$$ $$e\left(\frac{167}{660}\right)$$ $$e\left(\frac{91}{330}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{91}{220}\right)$$ $$e\left(\frac{167}{330}\right)$$ $$e\left(\frac{134}{165}\right)$$ $$e\left(\frac{349}{660}\right)$$ $$e\left(\frac{73}{220}\right)$$ $$e\left(\frac{91}{165}\right)$$
$$\chi_{4025}(4,\cdot)$$ 4025.dm 330 yes $$1$$ $$1$$ $$e\left(\frac{263}{330}\right)$$ $$e\left(\frac{91}{330}\right)$$ $$e\left(\frac{98}{165}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{91}{165}\right)$$ $$e\left(\frac{149}{165}\right)$$ $$e\left(\frac{287}{330}\right)$$ $$e\left(\frac{49}{110}\right)$$ $$e\left(\frac{31}{165}\right)$$
$$\chi_{4025}(6,\cdot)$$ 4025.cw 110 yes $$-1$$ $$1$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{42}{55}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{8}{55}\right)$$
$$\chi_{4025}(8,\cdot)$$ 4025.dg 220 no $$-1$$ $$1$$ $$e\left(\frac{153}{220}\right)$$ $$e\left(\frac{91}{220}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{19}{220}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{177}{220}\right)$$ $$e\left(\frac{147}{220}\right)$$ $$e\left(\frac{43}{55}\right)$$
$$\chi_{4025}(9,\cdot)$$ 4025.dm 330 yes $$1$$ $$1$$ $$e\left(\frac{91}{330}\right)$$ $$e\left(\frac{167}{330}\right)$$ $$e\left(\frac{91}{165}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{2}{165}\right)$$ $$e\left(\frac{103}{165}\right)$$ $$e\left(\frac{19}{330}\right)$$ $$e\left(\frac{73}{110}\right)$$ $$e\left(\frac{17}{165}\right)$$
$$\chi_{4025}(11,\cdot)$$ 4025.dh 330 yes $$-1$$ $$1$$ $$e\left(\frac{157}{165}\right)$$ $$e\left(\frac{134}{165}\right)$$ $$e\left(\frac{149}{165}\right)$$ $$e\left(\frac{42}{55}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{103}{165}\right)$$ $$e\left(\frac{49}{330}\right)$$ $$e\left(\frac{118}{165}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{133}{165}\right)$$
$$\chi_{4025}(12,\cdot)$$ 4025.do 660 yes $$1$$ $$1$$ $$e\left(\frac{617}{660}\right)$$ $$e\left(\frac{349}{660}\right)$$ $$e\left(\frac{287}{330}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{177}{220}\right)$$ $$e\left(\frac{19}{330}\right)$$ $$e\left(\frac{118}{165}\right)$$ $$e\left(\frac{263}{660}\right)$$ $$e\left(\frac{171}{220}\right)$$ $$e\left(\frac{122}{165}\right)$$
$$\chi_{4025}(13,\cdot)$$ 4025.de 220 yes $$1$$ $$1$$ $$e\left(\frac{49}{220}\right)$$ $$e\left(\frac{73}{220}\right)$$ $$e\left(\frac{49}{110}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{147}{220}\right)$$ $$e\left(\frac{73}{110}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{171}{220}\right)$$ $$e\left(\frac{101}{220}\right)$$ $$e\left(\frac{49}{55}\right)$$
$$\chi_{4025}(16,\cdot)$$ 4025.dc 165 yes $$1$$ $$1$$ $$e\left(\frac{98}{165}\right)$$ $$e\left(\frac{91}{165}\right)$$ $$e\left(\frac{31}{165}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{17}{165}\right)$$ $$e\left(\frac{133}{165}\right)$$ $$e\left(\frac{122}{165}\right)$$ $$e\left(\frac{49}{55}\right)$$ $$e\left(\frac{62}{165}\right)$$
$$\chi_{4025}(17,\cdot)$$ 4025.dp 660 yes $$-1$$ $$1$$ $$e\left(\frac{409}{660}\right)$$ $$e\left(\frac{533}{660}\right)$$ $$e\left(\frac{79}{330}\right)$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{189}{220}\right)$$ $$e\left(\frac{203}{330}\right)$$ $$e\left(\frac{307}{330}\right)$$ $$e\left(\frac{31}{660}\right)$$ $$e\left(\frac{67}{220}\right)$$ $$e\left(\frac{79}{165}\right)$$
$$\chi_{4025}(18,\cdot)$$ 4025.cz 132 no $$-1$$ $$1$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{4025}(19,\cdot)$$ 4025.dl 330 yes $$1$$ $$1$$ $$e\left(\frac{307}{330}\right)$$ $$e\left(\frac{7}{165}\right)$$ $$e\left(\frac{142}{165}\right)$$ $$e\left(\frac{107}{110}\right)$$ $$e\left(\frac{87}{110}\right)$$ $$e\left(\frac{14}{165}\right)$$ $$e\left(\frac{287}{330}\right)$$ $$e\left(\frac{149}{165}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{119}{165}\right)$$
$$\chi_{4025}(22,\cdot)$$ 4025.bj 20 no $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4025}(24,\cdot)$$ 4025.r 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4025}(26,\cdot)$$ 4025.cp 66 no $$-1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{16}{33}\right)$$
$$\chi_{4025}(27,\cdot)$$ 4025.de 220 yes $$1$$ $$1$$ $$e\left(\frac{91}{220}\right)$$ $$e\left(\frac{167}{220}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{19}{110}\right)$$ $$e\left(\frac{53}{220}\right)$$ $$e\left(\frac{57}{110}\right)$$ $$e\left(\frac{24}{55}\right)$$ $$e\left(\frac{129}{220}\right)$$ $$e\left(\frac{219}{220}\right)$$ $$e\left(\frac{36}{55}\right)$$
$$\chi_{4025}(29,\cdot)$$ 4025.cs 110 no $$1$$ $$1$$ $$e\left(\frac{81}{110}\right)$$ $$e\left(\frac{87}{110}\right)$$ $$e\left(\frac{26}{55}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{53}{55}\right)$$ $$e\left(\frac{29}{110}\right)$$ $$e\left(\frac{39}{110}\right)$$ $$e\left(\frac{52}{55}\right)$$
$$\chi_{4025}(31,\cdot)$$ 4025.di 330 yes $$-1$$ $$1$$ $$e\left(\frac{46}{165}\right)$$ $$e\left(\frac{109}{330}\right)$$ $$e\left(\frac{92}{165}\right)$$ $$e\left(\frac{67}{110}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{109}{165}\right)$$ $$e\left(\frac{86}{165}\right)$$ $$e\left(\frac{293}{330}\right)$$ $$e\left(\frac{101}{110}\right)$$ $$e\left(\frac{19}{165}\right)$$
$$\chi_{4025}(32,\cdot)$$ 4025.cz 132 no $$-1$$ $$1$$ $$e\left(\frac{65}{132}\right)$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{89}{132}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{32}{33}\right)$$
$$\chi_{4025}(33,\cdot)$$ 4025.dp 660 yes $$-1$$ $$1$$ $$e\left(\frac{59}{660}\right)$$ $$e\left(\frac{43}{660}\right)$$ $$e\left(\frac{59}{330}\right)$$ $$e\left(\frac{17}{110}\right)$$ $$e\left(\frac{59}{220}\right)$$ $$e\left(\frac{43}{330}\right)$$ $$e\left(\frac{317}{330}\right)$$ $$e\left(\frac{161}{660}\right)$$ $$e\left(\frac{57}{220}\right)$$ $$e\left(\frac{59}{165}\right)$$
$$\chi_{4025}(34,\cdot)$$ 4025.ct 110 yes $$1$$ $$1$$ $$e\left(\frac{57}{110}\right)$$ $$e\left(\frac{52}{55}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{49}{55}\right)$$ $$e\left(\frac{97}{110}\right)$$ $$e\left(\frac{54}{55}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{4}{55}\right)$$
$$\chi_{4025}(36,\cdot)$$ 4025.cf 55 no $$1$$ $$1$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{12}{55}\right)$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{16}{55}\right)$$
$$\chi_{4025}(37,\cdot)$$ 4025.dr 660 yes $$1$$ $$1$$ $$e\left(\frac{17}{660}\right)$$ $$e\left(\frac{499}{660}\right)$$ $$e\left(\frac{17}{330}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{17}{220}\right)$$ $$e\left(\frac{169}{330}\right)$$ $$e\left(\frac{41}{330}\right)$$ $$e\left(\frac{533}{660}\right)$$ $$e\left(\frac{201}{220}\right)$$ $$e\left(\frac{17}{165}\right)$$
$$\chi_{4025}(38,\cdot)$$ 4025.dp 660 yes $$-1$$ $$1$$ $$e\left(\frac{547}{660}\right)$$ $$e\left(\frac{119}{660}\right)$$ $$e\left(\frac{217}{330}\right)$$ $$e\left(\frac{1}{110}\right)$$ $$e\left(\frac{107}{220}\right)$$ $$e\left(\frac{119}{330}\right)$$ $$e\left(\frac{271}{330}\right)$$ $$e\left(\frac{553}{660}\right)$$ $$e\left(\frac{81}{220}\right)$$ $$e\left(\frac{52}{165}\right)$$
$$\chi_{4025}(39,\cdot)$$ 4025.dm 330 yes $$1$$ $$1$$ $$e\left(\frac{119}{330}\right)$$ $$e\left(\frac{193}{330}\right)$$ $$e\left(\frac{119}{165}\right)$$ $$e\left(\frac{52}{55}\right)$$ $$e\left(\frac{9}{110}\right)$$ $$e\left(\frac{28}{165}\right)$$ $$e\left(\frac{122}{165}\right)$$ $$e\left(\frac{101}{330}\right)$$ $$e\left(\frac{87}{110}\right)$$ $$e\left(\frac{73}{165}\right)$$
$$\chi_{4025}(41,\cdot)$$ 4025.cw 110 yes $$-1$$ $$1$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{101}{110}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{14}{55}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{103}{110}\right)$$ $$e\left(\frac{9}{55}\right)$$
$$\chi_{4025}(43,\cdot)$$ 4025.cc 44 no $$1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{4025}(44,\cdot)$$ 4025.dn 330 yes $$-1$$ $$1$$ $$e\left(\frac{247}{330}\right)$$ $$e\left(\frac{29}{330}\right)$$ $$e\left(\frac{82}{165}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{27}{110}\right)$$ $$e\left(\frac{29}{165}\right)$$ $$e\left(\frac{17}{330}\right)$$ $$e\left(\frac{193}{330}\right)$$ $$e\left(\frac{41}{110}\right)$$ $$e\left(\frac{164}{165}\right)$$
$$\chi_{4025}(47,\cdot)$$ 4025.cj 60 no $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{4025}(48,\cdot)$$ 4025.de 220 yes $$1$$ $$1$$ $$e\left(\frac{161}{220}\right)$$ $$e\left(\frac{177}{220}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{59}{110}\right)$$ $$e\left(\frac{43}{220}\right)$$ $$e\left(\frac{67}{110}\right)$$ $$e\left(\frac{34}{55}\right)$$ $$e\left(\frac{59}{220}\right)$$ $$e\left(\frac{49}{220}\right)$$ $$e\left(\frac{51}{55}\right)$$