from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7935, base_ring=CyclotomicField(506))
M = H._module
chi = DirichletCharacter(H, M([253,0,449]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,7935))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(7935\) | |
| Conductor: | \(1587\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(506\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1587.o | 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: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
First 31 of 220 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{7935}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{491}{506}\right)\) | \(e\left(\frac{238}{253}\right)\) | \(e\left(\frac{237}{506}\right)\) | \(e\left(\frac{461}{506}\right)\) | \(e\left(\frac{233}{253}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{223}{253}\right)\) | \(e\left(\frac{59}{253}\right)\) | \(e\left(\frac{399}{506}\right)\) |
| \(\chi_{7935}(56,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{325}{506}\right)\) | \(e\left(\frac{72}{253}\right)\) | \(e\left(\frac{431}{506}\right)\) | \(e\left(\frac{469}{506}\right)\) | \(e\left(\frac{96}{253}\right)\) | \(e\left(\frac{186}{253}\right)\) | \(e\left(\frac{125}{253}\right)\) | \(e\left(\frac{144}{253}\right)\) | \(e\left(\frac{71}{253}\right)\) | \(e\left(\frac{463}{506}\right)\) |
| \(\chi_{7935}(86,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{506}\right)\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{441}{506}\right)\) | \(e\left(\frac{339}{506}\right)\) | \(e\left(\frac{235}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{24}{253}\right)\) | \(e\left(\frac{226}{253}\right)\) | \(e\left(\frac{129}{253}\right)\) | \(e\left(\frac{435}{506}\right)\) |
| \(\chi_{7935}(176,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{506}\right)\) | \(e\left(\frac{89}{253}\right)\) | \(e\left(\frac{213}{506}\right)\) | \(e\left(\frac{267}{506}\right)\) | \(e\left(\frac{203}{253}\right)\) | \(e\left(\frac{251}{253}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{178}{253}\right)\) | \(e\left(\frac{21}{253}\right)\) | \(e\left(\frac{365}{506}\right)\) |
| \(\chi_{7935}(191,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{379}{506}\right)\) | \(e\left(\frac{126}{253}\right)\) | \(e\left(\frac{185}{506}\right)\) | \(e\left(\frac{125}{506}\right)\) | \(e\left(\frac{168}{253}\right)\) | \(e\left(\frac{199}{253}\right)\) | \(e\left(\frac{29}{253}\right)\) | \(e\left(\frac{252}{253}\right)\) | \(e\left(\frac{61}{253}\right)\) | \(e\left(\frac{241}{506}\right)\) |
| \(\chi_{7935}(221,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{506}\right)\) | \(e\left(\frac{31}{253}\right)\) | \(e\left(\frac{421}{506}\right)\) | \(e\left(\frac{93}{506}\right)\) | \(e\left(\frac{210}{253}\right)\) | \(e\left(\frac{59}{253}\right)\) | \(e\left(\frac{226}{253}\right)\) | \(e\left(\frac{62}{253}\right)\) | \(e\left(\frac{13}{253}\right)\) | \(e\left(\frac{491}{506}\right)\) |
| \(\chi_{7935}(251,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{213}{506}\right)\) | \(e\left(\frac{213}{253}\right)\) | \(e\left(\frac{379}{506}\right)\) | \(e\left(\frac{133}{506}\right)\) | \(e\left(\frac{31}{253}\right)\) | \(e\left(\frac{234}{253}\right)\) | \(e\left(\frac{43}{253}\right)\) | \(e\left(\frac{173}{253}\right)\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{305}{506}\right)\) |
| \(\chi_{7935}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{123}{506}\right)\) | \(e\left(\frac{123}{253}\right)\) | \(e\left(\frac{283}{506}\right)\) | \(e\left(\frac{369}{506}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{128}{253}\right)\) | \(e\left(\frac{203}{253}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{174}{253}\right)\) | \(e\left(\frac{169}{506}\right)\) |
| \(\chi_{7935}(296,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{506}\right)\) | \(e\left(\frac{43}{253}\right)\) | \(e\left(\frac{29}{506}\right)\) | \(e\left(\frac{129}{506}\right)\) | \(e\left(\frac{226}{253}\right)\) | \(e\left(\frac{90}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{67}{253}\right)\) | \(e\left(\frac{273}{506}\right)\) |
| \(\chi_{7935}(341,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{283}{506}\right)\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{285}{506}\right)\) | \(e\left(\frac{343}{506}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{204}{253}\right)\) | \(e\left(\frac{31}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{135}{253}\right)\) | \(e\left(\frac{467}{506}\right)\) |
| \(\chi_{7935}(356,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{315}{506}\right)\) | \(e\left(\frac{62}{253}\right)\) | \(e\left(\frac{83}{506}\right)\) | \(e\left(\frac{439}{506}\right)\) | \(e\left(\frac{167}{253}\right)\) | \(e\left(\frac{118}{253}\right)\) | \(e\left(\frac{199}{253}\right)\) | \(e\left(\frac{124}{253}\right)\) | \(e\left(\frac{26}{253}\right)\) | \(e\left(\frac{223}{506}\right)\) |
| \(\chi_{7935}(401,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{435}{506}\right)\) | \(e\left(\frac{182}{253}\right)\) | \(e\left(\frac{211}{506}\right)\) | \(e\left(\frac{293}{506}\right)\) | \(e\left(\frac{74}{253}\right)\) | \(e\left(\frac{175}{253}\right)\) | \(e\left(\frac{70}{253}\right)\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{67}{506}\right)\) |
| \(\chi_{7935}(431,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{267}{506}\right)\) | \(e\left(\frac{14}{253}\right)\) | \(e\left(\frac{133}{506}\right)\) | \(e\left(\frac{295}{506}\right)\) | \(e\left(\frac{103}{253}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{28}{253}\right)\) | \(e\left(\frac{63}{253}\right)\) | \(e\left(\frac{83}{506}\right)\) |
| \(\chi_{7935}(521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{331}{506}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{235}{506}\right)\) | \(e\left(\frac{487}{506}\right)\) | \(e\left(\frac{104}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{156}{253}\right)\) | \(e\left(\frac{98}{253}\right)\) | \(e\left(\frac{101}{506}\right)\) |
| \(\chi_{7935}(536,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{247}{506}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{235}{506}\right)\) | \(e\left(\frac{245}{253}\right)\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{241}{253}\right)\) | \(e\left(\frac{226}{253}\right)\) | \(e\left(\frac{109}{506}\right)\) |
| \(\chi_{7935}(566,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{471}{506}\right)\) | \(e\left(\frac{218}{253}\right)\) | \(e\left(\frac{47}{506}\right)\) | \(e\left(\frac{401}{506}\right)\) | \(e\left(\frac{122}{253}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{6}{253}\right)\) | \(e\left(\frac{183}{253}\right)\) | \(e\left(\frac{222}{253}\right)\) | \(e\left(\frac{425}{506}\right)\) |
| \(\chi_{7935}(596,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{506}\right)\) | \(e\left(\frac{169}{253}\right)\) | \(e\left(\frac{467}{506}\right)\) | \(e\left(\frac{1}{506}\right)\) | \(e\left(\frac{141}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{65}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{128}{253}\right)\) | \(e\left(\frac{261}{506}\right)\) |
| \(\chi_{7935}(626,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{343}{506}\right)\) | \(e\left(\frac{90}{253}\right)\) | \(e\left(\frac{349}{506}\right)\) | \(e\left(\frac{17}{506}\right)\) | \(e\left(\frac{120}{253}\right)\) | \(e\left(\frac{106}{253}\right)\) | \(e\left(\frac{93}{253}\right)\) | \(e\left(\frac{180}{253}\right)\) | \(e\left(\frac{152}{253}\right)\) | \(e\left(\frac{389}{506}\right)\) |
| \(\chi_{7935}(641,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{351}{506}\right)\) | \(e\left(\frac{98}{253}\right)\) | \(e\left(\frac{425}{506}\right)\) | \(e\left(\frac{41}{506}\right)\) | \(e\left(\frac{215}{253}\right)\) | \(e\left(\frac{211}{253}\right)\) | \(e\left(\frac{135}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) | \(e\left(\frac{188}{253}\right)\) | \(e\left(\frac{75}{506}\right)\) |
| \(\chi_{7935}(686,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{261}{506}\right)\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{329}{506}\right)\) | \(e\left(\frac{277}{506}\right)\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{105}{253}\right)\) | \(e\left(\frac{42}{253}\right)\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{445}{506}\right)\) |
| \(\chi_{7935}(701,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{506}\right)\) | \(e\left(\frac{139}{253}\right)\) | \(e\left(\frac{435}{506}\right)\) | \(e\left(\frac{417}{506}\right)\) | \(e\left(\frac{101}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{34}{253}\right)\) | \(e\left(\frac{25}{253}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{47}{506}\right)\) |
| \(\chi_{7935}(746,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{506}\right)\) | \(e\left(\frac{39}{253}\right)\) | \(e\left(\frac{497}{506}\right)\) | \(e\left(\frac{117}{506}\right)\) | \(e\left(\frac{52}{253}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{49}{253}\right)\) | \(e\left(\frac{177}{506}\right)\) |
| \(\chi_{7935}(776,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{421}{506}\right)\) | \(e\left(\frac{168}{253}\right)\) | \(e\left(\frac{331}{506}\right)\) | \(e\left(\frac{251}{506}\right)\) | \(e\left(\frac{224}{253}\right)\) | \(e\left(\frac{181}{253}\right)\) | \(e\left(\frac{123}{253}\right)\) | \(e\left(\frac{83}{253}\right)\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{237}{506}\right)\) |
| \(\chi_{7935}(866,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{506}\right)\) | \(e\left(\frac{67}{253}\right)\) | \(e\left(\frac{257}{506}\right)\) | \(e\left(\frac{201}{506}\right)\) | \(e\left(\frac{5}{253}\right)\) | \(e\left(\frac{152}{253}\right)\) | \(e\left(\frac{162}{253}\right)\) | \(e\left(\frac{134}{253}\right)\) | \(e\left(\frac{175}{253}\right)\) | \(e\left(\frac{343}{506}\right)\) |
| \(\chi_{7935}(911,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{405}{506}\right)\) | \(e\left(\frac{152}{253}\right)\) | \(e\left(\frac{179}{506}\right)\) | \(e\left(\frac{203}{506}\right)\) | \(e\left(\frac{34}{253}\right)\) | \(e\left(\frac{224}{253}\right)\) | \(e\left(\frac{39}{253}\right)\) | \(e\left(\frac{51}{253}\right)\) | \(e\left(\frac{178}{253}\right)\) | \(e\left(\frac{359}{506}\right)\) |
| \(\chi_{7935}(941,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{506}\right)\) | \(e\left(\frac{125}{253}\right)\) | \(e\left(\frac{49}{506}\right)\) | \(e\left(\frac{375}{506}\right)\) | \(e\left(\frac{251}{253}\right)\) | \(e\left(\frac{91}{253}\right)\) | \(e\left(\frac{87}{253}\right)\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{183}{253}\right)\) | \(e\left(\frac{217}{506}\right)\) |
| \(\chi_{7935}(971,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{506}\right)\) | \(e\left(\frac{57}{253}\right)\) | \(e\left(\frac{415}{506}\right)\) | \(e\left(\frac{171}{506}\right)\) | \(e\left(\frac{76}{253}\right)\) | \(e\left(\frac{84}{253}\right)\) | \(e\left(\frac{236}{253}\right)\) | \(e\left(\frac{114}{253}\right)\) | \(e\left(\frac{130}{253}\right)\) | \(e\left(\frac{103}{506}\right)\) |
| \(\chi_{7935}(986,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{153}{506}\right)\) | \(e\left(\frac{153}{253}\right)\) | \(e\left(\frac{315}{506}\right)\) | \(e\left(\frac{459}{506}\right)\) | \(e\left(\frac{204}{253}\right)\) | \(e\left(\frac{79}{253}\right)\) | \(e\left(\frac{234}{253}\right)\) | \(e\left(\frac{53}{253}\right)\) | \(e\left(\frac{56}{253}\right)\) | \(e\left(\frac{383}{506}\right)\) |
| \(\chi_{7935}(1031,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{506}\right)\) | \(e\left(\frac{239}{253}\right)\) | \(e\left(\frac{373}{506}\right)\) | \(e\left(\frac{211}{506}\right)\) | \(e\left(\frac{150}{253}\right)\) | \(e\left(\frac{6}{253}\right)\) | \(e\left(\frac{53}{253}\right)\) | \(e\left(\frac{225}{253}\right)\) | \(e\left(\frac{190}{253}\right)\) | \(e\left(\frac{423}{506}\right)\) |
| \(\chi_{7935}(1046,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{469}{506}\right)\) | \(e\left(\frac{216}{253}\right)\) | \(e\left(\frac{281}{506}\right)\) | \(e\left(\frac{395}{506}\right)\) | \(e\left(\frac{35}{253}\right)\) | \(e\left(\frac{52}{253}\right)\) | \(e\left(\frac{122}{253}\right)\) | \(e\left(\frac{179}{253}\right)\) | \(e\left(\frac{213}{253}\right)\) | \(e\left(\frac{377}{506}\right)\) |
| \(\chi_{7935}(1091,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{506}\right)\) | \(e\left(\frac{149}{253}\right)\) | \(e\left(\frac{277}{506}\right)\) | \(e\left(\frac{447}{506}\right)\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{153}{253}\right)\) | \(e\left(\frac{213}{253}\right)\) | \(e\left(\frac{45}{253}\right)\) | \(e\left(\frac{38}{253}\right)\) | \(e\left(\frac{287}{506}\right)\) |