from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2153, base_ring=CyclotomicField(1076))
M = H._module
chi = DirichletCharacter(H, M([955]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,2153))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2153\) | |
| Conductor: | \(2153\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1076\) | 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: | $\Q(\zeta_{1076})$ |
| Fixed field: | Number field defined by a degree 1076 polynomial (not computed) |
First 31 of 536 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2153}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{538}\right)\) | \(e\left(\frac{955}{1076}\right)\) | \(e\left(\frac{115}{269}\right)\) | \(e\left(\frac{1047}{1076}\right)\) | \(e\left(\frac{109}{1076}\right)\) | \(e\left(\frac{132}{269}\right)\) | \(e\left(\frac{345}{538}\right)\) | \(e\left(\frac{417}{538}\right)\) | \(e\left(\frac{201}{1076}\right)\) | \(e\left(\frac{515}{1076}\right)\) |
| \(\chi_{2153}(8,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{345}{538}\right)\) | \(e\left(\frac{713}{1076}\right)\) | \(e\left(\frac{76}{269}\right)\) | \(e\left(\frac{989}{1076}\right)\) | \(e\left(\frac{327}{1076}\right)\) | \(e\left(\frac{127}{269}\right)\) | \(e\left(\frac{497}{538}\right)\) | \(e\left(\frac{175}{538}\right)\) | \(e\left(\frac{603}{1076}\right)\) | \(e\left(\frac{469}{1076}\right)\) |
| \(\chi_{2153}(9,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{417}{538}\right)\) | \(e\left(\frac{1}{1076}\right)\) | \(e\left(\frac{148}{269}\right)\) | \(e\left(\frac{765}{1076}\right)\) | \(e\left(\frac{835}{1076}\right)\) | \(e\left(\frac{219}{269}\right)\) | \(e\left(\frac{175}{538}\right)\) | \(e\left(\frac{1}{538}\right)\) | \(e\left(\frac{523}{1076}\right)\) | \(e\left(\frac{885}{1076}\right)\) |
| \(\chi_{2153}(14,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{379}{538}\right)\) | \(e\left(\frac{855}{1076}\right)\) | \(e\left(\frac{110}{269}\right)\) | \(e\left(\frac{943}{1076}\right)\) | \(e\left(\frac{537}{1076}\right)\) | \(e\left(\frac{21}{269}\right)\) | \(e\left(\frac{61}{538}\right)\) | \(e\left(\frac{317}{538}\right)\) | \(e\left(\frac{625}{1076}\right)\) | \(e\left(\frac{247}{1076}\right)\) |
| \(\chi_{2153}(15,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{463}{538}\right)\) | \(e\left(\frac{383}{1076}\right)\) | \(e\left(\frac{194}{269}\right)\) | \(e\left(\frac{323}{1076}\right)\) | \(e\left(\frac{233}{1076}\right)\) | \(e\left(\frac{218}{269}\right)\) | \(e\left(\frac{313}{538}\right)\) | \(e\left(\frac{383}{538}\right)\) | \(e\left(\frac{173}{1076}\right)\) | \(e\left(\frac{15}{1076}\right)\) |
| \(\chi_{2153}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{323}{538}\right)\) | \(e\left(\frac{811}{1076}\right)\) | \(e\left(\frac{54}{269}\right)\) | \(e\left(\frac{639}{1076}\right)\) | \(e\left(\frac{381}{1076}\right)\) | \(e\left(\frac{69}{269}\right)\) | \(e\left(\frac{431}{538}\right)\) | \(e\left(\frac{273}{538}\right)\) | \(e\left(\frac{209}{1076}\right)\) | \(e\left(\frac{43}{1076}\right)\) |
| \(\chi_{2153}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{509}{538}\right)\) | \(e\left(\frac{765}{1076}\right)\) | \(e\left(\frac{240}{269}\right)\) | \(e\left(\frac{957}{1076}\right)\) | \(e\left(\frac{707}{1076}\right)\) | \(e\left(\frac{217}{269}\right)\) | \(e\left(\frac{451}{538}\right)\) | \(e\left(\frac{227}{538}\right)\) | \(e\left(\frac{899}{1076}\right)\) | \(e\left(\frac{221}{1076}\right)\) |
| \(\chi_{2153}(31,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{538}\right)\) | \(e\left(\frac{1039}{1076}\right)\) | \(e\left(\frac{173}{269}\right)\) | \(e\left(\frac{747}{1076}\right)\) | \(e\left(\frac{309}{1076}\right)\) | \(e\left(\frac{236}{269}\right)\) | \(e\left(\frac{519}{538}\right)\) | \(e\left(\frac{501}{538}\right)\) | \(e\left(\frac{17}{1076}\right)\) | \(e\left(\frac{611}{1076}\right)\) |
| \(\chi_{2153}(32,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{538}\right)\) | \(e\left(\frac{471}{1076}\right)\) | \(e\left(\frac{37}{269}\right)\) | \(e\left(\frac{931}{1076}\right)\) | \(e\left(\frac{545}{1076}\right)\) | \(e\left(\frac{122}{269}\right)\) | \(e\left(\frac{111}{538}\right)\) | \(e\left(\frac{471}{538}\right)\) | \(e\left(\frac{1005}{1076}\right)\) | \(e\left(\frac{423}{1076}\right)\) |
| \(\chi_{2153}(33,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{538}\right)\) | \(e\left(\frac{443}{1076}\right)\) | \(e\left(\frac{197}{269}\right)\) | \(e\left(\frac{1031}{1076}\right)\) | \(e\left(\frac{837}{1076}\right)\) | \(e\left(\frac{177}{269}\right)\) | \(e\left(\frac{53}{538}\right)\) | \(e\left(\frac{443}{538}\right)\) | \(e\left(\frac{349}{1076}\right)\) | \(e\left(\frac{391}{1076}\right)\) |
| \(\chi_{2153}(36,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{538}\right)\) | \(e\left(\frac{835}{1076}\right)\) | \(e\left(\frac{109}{269}\right)\) | \(e\left(\frac{707}{1076}\right)\) | \(e\left(\frac{1053}{1076}\right)\) | \(e\left(\frac{214}{269}\right)\) | \(e\left(\frac{327}{538}\right)\) | \(e\left(\frac{297}{538}\right)\) | \(e\left(\frac{925}{1076}\right)\) | \(e\left(\frac{839}{1076}\right)\) |
| \(\chi_{2153}(37,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{225}{538}\right)\) | \(e\left(\frac{1003}{1076}\right)\) | \(e\left(\frac{225}{269}\right)\) | \(e\left(\frac{107}{1076}\right)\) | \(e\left(\frac{377}{1076}\right)\) | \(e\left(\frac{153}{269}\right)\) | \(e\left(\frac{137}{538}\right)\) | \(e\left(\frac{465}{538}\right)\) | \(e\left(\frac{557}{1076}\right)\) | \(e\left(\frac{1031}{1076}\right)\) |
| \(\chi_{2153}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{349}{538}\right)\) | \(e\left(\frac{255}{1076}\right)\) | \(e\left(\frac{80}{269}\right)\) | \(e\left(\frac{319}{1076}\right)\) | \(e\left(\frac{953}{1076}\right)\) | \(e\left(\frac{162}{269}\right)\) | \(e\left(\frac{509}{538}\right)\) | \(e\left(\frac{255}{538}\right)\) | \(e\left(\frac{1017}{1076}\right)\) | \(e\left(\frac{791}{1076}\right)\) |
| \(\chi_{2153}(51,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{477}{538}\right)\) | \(e\left(\frac{125}{1076}\right)\) | \(e\left(\frac{208}{269}\right)\) | \(e\left(\frac{937}{1076}\right)\) | \(e\left(\frac{3}{1076}\right)\) | \(e\left(\frac{206}{269}\right)\) | \(e\left(\frac{355}{538}\right)\) | \(e\left(\frac{125}{538}\right)\) | \(e\left(\frac{815}{1076}\right)\) | \(e\left(\frac{873}{1076}\right)\) |
| \(\chi_{2153}(55,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{243}{538}\right)\) | \(e\left(\frac{825}{1076}\right)\) | \(e\left(\frac{243}{269}\right)\) | \(e\left(\frac{589}{1076}\right)\) | \(e\left(\frac{235}{1076}\right)\) | \(e\left(\frac{176}{269}\right)\) | \(e\left(\frac{191}{538}\right)\) | \(e\left(\frac{287}{538}\right)\) | \(e\left(\frac{1075}{1076}\right)\) | \(e\left(\frac{597}{1076}\right)\) |
| \(\chi_{2153}(56,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{538}\right)\) | \(e\left(\frac{613}{1076}\right)\) | \(e\left(\frac{71}{269}\right)\) | \(e\left(\frac{885}{1076}\right)\) | \(e\left(\frac{755}{1076}\right)\) | \(e\left(\frac{16}{269}\right)\) | \(e\left(\frac{213}{538}\right)\) | \(e\left(\frac{75}{538}\right)\) | \(e\left(\frac{1027}{1076}\right)\) | \(e\left(\frac{201}{1076}\right)\) |
| \(\chi_{2153}(58,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{39}{538}\right)\) | \(e\left(\frac{511}{1076}\right)\) | \(e\left(\frac{39}{269}\right)\) | \(e\left(\frac{327}{1076}\right)\) | \(e\left(\frac{589}{1076}\right)\) | \(e\left(\frac{5}{269}\right)\) | \(e\left(\frac{117}{538}\right)\) | \(e\left(\frac{511}{538}\right)\) | \(e\left(\frac{405}{1076}\right)\) | \(e\left(\frac{315}{1076}\right)\) |
| \(\chi_{2153}(59,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{353}{538}\right)\) | \(e\left(\frac{335}{1076}\right)\) | \(e\left(\frac{84}{269}\right)\) | \(e\left(\frac{187}{1076}\right)\) | \(e\left(\frac{1041}{1076}\right)\) | \(e\left(\frac{197}{269}\right)\) | \(e\left(\frac{521}{538}\right)\) | \(e\left(\frac{335}{538}\right)\) | \(e\left(\frac{893}{1076}\right)\) | \(e\left(\frac{575}{1076}\right)\) |
| \(\chi_{2153}(60,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{538}\right)\) | \(e\left(\frac{141}{1076}\right)\) | \(e\left(\frac{155}{269}\right)\) | \(e\left(\frac{265}{1076}\right)\) | \(e\left(\frac{451}{1076}\right)\) | \(e\left(\frac{213}{269}\right)\) | \(e\left(\frac{465}{538}\right)\) | \(e\left(\frac{141}{538}\right)\) | \(e\left(\frac{575}{1076}\right)\) | \(e\left(\frac{1045}{1076}\right)\) |
| \(\chi_{2153}(63,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{538}\right)\) | \(e\left(\frac{977}{1076}\right)\) | \(e\left(\frac{143}{269}\right)\) | \(e\left(\frac{661}{1076}\right)\) | \(e\left(\frac{187}{1076}\right)\) | \(e\left(\frac{108}{269}\right)\) | \(e\left(\frac{429}{538}\right)\) | \(e\left(\frac{439}{538}\right)\) | \(e\left(\frac{947}{1076}\right)\) | \(e\left(\frac{617}{1076}\right)\) |
| \(\chi_{2153}(73,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{538}\right)\) | \(e\left(\frac{741}{1076}\right)\) | \(e\left(\frac{185}{269}\right)\) | \(e\left(\frac{889}{1076}\right)\) | \(e\left(\frac{35}{1076}\right)\) | \(e\left(\frac{72}{269}\right)\) | \(e\left(\frac{17}{538}\right)\) | \(e\left(\frac{203}{538}\right)\) | \(e\left(\frac{183}{1076}\right)\) | \(e\left(\frac{501}{1076}\right)\) |
| \(\chi_{2153}(76,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{538}\right)\) | \(e\left(\frac{569}{1076}\right)\) | \(e\left(\frac{15}{269}\right)\) | \(e\left(\frac{581}{1076}\right)\) | \(e\left(\frac{599}{1076}\right)\) | \(e\left(\frac{64}{269}\right)\) | \(e\left(\frac{45}{538}\right)\) | \(e\left(\frac{31}{538}\right)\) | \(e\left(\frac{611}{1076}\right)\) | \(e\left(\frac{1073}{1076}\right)\) |
| \(\chi_{2153}(78,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{538}\right)\) | \(e\left(\frac{305}{1076}\right)\) | \(e\left(\frac{217}{269}\right)\) | \(e\left(\frac{909}{1076}\right)\) | \(e\left(\frac{739}{1076}\right)\) | \(e\left(\frac{83}{269}\right)\) | \(e\left(\frac{113}{538}\right)\) | \(e\left(\frac{305}{538}\right)\) | \(e\left(\frac{267}{1076}\right)\) | \(e\left(\frac{925}{1076}\right)\) |
| \(\chi_{2153}(79,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{397}{538}\right)\) | \(e\left(\frac{677}{1076}\right)\) | \(e\left(\frac{128}{269}\right)\) | \(e\left(\frac{349}{1076}\right)\) | \(e\left(\frac{395}{1076}\right)\) | \(e\left(\frac{44}{269}\right)\) | \(e\left(\frac{115}{538}\right)\) | \(e\left(\frac{139}{538}\right)\) | \(e\left(\frac{67}{1076}\right)\) | \(e\left(\frac{889}{1076}\right)\) |
| \(\chi_{2153}(85,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{523}{538}\right)\) | \(e\left(\frac{507}{1076}\right)\) | \(e\left(\frac{254}{269}\right)\) | \(e\left(\frac{495}{1076}\right)\) | \(e\left(\frac{477}{1076}\right)\) | \(e\left(\frac{205}{269}\right)\) | \(e\left(\frac{493}{538}\right)\) | \(e\left(\frac{507}{538}\right)\) | \(e\left(\frac{465}{1076}\right)\) | \(e\left(\frac{3}{1076}\right)\) |
| \(\chi_{2153}(89,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{253}{538}\right)\) | \(e\left(\frac{1025}{1076}\right)\) | \(e\left(\frac{253}{269}\right)\) | \(e\left(\frac{797}{1076}\right)\) | \(e\left(\frac{455}{1076}\right)\) | \(e\left(\frac{129}{269}\right)\) | \(e\left(\frac{221}{538}\right)\) | \(e\left(\frac{487}{538}\right)\) | \(e\left(\frac{227}{1076}\right)\) | \(e\left(\frac{57}{1076}\right)\) |
| \(\chi_{2153}(98,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{105}{538}\right)\) | \(e\left(\frac{755}{1076}\right)\) | \(e\left(\frac{105}{269}\right)\) | \(e\left(\frac{839}{1076}\right)\) | \(e\left(\frac{965}{1076}\right)\) | \(e\left(\frac{179}{269}\right)\) | \(e\left(\frac{315}{538}\right)\) | \(e\left(\frac{217}{538}\right)\) | \(e\left(\frac{1049}{1076}\right)\) | \(e\left(\frac{1055}{1076}\right)\) |
| \(\chi_{2153}(100,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{201}{538}\right)\) | \(e\left(\frac{523}{1076}\right)\) | \(e\left(\frac{201}{269}\right)\) | \(e\left(\frac{899}{1076}\right)\) | \(e\left(\frac{925}{1076}\right)\) | \(e\left(\frac{212}{269}\right)\) | \(e\left(\frac{65}{538}\right)\) | \(e\left(\frac{523}{538}\right)\) | \(e\left(\frac{225}{1076}\right)\) | \(e\left(\frac{175}{1076}\right)\) |
| \(\chi_{2153}(103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{435}{538}\right)\) | \(e\left(\frac{361}{1076}\right)\) | \(e\left(\frac{166}{269}\right)\) | \(e\left(\frac{709}{1076}\right)\) | \(e\left(\frac{155}{1076}\right)\) | \(e\left(\frac{242}{269}\right)\) | \(e\left(\frac{229}{538}\right)\) | \(e\left(\frac{361}{538}\right)\) | \(e\left(\frac{503}{1076}\right)\) | \(e\left(\frac{989}{1076}\right)\) |
| \(\chi_{2153}(105,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{189}{538}\right)\) | \(e\left(\frac{283}{1076}\right)\) | \(e\left(\frac{189}{269}\right)\) | \(e\left(\frac{219}{1076}\right)\) | \(e\left(\frac{661}{1076}\right)\) | \(e\left(\frac{107}{269}\right)\) | \(e\left(\frac{29}{538}\right)\) | \(e\left(\frac{283}{538}\right)\) | \(e\left(\frac{597}{1076}\right)\) | \(e\left(\frac{823}{1076}\right)\) |
| \(\chi_{2153}(107,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{485}{538}\right)\) | \(e\left(\frac{823}{1076}\right)\) | \(e\left(\frac{216}{269}\right)\) | \(e\left(\frac{135}{1076}\right)\) | \(e\left(\frac{717}{1076}\right)\) | \(e\left(\frac{7}{269}\right)\) | \(e\left(\frac{379}{538}\right)\) | \(e\left(\frac{285}{538}\right)\) | \(e\left(\frac{29}{1076}\right)\) | \(e\left(\frac{979}{1076}\right)\) |