from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(953, base_ring=CyclotomicField(238))
M = H._module
chi = DirichletCharacter(H, M([201]))
chi.galois_orbit()
[g,chi] = znchar(Mod(7,953))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(953\) | |
| Conductor: | \(953\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(238\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{119})$ |
| Fixed field: | Number field defined by a degree 238 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{953}(7,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{201}{238}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{165}{238}\right)\) | \(e\left(\frac{61}{238}\right)\) | \(e\left(\frac{1}{119}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{82}{119}\right)\) | \(e\left(\frac{25}{238}\right)\) | \(e\left(\frac{155}{238}\right)\) |
| \(\chi_{953}(26,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{117}{238}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{25}{238}\right)\) | \(e\left(\frac{103}{238}\right)\) | \(e\left(\frac{29}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{117}{119}\right)\) | \(e\left(\frac{11}{238}\right)\) | \(e\left(\frac{211}{238}\right)\) |
| \(\chi_{953}(29,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{223}{238}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{9}{238}\right)\) | \(e\left(\frac{237}{238}\right)\) | \(e\left(\frac{39}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{104}{119}\right)\) | \(e\left(\frac{23}{238}\right)\) | \(e\left(\frac{95}{238}\right)\) |
| \(\chi_{953}(34,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{93}{238}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{87}{238}\right)\) | \(e\left(\frac{149}{238}\right)\) | \(e\left(\frac{20}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{93}{119}\right)\) | \(e\left(\frac{143}{238}\right)\) | \(e\left(\frac{125}{238}\right)\) |
| \(\chi_{953}(50,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{55}{238}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{205}{238}\right)\) | \(e\left(\frac{83}{238}\right)\) | \(e\left(\frac{95}{119}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{55}{119}\right)\) | \(e\left(\frac{233}{238}\right)\) | \(e\left(\frac{207}{238}\right)\) |
| \(\chi_{953}(60,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{75}{238}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{193}{238}\right)\) | \(e\left(\frac{5}{238}\right)\) | \(e\left(\frac{43}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{75}{119}\right)\) | \(e\left(\frac{123}{238}\right)\) | \(e\left(\frac{1}{238}\right)\) |
| \(\chi_{953}(72,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{95}{238}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{181}{238}\right)\) | \(e\left(\frac{165}{238}\right)\) | \(e\left(\frac{110}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{95}{119}\right)\) | \(e\left(\frac{13}{238}\right)\) | \(e\left(\frac{33}{238}\right)\) |
| \(\chi_{953}(81,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{1}{238}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{47}{238}\right)\) | \(e\left(\frac{127}{238}\right)\) | \(e\left(\frac{45}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{119}\right)\) | \(e\left(\frac{173}{238}\right)\) | \(e\left(\frac{73}{238}\right)\) |
| \(\chi_{953}(82,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{103}{238}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{81}{238}\right)\) | \(e\left(\frac{229}{238}\right)\) | \(e\left(\frac{113}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{103}{119}\right)\) | \(e\left(\frac{207}{238}\right)\) | \(e\left(\frac{141}{238}\right)\) |
| \(\chi_{953}(105,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{213}{238}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{15}{238}\right)\) | \(e\left(\frac{157}{238}\right)\) | \(e\left(\frac{65}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{94}{119}\right)\) | \(e\left(\frac{197}{238}\right)\) | \(e\left(\frac{79}{238}\right)\) |
| \(\chi_{953}(110,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{121}{238}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{213}{238}\right)\) | \(e\left(\frac{135}{238}\right)\) | \(e\left(\frac{90}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{2}{119}\right)\) | \(e\left(\frac{227}{238}\right)\) | \(e\left(\frac{27}{238}\right)\) |
| \(\chi_{953}(112,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{89}{238}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{137}{238}\right)\) | \(e\left(\frac{117}{238}\right)\) | \(e\left(\frac{78}{119}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{89}{119}\right)\) | \(e\left(\frac{165}{238}\right)\) | \(e\left(\frac{71}{238}\right)\) |
| \(\chi_{953}(118,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{25}{238}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{223}{238}\right)\) | \(e\left(\frac{81}{238}\right)\) | \(e\left(\frac{54}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{25}{119}\right)\) | \(e\left(\frac{41}{238}\right)\) | \(e\left(\frac{159}{238}\right)\) |
| \(\chi_{953}(126,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{233}{238}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{3}{238}\right)\) | \(e\left(\frac{79}{238}\right)\) | \(e\left(\frac{13}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{114}{119}\right)\) | \(e\left(\frac{87}{238}\right)\) | \(e\left(\frac{111}{238}\right)\) |
| \(\chi_{953}(127,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{107}{238}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{31}{238}\right)\) | \(e\left(\frac{23}{238}\right)\) | \(e\left(\frac{55}{119}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{107}{119}\right)\) | \(e\left(\frac{185}{238}\right)\) | \(e\left(\frac{195}{238}\right)\) |
| \(\chi_{953}(129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{211}{238}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{159}{238}\right)\) | \(e\left(\frac{141}{238}\right)\) | \(e\left(\frac{94}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{89}{238}\right)\) | \(e\left(\frac{171}{238}\right)\) |
| \(\chi_{953}(132,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{141}{238}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{201}{238}\right)\) | \(e\left(\frac{57}{238}\right)\) | \(e\left(\frac{38}{119}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{22}{119}\right)\) | \(e\left(\frac{117}{238}\right)\) | \(e\left(\frac{59}{238}\right)\) |
| \(\chi_{953}(157,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{165}{238}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{139}{238}\right)\) | \(e\left(\frac{11}{238}\right)\) | \(e\left(\frac{47}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{46}{119}\right)\) | \(e\left(\frac{223}{238}\right)\) | \(e\left(\frac{145}{238}\right)\) |
| \(\chi_{953}(158,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{99}{238}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{131}{238}\right)\) | \(e\left(\frac{197}{238}\right)\) | \(e\left(\frac{52}{119}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{229}{238}\right)\) | \(e\left(\frac{87}{238}\right)\) |
| \(\chi_{953}(166,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{179}{238}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{83}{238}\right)\) | \(e\left(\frac{123}{238}\right)\) | \(e\left(\frac{82}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{60}{119}\right)\) | \(e\left(\frac{27}{238}\right)\) | \(e\left(\frac{215}{238}\right)\) |
| \(\chi_{953}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{171}{238}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{183}{238}\right)\) | \(e\left(\frac{59}{238}\right)\) | \(e\left(\frac{79}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{52}{119}\right)\) | \(e\left(\frac{71}{238}\right)\) | \(e\left(\frac{107}{238}\right)\) |
| \(\chi_{953}(196,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{227}{238}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{197}{238}\right)\) | \(e\left(\frac{31}{238}\right)\) | \(e\left(\frac{100}{119}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{1}{238}\right)\) | \(e\left(\frac{149}{238}\right)\) |
| \(\chi_{953}(206,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{29}{238}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{173}{238}\right)\) | \(e\left(\frac{113}{238}\right)\) | \(e\left(\frac{115}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{29}{119}\right)\) | \(e\left(\frac{19}{238}\right)\) | \(e\left(\frac{213}{238}\right)\) |
| \(\chi_{953}(212,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{31}{238}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{29}{238}\right)\) | \(e\left(\frac{129}{238}\right)\) | \(e\left(\frac{86}{119}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{31}{119}\right)\) | \(e\left(\frac{127}{238}\right)\) | \(e\left(\frac{121}{238}\right)\) |
| \(\chi_{953}(218,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{57}{238}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{61}{238}\right)\) | \(e\left(\frac{99}{238}\right)\) | \(e\left(\frac{66}{119}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{57}{119}\right)\) | \(e\left(\frac{103}{238}\right)\) | \(e\left(\frac{115}{238}\right)\) |
| \(\chi_{953}(231,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{41}{238}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{23}{238}\right)\) | \(e\left(\frac{209}{238}\right)\) | \(e\left(\frac{60}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{41}{119}\right)\) | \(e\left(\frac{191}{238}\right)\) | \(e\left(\frac{137}{238}\right)\) |
| \(\chi_{953}(262,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{13}{238}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{135}{238}\right)\) | \(e\left(\frac{223}{238}\right)\) | \(e\left(\frac{109}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{119}\right)\) | \(e\left(\frac{107}{238}\right)\) | \(e\left(\frac{235}{238}\right)\) |
| \(\chi_{953}(277,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{115}{238}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{169}{238}\right)\) | \(e\left(\frac{87}{238}\right)\) | \(e\left(\frac{58}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{115}{119}\right)\) | \(e\left(\frac{141}{238}\right)\) | \(e\left(\frac{65}{238}\right)\) |
| \(\chi_{953}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{123}{238}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{69}{238}\right)\) | \(e\left(\frac{151}{238}\right)\) | \(e\left(\frac{61}{119}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{4}{119}\right)\) | \(e\left(\frac{97}{238}\right)\) | \(e\left(\frac{173}{238}\right)\) |
| \(\chi_{953}(321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{43}{238}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{117}{238}\right)\) | \(e\left(\frac{225}{238}\right)\) | \(e\left(\frac{31}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{43}{119}\right)\) | \(e\left(\frac{61}{238}\right)\) | \(e\left(\frac{45}{238}\right)\) |
| \(\chi_{953}(325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{109}{238}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{125}{238}\right)\) | \(e\left(\frac{39}{238}\right)\) | \(e\left(\frac{26}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{109}{119}\right)\) | \(e\left(\frac{55}{238}\right)\) | \(e\left(\frac{103}{238}\right)\) |